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HcmV?d00001 diff --git a/_notebooks/about.ipynb b/_notebooks/about.ipynb index e57bddc8..9197b5af 100644 --- a/_notebooks/about.ipynb +++ b/_notebooks/about.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e9049757", + "id": "e2a7c0df", "metadata": {}, "source": [ "# About These Lectures" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "95b96ddc", + "id": "881a93f7", "metadata": {}, "source": [ "## About\n", @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "01df23a6", + "id": "78bb24f0", "metadata": {}, "source": [ "## Level\n", @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "f5392618", + "id": "fcf2789a", "metadata": {}, "source": [ "## Credits\n", @@ -96,7 +96,7 @@ } ], "metadata": { - "date": 1722488539.950746, + "date": 1722502936.2569392, "filename": "about.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/ak2.ipynb b/_notebooks/ak2.ipynb index c32ce82b..9d029f21 100644 --- a/_notebooks/ak2.ipynb +++ b/_notebooks/ak2.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d9489df4", + "id": "ad7e303f", "metadata": {}, "source": [ "# Transitions in an Overlapping Generations Model\n", @@ -13,7 +13,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84b07cc8", + "id": "ad5a8a63", "metadata": { "hide-output": false }, @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "9a001f60", + "id": "2afdf353", "metadata": {}, "source": [ "## Introduction\n", @@ -60,7 +60,7 @@ }, { "cell_type": "markdown", - "id": "86725aec", + "id": "14bd9039", "metadata": {}, "source": [ "## Setting\n", @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "7d88a270", + "id": "c1aaa674", "metadata": {}, "source": [ "## Production\n", @@ -163,7 +163,7 @@ }, { "cell_type": "markdown", - "id": "7243c266", + "id": "3438905a", "metadata": {}, "source": [ "## Government\n", @@ -197,7 +197,7 @@ }, { "cell_type": "markdown", - "id": "36509fe7", + "id": "9d5239a3", "metadata": {}, "source": [ "## Activities in Factor Markets\n", @@ -227,7 +227,7 @@ }, { "cell_type": "markdown", - "id": "2f87cb85", + "id": "feae07d5", "metadata": {}, "source": [ "## Representative firm’s problem\n", @@ -269,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "550111c5", + "id": "55ec611b", "metadata": {}, "source": [ "## Individuals’ problems" @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "2c6fb2dc", + "id": "356fa63b", "metadata": {}, "source": [ "### Initial old person\n", @@ -301,7 +301,7 @@ }, { "cell_type": "markdown", - "id": "83e962d3", + "id": "34f7c672", "metadata": {}, "source": [ "### Young person\n", @@ -378,7 +378,7 @@ }, { "cell_type": "markdown", - "id": "b52bd0c8", + "id": "1c70da5d", "metadata": {}, "source": [ "## Equilbrium\n", @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "ef240469", + "id": "7fe6195f", "metadata": {}, "source": [ "## Next steps\n", @@ -414,7 +414,7 @@ }, { "cell_type": "markdown", - "id": "69c8b337", + "id": "49b97c35", "metadata": {}, "source": [ "## Closed form solution\n", @@ -441,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "0765f856", + "id": "ea9c48b9", "metadata": {}, "source": [ "### Steady states\n", @@ -486,7 +486,7 @@ }, { "cell_type": "markdown", - "id": "41dcbedc", + "id": "35af6992", "metadata": {}, "source": [ "### Implementation" @@ -495,7 +495,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87b86785", + "id": "822d3daf", "metadata": { "hide-output": false }, @@ -509,7 +509,7 @@ }, { "cell_type": "markdown", - "id": "745528a3", + "id": "3797d7a7", "metadata": {}, "source": [ "For parameters $ \\alpha = 0.3 $ and $ \\beta = 0.5 $, let’s compute $ \\hat{K} $:" @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "962e8849", + "id": "90423e0e", "metadata": { "hide-output": false }, @@ -539,7 +539,7 @@ }, { "cell_type": "markdown", - "id": "6e9c3606", + "id": "f59e6451", "metadata": {}, "source": [ "Knowing $ \\hat K $, we can calculate other equilibrium objects.\n", @@ -550,7 +550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e86e93aa", + "id": "4bb3246b", "metadata": { "hide-output": false }, @@ -587,7 +587,7 @@ }, { "cell_type": "markdown", - "id": "7cf22268", + "id": "19d74414", "metadata": {}, "source": [ "We can use these helper functions to obtain steady state values $ \\hat{Y} $, $ \\hat{r} $, and $ \\hat{W} $ associated with steady state values $ \\hat{K} $ and $ \\hat{r} $." @@ -596,7 +596,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48d3ae2e", + "id": "1ff98113", "metadata": { "hide-output": false }, @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "babf731a", + "id": "3ab962b4", "metadata": {}, "source": [ "Since steady state government debt $ \\hat{D} $ is $ 0 $, all taxes are used to pay for government expenditures" @@ -617,7 +617,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f05988e", + "id": "fa3a1f48", "metadata": { "hide-output": false }, @@ -629,7 +629,7 @@ }, { "cell_type": "markdown", - "id": "dcd8c186", + "id": "a518c32b", "metadata": {}, "source": [ "We use the optimal consumption plans to find steady state consumptions for young and old" @@ -638,7 +638,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1e99fc4", + "id": "f0636243", "metadata": { "hide-output": false }, @@ -650,7 +650,7 @@ }, { "cell_type": "markdown", - "id": "c16e3e28", + "id": "e642dab4", "metadata": {}, "source": [ "Let’s store the steady state quantities and prices using an array called `init_ss`" @@ -659,7 +659,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4653c34", + "id": "b0a51bcd", "metadata": { "hide-output": false }, @@ -673,7 +673,7 @@ }, { "cell_type": "markdown", - "id": "43c502b2", + "id": "dcaaa047", "metadata": {}, "source": [ "### Transitions\n", @@ -716,7 +716,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2fe85cc", + "id": "c70a9585", "metadata": { "hide-output": false }, @@ -866,7 +866,7 @@ }, { "cell_type": "markdown", - "id": "da45d12c", + "id": "b9efa51f", "metadata": {}, "source": [ "We can create an instance `closed` for model parameters $ \\{\\alpha, \\beta\\} $ and use it for various fiscal policy experiments." @@ -875,7 +875,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c9122e6", + "id": "8277d773", "metadata": { "hide-output": false }, @@ -886,7 +886,7 @@ }, { "cell_type": "markdown", - "id": "7b6d5fce", + "id": "e3b6df6a", "metadata": {}, "source": [ "\n", @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "93dd6179", + "id": "298269c0", "metadata": {}, "source": [ "### Experiment 1: Tax cut\n", @@ -928,7 +928,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a5ec05c", + "id": "ad88d3b4", "metadata": { "hide-output": false }, @@ -950,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "ce614a4e", + "id": "e7a470db", "metadata": {}, "source": [ "Let’s use the `simulate` method of `closed` to compute dynamic transitions.\n", @@ -961,7 +961,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8e60824", + "id": "84548eae", "metadata": { "hide-output": false }, @@ -975,7 +975,7 @@ }, { "cell_type": "markdown", - "id": "b3e67491", + "id": "88313931", "metadata": {}, "source": [ "We can also experiment with a lower tax cut rate, such as $ 0.2 $." @@ -984,7 +984,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7c80aef", + "id": "ade3587a", "metadata": { "hide-output": false }, @@ -1006,7 +1006,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5124bac", + "id": "615f83ea", "metadata": { "hide-output": false }, @@ -1044,7 +1044,7 @@ }, { "cell_type": "markdown", - "id": "7c29f8a4", + "id": "8d6d1f20", "metadata": {}, "source": [ "The economy with lower tax cut rate at $ t=0 $ has the same transitional pattern, but is less distorted, and it converges to a new steady state with higher physical capital stock.\n", @@ -1055,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "471e5eb9", + "id": "3617de0f", "metadata": {}, "source": [ "### Experiment 2: Government asset accumulation\n", @@ -1072,7 +1072,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e76a8105", + "id": "d48bd540", "metadata": { "hide-output": false }, @@ -1090,7 +1090,7 @@ }, { "cell_type": "markdown", - "id": "fe0e1b1b", + "id": "ff24513d", "metadata": {}, "source": [ "As the government accumulates the asset and uses it in production, the rental rate on capital falls and private investment falls.\n", @@ -1101,7 +1101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce0257b0", + "id": "49c796e8", "metadata": { "hide-output": false }, @@ -1114,7 +1114,7 @@ }, { "cell_type": "markdown", - "id": "53279500", + "id": "0c946fde", "metadata": {}, "source": [ "We want to know how this policy experiment affects individuals.\n", @@ -1132,7 +1132,7 @@ }, { "cell_type": "markdown", - "id": "d72f7a29", + "id": "e2c91be4", "metadata": {}, "source": [ "### Experiment 3: Temporary expenditure cut\n", @@ -1147,7 +1147,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8396218", + "id": "36246f0a", "metadata": { "hide-output": false }, @@ -1168,7 +1168,7 @@ }, { "cell_type": "markdown", - "id": "facb92be", + "id": "e4baf8df", "metadata": {}, "source": [ "The economy quickly converges to a new steady state with higher physical capital stock, lower interest rate, higher wage rate, and higher consumptions for both the young and the old.\n", @@ -1180,7 +1180,7 @@ }, { "cell_type": "markdown", - "id": "48c3c766", + "id": "dd866769", "metadata": {}, "source": [ "## A computational strategy\n", @@ -1241,7 +1241,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5158508", + "id": "4de30c47", "metadata": { "hide-output": false }, @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "dff2afc4", + "id": "f11aba1b", "metadata": {}, "source": [ "We use `Cy_val` to compute the lifetime value of an arbitrary consumption plan, $ C_y $, given the intertemporal budget constraint.\n", @@ -1266,7 +1266,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17462ae6", + "id": "2d6ee47e", "metadata": { "hide-output": false }, @@ -1283,7 +1283,7 @@ }, { "cell_type": "markdown", - "id": "83b8fbc1", + "id": "1f485e1a", "metadata": {}, "source": [ "An optimal consumption plan $ C_y^* $ can be found by maximizing `Cy_val`.\n", @@ -1294,7 +1294,7 @@ { "cell_type": "code", "execution_count": null, - "id": "036db85d", + "id": "885ba9cf", "metadata": { "hide-output": false }, @@ -1313,7 +1313,7 @@ }, { "cell_type": "markdown", - "id": "535857c9", + "id": "1ab5315e", "metadata": {}, "source": [ "Let’s define a Python class `AK2` that computes the transition paths with the fixed-point algorithm.\n", @@ -1324,7 +1324,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb0c669b", + "id": "275d8751", "metadata": { "hide-output": false }, @@ -1500,7 +1500,7 @@ }, { "cell_type": "markdown", - "id": "64a71dee", + "id": "85056e45", "metadata": {}, "source": [ "We can initialize an instance of class `AK2` with model parameters $ \\{\\alpha, \\beta\\} $ and then use it to conduct fiscal policy experiments." @@ -1509,7 +1509,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e33b3674", + "id": "f79c2692", "metadata": { "hide-output": false }, @@ -1520,7 +1520,7 @@ }, { "cell_type": "markdown", - "id": "a1979bc0", + "id": "67d03924", "metadata": {}, "source": [ "We first examine that the “guess and verify” method leads to the same numerical results as we obtain with the closed form solution when lump sum taxes are muted" @@ -1529,7 +1529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7768de8a", + "id": "7bb22dc3", "metadata": { "hide-output": false }, @@ -1551,7 +1551,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d88884e5", + "id": "43aa3c3a", "metadata": { "hide-output": false }, @@ -1566,7 +1566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75ff8e56", + "id": "b37c6867", "metadata": { "hide-output": false }, @@ -1577,7 +1577,7 @@ }, { "cell_type": "markdown", - "id": "3ba6a162", + "id": "cdb4a07f", "metadata": {}, "source": [ "Next, we activate lump sum taxes.\n", @@ -1588,7 +1588,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6bc5307c", + "id": "352c1257", "metadata": { "hide-output": false }, @@ -1607,7 +1607,7 @@ }, { "cell_type": "markdown", - "id": "dc0becb3", + "id": "c6aec34d", "metadata": {}, "source": [ "Note how “crowding out” has been mitigated." @@ -1616,7 +1616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d82f77dc", + "id": "c1084246", "metadata": { "hide-output": false }, @@ -1654,7 +1654,7 @@ }, { "cell_type": "markdown", - "id": "d78e37fb", + "id": "2583aee4", "metadata": {}, "source": [ "Comparing to [Experiment 1: Tax cut](#exp-tax-cut), the government raises lump-sum taxes to finance the increasing debt interest payment, which is less distortionary comparing to raising the capital income tax rate." @@ -1662,7 +1662,7 @@ }, { "cell_type": "markdown", - "id": "71126ad2", + "id": "d676c929", "metadata": {}, "source": [ "### Experiment 4: Unfunded Social Security System\n", @@ -1689,7 +1689,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6ab15a63", + "id": "87a6f353", "metadata": { "hide-output": false }, @@ -1708,7 +1708,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bd315638", + "id": "4e046f40", "metadata": { "hide-output": false }, @@ -1746,7 +1746,7 @@ }, { "cell_type": "markdown", - "id": "574ddb9c", + "id": "ff117c64", "metadata": {}, "source": [ "An initial old person benefits especially when the social security system is launched because he receives a transfer but pays nothing for it.\n", @@ -1762,7 +1762,7 @@ } ], "metadata": { - "date": 1722488540.2177029, + "date": 1722502936.310943, "filename": "ak2.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/ar1_processes.ipynb b/_notebooks/ar1_processes.ipynb index dd6ddc6b..335db2bb 100644 --- a/_notebooks/ar1_processes.ipynb +++ b/_notebooks/ar1_processes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5d7c1d92", + "id": "c00b25b0", "metadata": {}, "source": [ "\n", @@ -13,7 +13,7 @@ }, { "cell_type": "markdown", - "id": "303327fa", + "id": "632bd827", "metadata": {}, "source": [ "# AR(1) Processes\n", @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "e932dd84", + "id": "3c70be23", "metadata": {}, "source": [ "## Overview\n", @@ -48,7 +48,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab137894", + "id": "0293e549", "metadata": { "hide-output": false }, @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "e73ad254", + "id": "2e82cdd2", "metadata": {}, "source": [ "## The AR(1) model\n", @@ -102,7 +102,7 @@ }, { "cell_type": "markdown", - "id": "b16aff4f", + "id": "a2d94760", "metadata": {}, "source": [ "### Moving average representation\n", @@ -138,7 +138,7 @@ }, { "cell_type": "markdown", - "id": "420d3834", + "id": "e1a1f16a", "metadata": {}, "source": [ "### Distribution dynamics\n", @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bfded352", + "id": "a70064f0", "metadata": { "hide-output": false }, @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "f5989c77", + "id": "af6260b7", "metadata": {}, "source": [ "Here’s the sequence of distributions:" @@ -211,7 +211,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef8dc7b6", + "id": "537d0e07", "metadata": { "hide-output": false }, @@ -238,7 +238,7 @@ }, { "cell_type": "markdown", - "id": "12e49b19", + "id": "b42707ef", "metadata": {}, "source": [ "## Stationarity and asymptotic stability\n", @@ -261,7 +261,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fda212f5", + "id": "7b112c47", "metadata": { "hide-output": false }, @@ -283,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "fc9a3dec", + "id": "83b93593", "metadata": {}, "source": [ "Moreover, the limit does not depend on the initial condition.\n", @@ -294,7 +294,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a1a9c088", + "id": "843ae0db", "metadata": { "hide-output": false }, @@ -307,7 +307,7 @@ }, { "cell_type": "markdown", - "id": "41f6d673", + "id": "2d83bc29", "metadata": {}, "source": [ "In fact it’s easy to show that such convergence will occur, regardless of the initial condition, whenever $ |a| < 1 $.\n", @@ -343,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55d87d38", + "id": "938c7389", "metadata": { "hide-output": false }, @@ -363,7 +363,7 @@ }, { "cell_type": "markdown", - "id": "b675d27d", + "id": "4f3d3f1a", "metadata": {}, "source": [ "As claimed, the sequence $ \\{ \\psi_t \\} $ converges to $ \\psi^* $.\n", @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "eab4eff8", + "id": "b5490255", "metadata": {}, "source": [ "### Stationary distributions\n", @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "0b9eed34", + "id": "62cdbbe9", "metadata": {}, "source": [ "## Ergodicity\n", @@ -462,7 +462,7 @@ }, { "cell_type": "markdown", - "id": "3465b086", + "id": "b2069f7d", "metadata": {}, "source": [ "## Exercises" @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "a43e9dcc", + "id": "43a8a4ae", "metadata": {}, "source": [ "## Exercise 33.1\n", @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "de78c158", + "id": "f2806a9e", "metadata": {}, "source": [ "## Solution to[ Exercise 33.1](https://intro.quantecon.org/#ar1p_ex1)\n", @@ -521,7 +521,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f2dd84ea", + "id": "deacd9ab", "metadata": { "hide-output": false }, @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "776220dc", + "id": "6a029c63", "metadata": {}, "source": [ "## Exercise 33.2\n", @@ -615,7 +615,7 @@ }, { "cell_type": "markdown", - "id": "86479e4d", + "id": "d245d0d2", "metadata": {}, "source": [ "## Solution to[ Exercise 33.2](https://intro.quantecon.org/#ar1p_ex2)\n", @@ -626,7 +626,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1a69bfc1", + "id": "a51e347e", "metadata": { "hide-output": false }, @@ -658,7 +658,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0df7989b", + "id": "f1f1bbe2", "metadata": { "hide-output": false }, @@ -679,7 +679,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5edc0fc1", + "id": "932aaded", "metadata": { "hide-output": false }, @@ -695,7 +695,7 @@ }, { "cell_type": "markdown", - "id": "e3d2030c", + "id": "516761d1", "metadata": {}, "source": [ "We see that the kernel density estimator is effective when the underlying\n", @@ -704,7 +704,7 @@ }, { "cell_type": "markdown", - "id": "fe8bbff2", + "id": "80b06f65", "metadata": {}, "source": [ "## Exercise 33.3\n", @@ -752,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "e9be329c", + "id": "bb98f968", "metadata": {}, "source": [ "## Solution to[ Exercise 33.3](https://intro.quantecon.org/#ar1p_ex3)\n", @@ -763,7 +763,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab122286", + "id": "573921d5", "metadata": { "hide-output": false }, @@ -779,7 +779,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27b97c03", + "id": "0f8837f5", "metadata": { "hide-output": false }, @@ -792,7 +792,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c60cbeb4", + "id": "d45d23d3", "metadata": { "hide-output": false }, @@ -805,7 +805,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2976a19e", + "id": "f495ef56", "metadata": { "hide-output": false }, @@ -818,7 +818,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04159eec", + "id": "f3039244", "metadata": { "hide-output": false }, @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "63ea9e16", + "id": "e051ba0b", "metadata": {}, "source": [ "The simulated distribution approximately coincides with the theoretical\n", @@ -851,7 +851,7 @@ } ], "metadata": { - "date": 1722488540.2488303, + "date": 1722502936.343179, "filename": "ar1_processes.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/business_cycle.ipynb b/_notebooks/business_cycle.ipynb index b1c1185e..8d1c65e0 100644 --- a/_notebooks/business_cycle.ipynb +++ b/_notebooks/business_cycle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d1033c83", + "id": "1ff69c05", "metadata": {}, "source": [ "# Business Cycles" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "cf73421b", + "id": "8838fd69", "metadata": {}, "source": [ "## Overview\n", @@ -29,7 +29,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8c35ad9", + "id": "5bf586a4", "metadata": { "hide-output": false }, @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "bde6e87d", + "id": "b8a69cec", "metadata": {}, "source": [ "We use the following imports" @@ -50,7 +50,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52bbe1b0", + "id": "accfee9c", "metadata": { "hide-output": false }, @@ -65,7 +65,7 @@ }, { "cell_type": "markdown", - "id": "ca2e3344", + "id": "fce97c63", "metadata": {}, "source": [ "Here’s some minor code to help with colors in our plots." @@ -74,7 +74,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c459fa0d", + "id": "12b52ece", "metadata": { "hide-output": false }, @@ -88,7 +88,7 @@ }, { "cell_type": "markdown", - "id": "859d05ff", + "id": "960f4620", "metadata": {}, "source": [ "## Data acquisition\n", @@ -104,7 +104,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e08430b3", + "id": "b455c1de", "metadata": { "hide-output": false }, @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "bcc828e7", + "id": "8cc55da8", "metadata": {}, "source": [ "Now we use this series ID to obtain the data." @@ -124,7 +124,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9652d0f", + "id": "0b3bd0dc", "metadata": { "hide-output": false }, @@ -138,7 +138,7 @@ }, { "cell_type": "markdown", - "id": "374ccdb4", + "id": "72d8dafd", "metadata": {}, "source": [ "We can look at the series’ metadata to learn more about the series (click to expand)." @@ -147,7 +147,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f21b30fa", + "id": "713223f4", "metadata": { "hide-output": false }, @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "c3a9bc14", + "id": "aa36fc1e", "metadata": {}, "source": [ "\n", @@ -167,7 +167,7 @@ }, { "cell_type": "markdown", - "id": "8f9af74f", + "id": "ccd831d3", "metadata": {}, "source": [ "## GDP growth rate\n", @@ -180,7 +180,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2d6ee35", + "id": "1a7c3eb9", "metadata": { "hide-output": false }, @@ -196,7 +196,7 @@ }, { "cell_type": "markdown", - "id": "5b355736", + "id": "21cf1944", "metadata": {}, "source": [ "Here’s a first look at the data" @@ -205,7 +205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bd87ff41", + "id": "c6706914", "metadata": { "hide-output": false }, @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "0fdedbe9", + "id": "9ab49e18", "metadata": {}, "source": [ "We write a function to generate plots for individual countries taking into account the recessions." @@ -225,7 +225,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca6d1785", + "id": "7a5ba37b", "metadata": { "hide-output": false }, @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "058e97b5", + "id": "b45ec335", "metadata": {}, "source": [ "Let’s start with the United States." @@ -313,7 +313,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8200844", + "id": "73ce5c58", "metadata": { "hide-output": false }, @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "2c1048a1", + "id": "def1cd80", "metadata": {}, "source": [ "GDP growth is positive on average and trending slightly downward over time.\n", @@ -349,7 +349,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e4c9ae4", + "id": "26d94d27", "metadata": { "hide-output": false }, @@ -366,7 +366,7 @@ }, { "cell_type": "markdown", - "id": "2d63b84c", + "id": "fcab0d39", "metadata": {}, "source": [ "Now let’s consider Japan, which experienced rapid growth in the 1960s and\n", @@ -379,7 +379,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25934f6c", + "id": "b52b190b", "metadata": { "hide-output": false }, @@ -396,7 +396,7 @@ }, { "cell_type": "markdown", - "id": "45acdbbb", + "id": "e225f5cb", "metadata": {}, "source": [ "Now let’s study Greece." @@ -405,7 +405,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb625427", + "id": "32ec1732", "metadata": { "hide-output": false }, @@ -422,7 +422,7 @@ }, { "cell_type": "markdown", - "id": "a4513f69", + "id": "02c28d7a", "metadata": {}, "source": [ "Greece experienced a very large drop in GDP growth around 2010-2011, during the peak\n", @@ -434,7 +434,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9f9ffc7", + "id": "f0753718", "metadata": { "hide-output": false }, @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "ef6b6229", + "id": "73409eb7", "metadata": {}, "source": [ "Notice that Argentina has experienced far more volatile cycles than\n", @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "3dda606a", + "id": "fe63c157", "metadata": {}, "source": [ "## Unemployment\n", @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07afe89f", + "id": "d3af4538", "metadata": { "hide-output": false }, @@ -499,7 +499,7 @@ }, { "cell_type": "markdown", - "id": "361eedfd", + "id": "fba2f246", "metadata": {}, "source": [ "Let’s plot the unemployment rate in the US from 1929 to 2022 with recessions\n", @@ -509,7 +509,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c266bd4", + "id": "4da490f5", "metadata": { "hide-output": false }, @@ -559,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "29257969", + "id": "01189ed5", "metadata": {}, "source": [ "The plot shows that\n", @@ -581,7 +581,7 @@ }, { "cell_type": "markdown", - "id": "5b9d7c18", + "id": "dc8a73af", "metadata": {}, "source": [ "## Synchronization\n", @@ -600,7 +600,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9fb6e3e1", + "id": "c6187e6e", "metadata": { "hide-output": false }, @@ -680,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "7ac6029b", + "id": "3b7722f3", "metadata": {}, "source": [ "Here we compare the GDP growth rate of developed economies and developing economies." @@ -689,7 +689,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d72958b0", + "id": "e53d65a7", "metadata": { "hide-output": false }, @@ -705,7 +705,7 @@ }, { "cell_type": "markdown", - "id": "78cf975c", + "id": "eaffee34", "metadata": {}, "source": [ "We use the United Kingdom, United States, Germany, and Japan as examples of developed economies." @@ -714,7 +714,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60c551da", + "id": "8155049a", "metadata": { "hide-output": false }, @@ -732,7 +732,7 @@ }, { "cell_type": "markdown", - "id": "c4767f7d", + "id": "010505fb", "metadata": {}, "source": [ "We choose Brazil, China, Argentina, and Mexico as representative developing economies." @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "126aa4d9", + "id": "0fc5a124", "metadata": { "hide-output": false }, @@ -758,7 +758,7 @@ }, { "cell_type": "markdown", - "id": "ea7aea3c", + "id": "7daa5039", "metadata": {}, "source": [ "The comparison of GDP growth rates above suggests that\n", @@ -780,7 +780,7 @@ { "cell_type": "code", "execution_count": null, - "id": "86a9762d", + "id": "22cb941a", "metadata": { "hide-output": false }, @@ -803,7 +803,7 @@ }, { "cell_type": "markdown", - "id": "0653503f", + "id": "47828bf6", "metadata": {}, "source": [ "We see that France, with its strong labor unions, typically experiences\n", @@ -814,7 +814,7 @@ }, { "cell_type": "markdown", - "id": "3cc91bda", + "id": "a175484f", "metadata": {}, "source": [ "## Leading indicators and correlated factors\n", @@ -828,7 +828,7 @@ }, { "cell_type": "markdown", - "id": "d550d44f", + "id": "a92358ce", "metadata": {}, "source": [ "### Consumption\n", @@ -848,7 +848,7 @@ { "cell_type": "code", "execution_count": null, - "id": "770bfdb2", + "id": "48911e34", "metadata": { "hide-output": false }, @@ -907,7 +907,7 @@ }, { "cell_type": "markdown", - "id": "618afa4f", + "id": "87c3cd0f", "metadata": {}, "source": [ "We see that\n", @@ -924,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "4aa35a4a", + "id": "6aeecc49", "metadata": {}, "source": [ "### Production\n", @@ -941,7 +941,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab6a2867", + "id": "36fe6201", "metadata": { "hide-output": false }, @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "f4a12725", + "id": "71466bc5", "metadata": {}, "source": [ "We observe the delayed contraction in the plot across recessions." @@ -980,7 +980,7 @@ }, { "cell_type": "markdown", - "id": "a7ec6f2f", + "id": "c0f975ca", "metadata": {}, "source": [ "### Credit level\n", @@ -1000,7 +1000,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15c0b3ec", + "id": "68eb3f5b", "metadata": { "hide-output": false }, @@ -1023,7 +1023,7 @@ }, { "cell_type": "markdown", - "id": "b7325ccd", + "id": "8f3eeedf", "metadata": {}, "source": [ "Note that the credit rises during economic expansions\n", @@ -1032,7 +1032,7 @@ } ], "metadata": { - "date": 1722488540.2741394, + "date": 1722502936.367467, "filename": "business_cycle.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/cagan_adaptive.ipynb b/_notebooks/cagan_adaptive.ipynb index 670fe138..83acad08 100644 --- a/_notebooks/cagan_adaptive.ipynb +++ b/_notebooks/cagan_adaptive.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c9e6c24e", + "id": "d1de25b9", "metadata": {}, "source": [ "# Monetarist Theory of Price Levels with Adaptive Expectations" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "1eb75c46", + "id": "7ac273a3", "metadata": {}, "source": [ "## Overview\n", @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "6487c021", + "id": "676a0057", "metadata": {}, "source": [ "## Structure of the model\n", @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "08947dc9", + "id": "e104c770", "metadata": {}, "source": [ "## Representing key equations with linear algebra\n", @@ -183,7 +183,7 @@ }, { "cell_type": "markdown", - "id": "11ad32b6", + "id": "b9e2be94", "metadata": {}, "source": [ "## Harvesting insights from our matrix formulation\n", @@ -295,7 +295,7 @@ }, { "cell_type": "markdown", - "id": "2b9cd234", + "id": "bd8f045b", "metadata": {}, "source": [ "## Forecast errors and model computation\n", @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ca03a6b", + "id": "e49bae3c", "metadata": { "hide-output": false }, @@ -342,7 +342,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09eb20fb", + "id": "6ee9e2b2", "metadata": { "hide-output": false }, @@ -359,7 +359,7 @@ }, { "cell_type": "markdown", - "id": "976c7e84", + "id": "99fc543e", "metadata": {}, "source": [ "We solve the model and plot variables of interests using the following functions." @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bae212a8", + "id": "c71a1c5c", "metadata": { "hide-output": false }, @@ -405,7 +405,7 @@ { "cell_type": "code", "execution_count": null, - "id": "774e46f5", + "id": "21599a5b", "metadata": { "hide-output": false }, @@ -442,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "65e2bf32", + "id": "e849ae29", "metadata": {}, "source": [ "## Technical condition for stability\n", @@ -471,7 +471,7 @@ { "cell_type": "code", "execution_count": null, - "id": "631f6d65", + "id": "4fe87a1c", "metadata": { "hide-output": false }, @@ -482,7 +482,7 @@ }, { "cell_type": "markdown", - "id": "ca2e3f0e", + "id": "62336337", "metadata": {}, "source": [ "## Experiments\n", @@ -492,7 +492,7 @@ }, { "cell_type": "markdown", - "id": "e7049e47", + "id": "ff36f81d", "metadata": {}, "source": [ "### Experiment 1\n", @@ -519,7 +519,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1d301b14", + "id": "63662d41", "metadata": { "hide-output": false }, @@ -538,7 +538,7 @@ }, { "cell_type": "markdown", - "id": "14711faa", + "id": "cbf26f33", "metadata": {}, "source": [ "We invite the reader to compare outcomes with those under rational expectations studied in [A Monetarist Theory of Price Levels](https://intro.quantecon.org/cagan_ree.html).\n", @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "b9a40065", + "id": "6962bba8", "metadata": {}, "source": [ "### Experiment 2\n", @@ -566,7 +566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f56a192d", + "id": "38e14087", "metadata": { "hide-output": false }, @@ -584,7 +584,7 @@ } ], "metadata": { - "date": 1722488540.296871, + "date": 1722502936.3899615, "filename": "cagan_adaptive.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/cagan_ree.ipynb b/_notebooks/cagan_ree.ipynb index ec8d6334..c2e8503d 100644 --- a/_notebooks/cagan_ree.ipynb +++ b/_notebooks/cagan_ree.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c1dcafa4", + "id": "836a7ca3", "metadata": {}, "source": [ "# A Monetarist Theory of Price Levels" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "7be9d40b", + "id": "1c3a14e6", "metadata": {}, "source": [ "## Overview\n", @@ -65,7 +65,7 @@ }, { "cell_type": "markdown", - "id": "4d3c4960", + "id": "dcf69e62", "metadata": {}, "source": [ "## Structure of the model\n", @@ -223,7 +223,7 @@ }, { "cell_type": "markdown", - "id": "8a557057", + "id": "8ded79af", "metadata": {}, "source": [ "## Continuation values\n", @@ -261,7 +261,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98727d9a", + "id": "851501a8", "metadata": { "hide-output": false }, @@ -274,7 +274,7 @@ }, { "cell_type": "markdown", - "id": "72a6f060", + "id": "0534b3a4", "metadata": {}, "source": [ "First, we store parameters in a `namedtuple`:" @@ -283,7 +283,7 @@ { "cell_type": "code", "execution_count": null, - "id": "214e118b", + "id": "88a21ac6", "metadata": { "hide-output": false }, @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "2648a3f9", + "id": "d1e83dd3", "metadata": {}, "source": [ "Now we can solve the model to compute $ \\pi_t $, $ m_t $ and $ p_t $ for $ t =1, \\ldots, T+1 $ using the matrix equation above" @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5805b18", + "id": "a5b2108a", "metadata": { "hide-output": false }, @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "07593c89", + "id": "665e98f3", "metadata": {}, "source": [ "### Some quantitative experiments\n", @@ -368,7 +368,7 @@ }, { "cell_type": "markdown", - "id": "82111306", + "id": "899badf4", "metadata": {}, "source": [ "#### Experiment 1: Foreseen sudden stabilization\n", @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d3bcd5b", + "id": "6cd127ab", "metadata": { "hide-output": false }, @@ -418,7 +418,7 @@ }, { "cell_type": "markdown", - "id": "b9426f4e", + "id": "8239f542", "metadata": {}, "source": [ "Now we use the following function to plot the result" @@ -427,7 +427,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b7fedee", + "id": "9548cbcf", "metadata": { "hide-output": false }, @@ -449,7 +449,7 @@ }, { "cell_type": "markdown", - "id": "6224614d", + "id": "d615e703", "metadata": {}, "source": [ "The plot of the money growth rate $ \\mu_t $ in the top level panel portrays\n", @@ -471,7 +471,7 @@ }, { "cell_type": "markdown", - "id": "9394b214", + "id": "345ab551", "metadata": {}, "source": [ "### The log price level\n", @@ -507,7 +507,7 @@ }, { "cell_type": "markdown", - "id": "e30c75b9", + "id": "e6834954", "metadata": {}, "source": [ "### What jumps?\n", @@ -540,7 +540,7 @@ }, { "cell_type": "markdown", - "id": "c3d92a41", + "id": "820596fa", "metadata": {}, "source": [ "#### Technical details about whether $ p $ or $ m $ jumps at $ T_1 $\n", @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "ce080a4a", + "id": "986435ec", "metadata": {}, "source": [ "#### $ m_{T_{1}} $ does not jump.\n", @@ -570,7 +570,7 @@ }, { "cell_type": "markdown", - "id": "dbc806da", + "id": "f6e7c138", "metadata": {}, "source": [ "#### $ m_{T_{1}} $ jumps.\n", @@ -590,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "c34a1f86", + "id": "e4a0f198", "metadata": {}, "source": [ "#### Experiment 2: an unforeseen sudden stabilization\n", @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7bf46d92", + "id": "228ade3b", "metadata": { "hide-output": false }, @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6980ba07", + "id": "d5049897", "metadata": { "hide-output": false }, @@ -720,7 +720,7 @@ }, { "cell_type": "markdown", - "id": "7e744eb0", + "id": "ec9ee417", "metadata": {}, "source": [ "We invite you to compare these graphs with corresponding ones for the foreseen stabilization analyzed in experiment 1 above.\n", @@ -748,7 +748,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8555fa03", + "id": "b24b965f", "metadata": { "hide-output": false }, @@ -776,7 +776,7 @@ }, { "cell_type": "markdown", - "id": "ea54580a", + "id": "e110c7fa", "metadata": {}, "source": [ "It is instructive to compare the preceding graphs with graphs of log price levels and inflation rates for data from four big inflations described in\n", @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "af43c64c", + "id": "1c6826e6", "metadata": {}, "source": [ "#### Experiment 3\n", @@ -817,7 +817,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6125a6db", + "id": "061ab019", "metadata": { "hide-output": false }, @@ -840,7 +840,7 @@ }, { "cell_type": "markdown", - "id": "0170ec1c", + "id": "1fb131c7", "metadata": {}, "source": [ "## Sequel\n", @@ -854,7 +854,7 @@ } ], "metadata": { - "date": 1722488540.3275425, + "date": 1722502936.421616, "filename": "cagan_ree.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/cobweb.ipynb b/_notebooks/cobweb.ipynb index 7333612e..5479c482 100644 --- a/_notebooks/cobweb.ipynb +++ b/_notebooks/cobweb.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e87b2d69", + "id": "e5fdfdb8", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "fea1833a", + "id": "38380acc", "metadata": {}, "source": [ "# The Cobweb Model\n", @@ -21,7 +21,7 @@ }, { "cell_type": "markdown", - "id": "fc8d4409", + "id": "68e73058", "metadata": {}, "source": [ "## Overview\n", @@ -69,7 +69,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6422d34f", + "id": "8254d7e5", "metadata": { "hide-output": false }, @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "68d92139", + "id": "aeedaf5b", "metadata": {}, "source": [ "## History\n", @@ -98,7 +98,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba7ef9a0", + "id": "1c504495", "metadata": { "hide-output": false }, @@ -119,7 +119,7 @@ }, { "cell_type": "markdown", - "id": "6d211151", + "id": "ac1c782d", "metadata": {}, "source": [ "## The model\n", @@ -154,7 +154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4894e1b", + "id": "1b9282b9", "metadata": { "hide-output": false }, @@ -182,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "2ccc0dd8", + "id": "0e668874", "metadata": {}, "source": [ "Now let’s plot." @@ -191,7 +191,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f90eaff1", + "id": "be6bd91b", "metadata": { "hide-output": false }, @@ -212,7 +212,7 @@ }, { "cell_type": "markdown", - "id": "30352e06", + "id": "9db94cdf", "metadata": {}, "source": [ "Market equilibrium requires that supply equals demand, or\n", @@ -258,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "eda9b028", + "id": "41290406", "metadata": {}, "source": [ "## Naive expectations\n", @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f72b662", + "id": "c169258d", "metadata": { "hide-output": false }, @@ -317,7 +317,7 @@ }, { "cell_type": "markdown", - "id": "b8779b45", + "id": "d0f6c898", "metadata": {}, "source": [ "Let’s try to understand how prices will evolve using a 45-degree diagram, which is a tool for studying one-dimensional dynamics.\n", @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1985afe3", + "id": "31cd0d07", "metadata": { "hide-output": false }, @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "bb62a0f8", + "id": "dae60a96", "metadata": {}, "source": [ "Now we can set up a market and plot the 45-degree diagram." @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c718a5c", + "id": "6a62365a", "metadata": { "hide-output": false }, @@ -429,7 +429,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4ae4ac66", + "id": "01e0d517", "metadata": { "hide-output": false }, @@ -440,7 +440,7 @@ }, { "cell_type": "markdown", - "id": "cdd11b6b", + "id": "8ccc9187", "metadata": {}, "source": [ "The plot shows the function $ g $ defined in [(25.3)](#equation-def-g) and the 45-degree line.\n", @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e81edf1", + "id": "4bfa6d33", "metadata": { "hide-output": false }, @@ -506,7 +506,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83990e9f", + "id": "bea28ef1", "metadata": { "hide-output": false }, @@ -517,7 +517,7 @@ }, { "cell_type": "markdown", - "id": "b8d63491", + "id": "598e251d", "metadata": {}, "source": [ "We see that a cycle has formed and the cycle is persistent.\n", @@ -532,7 +532,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90470114", + "id": "b289134d", "metadata": { "hide-output": false }, @@ -543,7 +543,7 @@ }, { "cell_type": "markdown", - "id": "2eba9689", + "id": "79e7e61f", "metadata": {}, "source": [ "## Adaptive expectations\n", @@ -593,7 +593,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1661e79", + "id": "9c2be63d", "metadata": { "hide-output": false }, @@ -609,7 +609,7 @@ }, { "cell_type": "markdown", - "id": "c09aa827", + "id": "84f4c00c", "metadata": {}, "source": [ "The function below plots price dynamics under adaptive expectations for different values of $ \\alpha $." @@ -618,7 +618,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4c8445d", + "id": "fbfa50be", "metadata": { "hide-output": false }, @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "d21acda0", + "id": "4906d94f", "metadata": {}, "source": [ "Let’s call the function with prices starting at $ p_0 = 5 $." @@ -652,7 +652,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d05d4744", + "id": "810f5754", "metadata": { "hide-output": false }, @@ -663,7 +663,7 @@ }, { "cell_type": "markdown", - "id": "729f3be8", + "id": "fe75fbb2", "metadata": {}, "source": [ "Note that if $ \\alpha=1 $, then adaptive expectations are just naive expectation.\n", @@ -676,7 +676,7 @@ }, { "cell_type": "markdown", - "id": "0260c3b9", + "id": "e74dd36d", "metadata": {}, "source": [ "## Exercises" @@ -684,7 +684,7 @@ }, { "cell_type": "markdown", - "id": "9529333b", + "id": "089294aa", "metadata": {}, "source": [ "## Exercise 25.1\n", @@ -696,7 +696,7 @@ }, { "cell_type": "markdown", - "id": "db26f4a1", + "id": "09c52612", "metadata": {}, "source": [ "## Solution to[ Exercise 25.1](https://intro.quantecon.org/#cobweb_ex1)" @@ -705,7 +705,7 @@ { "cell_type": "code", "execution_count": null, - "id": "977b2fbc", + "id": "2767c8d7", "metadata": { "hide-output": false }, @@ -743,7 +743,7 @@ { "cell_type": "code", "execution_count": null, - "id": "572abcd4", + "id": "fc65b200", "metadata": { "hide-output": false }, @@ -755,7 +755,7 @@ }, { "cell_type": "markdown", - "id": "1ad135b6", + "id": "1dceb335", "metadata": {}, "source": [ "## Exercise 25.2\n", @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "d279f9f1", + "id": "87393e42", "metadata": {}, "source": [ "## Solution to[ Exercise 25.2](https://intro.quantecon.org/#cobweb_ex2)" @@ -788,7 +788,7 @@ { "cell_type": "code", "execution_count": null, - "id": "24b9ba06", + "id": "618ba6cf", "metadata": { "hide-output": false }, @@ -805,7 +805,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f94b0c4b", + "id": "16281bcc", "metadata": { "hide-output": false }, @@ -839,7 +839,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a80f0d6c", + "id": "d249766f", "metadata": { "hide-output": false }, @@ -855,7 +855,7 @@ } ], "metadata": { - "date": 1722488540.3524177, + "date": 1722502936.44491, "filename": "cobweb.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/commod_price.ipynb b/_notebooks/commod_price.ipynb index 0d675a77..4629c1ce 100644 --- a/_notebooks/commod_price.ipynb +++ b/_notebooks/commod_price.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "62365158", + "id": "81ea97e1", "metadata": {}, "source": [ "# Commodity Prices" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "ed67b1d7", + "id": "aa3205ef", "metadata": {}, "source": [ "## Outline\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5888916", + "id": "6a229a34", "metadata": { "hide-output": false }, @@ -50,7 +50,7 @@ }, { "cell_type": "markdown", - "id": "8f1d6eb8", + "id": "b07fe538", "metadata": {}, "source": [ "We will use the following imports" @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e718a2b9", + "id": "6fad21fb", "metadata": { "hide-output": false }, @@ -75,7 +75,7 @@ }, { "cell_type": "markdown", - "id": "303981a1", + "id": "0f9c60c8", "metadata": {}, "source": [ "## Data\n", @@ -86,7 +86,7 @@ { "cell_type": "code", "execution_count": null, - "id": "53c36de3", + "id": "918c98e2", "metadata": { "hide-output": false }, @@ -98,7 +98,7 @@ { "cell_type": "code", "execution_count": null, - "id": "899eeab3", + "id": "17529a78", "metadata": { "hide-output": false }, @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "b47aaa7e", + "id": "f44a09f3", "metadata": {}, "source": [ "The figure shows surprisingly large movements in the price of cotton.\n", @@ -143,7 +143,7 @@ }, { "cell_type": "markdown", - "id": "dc6413b5", + "id": "58df301d", "metadata": {}, "source": [ "## The competitive storage model\n", @@ -175,7 +175,7 @@ }, { "cell_type": "markdown", - "id": "f3224ba3", + "id": "2ba18780", "metadata": {}, "source": [ "## The model\n", @@ -206,7 +206,7 @@ }, { "cell_type": "markdown", - "id": "678ad48c", + "id": "bf10e6ed", "metadata": {}, "source": [ "## Equilibrium\n", @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "39592ad5", + "id": "5f911bc8", "metadata": {}, "source": [ "### Equilibrium conditions\n", @@ -278,7 +278,7 @@ }, { "cell_type": "markdown", - "id": "baf81f41", + "id": "0bd93214", "metadata": {}, "source": [ "### An equilibrium function\n", @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "8ab9f776", + "id": "10ef058d", "metadata": {}, "source": [ "### Computing the equilibrium\n", @@ -423,7 +423,7 @@ }, { "cell_type": "markdown", - "id": "aaa8ed27", + "id": "4d8efdfd", "metadata": {}, "source": [ "## Code\n", @@ -439,7 +439,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ba091b3", + "id": "2e25bad5", "metadata": { "hide-output": false }, @@ -497,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "f2eb6a43", + "id": "468d5b48", "metadata": {}, "source": [ "The figure above shows the inverse demand curve $ P $, which is also $ p_0 $, as\n", @@ -510,7 +510,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7696960a", + "id": "1a3de444", "metadata": { "hide-output": false }, @@ -542,7 +542,7 @@ } ], "metadata": { - "date": 1722488540.3877714, + "date": 1722502936.4786136, "filename": "commod_price.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/complex_and_trig.ipynb b/_notebooks/complex_and_trig.ipynb index f6509a8b..38933b70 100644 --- a/_notebooks/complex_and_trig.ipynb +++ b/_notebooks/complex_and_trig.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "13f04665", + "id": "e8da3dfb", "metadata": {}, "source": [ "\n", @@ -13,7 +13,7 @@ }, { "cell_type": "markdown", - "id": "d3b3943f", + "id": "eb0d18cb", "metadata": {}, "source": [ "# Complex Numbers and Trigonometry" @@ -21,7 +21,7 @@ }, { "cell_type": "markdown", - "id": "235a2122", + "id": "894db063", "metadata": {}, "source": [ "## Overview\n", @@ -45,7 +45,7 @@ }, { "cell_type": "markdown", - "id": "3d46c47a", + "id": "08fa2357", "metadata": {}, "source": [ "### Complex Numbers\n", @@ -105,7 +105,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bda61c0c", + "id": "721a2cbb", "metadata": { "hide-output": false }, @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "6815b9ad", + "id": "532be2c3", "metadata": {}, "source": [ "### An Example\n", @@ -139,7 +139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdfbb05c", + "id": "8fe43e64", "metadata": { "hide-output": false }, @@ -186,7 +186,7 @@ }, { "cell_type": "markdown", - "id": "7f2840e7", + "id": "515c7312", "metadata": {}, "source": [ "## De Moivre’s Theorem\n", @@ -210,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "eba3f38e", + "id": "bd8096c3", "metadata": {}, "source": [ "## Applications of de Moivre’s Theorem" @@ -218,7 +218,7 @@ }, { "cell_type": "markdown", - "id": "0bedd838", + "id": "8edc83d9", "metadata": {}, "source": [ "### Example 1\n", @@ -249,7 +249,7 @@ }, { "cell_type": "markdown", - "id": "1ff7c410", + "id": "ccab1d35", "metadata": {}, "source": [ "### Example 2\n", @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "a79ec05e", + "id": "94fe815d", "metadata": {}, "source": [ "### Example 3\n", @@ -353,7 +353,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f218ccf1", + "id": "376d41be", "metadata": { "hide-output": false }, @@ -384,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "2e6ad09c", + "id": "2b4552d7", "metadata": {}, "source": [ "Using the code above, we compute that\n", @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21497bf3", + "id": "9fd97a90", "metadata": { "hide-output": false }, @@ -437,7 +437,7 @@ }, { "cell_type": "markdown", - "id": "ab478238", + "id": "bc4ad024", "metadata": {}, "source": [ "### Trigonometric Identities\n", @@ -496,7 +496,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0239668", + "id": "4a272b7a", "metadata": { "hide-output": false }, @@ -514,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "bf8fbf64", + "id": "79d7ef5c", "metadata": {}, "source": [ "### Trigonometric Integrals\n", @@ -571,7 +571,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4f477ce", + "id": "dd5293a9", "metadata": { "hide-output": false }, @@ -588,7 +588,7 @@ { "cell_type": "code", "execution_count": null, - "id": "accbeda4", + "id": "cc4a20d1", "metadata": { "hide-output": false }, @@ -601,7 +601,7 @@ }, { "cell_type": "markdown", - "id": "f292edf8", + "id": "33156647", "metadata": {}, "source": [ "### Exercises" @@ -609,7 +609,7 @@ }, { "cell_type": "markdown", - "id": "37b64d01", + "id": "42af81dc", "metadata": {}, "source": [ "### Exercise 9.1\n", @@ -627,7 +627,7 @@ }, { "cell_type": "markdown", - "id": "6e71ab5e", + "id": "c623768c", "metadata": {}, "source": [ "### Solution to[ Exercise 9.1](https://intro.quantecon.org/#complex_ex1)\n", @@ -638,7 +638,7 @@ { "cell_type": "code", "execution_count": null, - "id": "899870bf", + "id": "829fc0f8", "metadata": { "hide-output": false }, @@ -651,7 +651,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37a5ebad", + "id": "c9b92b8c", "metadata": { "hide-output": false }, @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a1e5d8cc", + "id": "d53fc628", "metadata": { "hide-output": false }, @@ -680,7 +680,7 @@ } ], "metadata": { - "date": 1722488540.4080875, + "date": 1722502936.4996426, "filename": "complex_and_trig.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/cons_smooth.ipynb b/_notebooks/cons_smooth.ipynb index 3e78808a..268104dd 100644 --- a/_notebooks/cons_smooth.ipynb +++ b/_notebooks/cons_smooth.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "feae4c4f", + "id": "6d0a82be", "metadata": {}, "source": [ "# Consumption Smoothing" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "481bb7b9", + "id": "e73d1b0a", "metadata": {}, "source": [ "## Overview\n", @@ -37,7 +37,7 @@ }, { "cell_type": "markdown", - "id": "87324459", + "id": "b4c83bef", "metadata": {}, "source": [ "## Analysis\n", @@ -48,7 +48,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1627655a", + "id": "e91ad807", "metadata": { "hide-output": false }, @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "ff92b0ce", + "id": "e48cfbaa", "metadata": {}, "source": [ "The model describes a consumer who lives from time $ t=0, 1, \\ldots, T $, receives a stream $ \\{y_t\\}_{t=0}^T $ of non-financial income and chooses a consumption stream $ \\{c_t\\}_{t=0}^T $.\n", @@ -156,7 +156,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8da7104", + "id": "c3e96349", "metadata": { "hide-output": false }, @@ -174,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "28eaae22", + "id": "292beca7", "metadata": {}, "source": [ "## Friedman-Hall consumption-smoothing model\n", @@ -230,7 +230,7 @@ }, { "cell_type": "markdown", - "id": "c141efb6", + "id": "1c681c94", "metadata": {}, "source": [ "## Mechanics of Consumption smoothing model\n", @@ -242,7 +242,7 @@ }, { "cell_type": "markdown", - "id": "7c9c714d", + "id": "18c963d0", "metadata": {}, "source": [ "### Step 1\n", @@ -257,7 +257,7 @@ }, { "cell_type": "markdown", - "id": "43826f73", + "id": "f9799ca0", "metadata": {}, "source": [ "### Step 2\n", @@ -271,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "fdde160e", + "id": "0019e382", "metadata": {}, "source": [ "### Step 3\n", @@ -317,7 +317,7 @@ { "cell_type": "code", "execution_count": null, - "id": "693923c8", + "id": "59e77eea", "metadata": { "hide-output": false }, @@ -346,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "84ba3ac4", + "id": "0392b413", "metadata": {}, "source": [ "We use an example where the consumer inherits $ a_0<0 $.\n", @@ -361,7 +361,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8981ef0a", + "id": "80d942df", "metadata": { "hide-output": false }, @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "7a5c4705", + "id": "32a26c78", "metadata": {}, "source": [ "The graphs below show paths of non-financial income, consumption, and financial assets." @@ -391,7 +391,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d376506", + "id": "c2642e41", "metadata": { "hide-output": false }, @@ -413,7 +413,7 @@ }, { "cell_type": "markdown", - "id": "6e26321d", + "id": "8768ffed", "metadata": {}, "source": [ "Note that $ a_{T+1} = 0 $, as anticipated.\n", @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8993483d", + "id": "76ca2157", "metadata": { "hide-output": false }, @@ -441,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "8c3505b3", + "id": "0afe91dd", "metadata": {}, "source": [ "### Experiments\n", @@ -456,7 +456,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8c84074", + "id": "d4c30faa", "metadata": { "hide-output": false }, @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "2fb26701", + "id": "c7066b6e", "metadata": {}, "source": [ "In the experiments below, please study how consumption and financial asset sequences vary accross different sequences for non-financial income." @@ -495,7 +495,7 @@ }, { "cell_type": "markdown", - "id": "cfa2d7c2", + "id": "1230d88b", "metadata": {}, "source": [ "#### Experiment 1: one-time gain/loss\n", @@ -508,7 +508,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17631b70", + "id": "f66c3d13", "metadata": { "hide-output": false }, @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f190caa", + "id": "aa166ca2", "metadata": { "hide-output": false }, @@ -537,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "ffd8f4c0", + "id": "3a9efed5", "metadata": {}, "source": [ "#### Experiment 2: permanent wage gain/loss\n", @@ -550,7 +550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e34fff4a", + "id": "a32bf584", "metadata": { "hide-output": false }, @@ -566,7 +566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be526567", + "id": "4c656482", "metadata": { "hide-output": false }, @@ -581,7 +581,7 @@ }, { "cell_type": "markdown", - "id": "287c6613", + "id": "8cac126e", "metadata": {}, "source": [ "#### Experiment 3: a late starter\n", @@ -592,7 +592,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43b9ed71", + "id": "703e84aa", "metadata": { "hide-output": false }, @@ -607,7 +607,7 @@ }, { "cell_type": "markdown", - "id": "c0720e05", + "id": "894de8ea", "metadata": {}, "source": [ "#### Experiment 4: geometric earner\n", @@ -620,7 +620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "886b3428", + "id": "35638fe6", "metadata": { "hide-output": false }, @@ -641,7 +641,7 @@ }, { "cell_type": "markdown", - "id": "dc60f740", + "id": "53bc84a5", "metadata": {}, "source": [ "Now we show the behavior when $ \\lambda = 0.95 $" @@ -650,7 +650,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17842830", + "id": "1e3970b2", "metadata": { "hide-output": false }, @@ -667,7 +667,7 @@ }, { "cell_type": "markdown", - "id": "3ae8705e", + "id": "090b5e77", "metadata": {}, "source": [ "What happens when $ \\lambda $ is negative" @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be7ebce8", + "id": "e683811b", "metadata": { "hide-output": false }, @@ -693,7 +693,7 @@ }, { "cell_type": "markdown", - "id": "fc70ca53", + "id": "525b617d", "metadata": {}, "source": [ "### Feasible consumption variations\n", @@ -770,7 +770,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8016547", + "id": "76f0092c", "metadata": { "hide-output": false }, @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "987bc68e", + "id": "05940ebc", "metadata": {}, "source": [ "We visualize variations for $ \\xi_1 \\in \\{.01, .05\\} $ and $ \\phi \\in \\{.95, 1.02\\} $" @@ -802,7 +802,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d96198c", + "id": "e2c38987", "metadata": { "hide-output": false }, @@ -843,7 +843,7 @@ }, { "cell_type": "markdown", - "id": "dca53a7f", + "id": "eb1d29aa", "metadata": {}, "source": [ "We can even use the Python `np.gradient` command to compute derivatives of welfare with respect to our two parameters.\n", @@ -856,7 +856,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6aac391", + "id": "b3993cea", "metadata": { "hide-output": false }, @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "ff4c085c", + "id": "14f44306", "metadata": {}, "source": [ "Then we can visualize the relationship between welfare and $ \\xi_1 $ and compute its derivatives" @@ -889,7 +889,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96d84b01", + "id": "88e8fc07", "metadata": { "hide-output": false }, @@ -912,7 +912,7 @@ }, { "cell_type": "markdown", - "id": "071ba5f5", + "id": "6f9422ee", "metadata": {}, "source": [ "The same can be done on $ \\phi $" @@ -921,7 +921,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b769d419", + "id": "d8e667c0", "metadata": { "hide-output": false }, @@ -944,7 +944,7 @@ }, { "cell_type": "markdown", - "id": "cee05487", + "id": "aac8ca2c", "metadata": {}, "source": [ "## Wrapping up the consumption-smoothing model\n", @@ -961,7 +961,7 @@ }, { "cell_type": "markdown", - "id": "de9d6575", + "id": "852fa06d", "metadata": {}, "source": [ "## Appendix: solving difference equations with linear algebra\n", @@ -980,7 +980,7 @@ }, { "cell_type": "markdown", - "id": "fbc5a78e", + "id": "d651734d", "metadata": {}, "source": [ "### First-order difference equation\n", @@ -1038,7 +1038,7 @@ }, { "cell_type": "markdown", - "id": "bdffdbf6", + "id": "0bac4098", "metadata": {}, "source": [ "### Exercise 12.1\n", @@ -1060,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "600c7e55", + "id": "633b151f", "metadata": {}, "source": [ "### Second order difference equation\n", @@ -1097,7 +1097,7 @@ }, { "cell_type": "markdown", - "id": "6cd6bf27", + "id": "1c9b873e", "metadata": {}, "source": [ "### Exercise 12.2\n", @@ -1108,7 +1108,7 @@ } ], "metadata": { - "date": 1722488540.4470646, + "date": 1722502936.5417886, "filename": "cons_smooth.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/eigen_I.ipynb b/_notebooks/eigen_I.ipynb index 32086ead..e6d643f9 100644 --- a/_notebooks/eigen_I.ipynb +++ b/_notebooks/eigen_I.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "675dc728", + "id": "c1faf63c", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "94c95745", + "id": "2ca781c7", "metadata": {}, "source": [ "# Eigenvalues and Eigenvectors\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "3575e304", + "id": "3ba8da8b", "metadata": {}, "source": [ "## Overview\n", @@ -49,7 +49,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7e9bbf9", + "id": "441d3f13", "metadata": { "hide-output": false }, @@ -65,7 +65,7 @@ }, { "cell_type": "markdown", - "id": "5665cd74", + "id": "4f83fc68", "metadata": {}, "source": [ "\n", @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "0ef0fe95", + "id": "feb7cf44", "metadata": {}, "source": [ "## Matrices as transformations\n", @@ -84,7 +84,7 @@ }, { "cell_type": "markdown", - "id": "b7e27714", + "id": "ed05eb46", "metadata": {}, "source": [ "### Mapping vectors to vectors\n", @@ -116,7 +116,7 @@ }, { "cell_type": "markdown", - "id": "de8bb8d5", + "id": "e3c4ac0a", "metadata": {}, "source": [ "### Square matrices\n", @@ -164,7 +164,7 @@ { "cell_type": "code", "execution_count": null, - "id": "58eb3e21", + "id": "13da4ca5", "metadata": { "hide-output": false }, @@ -177,7 +177,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87646095", + "id": "770289b5", "metadata": { "hide-output": false }, @@ -224,7 +224,7 @@ }, { "cell_type": "markdown", - "id": "e0642904", + "id": "be513e61", "metadata": {}, "source": [ "One way to understand this transformation is that $ A $\n", @@ -235,7 +235,7 @@ }, { "cell_type": "markdown", - "id": "ffe2ccac", + "id": "1fc1488c", "metadata": {}, "source": [ "## Types of transformations\n", @@ -259,7 +259,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43a87187", + "id": "29aa79a2", "metadata": { "hide-output": false }, @@ -355,7 +355,7 @@ }, { "cell_type": "markdown", - "id": "c5ef960e", + "id": "80b2cc37", "metadata": {}, "source": [ "### Scaling\n", @@ -378,7 +378,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79ae7797", + "id": "7e54b6e4", "metadata": { "hide-output": false }, @@ -392,7 +392,7 @@ }, { "cell_type": "markdown", - "id": "e542bb67", + "id": "6b106f5e", "metadata": {}, "source": [ "### Shearing\n", @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5109bce2", + "id": "6ca929b5", "metadata": { "hide-output": false }, @@ -427,7 +427,7 @@ }, { "cell_type": "markdown", - "id": "e2724277", + "id": "56483350", "metadata": {}, "source": [ "### Rotation\n", @@ -449,7 +449,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74d71025", + "id": "a09c535a", "metadata": { "hide-output": false }, @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "e66edf9b", + "id": "af7923c7", "metadata": {}, "source": [ "### Permutation\n", @@ -483,7 +483,7 @@ { "cell_type": "code", "execution_count": null, - "id": "58b75b33", + "id": "266ed220", "metadata": { "hide-output": false }, @@ -495,7 +495,7 @@ }, { "cell_type": "markdown", - "id": "c9ba0ece", + "id": "77de7ae9", "metadata": {}, "source": [ "More examples of common transition matrices can be found [here](https://en.wikipedia.org/wiki/Transformation_matrix#Examples_in_2_dimensions)." @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "eac9902a", + "id": "8cdbd165", "metadata": {}, "source": [ "## Matrix multiplication as composition\n", @@ -514,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "95982d37", + "id": "8ea4e1c6", "metadata": {}, "source": [ "### Linear compositions\n", @@ -645,7 +645,7 @@ }, { "cell_type": "markdown", - "id": "01650d6a", + "id": "34dd75f2", "metadata": {}, "source": [ "### Examples\n", @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de1fd77a", + "id": "571b2b3d", "metadata": { "hide-output": false }, @@ -706,7 +706,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6792373d", + "id": "d58bfa9f", "metadata": { "hide-output": false }, @@ -720,7 +720,7 @@ }, { "cell_type": "markdown", - "id": "8a4197a2", + "id": "bcb39c2d", "metadata": {}, "source": [ "#### Shear then rotate" @@ -729,7 +729,7 @@ { "cell_type": "code", "execution_count": null, - "id": "653b4dce", + "id": "0a828899", "metadata": { "hide-output": false }, @@ -740,7 +740,7 @@ }, { "cell_type": "markdown", - "id": "f0c05b6d", + "id": "6b1a861f", "metadata": {}, "source": [ "#### Rotate then shear" @@ -749,7 +749,7 @@ { "cell_type": "code", "execution_count": null, - "id": "837d1bb0", + "id": "b72f4870", "metadata": { "hide-output": false }, @@ -760,7 +760,7 @@ }, { "cell_type": "markdown", - "id": "f1a7ae5b", + "id": "4858c9af", "metadata": {}, "source": [ "It is evident that the transformation $ AB $ is not the same as the transformation $ BA $." @@ -768,7 +768,7 @@ }, { "cell_type": "markdown", - "id": "cbb9eaf6", + "id": "4c56267d", "metadata": {}, "source": [ "## Iterating on a fixed map\n", @@ -795,7 +795,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1d3da19", + "id": "9e33240a", "metadata": { "hide-output": false }, @@ -848,7 +848,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b60d410c", + "id": "18674493", "metadata": { "hide-output": false }, @@ -865,7 +865,7 @@ }, { "cell_type": "markdown", - "id": "806982f8", + "id": "859d55c4", "metadata": {}, "source": [ "Here with each iteration the vectors get shorter, i.e., move closer to the origin.\n", @@ -876,7 +876,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8b359b4", + "id": "43b274b9", "metadata": { "hide-output": false }, @@ -893,7 +893,7 @@ }, { "cell_type": "markdown", - "id": "bd78ebe2", + "id": "73c0698f", "metadata": {}, "source": [ "Here with each iteration vectors do not tend to get longer or shorter.\n", @@ -905,7 +905,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d801ca1a", + "id": "1cfff9d3", "metadata": { "hide-output": false }, @@ -922,7 +922,7 @@ }, { "cell_type": "markdown", - "id": "78361b2f", + "id": "91a3c7e2", "metadata": {}, "source": [ "Here with each iteration vectors tend to get longer, i.e., farther from the\n", @@ -940,7 +940,7 @@ }, { "cell_type": "markdown", - "id": "fa548969", + "id": "23c51aa6", "metadata": {}, "source": [ "## Eigenvalues\n", @@ -952,7 +952,7 @@ }, { "cell_type": "markdown", - "id": "bd3b9b9a", + "id": "2150188a", "metadata": {}, "source": [ "### Definitions\n", @@ -979,7 +979,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ea7cac4", + "id": "bc026373", "metadata": { "hide-output": false }, @@ -1033,7 +1033,7 @@ }, { "cell_type": "markdown", - "id": "16814aeb", + "id": "0e5c21ad", "metadata": {}, "source": [ "### Complex values\n", @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "27ed457e", + "id": "8af754bc", "metadata": {}, "source": [ "### Some mathematical details\n", @@ -1080,7 +1080,7 @@ }, { "cell_type": "markdown", - "id": "b3019d7b", + "id": "d2038674", "metadata": {}, "source": [ "### Facts\n", @@ -1098,7 +1098,7 @@ }, { "cell_type": "markdown", - "id": "a95e6fe7", + "id": "f73741b9", "metadata": {}, "source": [ "### Computation\n", @@ -1109,7 +1109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54acd8c9", + "id": "62df8ccd", "metadata": { "hide-output": false }, @@ -1128,7 +1128,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a527d8f9", + "id": "9ebc0937", "metadata": { "hide-output": false }, @@ -1139,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "376c343d", + "id": "ba2977f2", "metadata": {}, "source": [ "Note that the *columns* of `evecs` are the eigenvectors.\n", @@ -1158,7 +1158,7 @@ }, { "cell_type": "markdown", - "id": "ee1d6118", + "id": "10c696d9", "metadata": {}, "source": [ "## The Neumann Series Lemma\n", @@ -1171,7 +1171,7 @@ }, { "cell_type": "markdown", - "id": "343c67f5", + "id": "e6fb681f", "metadata": {}, "source": [ "### Scalar series\n", @@ -1195,7 +1195,7 @@ }, { "cell_type": "markdown", - "id": "0c14b695", + "id": "4829d9ba", "metadata": {}, "source": [ "### Matrix series\n", @@ -1225,7 +1225,7 @@ }, { "cell_type": "markdown", - "id": "f568176f", + "id": "5f7687f8", "metadata": {}, "source": [ "### (Neumann Series Lemma)\n", @@ -1250,7 +1250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a25b2a7", + "id": "ff28a6df", "metadata": { "hide-output": false }, @@ -1267,7 +1267,7 @@ }, { "cell_type": "markdown", - "id": "009f113c", + "id": "5ad2729a", "metadata": {}, "source": [ "The spectral radius $ r(A) $ obtained is less than 1.\n", @@ -1278,7 +1278,7 @@ { "cell_type": "code", "execution_count": null, - "id": "543b3b14", + "id": "65057385", "metadata": { "hide-output": false }, @@ -1291,7 +1291,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5ef013c", + "id": "3e3b002e", "metadata": { "hide-output": false }, @@ -1303,7 +1303,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9afbc46b", + "id": "115755f2", "metadata": { "hide-output": false }, @@ -1318,7 +1318,7 @@ }, { "cell_type": "markdown", - "id": "6ba10c34", + "id": "c5b77706", "metadata": {}, "source": [ "Let’s check equality between the sum and the inverse methods." @@ -1327,7 +1327,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33c22ce7", + "id": "86e91817", "metadata": { "hide-output": false }, @@ -1338,7 +1338,7 @@ }, { "cell_type": "markdown", - "id": "03925292", + "id": "ceedaf6b", "metadata": {}, "source": [ "Although we truncate the infinite sum at $ k = 50 $, both methods give us the same\n", @@ -1347,7 +1347,7 @@ }, { "cell_type": "markdown", - "id": "e27cd312", + "id": "f4c49369", "metadata": {}, "source": [ "## Exercises" @@ -1355,7 +1355,7 @@ }, { "cell_type": "markdown", - "id": "dd190d14", + "id": "2895a5b7", "metadata": {}, "source": [ "## Exercise 16.1\n", @@ -1377,7 +1377,7 @@ }, { "cell_type": "markdown", - "id": "24958eab", + "id": "763fd61b", "metadata": {}, "source": [ "## Solution to[ Exercise 16.1](https://intro.quantecon.org/#eig1_ex1)\n", @@ -1390,7 +1390,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ded852f6", + "id": "a8a41bd4", "metadata": { "hide-output": false }, @@ -1438,7 +1438,7 @@ }, { "cell_type": "markdown", - "id": "94d3f64b", + "id": "cbccce1a", "metadata": {}, "source": [ "Then we can look at the trajectory of the eigenvector approximation." @@ -1447,7 +1447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c15ee0a4", + "id": "f3c1d9bf", "metadata": { "hide-output": false }, @@ -1485,7 +1485,7 @@ }, { "cell_type": "markdown", - "id": "0500a847", + "id": "b026cea9", "metadata": {}, "source": [ "## Exercise 16.2\n", @@ -1499,7 +1499,7 @@ }, { "cell_type": "markdown", - "id": "5485b329", + "id": "7950313d", "metadata": {}, "source": [ "## Solution to[ Exercise 16.2](https://intro.quantecon.org/#eig1_ex2)" @@ -1508,7 +1508,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c6139cb9", + "id": "89c80669", "metadata": { "hide-output": false }, @@ -1530,7 +1530,7 @@ }, { "cell_type": "markdown", - "id": "00abd4fe", + "id": "d3d77343", "metadata": {}, "source": [ "The result seems to converge to the eigenvector of $ A $ with the largest eigenvalue.\n", @@ -1543,7 +1543,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55d5be43", + "id": "4f8aef09", "metadata": { "hide-output": false }, @@ -1587,7 +1587,7 @@ }, { "cell_type": "markdown", - "id": "6c8853fe", + "id": "abaa1f85", "metadata": {}, "source": [ "Note that the vector field converges to the eigenvector of $ A $ with the largest eigenvalue and diverges from the eigenvector of $ A $ with the smallest eigenvalue.\n", @@ -1601,7 +1601,7 @@ }, { "cell_type": "markdown", - "id": "195152ae", + "id": "8dfd40b6", "metadata": {}, "source": [ "## Exercise 16.3\n", @@ -1613,7 +1613,7 @@ }, { "cell_type": "markdown", - "id": "2775e7f9", + "id": "a3ff4b4b", "metadata": {}, "source": [ "## Solution to[ Exercise 16.3](https://intro.quantecon.org/#eig1_ex3)\n", @@ -1624,7 +1624,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be55502d", + "id": "074ccaf1", "metadata": { "hide-output": false }, @@ -1693,7 +1693,7 @@ }, { "cell_type": "markdown", - "id": "5ad06ac8", + "id": "8cc1a610", "metadata": {}, "source": [ "The vector fields explain why we observed the trajectories of the vector $ v $ multiplied by $ A $ iteratively before.\n", @@ -1706,7 +1706,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f185d9de", + "id": "46c3aa60", "metadata": { "hide-output": false }, @@ -1770,7 +1770,7 @@ } ], "metadata": { - "date": 1722488540.4917877, + "date": 1722502936.5894413, "filename": "eigen_I.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/eigen_II.ipynb b/_notebooks/eigen_II.ipynb index cba71291..98a48d5f 100644 --- a/_notebooks/eigen_II.ipynb +++ b/_notebooks/eigen_II.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f479ef44", + "id": "6ab3973b", "metadata": {}, "source": [ "# The Perron-Frobenius Theorem\n", @@ -15,7 +15,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f32d2a0d", + "id": "85829dad", "metadata": { "hide-output": false }, @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "e1ed34b5", + "id": "d11d2543", "metadata": {}, "source": [ "In this lecture we will begin with the foundational concepts in spectral theory.\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27f8f97f", + "id": "4ad49ab5", "metadata": { "hide-output": false }, @@ -53,7 +53,7 @@ }, { "cell_type": "markdown", - "id": "9b682b84", + "id": "f1ddba40", "metadata": {}, "source": [ "## Nonnegative matrices\n", @@ -76,7 +76,7 @@ }, { "cell_type": "markdown", - "id": "f20e7bf3", + "id": "563edbd2", "metadata": {}, "source": [ "### Irreducible matrices\n", @@ -125,7 +125,7 @@ }, { "cell_type": "markdown", - "id": "419b8ae9", + "id": "4be9379a", "metadata": {}, "source": [ "### Left eigenvectors\n", @@ -154,7 +154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32b2b158", + "id": "6988d268", "metadata": { "hide-output": false }, @@ -179,7 +179,7 @@ }, { "cell_type": "markdown", - "id": "eadf5d58", + "id": "15505d38", "metadata": {}, "source": [ "We can also use `scipy.linalg.eig` with argument `left=True` to find left eigenvectors directly" @@ -188,7 +188,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5d6451b", + "id": "22e4009d", "metadata": { "hide-output": false }, @@ -203,7 +203,7 @@ }, { "cell_type": "markdown", - "id": "10a20456", + "id": "01004480", "metadata": {}, "source": [ "The eigenvalues are the same while the eigenvectors themselves are different.\n", @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "9a304c05", + "id": "dc688a7c", "metadata": {}, "source": [ "### The Perron-Frobenius theorem\n", @@ -234,7 +234,7 @@ }, { "cell_type": "markdown", - "id": "806e83bf", + "id": "41d16edf", "metadata": {}, "source": [ "### (Perron-Frobenius Theorem)\n", @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "b3a589a6", + "id": "2815635b", "metadata": {}, "source": [ "#### Example: Irreducible matrix\n", @@ -277,7 +277,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6304e4fa", + "id": "a934bc70", "metadata": { "hide-output": false }, @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "09ea5b35", + "id": "c889adcc", "metadata": {}, "source": [ "We can compute the dominant eigenvalue and the corresponding eigenvector" @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3231a186", + "id": "2ae6b2f6", "metadata": { "hide-output": false }, @@ -310,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "1cb55e8f", + "id": "d7514919", "metadata": {}, "source": [ "Now we can see the claims of the Perron-Frobenius Theorem holds for the irreducible matrix $ A $:\n", @@ -328,7 +328,7 @@ }, { "cell_type": "markdown", - "id": "81b4ac22", + "id": "5a5d15ce", "metadata": {}, "source": [ "### Primitive matrices\n", @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "ae474303", + "id": "b79a2099", "metadata": {}, "source": [ "### (Continous of Perron-Frobenius Theorem)\n", @@ -384,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "a6486c6c", + "id": "59340d7d", "metadata": {}, "source": [ "#### Example 1: Primitive matrix\n", @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e03eab3", + "id": "68aea8e1", "metadata": { "hide-output": false }, @@ -410,7 +410,7 @@ }, { "cell_type": "markdown", - "id": "41806651", + "id": "a302ff45", "metadata": {}, "source": [ "We compute the dominant eigenvalue and the corresponding eigenvector" @@ -419,7 +419,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2a2a1f0", + "id": "52d9d8bc", "metadata": { "hide-output": false }, @@ -430,7 +430,7 @@ }, { "cell_type": "markdown", - "id": "665b2c72", + "id": "cb7f14bb", "metadata": {}, "source": [ "Now let’s give some examples to see if the claims of the Perron-Frobenius Theorem hold for the primitive matrix $ B $:\n", @@ -449,7 +449,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2be77de1", + "id": "080b5802", "metadata": { "hide-output": false }, @@ -521,7 +521,7 @@ }, { "cell_type": "markdown", - "id": "4507eadf", + "id": "e8b137b0", "metadata": {}, "source": [ "The convergence is not observed in cases of non-primitive matrices.\n", @@ -532,7 +532,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7935b39d", + "id": "5ddd4636", "metadata": { "hide-output": false }, @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "abd9c1d2", + "id": "701a184c", "metadata": {}, "source": [ "The result shows that the matrix is not primitive as it is not everywhere positive.\n", @@ -568,7 +568,7 @@ }, { "cell_type": "markdown", - "id": "e071056c", + "id": "0f74cdc5", "metadata": {}, "source": [ "#### Example 2: Connection to Markov chains\n", @@ -583,7 +583,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c5c4934", + "id": "b108de77", "metadata": { "hide-output": false }, @@ -599,7 +599,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47b201eb", + "id": "4ac3a294", "metadata": { "hide-output": false }, @@ -613,7 +613,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87243e62", + "id": "aad7736f", "metadata": { "hide-output": false }, @@ -629,7 +629,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f1c23c1", + "id": "f9339688", "metadata": { "hide-output": false }, @@ -642,7 +642,7 @@ }, { "cell_type": "markdown", - "id": "d541f581", + "id": "0f9e97ac", "metadata": {}, "source": [ "We can also verify other properties hinted by Perron-Frobenius in these stochastic matrices.\n", @@ -691,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "983c4ca2", + "id": "e78a95f0", "metadata": {}, "source": [ "## Exercises" @@ -699,7 +699,7 @@ }, { "cell_type": "markdown", - "id": "6d53452a", + "id": "c8dd3d48", "metadata": {}, "source": [ "## (Leontief’s Input-Output Model)Exercise 39.1\n", @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "d654de6f", + "id": "72bae54d", "metadata": {}, "source": [ "## Solution to[ Exercise 39.1 (Leontief’s Input-Output Model)](https://intro.quantecon.org/#eig_ex1)" @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f5a0e58", + "id": "0f3362df", "metadata": { "hide-output": false }, @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "79589beb", + "id": "2b7a76d4", "metadata": {}, "source": [ "Since we have $ r(A) < 1 $ we can thus find the solution using the Neumann Series Lemma." @@ -802,7 +802,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d0f4dcf9", + "id": "3d25ea93", "metadata": { "hide-output": false }, @@ -821,7 +821,7 @@ } ], "metadata": { - "date": 1722488540.5245233, + "date": 1722502936.6237442, "filename": "eigen_II.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/equalizing_difference.ipynb b/_notebooks/equalizing_difference.ipynb index 43733bf6..ad7b203d 100644 --- a/_notebooks/equalizing_difference.ipynb +++ b/_notebooks/equalizing_difference.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "53808b57", + "id": "8f7fdf0c", "metadata": {}, "source": [ "# Equalizing Difference Model" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "5828fae5", + "id": "5f5d784a", "metadata": {}, "source": [ "## Overview\n", @@ -49,7 +49,7 @@ { "cell_type": "code", "execution_count": null, - "id": "923b782d", + "id": "0a2a6b09", "metadata": { "hide-output": false }, @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "15211e0b", + "id": "956f2294", "metadata": {}, "source": [ "## The indifference condition\n", @@ -93,7 +93,7 @@ }, { "cell_type": "markdown", - "id": "691db277", + "id": "43509612", "metadata": {}, "source": [ "### Present value of a high school educated worker\n", @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "520d9e50", + "id": "b4b39140", "metadata": {}, "source": [ "### Present value of a college-bound new high school graduate\n", @@ -190,7 +190,7 @@ }, { "cell_type": "markdown", - "id": "39eecef1", + "id": "70edff4f", "metadata": {}, "source": [ "## Computations\n", @@ -204,7 +204,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f5676c7e", + "id": "b11c0304", "metadata": { "hide-output": false }, @@ -235,7 +235,7 @@ }, { "cell_type": "markdown", - "id": "d125b2f3", + "id": "633c0636", "metadata": {}, "source": [ "Using vectorization instead of loops,\n", @@ -249,7 +249,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b1fe7a1", + "id": "0ed802d0", "metadata": { "hide-output": false }, @@ -263,7 +263,7 @@ }, { "cell_type": "markdown", - "id": "25f7669b", + "id": "c7c4022d", "metadata": {}, "source": [ "Let’s not charge for college and recompute $ \\phi $.\n", @@ -274,7 +274,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba14ec21", + "id": "febd467a", "metadata": { "hide-output": false }, @@ -288,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "f0408bee", + "id": "5f83d43c", "metadata": {}, "source": [ "Let us construct some graphs that show us how the initial college-high-school wage ratio $ \\phi $ would change if one of its determinants were to change.\n", @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "128c8687", + "id": "0d27be7c", "metadata": { "hide-output": false }, @@ -317,7 +317,7 @@ }, { "cell_type": "markdown", - "id": "b6ea2d7f", + "id": "0617c0fb", "metadata": {}, "source": [ "Evidently, the initial wage ratio $ \\phi $ must rise to compensate a prospective high school student for **waiting** to start receiving income – remember that while she is earning nothing in years $ t=0, 1, 2, 3 $, the high school worker is earning a salary.\n", @@ -329,7 +329,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cc1583c6", + "id": "9d552e6b", "metadata": { "hide-output": false }, @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "10cddb84", + "id": "431bcfbd", "metadata": {}, "source": [ "Notice how the initial wage gap falls when the rate of growth $ \\gamma_c $ of college wages rises.\n", @@ -362,7 +362,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41a681a7", + "id": "ee87244d", "metadata": { "hide-output": false }, @@ -380,7 +380,7 @@ }, { "cell_type": "markdown", - "id": "d4a3f7f4", + "id": "76b086d4", "metadata": {}, "source": [ "## Entrepreneur-worker interpretation\n", @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d7f3615f", + "id": "56ca298c", "metadata": { "hide-output": false }, @@ -449,7 +449,7 @@ }, { "cell_type": "markdown", - "id": "439d7504", + "id": "cc40b2b7", "metadata": {}, "source": [ "If the probability that a new business succeeds is $ 0.2 $, let’s compute the initial wage premium for successful entrepreneurs." @@ -458,7 +458,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec0f45de", + "id": "e9ac66db", "metadata": { "hide-output": false }, @@ -472,7 +472,7 @@ }, { "cell_type": "markdown", - "id": "9344015e", + "id": "f472c19d", "metadata": {}, "source": [ "Now let’s study how the initial wage premium for successful entrepreneurs depend on the success probability." @@ -481,7 +481,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ae8c8412", + "id": "fd5302a4", "metadata": { "hide-output": false }, @@ -499,7 +499,7 @@ }, { "cell_type": "markdown", - "id": "3bf3baf3", + "id": "120aa9ba", "metadata": {}, "source": [ "Does the graph make sense to you?" @@ -507,7 +507,7 @@ }, { "cell_type": "markdown", - "id": "caa52367", + "id": "84cef0dd", "metadata": {}, "source": [ "## An application of calculus\n", @@ -530,7 +530,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e346b7a2", + "id": "3f706f93", "metadata": { "hide-output": false }, @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "cf0a6563", + "id": "94f74588", "metadata": {}, "source": [ "Define function $ A_h $" @@ -551,7 +551,7 @@ { "cell_type": "code", "execution_count": null, - "id": "024b1cfa", + "id": "ca107a89", "metadata": { "hide-output": false }, @@ -563,7 +563,7 @@ }, { "cell_type": "markdown", - "id": "c586a846", + "id": "245998de", "metadata": {}, "source": [ "Define function $ A_c $" @@ -572,7 +572,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f344664e", + "id": "85d02a7d", "metadata": { "hide-output": false }, @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "ee1b63ba", + "id": "2172f551", "metadata": {}, "source": [ "Now, define $ \\phi $" @@ -593,7 +593,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5ec6554e", + "id": "6cda6dcb", "metadata": { "hide-output": false }, @@ -605,7 +605,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f76365a", + "id": "43e13658", "metadata": { "hide-output": false }, @@ -616,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "c7e69d23", + "id": "827a99d1", "metadata": {}, "source": [ "We begin by setting default parameter values." @@ -625,7 +625,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afcff83d", + "id": "d0f6e83b", "metadata": { "hide-output": false }, @@ -640,7 +640,7 @@ }, { "cell_type": "markdown", - "id": "4de79721", + "id": "906a0f98", "metadata": {}, "source": [ "Now let’s compute $ \\frac{\\partial \\phi}{\\partial D} $ and then evaluate it at the default values" @@ -649,7 +649,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6a671a8", + "id": "d20adc70", "metadata": { "hide-output": false }, @@ -662,7 +662,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fafa3467", + "id": "5cae019e", "metadata": { "hide-output": false }, @@ -675,7 +675,7 @@ }, { "cell_type": "markdown", - "id": "3ffe2d8d", + "id": "9be7bd89", "metadata": {}, "source": [ "Thus, as with our earlier graph, we find that raising $ R $ increases the initial college wage premium $ \\phi $.\n", @@ -686,7 +686,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d13a02f6", + "id": "c01e3735", "metadata": { "hide-output": false }, @@ -699,7 +699,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88900be5", + "id": "84a15c1b", "metadata": { "hide-output": false }, @@ -712,7 +712,7 @@ }, { "cell_type": "markdown", - "id": "4f385574", + "id": "0678aa91", "metadata": {}, "source": [ "We find that raising $ T $ decreases the initial college wage premium $ \\phi $.\n", @@ -725,7 +725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7235bd7c", + "id": "60adcc6a", "metadata": { "hide-output": false }, @@ -738,7 +738,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73ef7891", + "id": "50c707d0", "metadata": { "hide-output": false }, @@ -751,7 +751,7 @@ }, { "cell_type": "markdown", - "id": "7e4d2fb0", + "id": "065c5d80", "metadata": {}, "source": [ "We find that raising $ \\gamma_h $ increases the initial college wage premium $ \\phi $, in line with our earlier graphical analysis.\n", @@ -762,7 +762,7 @@ { "cell_type": "code", "execution_count": null, - "id": "296697ea", + "id": "57e40a35", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07667567", + "id": "d2908501", "metadata": { "hide-output": false }, @@ -788,7 +788,7 @@ }, { "cell_type": "markdown", - "id": "e11775a5", + "id": "e43a1c1b", "metadata": {}, "source": [ "We find that raising $ \\gamma_c $ decreases the initial college wage premium $ \\phi $, in line with our earlier graphical analysis.\n", @@ -799,7 +799,7 @@ { "cell_type": "code", "execution_count": null, - "id": "216c3ec0", + "id": "fd83dbde", "metadata": { "hide-output": false }, @@ -812,7 +812,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a167ccc", + "id": "03a22ca5", "metadata": { "hide-output": false }, @@ -825,7 +825,7 @@ }, { "cell_type": "markdown", - "id": "1d46d9c5", + "id": "b012a97a", "metadata": {}, "source": [ "We find that raising the gross interest rate $ R $ increases the initial college wage premium $ \\phi $, in line with our earlier graphical analysis." @@ -833,7 +833,7 @@ } ], "metadata": { - "date": 1722488540.5540674, + "date": 1722502937.0598662, "filename": "equalizing_difference.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/french_rev.ipynb b/_notebooks/french_rev.ipynb index 8aa5ad77..8d9fc426 100644 --- a/_notebooks/french_rev.ipynb +++ b/_notebooks/french_rev.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "71a1e48d", + "id": "cb3e4d42", "metadata": {}, "source": [ "# Inflation During French Revolution" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "40b0beb7", + "id": "e51c4823", "metadata": {}, "source": [ "## Overview\n", @@ -47,7 +47,7 @@ }, { "cell_type": "markdown", - "id": "b1e92b4c", + "id": "eab081ee", "metadata": {}, "source": [ "## Data Sources\n", @@ -62,7 +62,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15022a76", + "id": "a45e7bb4", "metadata": { "hide-output": false }, @@ -83,7 +83,7 @@ }, { "cell_type": "markdown", - "id": "214bf708", + "id": "b35fda65", "metadata": {}, "source": [ "## Government Expenditures and Taxes Collected\n", @@ -94,7 +94,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83ed0ecf", + "id": "cced3b6f", "metadata": { "hide-output": false }, @@ -131,7 +131,7 @@ }, { "cell_type": "markdown", - "id": "3cda636c", + "id": "b67f126e", "metadata": {}, "source": [ "During the 18th century, Britain and France fought four large wars.\n", @@ -151,7 +151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3a91131", + "id": "15cafb68", "metadata": { "hide-output": false }, @@ -188,7 +188,7 @@ }, { "cell_type": "markdown", - "id": "d0bfdc76", + "id": "e1537136", "metadata": {}, "source": [ "Figures Fig. 5.2 and Fig. 5.4 summarize British and French government fiscal policies during the century before the start the French Revolution in 1789.\n", @@ -237,7 +237,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d0a247f8", + "id": "abef069c", "metadata": { "hide-output": false }, @@ -274,7 +274,7 @@ }, { "cell_type": "markdown", - "id": "0c580819", + "id": "82e6a00b", "metadata": {}, "source": [ "Figure Fig. 5.3 shows that interest payments on government debt (i.e., so-called ‘‘debt service’’) were high fractions of government tax revenues in both Great Britain and France.\n", @@ -288,7 +288,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8bbdc3b", + "id": "48755cdd", "metadata": { "hide-output": false }, @@ -304,7 +304,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56c8e3c5", + "id": "3e75e27a", "metadata": { "hide-output": false }, @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "385b063c", + "id": "a1829781", "metadata": {}, "source": [ "Fig. 5.4 shows that in 1788 on the eve of the French Revolution government expenditures exceeded tax revenues.\n", @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "82fac168", + "id": "7189a591", "metadata": {}, "source": [ "## Nationalization, Privatization, Debt Reduction\n", @@ -455,7 +455,7 @@ }, { "cell_type": "markdown", - "id": "bd7143ec", + "id": "72aff03a", "metadata": {}, "source": [ "## Remaking the tax code and tax administration\n", @@ -481,7 +481,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf5808bc", + "id": "43e0e6f2", "metadata": { "hide-output": false }, @@ -508,7 +508,7 @@ }, { "cell_type": "markdown", - "id": "d6dd03bd", + "id": "4b7a03f2", "metadata": {}, "source": [ "According to Fig. 5.5, tax revenues per capita did not rise to their pre 1789 levels\n", @@ -525,7 +525,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f003e348", + "id": "640df46c", "metadata": { "hide-output": false }, @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "1ccf1c0e", + "id": "bf5a1d66", "metadata": {}, "source": [ "To cover the disrepancies between government expenditures and tax revenues revealed in Fig. 5.6, the French revolutionaries printed paper money and spent it.\n", @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b68264a1", + "id": "a816f392", "metadata": { "hide-output": false }, @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "645e725a", + "id": "ad03f9cd", "metadata": {}, "source": [ "Fig. 5.7 compares the revenues raised by printing money from 1789 to 1796 with tax revenues that the Ancient Regime had raised in 1788.\n", @@ -652,7 +652,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cec7a82a", + "id": "c2c8d9af", "metadata": { "hide-output": false }, @@ -692,7 +692,7 @@ }, { "cell_type": "markdown", - "id": "9fa5a883", + "id": "e63daf34", "metadata": {}, "source": [ "We have partioned Fig. 5.8 that shows the log of the price level and Fig. 5.9\n", @@ -730,7 +730,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc1d246e", + "id": "0bad050c", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ }, { "cell_type": "markdown", - "id": "9a76d3c9", + "id": "84f59bc9", "metadata": {}, "source": [ "The three clouds of points in Figure\n", @@ -794,7 +794,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de11301a", + "id": "078c2fca", "metadata": { "hide-output": false }, @@ -811,7 +811,7 @@ { "cell_type": "code", "execution_count": null, - "id": "428591d1", + "id": "e75d1eca", "metadata": { "hide-output": false }, @@ -829,7 +829,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9b9fa3f", + "id": "dc777b39", "metadata": { "hide-output": false }, @@ -849,7 +849,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0770afdd", + "id": "4085472d", "metadata": { "hide-output": false }, @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "da96b353", + "id": "9669f768", "metadata": {}, "source": [ "The three clouds of points in Figure\n", @@ -901,7 +901,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27c8eee2", + "id": "5a2af802", "metadata": { "hide-output": false }, @@ -921,7 +921,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c155eaab", + "id": "c24cd741", "metadata": { "hide-output": false }, @@ -950,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "34b9fc18", + "id": "71af6ab2", "metadata": {}, "source": [ "Now let’s regress inflation on real balances during the **real bills** period and plot the regression\n", @@ -960,7 +960,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b48b525", + "id": "6e5a0d66", "metadata": { "hide-output": false }, @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "466f3ce8", + "id": "26f6badf", "metadata": {}, "source": [ "The regression line in Fig. 5.12 shows that large increases in real balances of\n", @@ -1013,7 +1013,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f372629", + "id": "14ee824a", "metadata": { "hide-output": false }, @@ -1045,7 +1045,7 @@ }, { "cell_type": "markdown", - "id": "5806c717", + "id": "0220e5fb", "metadata": {}, "source": [ "The regression line in Fig. 5.13 shows that large increases in real balances of\n", @@ -1066,7 +1066,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9d87ac8", + "id": "3aee8fd4", "metadata": { "hide-output": false }, @@ -1098,7 +1098,7 @@ }, { "cell_type": "markdown", - "id": "b66cbb85", + "id": "46de2b81", "metadata": {}, "source": [ "Fig. 5.14 shows the results of regressing inflation on real balances during the\n", @@ -1108,7 +1108,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c206a5e", + "id": "8a8471aa", "metadata": { "hide-output": false }, @@ -1140,7 +1140,7 @@ }, { "cell_type": "markdown", - "id": "9e6f39d0", + "id": "3aebd906", "metadata": {}, "source": [ "Fig. 5.14 shows the results of regressing real balances on inflation during the\n", @@ -1149,7 +1149,7 @@ } ], "metadata": { - "date": 1722488541.1360345, + "date": 1722502937.474606, "filename": "french_rev.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/geom_series.ipynb b/_notebooks/geom_series.ipynb index c4a2d4ce..048b8a1d 100644 --- a/_notebooks/geom_series.ipynb +++ b/_notebooks/geom_series.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "44356fbb", + "id": "4ac0b3bf", "metadata": {}, "source": [ "\n", @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "aebea892", + "id": "90f6adc5", "metadata": {}, "source": [ "# Geometric Series for Elementary Economics" @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "b4126040", + "id": "63205d89", "metadata": {}, "source": [ "## Overview\n", @@ -55,7 +55,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0dc7668", + "id": "03105150", "metadata": { "hide-output": false }, @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "0947a420", + "id": "0d4782ee", "metadata": {}, "source": [ "## Key formulas\n", @@ -90,7 +90,7 @@ }, { "cell_type": "markdown", - "id": "dd4070ba", + "id": "904cb8d7", "metadata": {}, "source": [ "### Infinite geometric series\n", @@ -118,7 +118,7 @@ }, { "cell_type": "markdown", - "id": "21e3ec47", + "id": "a40b33a0", "metadata": {}, "source": [ "### Finite geometric series\n", @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "5f234d40", + "id": "4478f213", "metadata": {}, "source": [ "## Example: The Money Multiplier in Fractional Reserve Banking\n", @@ -184,7 +184,7 @@ }, { "cell_type": "markdown", - "id": "aeb15c66", + "id": "0eb4c77d", "metadata": {}, "source": [ "### A simple model\n", @@ -298,7 +298,7 @@ }, { "cell_type": "markdown", - "id": "952b7619", + "id": "478c0309", "metadata": {}, "source": [ "### Money multiplier\n", @@ -318,7 +318,7 @@ }, { "cell_type": "markdown", - "id": "1f5a2be4", + "id": "82b37340", "metadata": {}, "source": [ "## Example: The Keynesian Multiplier\n", @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "2f1b38f0", + "id": "5a004484", "metadata": {}, "source": [ "### Static version\n", @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "a3850038", + "id": "b09f2953", "metadata": {}, "source": [ "### Dynamic version\n", @@ -508,7 +508,7 @@ }, { "cell_type": "markdown", - "id": "46d87b11", + "id": "785989c4", "metadata": {}, "source": [ "## Example: Interest Rates and Present Values\n", @@ -580,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "1dbbb39f", + "id": "1d1c9ad9", "metadata": {}, "source": [ "### Accumulation\n", @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "a6f06121", + "id": "7feaeaef", "metadata": {}, "source": [ "### Discounting\n", @@ -636,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "0530a156", + "id": "0182f4fb", "metadata": {}, "source": [ "### Application to asset pricing\n", @@ -754,7 +754,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29e768f3", + "id": "c29d9a7c", "metadata": { "hide-output": false }, @@ -784,7 +784,7 @@ }, { "cell_type": "markdown", - "id": "29b7cc84", + "id": "98a22b9f", "metadata": {}, "source": [ "Now that we have defined our functions, we can plot some outcomes.\n", @@ -795,7 +795,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4a13d22", + "id": "0d6c3f68", "metadata": { "hide-output": false }, @@ -828,7 +828,7 @@ }, { "cell_type": "markdown", - "id": "d3a676a1", + "id": "6c16fd52", "metadata": {}, "source": [ "Evidently our approximations perform well for small values of $ T $.\n", @@ -842,7 +842,7 @@ { "cell_type": "code", "execution_count": null, - "id": "874b9b0c", + "id": "81826b2e", "metadata": { "hide-output": false }, @@ -864,7 +864,7 @@ }, { "cell_type": "markdown", - "id": "10072b76", + "id": "d9d0891b", "metadata": {}, "source": [ "The graph above shows how as duration $ T \\rightarrow +\\infty $,\n", @@ -878,7 +878,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9a69cbbe", + "id": "1d972fb0", "metadata": { "hide-output": false }, @@ -903,7 +903,7 @@ }, { "cell_type": "markdown", - "id": "4f441fd7", + "id": "864852c3", "metadata": {}, "source": [ "This graph gives a big hint for why the condition $ r > g $ is\n", @@ -920,7 +920,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d756bb82", + "id": "de9c6944", "metadata": { "hide-output": false }, @@ -951,7 +951,7 @@ }, { "cell_type": "markdown", - "id": "c1240334", + "id": "2cf2562e", "metadata": {}, "source": [ "We can use a little calculus to study how the present value $ p_0 $\n", @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6ab1db5", + "id": "730a09eb", "metadata": { "hide-output": false }, @@ -990,7 +990,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d53e1575", + "id": "5e6917a4", "metadata": { "hide-output": false }, @@ -1004,7 +1004,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d818cc9", + "id": "91ca68d8", "metadata": { "hide-output": false }, @@ -1017,7 +1017,7 @@ }, { "cell_type": "markdown", - "id": "62760dee", + "id": "833de307", "metadata": {}, "source": [ "We can see that for $ \\frac{\\partial p_0}{\\partial r}<0 $ as long as\n", @@ -1030,7 +1030,7 @@ }, { "cell_type": "markdown", - "id": "71d558ec", + "id": "1f905f15", "metadata": {}, "source": [ "## Back to the Keynesian multiplier\n", @@ -1043,7 +1043,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85652f0b", + "id": "7d1c849c", "metadata": { "hide-output": false }, @@ -1076,7 +1076,7 @@ }, { "cell_type": "markdown", - "id": "29884a9b", + "id": "f7d559bb", "metadata": {}, "source": [ "In this model, income grows over time, until it gradually converges to\n", @@ -1090,7 +1090,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47f6ee43", + "id": "27751301", "metadata": { "hide-output": false }, @@ -1111,7 +1111,7 @@ }, { "cell_type": "markdown", - "id": "0ee0887c", + "id": "10e82103", "metadata": {}, "source": [ "Increasing the marginal propensity to consume $ b $ increases the\n", @@ -1123,7 +1123,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8fa4b75c", + "id": "a9ecd458", "metadata": { "hide-output": false }, @@ -1154,7 +1154,7 @@ }, { "cell_type": "markdown", - "id": "10a3e248", + "id": "e0e0c6c7", "metadata": {}, "source": [ "Notice here, whether government spending increases from 0.3 to 0.4 or\n", @@ -1164,7 +1164,7 @@ } ], "metadata": { - "date": 1722488541.1764092, + "date": 1722502937.5146832, "filename": "geom_series.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/greek_square.ipynb b/_notebooks/greek_square.ipynb index 115cccbb..422fffa4 100644 --- a/_notebooks/greek_square.ipynb +++ b/_notebooks/greek_square.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "890e87b4", + "id": "dd8e4c3b", "metadata": {}, "source": [ "# Computing Square Roots" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "23dfc0ee", + "id": "95e0bb2f", "metadata": {}, "source": [ "## Introduction\n", @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "0e61c368", + "id": "e4e41be3", "metadata": {}, "source": [ "## Perfect squares and irrational numbers\n", @@ -60,7 +60,7 @@ }, { "cell_type": "markdown", - "id": "3b2e2bac", + "id": "781c46d4", "metadata": {}, "source": [ "## Second-order linear difference equations\n", @@ -204,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "ac9264a1", + "id": "7395b269", "metadata": {}, "source": [ "## Algorithm of the Ancient Greeks\n", @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "7800cd2c", + "id": "1b87a793", "metadata": {}, "source": [ "## Implementation\n", @@ -375,7 +375,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c146cfc8", + "id": "e882ea83", "metadata": { "hide-output": false }, @@ -388,7 +388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8aa82ff", + "id": "b584b6f9", "metadata": { "hide-output": false }, @@ -448,7 +448,7 @@ }, { "cell_type": "markdown", - "id": "e419fa1f", + "id": "e7716079", "metadata": {}, "source": [ "Now we consider cases where $ (\\eta_1, \\eta_2) = (0, 1) $ and $ (\\eta_1, \\eta_2) = (1, 0) $" @@ -457,7 +457,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8282190e", + "id": "f1aacdc9", "metadata": { "hide-output": false }, @@ -471,7 +471,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22da9685", + "id": "4c9d686d", "metadata": { "hide-output": false }, @@ -490,7 +490,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0910980", + "id": "bac5e6a0", "metadata": { "hide-output": false }, @@ -505,7 +505,7 @@ }, { "cell_type": "markdown", - "id": "b70c591e", + "id": "c784ec8c", "metadata": {}, "source": [ "We find that convergence is immediate.\n", @@ -515,7 +515,7 @@ }, { "cell_type": "markdown", - "id": "146ab1ca", + "id": "07f8232e", "metadata": {}, "source": [ "## Vectorizing the difference equation\n", @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0750fc4c", + "id": "44ce1279", "metadata": { "hide-output": false }, @@ -606,7 +606,7 @@ }, { "cell_type": "markdown", - "id": "d7ffd487", + "id": "b40f0d4b", "metadata": {}, "source": [ "Let’s compare the eigenvalues to the roots [(17.15)](#equation-eq-secretweapon) of equation\n", @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b3e32be", + "id": "bad42498", "metadata": { "hide-output": false }, @@ -628,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "290426dd", + "id": "17bf1bb0", "metadata": {}, "source": [ "Hence we confirmed [(17.17)](#equation-eq-eigen-sqrt).\n", @@ -654,7 +654,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5517debf", + "id": "370e6aa3", "metadata": { "hide-output": false }, @@ -688,7 +688,7 @@ }, { "cell_type": "markdown", - "id": "e815c371", + "id": "1651220f", "metadata": {}, "source": [ "## Invariant subspace approach\n", @@ -785,7 +785,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb534362", + "id": "654de831", "metadata": { "hide-output": false }, @@ -801,7 +801,7 @@ }, { "cell_type": "markdown", - "id": "3eb94a04", + "id": "7cb5f17b", "metadata": {}, "source": [ "We find $ x_{1,0}^* = 0 $.\n", @@ -812,7 +812,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89620d86", + "id": "9501a885", "metadata": { "hide-output": false }, @@ -828,7 +828,7 @@ }, { "cell_type": "markdown", - "id": "f1ce0bc8", + "id": "8cda45ba", "metadata": {}, "source": [ "We find $ x_{2,0}^* = 0 $." @@ -837,7 +837,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c44fca2c", + "id": "1dd8fd8b", "metadata": { "hide-output": false }, @@ -855,7 +855,7 @@ }, { "cell_type": "markdown", - "id": "5c4842ab", + "id": "288321ae", "metadata": {}, "source": [ "The following graph shows the ratios $ y_t / y_{t-1} $ for the two cases.\n", @@ -866,7 +866,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d9149c2", + "id": "4ca432d1", "metadata": { "hide-output": false }, @@ -903,7 +903,7 @@ }, { "cell_type": "markdown", - "id": "a783d963", + "id": "89cd387d", "metadata": {}, "source": [ "## Concluding remarks\n", @@ -918,7 +918,7 @@ } ], "metadata": { - "date": 1722488541.206275, + "date": 1722502937.543686, "filename": "greek_square.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/heavy_tails.ipynb b/_notebooks/heavy_tails.ipynb index 2a721b57..c076b3e2 100644 --- a/_notebooks/heavy_tails.ipynb +++ b/_notebooks/heavy_tails.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5093485a", + "id": "ec2426a3", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "bf14a8f6", + "id": "4181d80b", "metadata": {}, "source": [ "# Heavy-Tailed Distributions\n", @@ -22,7 +22,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a31cb534", + "id": "77c35cbf", "metadata": { "hide-output": false }, @@ -33,7 +33,7 @@ }, { "cell_type": "markdown", - "id": "9e4d4aae", + "id": "5ec153ac", "metadata": {}, "source": [ "We use the following imports." @@ -42,7 +42,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a9af33c", + "id": "6aeeff7f", "metadata": { "hide-output": false }, @@ -62,7 +62,7 @@ }, { "cell_type": "markdown", - "id": "282080e5", + "id": "38e3f387", "metadata": {}, "source": [ "## Overview\n", @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "9a50370c", + "id": "5b172d04", "metadata": {}, "source": [ "### Introduction: light tails\n", @@ -113,7 +113,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e19e86b5", + "id": "aa78f01f", "metadata": { "hide-output": false }, @@ -130,7 +130,7 @@ }, { "cell_type": "markdown", - "id": "3d0b1ebf", + "id": "7a3877f6", "metadata": {}, "source": [ "Notice how\n", @@ -145,7 +145,7 @@ { "cell_type": "code", "execution_count": null, - "id": "30a5421d", + "id": "b6696a91", "metadata": { "hide-output": false }, @@ -156,7 +156,7 @@ }, { "cell_type": "markdown", - "id": "6afb02e1", + "id": "d109d349", "metadata": {}, "source": [ "Here’s another view of draws from the same distribution:" @@ -165,7 +165,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a842b179", + "id": "a88212f7", "metadata": { "hide-output": false }, @@ -184,7 +184,7 @@ }, { "cell_type": "markdown", - "id": "01f2b4a0", + "id": "b781d932", "metadata": {}, "source": [ "We have plotted each individual draw $ X_i $ against $ i $.\n", @@ -208,7 +208,7 @@ }, { "cell_type": "markdown", - "id": "cc1893c4", + "id": "47562683", "metadata": {}, "source": [ "### When are light tails valid?\n", @@ -237,7 +237,7 @@ }, { "cell_type": "markdown", - "id": "56df15ee", + "id": "f4f46be0", "metadata": {}, "source": [ "### Returns on assets\n", @@ -257,7 +257,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e74a935", + "id": "7398e792", "metadata": { "hide-output": false }, @@ -269,7 +269,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3bf0bb53", + "id": "c5fbe4ee", "metadata": { "hide-output": false }, @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "4276571d", + "id": "9a926686", "metadata": {}, "source": [ "This data looks different to the draws from the normal distribution we saw above.\n", @@ -303,7 +303,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28c32969", + "id": "6c636d3f", "metadata": { "hide-output": false }, @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8dcd6dd", + "id": "ca070d0a", "metadata": { "hide-output": false }, @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "c8121b87", + "id": "0b2da196", "metadata": {}, "source": [ "The histogram also looks different to the histogram of the normal\n", @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3bf519b", + "id": "243ce6c6", "metadata": { "hide-output": false }, @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "957b5554", + "id": "f2d09128", "metadata": {}, "source": [ "If we look at higher frequency returns data (e.g., tick-by-tick), we often see\n", @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "b7526569", + "id": "9535ebd8", "metadata": {}, "source": [ "### Other data\n", @@ -415,7 +415,7 @@ }, { "cell_type": "markdown", - "id": "ba694af2", + "id": "ea8d2f80", "metadata": {}, "source": [ "### Why should we care?\n", @@ -437,7 +437,7 @@ }, { "cell_type": "markdown", - "id": "3f7b9956", + "id": "d0a55343", "metadata": {}, "source": [ "## Visual comparisons\n", @@ -453,7 +453,7 @@ }, { "cell_type": "markdown", - "id": "273d78c2", + "id": "1ed20d4a", "metadata": {}, "source": [ "### Simulations\n", @@ -471,7 +471,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8e168b8a", + "id": "c5248c6e", "metadata": { "hide-output": false }, @@ -507,7 +507,7 @@ }, { "cell_type": "markdown", - "id": "aa31816d", + "id": "05f36251", "metadata": {}, "source": [ "In the top subfigure, the standard deviation of the normal distribution is 2,\n", @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "0600e3da", + "id": "2ca69870", "metadata": {}, "source": [ "### Nonnegative distributions\n", @@ -542,7 +542,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ea7858a", + "id": "47adf455", "metadata": { "hide-output": false }, @@ -563,7 +563,7 @@ }, { "cell_type": "markdown", - "id": "a0168834", + "id": "0e2259ee", "metadata": {}, "source": [ "Another nonnegative distribution is the [Pareto distribution](https://en.wikipedia.org/wiki/Pareto_distribution).\n", @@ -607,7 +607,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b5e7f40", + "id": "b0977ce1", "metadata": { "hide-output": false }, @@ -628,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "ed88d4bb", + "id": "38b562f7", "metadata": {}, "source": [ "Notice how extreme outcomes are more common." @@ -636,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "a5711433", + "id": "2b9774f5", "metadata": {}, "source": [ "### Counter CDFs\n", @@ -674,7 +674,7 @@ }, { "cell_type": "markdown", - "id": "3bf31fbd", + "id": "df8ad557", "metadata": {}, "source": [ "### Exercise 21.1\n", @@ -684,7 +684,7 @@ }, { "cell_type": "markdown", - "id": "59851619", + "id": "d95542ec", "metadata": {}, "source": [ "### Solution to[ Exercise 21.1](https://intro.quantecon.org/#ht_ex_x1)\n", @@ -709,7 +709,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20867bd3", + "id": "b2ce015c", "metadata": { "hide-output": false }, @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "559096d7", + "id": "4be71dbb", "metadata": {}, "source": [ "Here’s a log-log plot of the same functions, which makes visual comparison\n", @@ -738,7 +738,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19b72815", + "id": "b8f922f7", "metadata": { "hide-output": false }, @@ -756,7 +756,7 @@ }, { "cell_type": "markdown", - "id": "be69477e", + "id": "a34ca344", "metadata": {}, "source": [ "In the log-log plot, the Pareto CCDF is linear, while the exponential one is\n", @@ -768,7 +768,7 @@ }, { "cell_type": "markdown", - "id": "4df00e88", + "id": "d9f420cc", "metadata": {}, "source": [ "### Empirical CCDFs\n", @@ -787,7 +787,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8518ac51", + "id": "5a3006aa", "metadata": { "hide-output": false }, @@ -800,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "ee7d0cf5", + "id": "95d623eb", "metadata": {}, "source": [ "Here’s a figure containing some empirical CCDFs from simulated data." @@ -809,7 +809,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa446359", + "id": "ab35c7c1", "metadata": { "hide-output": false }, @@ -850,7 +850,7 @@ }, { "cell_type": "markdown", - "id": "cf4607d5", + "id": "a8011d5a", "metadata": {}, "source": [ "As with the CCDF, the empirical CCDF from the Pareto distributions is\n", @@ -861,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "9fbef616", + "id": "849f1f05", "metadata": {}, "source": [ "#### Q-Q Plots\n", @@ -876,7 +876,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6ec2c2a3", + "id": "dcf6d910", "metadata": { "hide-output": false }, @@ -889,7 +889,7 @@ }, { "cell_type": "markdown", - "id": "b7b308fc", + "id": "edd108fb", "metadata": {}, "source": [ "We can now compare this with the exponential, log-normal, and Pareto distributions" @@ -898,7 +898,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d7c639a", + "id": "79faf0ce", "metadata": { "hide-output": false }, @@ -917,7 +917,7 @@ }, { "cell_type": "markdown", - "id": "4b90f06f", + "id": "832ded3f", "metadata": {}, "source": [ "### Power laws\n", @@ -958,7 +958,7 @@ }, { "cell_type": "markdown", - "id": "c1fb2cbf", + "id": "8f9225d7", "metadata": {}, "source": [ "## Heavy tails in economic cross-sections\n", @@ -979,7 +979,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ae33eec", + "id": "d3a42a2a", "metadata": { "hide-output": false }, @@ -1045,7 +1045,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55fbca04", + "id": "b36835b0", "metadata": { "hide-output": false }, @@ -1074,7 +1074,7 @@ }, { "cell_type": "markdown", - "id": "1f7fff2c", + "id": "1d63071b", "metadata": {}, "source": [ "### Firm size\n", @@ -1085,7 +1085,7 @@ { "cell_type": "code", "execution_count": null, - "id": "03d40857", + "id": "7cde5d05", "metadata": { "hide-output": false }, @@ -1105,7 +1105,7 @@ }, { "cell_type": "markdown", - "id": "949628c9", + "id": "fa6ddb37", "metadata": {}, "source": [ "### City size\n", @@ -1118,7 +1118,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c867240", + "id": "82033118", "metadata": { "hide-output": false }, @@ -1138,7 +1138,7 @@ }, { "cell_type": "markdown", - "id": "92a3f918", + "id": "11860f4a", "metadata": {}, "source": [ "### Wealth\n", @@ -1151,7 +1151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d986af3", + "id": "59fab41a", "metadata": { "hide-output": false }, @@ -1184,7 +1184,7 @@ }, { "cell_type": "markdown", - "id": "ae280c9f", + "id": "7847318f", "metadata": {}, "source": [ "### GDP\n", @@ -1197,7 +1197,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cda20b1e", + "id": "2bc88c58", "metadata": { "hide-output": false }, @@ -1219,7 +1219,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4722737d", + "id": "9b52b53c", "metadata": { "hide-output": false }, @@ -1235,7 +1235,7 @@ }, { "cell_type": "markdown", - "id": "f017d0e5", + "id": "61c32b8b", "metadata": {}, "source": [ "The plot is concave rather than linear, so the distribution has light tails.\n", @@ -1248,7 +1248,7 @@ }, { "cell_type": "markdown", - "id": "176284dd", + "id": "7a245248", "metadata": {}, "source": [ "## Failure of the LLN\n", @@ -1282,7 +1282,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d13a7722", + "id": "cb45dd6d", "metadata": { "hide-output": false }, @@ -1314,7 +1314,7 @@ }, { "cell_type": "markdown", - "id": "d8c58aeb", + "id": "e5fae9f8", "metadata": {}, "source": [ "The sequence shows no sign of converging.\n", @@ -1327,7 +1327,7 @@ }, { "cell_type": "markdown", - "id": "5e086dc3", + "id": "e8834616", "metadata": {}, "source": [ "## Why do heavy tails matter?\n", @@ -1345,7 +1345,7 @@ }, { "cell_type": "markdown", - "id": "1975f931", + "id": "b1623048", "metadata": {}, "source": [ "### Diversification\n", @@ -1392,7 +1392,7 @@ }, { "cell_type": "markdown", - "id": "a87cbd7f", + "id": "16152631", "metadata": {}, "source": [ "### Fiscal policy\n", @@ -1410,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "db730ba3", + "id": "85d09048", "metadata": {}, "source": [ "## Classifying tail properties\n", @@ -1432,7 +1432,7 @@ }, { "cell_type": "markdown", - "id": "b450bf4c", + "id": "03fe4795", "metadata": {}, "source": [ "### Light and heavy tails\n", @@ -1485,7 +1485,7 @@ }, { "cell_type": "markdown", - "id": "bc75c01e", + "id": "363a42fe", "metadata": {}, "source": [ "## Further reading\n", @@ -1506,7 +1506,7 @@ }, { "cell_type": "markdown", - "id": "ec5ba42b", + "id": "cfa031b5", "metadata": {}, "source": [ "## Exercises" @@ -1514,7 +1514,7 @@ }, { "cell_type": "markdown", - "id": "f2bf0323", + "id": "b84856f0", "metadata": {}, "source": [ "## Exercise 21.2\n", @@ -1525,7 +1525,7 @@ }, { "cell_type": "markdown", - "id": "f7c877df", + "id": "ab0d06b2", "metadata": {}, "source": [ "## Solution to[ Exercise 21.2](https://intro.quantecon.org/#ht_ex2)\n", @@ -1556,7 +1556,7 @@ }, { "cell_type": "markdown", - "id": "b7084028", + "id": "134f7ef2", "metadata": {}, "source": [ "## Exercise 21.3\n", @@ -1572,7 +1572,7 @@ }, { "cell_type": "markdown", - "id": "dec370c0", + "id": "c2f9fb4f", "metadata": {}, "source": [ "## Solution to[ Exercise 21.3](https://intro.quantecon.org/#ht_ex3)" @@ -1581,7 +1581,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bbaa96d1", + "id": "8962265b", "metadata": { "hide-output": false }, @@ -1610,7 +1610,7 @@ }, { "cell_type": "markdown", - "id": "df047659", + "id": "c1890ca4", "metadata": {}, "source": [ "## Exercise 21.4\n", @@ -1672,7 +1672,7 @@ }, { "cell_type": "markdown", - "id": "420efc38", + "id": "b0f4bbe5", "metadata": {}, "source": [ "## Solution to[ Exercise 21.4](https://intro.quantecon.org/#ht_ex5)\n", @@ -1711,7 +1711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1cb72667", + "id": "9f19b91f", "metadata": { "hide-output": false }, @@ -1736,7 +1736,7 @@ }, { "cell_type": "markdown", - "id": "34e61b16", + "id": "553e01eb", "metadata": {}, "source": [ "Let’s compute the lognormal parameters:" @@ -1745,7 +1745,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b044e246", + "id": "38daafe9", "metadata": { "hide-output": false }, @@ -1758,7 +1758,7 @@ }, { "cell_type": "markdown", - "id": "acac53b0", + "id": "b9bb2573", "metadata": {}, "source": [ "Here’s a function to compute a single estimate of tax revenue for a particular\n", @@ -1768,7 +1768,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e90e6ca", + "id": "9e671d79", "metadata": { "hide-output": false }, @@ -1787,7 +1787,7 @@ }, { "cell_type": "markdown", - "id": "946f3638", + "id": "956753ee", "metadata": {}, "source": [ "Now let’s generate the violin plot." @@ -1796,7 +1796,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b846d4d3", + "id": "8e10afd2", "metadata": { "hide-output": false }, @@ -1823,7 +1823,7 @@ }, { "cell_type": "markdown", - "id": "e8798b78", + "id": "f4b26851", "metadata": {}, "source": [ "Finally, let’s print the means and standard deviations." @@ -1832,7 +1832,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e9e11d4", + "id": "ca394927", "metadata": { "hide-output": false }, @@ -1844,7 +1844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af1853ba", + "id": "a526822c", "metadata": { "hide-output": false }, @@ -1855,7 +1855,7 @@ }, { "cell_type": "markdown", - "id": "76991e92", + "id": "ad277a0a", "metadata": {}, "source": [ "Looking at the output of the code, our main conclusion is that the Pareto\n", @@ -1864,7 +1864,7 @@ }, { "cell_type": "markdown", - "id": "cb8f9368", + "id": "866e2572", "metadata": {}, "source": [ "## Exercise 21.5\n", @@ -1886,7 +1886,7 @@ }, { "cell_type": "markdown", - "id": "8c68b48f", + "id": "1a29b6f8", "metadata": {}, "source": [ "## Solution to[ Exercise 21.5](https://intro.quantecon.org/#ht_ex_cauchy)\n", @@ -1912,7 +1912,7 @@ } ], "metadata": { - "date": 1722488541.271759, + "date": 1722502937.6104822, "filename": "heavy_tails.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/inequality.ipynb b/_notebooks/inequality.ipynb index 0f9bbdaf..4cc3cf51 100644 --- a/_notebooks/inequality.ipynb +++ b/_notebooks/inequality.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "83a04d00", + "id": "cc0debd9", "metadata": {}, "source": [ "# Income and Wealth Inequality" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "b599d2ab", + "id": "628c83e6", "metadata": {}, "source": [ "## Overview\n", @@ -43,7 +43,7 @@ }, { "cell_type": "markdown", - "id": "017b957f", + "id": "597105d9", "metadata": {}, "source": [ "### Some history\n", @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "67fd1fb5", + "id": "d5ebd938", "metadata": {}, "source": [ "### Measurement\n", @@ -88,7 +88,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87ee96fd", + "id": "ec81a3e6", "metadata": { "hide-output": false }, @@ -99,7 +99,7 @@ }, { "cell_type": "markdown", - "id": "064fff89", + "id": "f2b47c1a", "metadata": {}, "source": [ "We will also use the following imports." @@ -108,7 +108,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83f329ba", + "id": "281821a4", "metadata": { "hide-output": false }, @@ -124,7 +124,7 @@ }, { "cell_type": "markdown", - "id": "05fc9a7f", + "id": "af864acd", "metadata": {}, "source": [ "## The Lorenz curve\n", @@ -136,7 +136,7 @@ }, { "cell_type": "markdown", - "id": "f099e265", + "id": "a4be48f5", "metadata": {}, "source": [ "### Definition\n", @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "a814276d", + "id": "69c41afb", "metadata": {}, "source": [ "### \n", @@ -187,7 +187,7 @@ }, { "cell_type": "markdown", - "id": "e81bd2f8", + "id": "7f3b964a", "metadata": {}, "source": [ "### Lorenz curves of simulated data\n", @@ -205,7 +205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdd3fe8a", + "id": "81b8fb41", "metadata": { "hide-output": false }, @@ -259,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "fc0d47cc", + "id": "c5467d36", "metadata": {}, "source": [ "In the next figure, we generate $ n=2000 $ draws from a lognormal\n", @@ -277,7 +277,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47501f0a", + "id": "80a77f5b", "metadata": { "hide-output": false }, @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "8381275a", + "id": "df56cc93", "metadata": {}, "source": [ "### Lorenz curves for US data\n", @@ -320,7 +320,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f75d9559", + "id": "cafbfc4b", "metadata": { "hide-output": false }, @@ -334,7 +334,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a68a716", + "id": "06bd8171", "metadata": { "hide-output": false }, @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "92acc895", + "id": "18a90cb9", "metadata": {}, "source": [ "The next code block uses data stored in dataframe `df_income_wealth` to generate the Lorenz curves.\n", @@ -357,7 +357,7 @@ { "cell_type": "code", "execution_count": null, - "id": "58bbcc8e", + "id": "af3a979b", "metadata": { "hide-output": false }, @@ -403,7 +403,7 @@ }, { "cell_type": "markdown", - "id": "cc035664", + "id": "e4e35772", "metadata": {}, "source": [ "Now we plot Lorenz curves for net wealth, total income and labor income in the\n", @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "353cccf1", + "id": "b342392c", "metadata": { "hide-output": false }, @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "3fb3734e", + "id": "3d4bbef6", "metadata": {}, "source": [ "One key finding from this figure is that wealth inequality is more extreme than income inequality." @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "226dffca", + "id": "97fad8a4", "metadata": {}, "source": [ "## The Gini coefficient\n", @@ -458,7 +458,7 @@ }, { "cell_type": "markdown", - "id": "2996332d", + "id": "986327dc", "metadata": {}, "source": [ "### Definition\n", @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "3062e568", + "id": "6c2d1bb2", "metadata": {}, "source": [ "### \n", @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e45ab754", + "id": "e70d2674", "metadata": { "hide-output": false }, @@ -514,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "ffcced89", + "id": "361004aa", "metadata": {}, "source": [ "In fact the Gini coefficient can also be expressed as\n", @@ -530,7 +530,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5a58184", + "id": "de383ae0", "metadata": { "hide-output": false }, @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "714650b4", + "id": "f211e72e", "metadata": {}, "source": [ "The World in Data project has a [graphical exploration of the Lorenz curve and the Gini coefficient](https://ourworldindata.org/what-is-the-gini-coefficient)" @@ -562,7 +562,7 @@ }, { "cell_type": "markdown", - "id": "26e917d5", + "id": "3af8f98f", "metadata": {}, "source": [ "### Gini coefficient of simulated data\n", @@ -578,7 +578,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca30bcfe", + "id": "8498aabb", "metadata": { "hide-output": false }, @@ -614,7 +614,7 @@ }, { "cell_type": "markdown", - "id": "7fd52e72", + "id": "6a7ac71f", "metadata": {}, "source": [ "Now we can compute the Gini coefficients for five different populations.\n", @@ -636,7 +636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca922929", + "id": "3da0c12b", "metadata": { "hide-output": false }, @@ -657,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "2f6a1133", + "id": "d2698896", "metadata": {}, "source": [ "Let’s build a function that returns a figure (so that we can use it later in the lecture)." @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "754cbf98", + "id": "fe9948a9", "metadata": { "hide-output": false }, @@ -684,7 +684,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9d6c7af", + "id": "d12de0d7", "metadata": { "hide-output": false }, @@ -700,7 +700,7 @@ }, { "cell_type": "markdown", - "id": "e24ab5bf", + "id": "ccd8ac13", "metadata": {}, "source": [ "The plots show that inequality rises with $ \\sigma $, according to the Gini\n", @@ -709,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "3fb8cf2d", + "id": "c0d99261", "metadata": {}, "source": [ "### Gini coefficient for income (US data)\n", @@ -724,7 +724,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b641bbbf", + "id": "356c5723", "metadata": { "hide-output": false }, @@ -735,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "4369d059", + "id": "a5b5f5a5", "metadata": {}, "source": [ "We now know the series ID is `SI.POV.GINI`.\n", @@ -748,7 +748,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4589739", + "id": "57aee051", "metadata": { "hide-output": false }, @@ -771,7 +771,7 @@ }, { "cell_type": "markdown", - "id": "8021d5c3", + "id": "abd605b4", "metadata": {}, "source": [ "We can see in Fig. 6.6 that across 50 years of data and all countries the measure varies between 20 and 65.\n", @@ -782,7 +782,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52d2ec49", + "id": "217fc9dd", "metadata": { "hide-output": false }, @@ -796,7 +796,7 @@ }, { "cell_type": "markdown", - "id": "193095e8", + "id": "db407773", "metadata": {}, "source": [ "(This package often returns data with year information contained in the columns. This is not always convenient for simple plotting with pandas so it can be useful to transpose the results before plotting.)" @@ -805,7 +805,7 @@ { "cell_type": "code", "execution_count": null, - "id": "02bc8896", + "id": "bce04783", "metadata": { "hide-output": false }, @@ -817,7 +817,7 @@ }, { "cell_type": "markdown", - "id": "c5e66fb5", + "id": "74c21bdd", "metadata": {}, "source": [ "Let us take a look at the data for the US." @@ -826,7 +826,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a31ea81", + "id": "29267ee1", "metadata": { "hide-output": false }, @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "9a4b81aa", + "id": "e76398ca", "metadata": {}, "source": [ "As can be seen in Fig. 6.7, the income Gini\n", @@ -854,7 +854,7 @@ }, { "cell_type": "markdown", - "id": "4377d9a5", + "id": "3ed42846", "metadata": {}, "source": [ "### Gini coefficient for wealth\n", @@ -869,7 +869,7 @@ { "cell_type": "code", "execution_count": null, - "id": "71422f84", + "id": "8511eb26", "metadata": { "hide-output": false }, @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "f766c1c3", + "id": "a3b36c15", "metadata": {}, "source": [ "[This notebook](https://github.com/QuantEcon/lecture-python-intro/tree/main/lectures/_static/lecture_specific/inequality/data.ipynb) can be used to compute this information over the full dataset." @@ -889,7 +889,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0c0aa2c", + "id": "8561ed39", "metadata": { "hide-output": false }, @@ -902,7 +902,7 @@ }, { "cell_type": "markdown", - "id": "89a408c7", + "id": "4503d6a8", "metadata": {}, "source": [ "Let’s plot the Gini coefficients for net wealth." @@ -911,7 +911,7 @@ { "cell_type": "code", "execution_count": null, - "id": "139b6739", + "id": "f125c28f", "metadata": { "hide-output": false }, @@ -926,7 +926,7 @@ }, { "cell_type": "markdown", - "id": "bd3bd911", + "id": "eaba8bf7", "metadata": {}, "source": [ "The time series for the wealth Gini exhibits a U-shape, falling until the early\n", @@ -939,7 +939,7 @@ }, { "cell_type": "markdown", - "id": "0bd13812", + "id": "b717bbd1", "metadata": {}, "source": [ "### Cross-country comparisons of income inequality\n", @@ -954,7 +954,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b13d3d02", + "id": "156075e1", "metadata": { "hide-output": false }, @@ -966,7 +966,7 @@ }, { "cell_type": "markdown", - "id": "bae9c2cd", + "id": "46f5df89", "metadata": {}, "source": [ "There are 167 countries represented in this dataset.\n", @@ -977,7 +977,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f09a788b", + "id": "70a0478c", "metadata": { "hide-output": false }, @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "d3c79634", + "id": "dde65d2d", "metadata": {}, "source": [ "We see that Norway has a shorter time series.\n", @@ -1003,7 +1003,7 @@ { "cell_type": "code", "execution_count": null, - "id": "67e88314", + "id": "c4fbd076", "metadata": { "hide-output": false }, @@ -1014,7 +1014,7 @@ }, { "cell_type": "markdown", - "id": "63243697", + "id": "87a78d8e", "metadata": {}, "source": [ "The data for Norway in this dataset goes back to 1979 but there are gaps in the time series and matplotlib is not showing those data points.\n", @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6c6d3bb", + "id": "0985315e", "metadata": { "hide-output": false }, @@ -1041,7 +1041,7 @@ }, { "cell_type": "markdown", - "id": "0ccf46fc", + "id": "336066f1", "metadata": {}, "source": [ "From this plot we can observe that the US has a higher Gini coefficient (i.e.\n", @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "28ca29f9", + "id": "7a114977", "metadata": {}, "source": [ "### Gini Coefficient and GDP per capita (over time)\n", @@ -1066,7 +1066,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aef24065", + "id": "2417eec5", "metadata": { "hide-output": false }, @@ -1081,7 +1081,7 @@ }, { "cell_type": "markdown", - "id": "9b5677d5", + "id": "d9e6e21b", "metadata": {}, "source": [ "We can rearrange the data so that we can plot GDP per capita and the Gini coefficient across years" @@ -1090,7 +1090,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98586371", + "id": "4d8e7a28", "metadata": { "hide-output": false }, @@ -1103,7 +1103,7 @@ }, { "cell_type": "markdown", - "id": "616ad2c5", + "id": "d85084b6", "metadata": {}, "source": [ "Now we can get the GDP per capita data into a shape that can be merged with `plot_data`" @@ -1112,7 +1112,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0710a65c", + "id": "2fef025f", "metadata": { "hide-output": false }, @@ -1127,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "6093f124", + "id": "4d36e62c", "metadata": {}, "source": [ "Now we use Plotly to build a plot with GDP per capita on the y-axis and the Gini coefficient on the x-axis." @@ -1136,7 +1136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fea76a8d", + "id": "5aa1ee9f", "metadata": { "hide-output": false }, @@ -1148,7 +1148,7 @@ }, { "cell_type": "markdown", - "id": "0abbfad6", + "id": "c3d94401", "metadata": {}, "source": [ "The time series for all three countries start and stop in different years. We will add a year mask to the data to\n", @@ -1158,7 +1158,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2af49662", + "id": "8bf025d7", "metadata": { "hide-output": false }, @@ -1171,7 +1171,7 @@ }, { "cell_type": "markdown", - "id": "ca9ef732", + "id": "ac7eb1b5", "metadata": {}, "source": [ "\n", @@ -1181,7 +1181,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6679e17", + "id": "45828008", "metadata": { "hide-output": false }, @@ -1201,7 +1201,7 @@ }, { "cell_type": "markdown", - "id": "a066eb24", + "id": "181a2b0f", "metadata": {}, "source": [ "This plot shows that all three Western economies GDP per capita has grown over\n", @@ -1216,7 +1216,7 @@ }, { "cell_type": "markdown", - "id": "abf22a74", + "id": "e042145c", "metadata": {}, "source": [ "## Top shares\n", @@ -1228,7 +1228,7 @@ }, { "cell_type": "markdown", - "id": "f2b2efc6", + "id": "82ec4c71", "metadata": {}, "source": [ "### Definition\n", @@ -1241,7 +1241,7 @@ }, { "cell_type": "markdown", - "id": "476c195f", + "id": "c1ccb1a4", "metadata": {}, "source": [ "### \n", @@ -1264,7 +1264,7 @@ { "cell_type": "code", "execution_count": null, - "id": "259e43e5", + "id": "ca50ecae", "metadata": { "hide-output": false }, @@ -1312,7 +1312,7 @@ }, { "cell_type": "markdown", - "id": "3bb52a7d", + "id": "ae6e44f2", "metadata": {}, "source": [ "Then let’s plot the top shares." @@ -1321,7 +1321,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3c651f5", + "id": "3df1ac5f", "metadata": { "hide-output": false }, @@ -1342,7 +1342,7 @@ }, { "cell_type": "markdown", - "id": "df60ac15", + "id": "bc534515", "metadata": {}, "source": [ "## Exercises" @@ -1350,7 +1350,7 @@ }, { "cell_type": "markdown", - "id": "8be4a2a4", + "id": "a3431ec6", "metadata": {}, "source": [ "## Exercise 6.1\n", @@ -1374,7 +1374,7 @@ }, { "cell_type": "markdown", - "id": "38d78b86", + "id": "d1af2d5c", "metadata": {}, "source": [ "## Solution to[ Exercise 6.1](https://intro.quantecon.org/#inequality_ex1)\n", @@ -1385,7 +1385,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28135b1b", + "id": "ae3fc1eb", "metadata": { "hide-output": false }, @@ -1402,7 +1402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4196d313", + "id": "3ad9fd33", "metadata": { "hide-output": false }, @@ -1430,7 +1430,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16286da1", + "id": "e53c769f", "metadata": { "hide-output": false }, @@ -1447,7 +1447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c50498ff", + "id": "690abd3f", "metadata": { "hide-output": false }, @@ -1464,7 +1464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51b56819", + "id": "fa2ac3ce", "metadata": { "hide-output": false }, @@ -1480,7 +1480,7 @@ }, { "cell_type": "markdown", - "id": "5a518093", + "id": "08b1b5d9", "metadata": {}, "source": [ "## Exercise 6.2\n", @@ -1494,7 +1494,7 @@ }, { "cell_type": "markdown", - "id": "e9b86c77", + "id": "958aeb78", "metadata": {}, "source": [ "## Solution to[ Exercise 6.2](https://intro.quantecon.org/#inequality_ex2)\n", @@ -1505,7 +1505,7 @@ { "cell_type": "code", "execution_count": null, - "id": "359569a6", + "id": "56f6fa9f", "metadata": { "hide-output": false }, @@ -1519,7 +1519,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41471e5b", + "id": "49691eed", "metadata": { "hide-output": false }, @@ -1533,7 +1533,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bdd83ccb", + "id": "4fc42038", "metadata": { "hide-output": false }, @@ -1553,7 +1553,7 @@ }, { "cell_type": "markdown", - "id": "b61be8c4", + "id": "86360d25", "metadata": {}, "source": [ "## Exercise 6.3\n", @@ -1571,7 +1571,7 @@ }, { "cell_type": "markdown", - "id": "134abe31", + "id": "1a6b621a", "metadata": {}, "source": [ "## Solution to[ Exercise 6.3](https://intro.quantecon.org/#inequality_ex3)\n", @@ -1582,7 +1582,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a61f9c36", + "id": "1ef057b6", "metadata": { "hide-output": false }, @@ -1594,7 +1594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77f0e611", + "id": "7a65ee07", "metadata": { "hide-output": false }, @@ -1605,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "48da8bcc", + "id": "9ed483db", "metadata": {}, "source": [ "We will focus on wealth variable `n_wealth` to compute a Gini coefficient for the year 2016." @@ -1614,7 +1614,7 @@ { "cell_type": "code", "execution_count": null, - "id": "115b7de5", + "id": "0d88710d", "metadata": { "hide-output": false }, @@ -1626,7 +1626,7 @@ { "cell_type": "code", "execution_count": null, - "id": "070c5e18", + "id": "7870a8c8", "metadata": { "hide-output": false }, @@ -1637,7 +1637,7 @@ }, { "cell_type": "markdown", - "id": "e958597f", + "id": "ce871743", "metadata": {}, "source": [ "We can first compute the Gini coefficient using the function defined in the lecture above." @@ -1646,7 +1646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "808cf4e3", + "id": "933a1da2", "metadata": { "hide-output": false }, @@ -1657,7 +1657,7 @@ }, { "cell_type": "markdown", - "id": "00551662", + "id": "a87be4c5", "metadata": {}, "source": [ "Now we can write a vectorized version using `numpy`" @@ -1666,7 +1666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b24af9c", + "id": "5bf7af9c", "metadata": { "hide-output": false }, @@ -1683,7 +1683,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6621df65", + "id": "b55577b5", "metadata": { "hide-output": false }, @@ -1694,7 +1694,7 @@ }, { "cell_type": "markdown", - "id": "51db9158", + "id": "349f4dc9", "metadata": {}, "source": [ "Let’s simulate five populations by drawing from a lognormal distribution as before" @@ -1703,7 +1703,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2bd906d8", + "id": "77fdd3c6", "metadata": { "hide-output": false }, @@ -1719,7 +1719,7 @@ }, { "cell_type": "markdown", - "id": "7edd20e4", + "id": "d4435aed", "metadata": {}, "source": [ "We can compute the Gini coefficient for these five populations using the vectorized function, the computation time is shown below:" @@ -1728,7 +1728,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8255f8eb", + "id": "17c73248", "metadata": { "hide-output": false }, @@ -1742,7 +1742,7 @@ }, { "cell_type": "markdown", - "id": "890246e6", + "id": "96af3011", "metadata": {}, "source": [ "This shows the vectorized function is much faster.\n", @@ -1752,7 +1752,7 @@ { "cell_type": "code", "execution_count": null, - "id": "45a4b746", + "id": "590d7fb1", "metadata": { "hide-output": false }, @@ -1763,7 +1763,7 @@ } ], "metadata": { - "date": 1722488541.3817422, + "date": 1722502937.728578, "filename": "inequality.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/inflation_history.ipynb b/_notebooks/inflation_history.ipynb index 4a304979..9e3bc2b9 100644 --- a/_notebooks/inflation_history.ipynb +++ b/_notebooks/inflation_history.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8624c715", + "id": "5842f43b", "metadata": {}, "source": [ "# Price Level Histories\n", @@ -17,7 +17,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f44b6fd", + "id": "0ca88426", "metadata": { "hide-output": false }, @@ -29,7 +29,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e7af340", + "id": "486706e4", "metadata": { "hide-output": false }, @@ -44,7 +44,7 @@ }, { "cell_type": "markdown", - "id": "3d565f9b", + "id": "6d71e3ff", "metadata": {}, "source": [ "We can then import the Python modules we will use." @@ -53,7 +53,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5ae8b69", + "id": "520f50ae", "metadata": { "hide-output": false }, @@ -67,7 +67,7 @@ }, { "cell_type": "markdown", - "id": "e0863421", + "id": "df2cda3f", "metadata": {}, "source": [ "The rate of growth of the price level is called **inflation** in the popular press and in discussions among central bankers and treasury officials.\n", @@ -89,7 +89,7 @@ }, { "cell_type": "markdown", - "id": "3c1c479d", + "id": "f6d531ff", "metadata": {}, "source": [ "## Four centuries of price levels\n", @@ -114,7 +114,7 @@ { "cell_type": "code", "execution_count": null, - "id": "149cbc84", + "id": "11696d42", "metadata": { "hide-output": false }, @@ -131,7 +131,7 @@ }, { "cell_type": "markdown", - "id": "51fce25f", + "id": "1bf14b3c", "metadata": {}, "source": [ "We first plot price levels over the period 1600-1914.\n", @@ -142,7 +142,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd907ca2", + "id": "5abd2477", "metadata": { "hide-output": false }, @@ -169,7 +169,7 @@ }, { "cell_type": "markdown", - "id": "178858aa", + "id": "38a40055", "metadata": {}, "source": [ "We say “most years” because there were temporary lapses from the gold or silver standard.\n", @@ -226,7 +226,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf8270de", + "id": "d6ace0a3", "metadata": { "hide-output": false }, @@ -250,7 +250,7 @@ }, { "cell_type": "markdown", - "id": "d0f5fda7", + "id": "a8d1d2ab", "metadata": {}, "source": [ "Fig. 4.2 shows that paper-money-printing central banks didn’t do as well as the gold and standard silver standard in anchoring price levels.\n", @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "0b40019e", + "id": "0e9b71d9", "metadata": {}, "source": [ "## Four big inflations\n", @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1e5d29f", + "id": "598a429e", "metadata": { "hide-output": false }, @@ -363,7 +363,7 @@ }, { "cell_type": "markdown", - "id": "d3c137ee", + "id": "eef877ea", "metadata": {}, "source": [ "Now we write plotting functions `pe_plot` and `pr_plot` that will build figures that show the price level, exchange rates,\n", @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7964a7a4", + "id": "30d419cd", "metadata": { "hide-output": false }, @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "ee97117b", + "id": "5159b03c", "metadata": {}, "source": [ "We prepare the data for each country" @@ -447,7 +447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31c2ed9f", + "id": "d0ae9b7c", "metadata": { "hide-output": false }, @@ -490,7 +490,7 @@ }, { "cell_type": "markdown", - "id": "592b338e", + "id": "c33274b8", "metadata": {}, "source": [ "Now let’s construct graphs for our four countries.\n", @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "07a2a97d", + "id": "190192d9", "metadata": {}, "source": [ "### Austria\n", @@ -524,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fa56e9b", + "id": "72e3bde7", "metadata": { "hide-output": false }, @@ -546,7 +546,7 @@ { "cell_type": "code", "execution_count": null, - "id": "801f0ab6", + "id": "207db0aa", "metadata": { "hide-output": false }, @@ -561,7 +561,7 @@ }, { "cell_type": "markdown", - "id": "bfd7c699", + "id": "d3d6fd54", "metadata": {}, "source": [ "Staring at Fig. 4.3 and Fig. 4.4 conveys the following impressions to the authors of this lecture at QuantEcon.\n", @@ -576,7 +576,7 @@ }, { "cell_type": "markdown", - "id": "92fb654c", + "id": "b8ccd04b", "metadata": {}, "source": [ "### Hungary\n", @@ -589,7 +589,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6057eb16", + "id": "d4fe9c30", "metadata": { "hide-output": false }, @@ -611,7 +611,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59f3c266", + "id": "16cfd3ae", "metadata": { "hide-output": false }, @@ -626,7 +626,7 @@ }, { "cell_type": "markdown", - "id": "c3ee08b0", + "id": "0965f6a8", "metadata": {}, "source": [ "### Poland\n", @@ -646,7 +646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea8b3f1c", + "id": "ebf4023a", "metadata": { "hide-output": false }, @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "128d3d3a", + "id": "2b01cfb6", "metadata": { "hide-output": false }, @@ -699,7 +699,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62969dcc", + "id": "fc58a6bc", "metadata": { "hide-output": false }, @@ -714,7 +714,7 @@ }, { "cell_type": "markdown", - "id": "bd847070", + "id": "e0c6c631", "metadata": {}, "source": [ "### Germany\n", @@ -728,7 +728,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1433548", + "id": "fb65bad0", "metadata": { "hide-output": false }, @@ -751,7 +751,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c88e144", + "id": "7c7be261", "metadata": { "hide-output": false }, @@ -780,7 +780,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a1faf0ed", + "id": "9198b540", "metadata": { "hide-output": false }, @@ -795,7 +795,7 @@ }, { "cell_type": "markdown", - "id": "c25e4ccc", + "id": "62d1ce68", "metadata": {}, "source": [ "## Starting and stopping big inflations\n", @@ -845,7 +845,7 @@ } ], "metadata": { - "date": 1722488541.6848342, + "date": 1722502938.135984, "filename": "inflation_history.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/input_output.ipynb b/_notebooks/input_output.ipynb index 5c515550..fea2ef25 100644 --- a/_notebooks/input_output.ipynb +++ b/_notebooks/input_output.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "1735be9d", + "id": "b6aecbca", "metadata": {}, "source": [ "# Input-Output Models" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "508ade66", + "id": "e60f83b5", "metadata": {}, "source": [ "## Overview\n", @@ -21,7 +21,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d10f9779", + "id": "dbc97565", "metadata": { "hide-output": false }, @@ -35,7 +35,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0e76b4c", + "id": "a756c19e", "metadata": { "hide-output": false }, @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "601d56ec", + "id": "5ea85a07", "metadata": {}, "source": [ "The following figure illustrates a network of linkages among 15 sectors\n", @@ -68,7 +68,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4dbe18bb", + "id": "1092df96", "metadata": { "hide-output": false }, @@ -101,7 +101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c1f785c", + "id": "180da13c", "metadata": { "hide-output": false }, @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "53119f86", + "id": "020d34b1", "metadata": {}, "source": [ "|Label|Sector|Label|Sector|Label|Sector|\n", @@ -150,7 +150,7 @@ }, { "cell_type": "markdown", - "id": "257a536c", + "id": "c8460ffa", "metadata": {}, "source": [ "## Input output analysis\n", @@ -176,7 +176,7 @@ }, { "cell_type": "markdown", - "id": "ac70f80b", + "id": "c91e0aec", "metadata": {}, "source": [ "### Two goods\n", @@ -188,7 +188,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcf4168c", + "id": "848af732", "metadata": { "hide-output": false }, @@ -231,7 +231,7 @@ }, { "cell_type": "markdown", - "id": "4e3ed8ce", + "id": "ebc19d22", "metadata": {}, "source": [ "**Feasible allocations must satisfy**\n", @@ -250,7 +250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2210c06d", + "id": "16b869b5", "metadata": { "hide-output": false }, @@ -287,7 +287,7 @@ }, { "cell_type": "markdown", - "id": "fdb41d91", + "id": "09d805b2", "metadata": {}, "source": [ "More generally, constraints on production are\n", @@ -344,7 +344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76029e62", + "id": "5e2b031f", "metadata": { "hide-output": false }, @@ -358,7 +358,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c91c5ed8", + "id": "b65f5bd7", "metadata": { "hide-output": false }, @@ -371,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "5d0cd26d", + "id": "dea902cd", "metadata": {}, "source": [ "Let’s check the **Hawkins-Simon conditions**" @@ -380,7 +380,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75ce08aa", + "id": "8ea27fc4", "metadata": { "hide-output": false }, @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "af486e8c", + "id": "319cb91b", "metadata": {}, "source": [ "Now, let’s compute the **Leontief inverse** matrix" @@ -400,7 +400,7 @@ { "cell_type": "code", "execution_count": null, - "id": "953a0d2a", + "id": "e41d222c", "metadata": { "hide-output": false }, @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcf59c58", + "id": "44889221", "metadata": { "hide-output": false }, @@ -425,7 +425,7 @@ }, { "cell_type": "markdown", - "id": "1fb5b2e8", + "id": "636d2aee", "metadata": {}, "source": [ "## Production possibility frontier\n", @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": null, - "id": "653ce0d6", + "id": "c0381c99", "metadata": { "hide-output": false }, @@ -483,7 +483,7 @@ }, { "cell_type": "markdown", - "id": "50553f0c", + "id": "4420df2d", "metadata": {}, "source": [ "Thus, the production possibility frontier for this economy is\n", @@ -495,7 +495,7 @@ }, { "cell_type": "markdown", - "id": "a30a8576", + "id": "9114a945", "metadata": {}, "source": [ "## Prices\n", @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "554cac06", + "id": "2998cb34", "metadata": {}, "source": [ "## Linear programs\n", @@ -590,7 +590,7 @@ { "cell_type": "code", "execution_count": null, - "id": "499c5a00", + "id": "31eda075", "metadata": { "hide-output": false }, @@ -626,7 +626,7 @@ }, { "cell_type": "markdown", - "id": "efb09dac", + "id": "4d331aed", "metadata": {}, "source": [ "## Leontief inverse\n", @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "105deb37", + "id": "4851db26", "metadata": {}, "source": [ "### Demand shocks\n", @@ -664,7 +664,7 @@ }, { "cell_type": "markdown", - "id": "298538ea", + "id": "5ec2dc1d", "metadata": {}, "source": [ "## Applications of graph theory\n", @@ -686,7 +686,7 @@ }, { "cell_type": "markdown", - "id": "aa221bac", + "id": "7dc91981", "metadata": {}, "source": [ "### Eigenvector centrality\n", @@ -705,7 +705,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3efdc2ee", + "id": "2dbac6a2", "metadata": { "hide-output": false }, @@ -719,7 +719,7 @@ }, { "cell_type": "markdown", - "id": "877ac616", + "id": "f7eba1ec", "metadata": {}, "source": [ "A higher measure indicates higher importance as a supplier.\n", @@ -731,7 +731,7 @@ }, { "cell_type": "markdown", - "id": "5705ab1e", + "id": "44b2119b", "metadata": {}, "source": [ "### Output multipliers\n", @@ -769,7 +769,7 @@ { "cell_type": "code", "execution_count": null, - "id": "929f3213", + "id": "d9f8dcc2", "metadata": { "hide-output": false }, @@ -787,7 +787,7 @@ }, { "cell_type": "markdown", - "id": "e2666374", + "id": "f556a5cb", "metadata": {}, "source": [ "We observe that manufacturing and agriculture are highest ranking sectors." @@ -795,7 +795,7 @@ }, { "cell_type": "markdown", - "id": "27150463", + "id": "923db9c7", "metadata": {}, "source": [ "## Exercises" @@ -803,7 +803,7 @@ }, { "cell_type": "markdown", - "id": "5a37846c", + "id": "43a34596", "metadata": {}, "source": [ "## Exercise 40.1\n", @@ -844,7 +844,7 @@ }, { "cell_type": "markdown", - "id": "bb5fc31d", + "id": "8023f146", "metadata": {}, "source": [ "## Solution to[ Exercise 40.1](https://intro.quantecon.org/#io_ex1)\n", @@ -858,7 +858,7 @@ }, { "cell_type": "markdown", - "id": "f3eba09f", + "id": "754ab4a5", "metadata": {}, "source": [ "## Exercise 40.2\n", @@ -868,7 +868,7 @@ }, { "cell_type": "markdown", - "id": "3e15b967", + "id": "e58f7ba2", "metadata": {}, "source": [ "## Solution to[ Exercise 40.2](https://intro.quantecon.org/#io_ex2)" @@ -877,7 +877,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88d3e05f", + "id": "7df71499", "metadata": { "hide-output": false }, @@ -891,7 +891,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a4bd474", + "id": "a1d0599c", "metadata": { "hide-output": false }, @@ -905,7 +905,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f3256cb", + "id": "b0019243", "metadata": { "hide-output": false }, @@ -917,7 +917,7 @@ }, { "cell_type": "markdown", - "id": "8cd8b0ed", + "id": "ec0033a2", "metadata": {}, "source": [ "Thus the production possibility frontier is given by\n", @@ -929,7 +929,7 @@ } ], "metadata": { - "date": 1722488541.7257688, + "date": 1722502938.1758358, "filename": "input_output.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/intro.ipynb b/_notebooks/intro.ipynb index cb13515f..2e0d591b 100644 --- a/_notebooks/intro.ipynb +++ b/_notebooks/intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f6d2862e", + "id": "1aeab9cd", "metadata": {}, "source": [ "# A First Course in Quantitative Economics with Python\n", @@ -12,7 +12,7 @@ }, { "cell_type": "markdown", - "id": "7c96f05b", + "id": "66742a73", "metadata": {}, "source": [ "# Introduction\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "06a3ef01", + "id": "985f619c", "metadata": {}, "source": [ "# Economic Data\n", @@ -36,7 +36,7 @@ }, { "cell_type": "markdown", - "id": "a37d2557", + "id": "92671af8", "metadata": {}, "source": [ "# Foundations\n", @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "7d319fa5", + "id": "abb7174c", "metadata": {}, "source": [ "# Linear Dynamics: Finite Horizons\n", @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "7ddb2aed", + "id": "f1b6e7a7", "metadata": {}, "source": [ "# Linear Dynamics: Infinite Horizons\n", @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "b73cc44e", + "id": "7e3da106", "metadata": {}, "source": [ "# Probability and Distributions\n", @@ -88,7 +88,7 @@ }, { "cell_type": "markdown", - "id": "f7f7343e", + "id": "d6cbe590", "metadata": {}, "source": [ "# Nonlinear Dynamics\n", @@ -102,7 +102,7 @@ }, { "cell_type": "markdown", - "id": "59718558", + "id": "1210fb09", "metadata": {}, "source": [ "# Monetary-Fiscal Policy Interactions\n", @@ -116,7 +116,7 @@ }, { "cell_type": "markdown", - "id": "4f6cc655", + "id": "1f3b5f69", "metadata": {}, "source": [ "# Stochastic Dynamics\n", @@ -129,7 +129,7 @@ }, { "cell_type": "markdown", - "id": "235065d2", + "id": "0df6f1b6", "metadata": {}, "source": [ "# Optimization\n", @@ -140,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "947806d9", + "id": "82ae11c2", "metadata": {}, "source": [ "# Modeling in Higher Dimensions\n", @@ -153,7 +153,7 @@ }, { "cell_type": "markdown", - "id": "24e01398", + "id": "d25f3e0e", "metadata": {}, "source": [ "# Markets and Competitive Equilibrium\n", @@ -164,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "2fa7d522", + "id": "615dd9ce", "metadata": {}, "source": [ "# Estimation\n", @@ -175,7 +175,7 @@ }, { "cell_type": "markdown", - "id": "635ba873", + "id": "92c13743", "metadata": {}, "source": [ "# Other\n", @@ -187,7 +187,7 @@ } ], "metadata": { - "date": 1722488541.7621598, + "date": 1722502938.206917, "filename": "intro.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/intro_supply_demand.ipynb b/_notebooks/intro_supply_demand.ipynb index 7f63aa80..06c1ae13 100644 --- a/_notebooks/intro_supply_demand.ipynb +++ b/_notebooks/intro_supply_demand.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c43477c6", + "id": "80d97398", "metadata": {}, "source": [ "# Introduction to Supply and Demand" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "79d656d8", + "id": "abe787ec", "metadata": {}, "source": [ "## Overview\n", @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "63921530", + "id": "8e4255cf", "metadata": {}, "source": [ "### Why does this model matter?\n", @@ -46,7 +46,7 @@ }, { "cell_type": "markdown", - "id": "52aad357", + "id": "de460d71", "metadata": {}, "source": [ "### Topics and infrastructure\n", @@ -68,7 +68,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98c7e6e9", + "id": "79302554", "metadata": { "hide-output": false }, @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "f390e36b", + "id": "6404f263", "metadata": {}, "source": [ "## Consumer surplus\n", @@ -93,7 +93,7 @@ }, { "cell_type": "markdown", - "id": "33696c03", + "id": "a99fa284", "metadata": {}, "source": [ "### A discrete example\n", @@ -133,7 +133,7 @@ { "cell_type": "code", "execution_count": null, - "id": "11db707a", + "id": "2013d8f8", "metadata": { "hide-output": false }, @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "14a5f8c9", + "id": "68d9d4f9", "metadata": {}, "source": [ "The total consumer surplus in this market is\n", @@ -174,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "95fbbe2b", + "id": "7be46f56", "metadata": {}, "source": [ "### A comment on quantity.\n", @@ -190,7 +190,7 @@ }, { "cell_type": "markdown", - "id": "9dcd6403", + "id": "4e466067", "metadata": {}, "source": [ "### A continuous approximation\n", @@ -213,7 +213,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75bbaeff", + "id": "72562d55", "metadata": { "hide-output": false }, @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "4e19d857", + "id": "81c18319", "metadata": {}, "source": [ "Reasoning by analogy with the discrete case, the area under the demand curve and above the price is called the **consumer surplus**, and is a measure of total gains from trade on the part of consumers.\n", @@ -252,7 +252,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5475d6f1", + "id": "eee6511c", "metadata": { "hide-output": false }, @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "8d7b67d3", + "id": "7819bcf1", "metadata": {}, "source": [ "The value $ q^* $ is where the inverse demand curve meets price." @@ -289,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "9c951e3e", + "id": "247611b3", "metadata": {}, "source": [ "## Producer surplus\n", @@ -299,7 +299,7 @@ }, { "cell_type": "markdown", - "id": "4e6cac4e", + "id": "d9c647c1", "metadata": {}, "source": [ "### The discrete case\n", @@ -310,7 +310,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6a32ed4c", + "id": "24f3ecf6", "metadata": { "hide-output": false }, @@ -332,7 +332,7 @@ }, { "cell_type": "markdown", - "id": "7441c46d", + "id": "de2eb013", "metadata": {}, "source": [ "Let $ v_i $ be the price at which producer $ i $ is willing to sell the good.\n", @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3da7c13c", + "id": "35996ffb", "metadata": { "hide-output": false }, @@ -398,7 +398,7 @@ }, { "cell_type": "markdown", - "id": "c28c9637", + "id": "c5709acc", "metadata": {}, "source": [ "\n", @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "79cdb360", + "id": "01ac9a35", "metadata": {}, "source": [ "## Integration\n", @@ -428,7 +428,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bed4ce01", + "id": "ceb00621", "metadata": { "hide-output": false }, @@ -452,7 +452,7 @@ }, { "cell_type": "markdown", - "id": "4b3d8c96", + "id": "ddbaf387", "metadata": {}, "source": [ "There are many rules for calculating integrals, with different rules applying to different choices of $ f $.\n", @@ -474,7 +474,7 @@ }, { "cell_type": "markdown", - "id": "538cf5fe", + "id": "164021c8", "metadata": {}, "source": [ "## Supply and demand\n", @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5942716c", + "id": "748ef4b0", "metadata": { "hide-output": false }, @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "a8d8899e", + "id": "b5c99098", "metadata": {}, "source": [ "The function below creates an instance of a Market namedtuple with default values." @@ -539,7 +539,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c1b5e0f", + "id": "2272b59d", "metadata": { "hide-output": false }, @@ -551,7 +551,7 @@ }, { "cell_type": "markdown", - "id": "325f77d9", + "id": "a472bbfe", "metadata": {}, "source": [ "This `market` can then be used by our `inverse_demand` and `inverse_supply` functions." @@ -560,7 +560,7 @@ { "cell_type": "code", "execution_count": null, - "id": "93345e10", + "id": "532d77a0", "metadata": { "hide-output": false }, @@ -575,7 +575,7 @@ }, { "cell_type": "markdown", - "id": "7c303f16", + "id": "6060321f", "metadata": {}, "source": [ "Here is a plot of these two functions using `market`." @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33acd46a", + "id": "8bdca576", "metadata": { "hide-output": false }, @@ -611,7 +611,7 @@ }, { "cell_type": "markdown", - "id": "389c43ed", + "id": "9a4a7e79", "metadata": {}, "source": [ "In the above graph, an **equilibrium** price-quantity pair occurs at the intersection of the supply and demand curves." @@ -619,7 +619,7 @@ }, { "cell_type": "markdown", - "id": "40c36b06", + "id": "1e77fd69", "metadata": {}, "source": [ "### Consumer surplus\n", @@ -643,7 +643,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0415eb8c", + "id": "2e9241ea", "metadata": { "hide-output": false }, @@ -677,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "02a6ca1b", + "id": "f826a098", "metadata": {}, "source": [ "Consumer surplus provides a measure of total consumer welfare at quantity $ q $.\n", @@ -700,7 +700,7 @@ }, { "cell_type": "markdown", - "id": "cba09aff", + "id": "dd381336", "metadata": {}, "source": [ "### Producer surplus\n", @@ -723,7 +723,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5ce476b", + "id": "a97761ff", "metadata": { "hide-output": false }, @@ -757,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "eae7ff47", + "id": "cb40c437", "metadata": {}, "source": [ "Producer surplus measures total producer welfare at quantity $ q $\n", @@ -780,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "3455bb10", + "id": "763c4c90", "metadata": {}, "source": [ "### Social welfare\n", @@ -807,7 +807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fdb78f05", + "id": "79cdb6f8", "metadata": { "hide-output": false }, @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "c25943ba", + "id": "bdf0a8aa", "metadata": {}, "source": [ "The next figure plots welfare as a function of $ q $." @@ -829,7 +829,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0e720b2", + "id": "8eead0a7", "metadata": { "hide-output": false }, @@ -845,7 +845,7 @@ }, { "cell_type": "markdown", - "id": "3faee7bc", + "id": "7370f2d3", "metadata": {}, "source": [ "Let’s now give a social planner the task of maximizing social welfare.\n", @@ -872,7 +872,7 @@ }, { "cell_type": "markdown", - "id": "be240233", + "id": "1b4754f1", "metadata": {}, "source": [ "### Competitive equilibrium\n", @@ -912,7 +912,7 @@ }, { "cell_type": "markdown", - "id": "6b148f25", + "id": "38960e10", "metadata": {}, "source": [ "## Generalizations\n", @@ -932,7 +932,7 @@ }, { "cell_type": "markdown", - "id": "507c6804", + "id": "a4c3f4f0", "metadata": {}, "source": [ "## Exercises\n", @@ -953,7 +953,7 @@ }, { "cell_type": "markdown", - "id": "535f17ab", + "id": "932d7b42", "metadata": {}, "source": [ "## Exercise 7.1\n", @@ -966,7 +966,7 @@ }, { "cell_type": "markdown", - "id": "b7e5e547", + "id": "200e8585", "metadata": {}, "source": [ "## Solution to[ Exercise 7.1](https://intro.quantecon.org/#isd_ex1)\n", @@ -977,7 +977,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7485aedb", + "id": "3338aaab", "metadata": { "hide-output": false }, @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "87f8881a", + "id": "0031aed0", "metadata": {}, "source": [ "Here is a plot of inverse supply and demand." @@ -1001,7 +1001,7 @@ { "cell_type": "code", "execution_count": null, - "id": "614c8626", + "id": "26eb2038", "metadata": { "hide-output": false }, @@ -1027,7 +1027,7 @@ }, { "cell_type": "markdown", - "id": "aa866c34", + "id": "7ef45f80", "metadata": {}, "source": [ "## Exercise 7.2\n", @@ -1067,7 +1067,7 @@ }, { "cell_type": "markdown", - "id": "eca93dab", + "id": "acfb2ec4", "metadata": {}, "source": [ "## Solution to[ Exercise 7.2](https://intro.quantecon.org/#isd_ex2)\n", @@ -1086,7 +1086,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ea725a5", + "id": "f94be50a", "metadata": { "hide-output": false }, @@ -1101,7 +1101,7 @@ }, { "cell_type": "markdown", - "id": "cefda6c3", + "id": "8d14704d", "metadata": {}, "source": [ "The next figure plots welfare as a function of $ q $." @@ -1110,7 +1110,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3464602d", + "id": "50c8149e", "metadata": { "hide-output": false }, @@ -1125,7 +1125,7 @@ }, { "cell_type": "markdown", - "id": "e6e05058", + "id": "03299983", "metadata": {}, "source": [ "## Exercise 7.3\n", @@ -1142,7 +1142,7 @@ }, { "cell_type": "markdown", - "id": "e5f29012", + "id": "fa8a4f55", "metadata": {}, "source": [ "## Solution to[ Exercise 7.3](https://intro.quantecon.org/#isd_ex3)" @@ -1151,7 +1151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b9ba0c8", + "id": "902a66a4", "metadata": { "hide-output": false }, @@ -1169,7 +1169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "caa096d1", + "id": "f3b80b98", "metadata": { "hide-output": false }, @@ -1181,7 +1181,7 @@ }, { "cell_type": "markdown", - "id": "97cf181b", + "id": "a1fc5701", "metadata": {}, "source": [ "## Exercise 7.4\n", @@ -1211,7 +1211,7 @@ }, { "cell_type": "markdown", - "id": "1a555aa6", + "id": "66877c7a", "metadata": {}, "source": [ "## Solution to[ Exercise 7.4](https://intro.quantecon.org/#isd_ex4)" @@ -1220,7 +1220,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75cc0c2b", + "id": "8ce08094", "metadata": { "hide-output": false }, @@ -1237,7 +1237,7 @@ } ], "metadata": { - "date": 1722488541.7995274, + "date": 1722502938.2438278, "filename": "intro_supply_demand.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/laffer_adaptive.ipynb b/_notebooks/laffer_adaptive.ipynb index fc9d8376..d907a732 100644 --- a/_notebooks/laffer_adaptive.ipynb +++ b/_notebooks/laffer_adaptive.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "a3fd0c78", + "id": "08db971c", "metadata": {}, "source": [ "# Laffer Curves with Adaptive Expectations" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "fe331345", + "id": "2abf08a3", "metadata": {}, "source": [ "## Overview\n", @@ -56,7 +56,7 @@ }, { "cell_type": "markdown", - "id": "b93ea876", + "id": "5c3b13d8", "metadata": {}, "source": [ "## The Model\n", @@ -109,7 +109,7 @@ }, { "cell_type": "markdown", - "id": "871a4843", + "id": "2d2c625e", "metadata": {}, "source": [ "## Computing An Equilibrium Sequence\n", @@ -140,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "4308649b", + "id": "191467ce", "metadata": {}, "source": [ "## Claims or Conjectures\n", @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "7cd343dc", + "id": "584e6d2a", "metadata": {}, "source": [ "## Limiting Values of Inflation Rate\n", @@ -205,7 +205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0366d119", + "id": "c1989ccc", "metadata": { "hide-output": false }, @@ -223,7 +223,7 @@ }, { "cell_type": "markdown", - "id": "88f0e439", + "id": "65dc9bd1", "metadata": {}, "source": [ "Let’s create a `namedtuple` to store the parameters of the model" @@ -232,7 +232,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8d4907b", + "id": "c16735d1", "metadata": { "hide-output": false }, @@ -253,7 +253,7 @@ }, { "cell_type": "markdown", - "id": "a1dea988", + "id": "c506421e", "metadata": {}, "source": [ "Now we write code that computes steady-state $ \\bar \\pi $s." @@ -262,7 +262,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f692f7f", + "id": "378d6826", "metadata": { "hide-output": false }, @@ -284,7 +284,7 @@ }, { "cell_type": "markdown", - "id": "75e91346", + "id": "2f958f81", "metadata": {}, "source": [ "We find two steady state $ \\bar \\pi $ values" @@ -292,7 +292,7 @@ }, { "cell_type": "markdown", - "id": "ccd417f3", + "id": "361557cd", "metadata": {}, "source": [ "## Steady State Laffer Curve\n", @@ -303,7 +303,7 @@ { "cell_type": "code", "execution_count": null, - "id": "874c66f1", + "id": "e80a2703", "metadata": { "hide-output": false }, @@ -343,7 +343,7 @@ }, { "cell_type": "markdown", - "id": "37e47d38", + "id": "25d576ee", "metadata": {}, "source": [ "## Associated Initial Price Levels\n", @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84d38008", + "id": "0ebe4f71", "metadata": { "hide-output": false }, @@ -378,7 +378,7 @@ }, { "cell_type": "markdown", - "id": "f9d65ca5", + "id": "f1c67361", "metadata": {}, "source": [ "### Verification\n", @@ -391,7 +391,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42c0755d", + "id": "bf940434", "metadata": { "hide-output": false }, @@ -431,7 +431,7 @@ }, { "cell_type": "markdown", - "id": "7e644188", + "id": "b7c77bd9", "metadata": {}, "source": [ "Compute limiting values starting from $ p_{-1} $ associated with $ \\pi_l $" @@ -440,7 +440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35a89491", + "id": "e6a9e0dc", "metadata": { "hide-output": false }, @@ -460,7 +460,7 @@ }, { "cell_type": "markdown", - "id": "328efffe", + "id": "2444acfa", "metadata": {}, "source": [ "Compute limiting values starting from $ p_{-1} $ associated with $ \\pi_u $" @@ -469,7 +469,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fa7a735", + "id": "108d7bf6", "metadata": { "hide-output": false }, @@ -489,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "89172a8c", + "id": "fe3c2f84", "metadata": {}, "source": [ "## Slippery Side of Laffer Curve Dynamics\n", @@ -507,7 +507,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8713d25", + "id": "257cb868", "metadata": { "hide-output": false }, @@ -548,7 +548,7 @@ }, { "cell_type": "markdown", - "id": "4ef85c41", + "id": "61612ad9", "metadata": {}, "source": [ "Let’s simulate the result generated by varying the initial $ \\pi_{-1} $ and corresponding $ p_{-1} $" @@ -557,7 +557,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97140b44", + "id": "17c71689", "metadata": { "hide-output": false }, @@ -575,7 +575,7 @@ } ], "metadata": { - "date": 1722488541.827119, + "date": 1722502938.270077, "filename": "laffer_adaptive.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/lake_model.ipynb b/_notebooks/lake_model.ipynb index 89560bf9..684677e3 100644 --- a/_notebooks/lake_model.ipynb +++ b/_notebooks/lake_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "01160742", + "id": "76a3b8b2", "metadata": {}, "source": [ "# A Lake Model of Employment" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "58b141c1", + "id": "1d49a674", "metadata": {}, "source": [ "## Outline\n", @@ -21,7 +21,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba668c38", + "id": "429133c2", "metadata": { "hide-output": false }, @@ -33,7 +33,7 @@ }, { "cell_type": "markdown", - "id": "fe386f4b", + "id": "9e4c5b42", "metadata": {}, "source": [ "## The Lake model\n", @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "7be50c68", + "id": "07b52abf", "metadata": {}, "source": [ "## Dynamics\n", @@ -119,7 +119,7 @@ }, { "cell_type": "markdown", - "id": "314779af", + "id": "679c1f05", "metadata": {}, "source": [ "### Visualising the long-run outcomes\n", @@ -130,7 +130,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b76107bd", + "id": "a7e46dc2", "metadata": { "hide-output": false }, @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "377a9672", + "id": "48b77717", "metadata": { "hide-output": false }, @@ -233,7 +233,7 @@ }, { "cell_type": "markdown", - "id": "18e320b1", + "id": "3c11e0fd", "metadata": {}, "source": [ "Not surprisingly, we observe that labor force $ n_t $ increases at a constant rate.\n", @@ -264,7 +264,7 @@ }, { "cell_type": "markdown", - "id": "c80f241e", + "id": "90b23413", "metadata": {}, "source": [ "### The application of Perron-Frobenius theorem\n", @@ -289,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "b78b8deb", + "id": "7f26dba6", "metadata": {}, "source": [ "#### Dominant eigenvector\n", @@ -358,7 +358,7 @@ { "cell_type": "code", "execution_count": null, - "id": "703c4b04", + "id": "f20fc913", "metadata": { "hide-output": false }, @@ -439,7 +439,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7a38bfc", + "id": "7b1fab89", "metadata": { "hide-output": false }, @@ -452,7 +452,7 @@ }, { "cell_type": "markdown", - "id": "1f4d98cb", + "id": "de5b7eca", "metadata": {}, "source": [ "Since $ \\bar{x} $ is an eigenvector corresponding to the eigenvalue $ r(A) $, all the vectors in the set\n", @@ -468,7 +468,7 @@ }, { "cell_type": "markdown", - "id": "9e695665", + "id": "ad8f50d6", "metadata": {}, "source": [ "#### Negative growth rate\n", @@ -487,7 +487,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5064a5a", + "id": "9e6f5f02", "metadata": { "hide-output": false }, @@ -499,7 +499,7 @@ }, { "cell_type": "markdown", - "id": "d87efc1e", + "id": "0e3d5952", "metadata": {}, "source": [ "Thus, while the sequence of iterates still moves towards the dominant eigenvector $ \\bar{x} $, in this case\n", @@ -513,7 +513,7 @@ }, { "cell_type": "markdown", - "id": "fb21d115", + "id": "9847704f", "metadata": {}, "source": [ "### Properties\n", @@ -572,7 +572,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c892e998", + "id": "ecc6b7b6", "metadata": { "hide-output": false }, @@ -614,7 +614,7 @@ }, { "cell_type": "markdown", - "id": "c978c133", + "id": "6c8301e9", "metadata": {}, "source": [ "To provide more intuition for convergence, we further explain the convergence below without the Perron-Frobenius theorem.\n", @@ -649,7 +649,7 @@ }, { "cell_type": "markdown", - "id": "3aad2600", + "id": "04ec6d07", "metadata": {}, "source": [ "## Exercise" @@ -657,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "a03850a2", + "id": "cf24e224", "metadata": {}, "source": [ "## (Evolution of unemployment and employment rate)Exercise 41.1\n", @@ -673,7 +673,7 @@ }, { "cell_type": "markdown", - "id": "e07ace04", + "id": "87571c0a", "metadata": {}, "source": [ "## Solution to[ Exercise 41.1 (Evolution of unemployment and employment rate)](https://intro.quantecon.org/#lake_model_ex1)\n", @@ -691,7 +691,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b9b949b", + "id": "21971a9b", "metadata": { "hide-output": false }, @@ -714,7 +714,7 @@ } ], "metadata": { - "date": 1722488541.8492994, + "date": 1722502938.2917242, "filename": "lake_model.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/linear_equations.ipynb b/_notebooks/linear_equations.ipynb index 29cf3a4c..19a75cd2 100644 --- a/_notebooks/linear_equations.ipynb +++ b/_notebooks/linear_equations.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "2b7f1855", + "id": "78b2ac5c", "metadata": {}, "source": [ "# Linear Equations and Matrix Algebra\n", @@ -13,7 +13,7 @@ }, { "cell_type": "markdown", - "id": "4aa33a55", + "id": "9b08d532", "metadata": {}, "source": [ "## Overview\n", @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "efde8686", + "id": "bef6c95d", "metadata": { "hide-output": false }, @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "0f0998da", + "id": "89a4e73c", "metadata": {}, "source": [ "## A two good example\n", @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "e16616a4", + "id": "14a9eaa3", "metadata": {}, "source": [ "### Pencil and paper methods\n", @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "00a878bf", + "id": "0f0716b4", "metadata": {}, "source": [ "### Looking forward\n", @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "4926273b", + "id": "72867c3f", "metadata": {}, "source": [ "## Vectors\n", @@ -177,7 +177,7 @@ }, { "cell_type": "markdown", - "id": "c7f39ab6", + "id": "066f4a97", "metadata": {}, "source": [ "## \n", @@ -194,7 +194,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e167ce2c", + "id": "cf952f51", "metadata": { "hide-output": false }, @@ -222,7 +222,7 @@ }, { "cell_type": "markdown", - "id": "0fccbeec", + "id": "5db654e9", "metadata": {}, "source": [ "### Vector operations\n", @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "de45c9c1", + "id": "f32f73a9", "metadata": {}, "source": [ "### \n", @@ -296,7 +296,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42035721", + "id": "8f6a1dbf", "metadata": { "hide-output": false }, @@ -337,7 +337,7 @@ }, { "cell_type": "markdown", - "id": "630a2254", + "id": "2b9db0d8", "metadata": {}, "source": [ "Scalar multiplication is an operation that multiplies a vector $ x $ with a scalar elementwise." @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "8305d58e", + "id": "5df863c4", "metadata": {}, "source": [ "### \n", @@ -386,7 +386,7 @@ { "cell_type": "code", "execution_count": null, - "id": "102849f0", + "id": "63f9148c", "metadata": { "hide-output": false }, @@ -424,7 +424,7 @@ }, { "cell_type": "markdown", - "id": "66432335", + "id": "eab80272", "metadata": {}, "source": [ "In Python, a vector can be represented as a list or tuple,\n", @@ -440,7 +440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc68b2be", + "id": "03cf5edd", "metadata": { "hide-output": false }, @@ -454,7 +454,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7472769", + "id": "1e2171b9", "metadata": { "hide-output": false }, @@ -465,7 +465,7 @@ }, { "cell_type": "markdown", - "id": "f4cdb7bf", + "id": "bda48761", "metadata": {}, "source": [ "### Inner product and norm\n", @@ -504,7 +504,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b928da78", + "id": "9a80a7af", "metadata": { "hide-output": false }, @@ -516,7 +516,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b24fbe52", + "id": "abd7d1b0", "metadata": { "hide-output": false }, @@ -528,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56f191ac", + "id": "8d788302", "metadata": { "hide-output": false }, @@ -540,7 +540,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85f7c5da", + "id": "e920ceed", "metadata": { "hide-output": false }, @@ -551,7 +551,7 @@ }, { "cell_type": "markdown", - "id": "bcc78229", + "id": "812e4222", "metadata": {}, "source": [ "## Matrix operations\n", @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "e3bd1867", + "id": "c5c8af8d", "metadata": {}, "source": [ "### Addition and scalar multiplication\n", @@ -580,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "26786408", + "id": "5e6a8adb", "metadata": {}, "source": [ "### \n", @@ -618,7 +618,7 @@ }, { "cell_type": "markdown", - "id": "c2d41fa2", + "id": "1b00e8c1", "metadata": {}, "source": [ "### \n", @@ -669,7 +669,7 @@ }, { "cell_type": "markdown", - "id": "283cff35", + "id": "e21ac614", "metadata": {}, "source": [ "### Matrix multiplication\n", @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "532edb0c", + "id": "1155c557", "metadata": {}, "source": [ "### \n", @@ -792,7 +792,7 @@ }, { "cell_type": "markdown", - "id": "6df2d342", + "id": "136f743f", "metadata": {}, "source": [ "### Matrices in NumPy\n", @@ -807,7 +807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7054430e", + "id": "93f018c2", "metadata": { "hide-output": false }, @@ -822,7 +822,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b1044ce", + "id": "f012155c", "metadata": { "hide-output": false }, @@ -836,7 +836,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b5131de", + "id": "6530fb26", "metadata": { "hide-output": false }, @@ -847,7 +847,7 @@ }, { "cell_type": "markdown", - "id": "687a3d14", + "id": "9127fa3f", "metadata": {}, "source": [ "The `shape` attribute is a tuple giving the number of rows and columns —\n", @@ -865,7 +865,7 @@ { "cell_type": "code", "execution_count": null, - "id": "405be6fd", + "id": "1c1960c1", "metadata": { "hide-output": false }, @@ -879,7 +879,7 @@ { "cell_type": "code", "execution_count": null, - "id": "930dfcc9", + "id": "8f5d1096", "metadata": { "hide-output": false }, @@ -890,7 +890,7 @@ }, { "cell_type": "markdown", - "id": "187e913a", + "id": "64f7ac91", "metadata": {}, "source": [ "To multiply matrices we use the `@` symbol.\n", @@ -902,7 +902,7 @@ }, { "cell_type": "markdown", - "id": "18027526", + "id": "5b0c9ca8", "metadata": {}, "source": [ "### Two good model in matrix form\n", @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "2137b56f", + "id": "42e0a918", "metadata": {}, "source": [ "### More goods\n", @@ -1040,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "d2a946e4", + "id": "e232610f", "metadata": {}, "source": [ "### General linear systems\n", @@ -1094,7 +1094,7 @@ }, { "cell_type": "markdown", - "id": "6c813cc4", + "id": "5591cde7", "metadata": {}, "source": [ "### \n", @@ -1118,7 +1118,7 @@ }, { "cell_type": "markdown", - "id": "4fb3a83a", + "id": "9a2ce210", "metadata": {}, "source": [ "## Solving systems of equations\n", @@ -1143,7 +1143,7 @@ }, { "cell_type": "markdown", - "id": "3e7b0856", + "id": "e3d83bb3", "metadata": {}, "source": [ "### No solution\n", @@ -1165,7 +1165,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8c64582f", + "id": "c99b1b91", "metadata": { "hide-output": false }, @@ -1181,7 +1181,7 @@ }, { "cell_type": "markdown", - "id": "c3f363f1", + "id": "e9b84bab", "metadata": {}, "source": [ "Clearly, these are parallel lines and hence we will never find a point $ x \\in \\mathbb{R}^2 $\n", @@ -1223,7 +1223,7 @@ }, { "cell_type": "markdown", - "id": "effe43ee", + "id": "45edae8f", "metadata": {}, "source": [ "### Many solutions\n", @@ -1260,7 +1260,7 @@ }, { "cell_type": "markdown", - "id": "5c01af0d", + "id": "b9ecec2d", "metadata": {}, "source": [ "### Nonsingular matrices\n", @@ -1310,7 +1310,7 @@ }, { "cell_type": "markdown", - "id": "2726ba0b", + "id": "ad80e6a2", "metadata": {}, "source": [ "### Linear equations with NumPy\n", @@ -1335,7 +1335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdfc9059", + "id": "0a228813", "metadata": { "hide-output": false }, @@ -1347,7 +1347,7 @@ }, { "cell_type": "markdown", - "id": "3bafb450", + "id": "39aa3995", "metadata": {}, "source": [ "Now we change this to a NumPy array." @@ -1356,7 +1356,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3622840", + "id": "f58b9d9e", "metadata": { "hide-output": false }, @@ -1368,7 +1368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f54bfe09", + "id": "ff9dad68", "metadata": { "hide-output": false }, @@ -1382,7 +1382,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c125218", + "id": "903e5260", "metadata": { "hide-output": false }, @@ -1395,7 +1395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "91586ad0", + "id": "90fb600d", "metadata": { "hide-output": false }, @@ -1410,7 +1410,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21d97c55", + "id": "3869ab49", "metadata": { "hide-output": false }, @@ -1423,7 +1423,7 @@ { "cell_type": "code", "execution_count": null, - "id": "addf94b6", + "id": "bb8c52fe", "metadata": { "hide-output": false }, @@ -1436,7 +1436,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5ce621c2", + "id": "c76a57d3", "metadata": { "hide-output": false }, @@ -1448,7 +1448,7 @@ }, { "cell_type": "markdown", - "id": "1aadf2e2", + "id": "8e9c71fc", "metadata": {}, "source": [ "Notice that we get the same solutions as the pencil and paper case.\n", @@ -1459,7 +1459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0a9888f", + "id": "d0968c14", "metadata": { "hide-output": false }, @@ -1473,7 +1473,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aa8e4bdd", + "id": "5870cad0", "metadata": { "hide-output": false }, @@ -1485,7 +1485,7 @@ }, { "cell_type": "markdown", - "id": "b3b8f77a", + "id": "8d21adb8", "metadata": {}, "source": [ "Observe how we can solve for $ x = A^{-1} y $ by either via `inv(A) @ y`, or using `solve(A, y)`.\n", @@ -1495,7 +1495,7 @@ }, { "cell_type": "markdown", - "id": "39ee822b", + "id": "679b7820", "metadata": {}, "source": [ "## Exercises" @@ -1503,7 +1503,7 @@ }, { "cell_type": "markdown", - "id": "c83645d1", + "id": "74633671", "metadata": {}, "source": [ "## Exercise 8.1\n", @@ -1541,7 +1541,7 @@ }, { "cell_type": "markdown", - "id": "16528720", + "id": "d941e971", "metadata": {}, "source": [ "## Solution to[ Exercise 8.1](https://intro.quantecon.org/#lin_eqs_ex1)\n", @@ -1586,7 +1586,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8ff4975", + "id": "f0755523", "metadata": { "hide-output": false }, @@ -1608,7 +1608,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c943d10", + "id": "68398350", "metadata": { "hide-output": false }, @@ -1626,7 +1626,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b473716e", + "id": "1c70b89b", "metadata": { "hide-output": false }, @@ -1640,7 +1640,7 @@ }, { "cell_type": "markdown", - "id": "f8697976", + "id": "dceba82f", "metadata": {}, "source": [ "The solution is given by:\n", @@ -1649,7 +1649,7 @@ }, { "cell_type": "markdown", - "id": "89a59146", + "id": "d299ecad", "metadata": {}, "source": [ "## Exercise 8.2\n", @@ -1737,7 +1737,7 @@ }, { "cell_type": "markdown", - "id": "53485a13", + "id": "16b89e2e", "metadata": {}, "source": [ "## Solution to[ Exercise 8.2](https://intro.quantecon.org/#lin_eqs_ex2)" @@ -1746,7 +1746,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc5f8370", + "id": "1b2f0cf9", "metadata": { "hide-output": false }, @@ -1759,7 +1759,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81fde9fc", + "id": "d39fa9ff", "metadata": { "hide-output": false }, @@ -1782,7 +1782,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99b2ddc5", + "id": "24b56f5d", "metadata": { "hide-output": false }, @@ -1795,7 +1795,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a9011a2a", + "id": "eead8d80", "metadata": { "hide-output": false }, @@ -1807,7 +1807,7 @@ }, { "cell_type": "markdown", - "id": "1745d73c", + "id": "33cbea6e", "metadata": {}, "source": [ "Here is a visualization of how the least squares method approximates the equation of a line connecting a set of points.\n", @@ -1818,7 +1818,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ec03bd9", + "id": "6201bb41", "metadata": { "hide-output": false }, @@ -1840,7 +1840,7 @@ }, { "cell_type": "markdown", - "id": "fcab3d05", + "id": "153c4c0b", "metadata": {}, "source": [ "### Further reading\n", @@ -1852,7 +1852,7 @@ } ], "metadata": { - "date": 1722488541.9002523, + "date": 1722502938.34152, "filename": "linear_equations.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/lln_clt.ipynb b/_notebooks/lln_clt.ipynb index 27f4cd3d..5d807f9a 100644 --- a/_notebooks/lln_clt.ipynb +++ b/_notebooks/lln_clt.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "bc5b8274", + "id": "b880128c", "metadata": {}, "source": [ "# LLN and CLT" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "de775db5", + "id": "3fae1652", "metadata": {}, "source": [ "## Overview\n", @@ -37,7 +37,7 @@ { "cell_type": "code", "execution_count": null, - "id": "70bf6436", + "id": "7232d1db", "metadata": { "hide-output": false }, @@ -50,7 +50,7 @@ }, { "cell_type": "markdown", - "id": "191b4a82", + "id": "6d156307", "metadata": {}, "source": [ "\n", @@ -59,7 +59,7 @@ }, { "cell_type": "markdown", - "id": "f4b4dbed", + "id": "979763c7", "metadata": {}, "source": [ "## The law of large numbers\n", @@ -72,7 +72,7 @@ }, { "cell_type": "markdown", - "id": "8cc7b1f9", + "id": "8a8ddd73", "metadata": {}, "source": [ "### The LLN in action\n", @@ -82,7 +82,7 @@ }, { "cell_type": "markdown", - "id": "07817dcd", + "id": "243dcdc9", "metadata": {}, "source": [ "### \n", @@ -112,7 +112,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6d39b6e", + "id": "50d64896", "metadata": { "hide-output": false }, @@ -125,7 +125,7 @@ }, { "cell_type": "markdown", - "id": "f09520a7", + "id": "cad48d60", "metadata": {}, "source": [ "In this setting, the LLN tells us if we flip the coin many times, the fraction\n", @@ -139,7 +139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4fad1f12", + "id": "57bce456", "metadata": { "hide-output": false }, @@ -152,7 +152,7 @@ }, { "cell_type": "markdown", - "id": "706a9770", + "id": "6680764f", "metadata": {}, "source": [ "If we change $ p $ the claim still holds:" @@ -161,7 +161,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16e99eb8", + "id": "3d336108", "metadata": { "hide-output": false }, @@ -174,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "1bcced98", + "id": "a6d60e4e", "metadata": {}, "source": [ "Let’s connect this to the discussion above, where we said the sample average\n", @@ -210,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "9080e20a", + "id": "e009f060", "metadata": {}, "source": [ "### Statement of the LLN\n", @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "54982485", + "id": "8d91cc13", "metadata": {}, "source": [ "### \n", @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "e6005690", + "id": "4ce2b8d4", "metadata": {}, "source": [ "### Comments on the theorem\n", @@ -301,7 +301,7 @@ }, { "cell_type": "markdown", - "id": "7db90a5a", + "id": "ada68c11", "metadata": {}, "source": [ "### Illustration\n", @@ -347,7 +347,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10045f13", + "id": "4bad1d54", "metadata": { "hide-output": false }, @@ -365,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "44f550bb", + "id": "c2afbd39", "metadata": {}, "source": [ "Now we write a function to generate $ m $ sample means and histogram them." @@ -374,7 +374,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a214717f", + "id": "4f900e37", "metadata": { "hide-output": false }, @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "2f36a064", + "id": "68bc7b77", "metadata": {}, "source": [ "Now we call the function." @@ -414,7 +414,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b75d027", + "id": "23c48822", "metadata": { "hide-output": false }, @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "f73bbab1", + "id": "e3d56576", "metadata": {}, "source": [ "We can see that the distribution of $ \\bar X $ is clustered around $ \\mathbb E X $\n", @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3379a5f", + "id": "f158081d", "metadata": { "hide-output": false }, @@ -480,7 +480,7 @@ }, { "cell_type": "markdown", - "id": "e295243c", + "id": "890b212f", "metadata": {}, "source": [ "Let’s try with a normal distribution." @@ -489,7 +489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d7a5557a", + "id": "8a14022c", "metadata": { "hide-output": false }, @@ -500,7 +500,7 @@ }, { "cell_type": "markdown", - "id": "8760c484", + "id": "0c52ea7d", "metadata": {}, "source": [ "As $ n $ gets large, more probability mass clusters around the population mean $ \\mu $.\n", @@ -511,7 +511,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2b7fec25", + "id": "93f5ac2c", "metadata": { "hide-output": false }, @@ -522,7 +522,7 @@ }, { "cell_type": "markdown", - "id": "7ef092ae", + "id": "fe3183a2", "metadata": {}, "source": [ "We get a similar result." @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "3d89f43c", + "id": "9654d8fb", "metadata": {}, "source": [ "## Breaking the LLN\n", @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "1fec2ed1", + "id": "ac40109e", "metadata": {}, "source": [ "### Infinite first moment\n", @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "863633c2", + "id": "62a9da77", "metadata": {}, "source": [ "### Failure of the IID condition\n", @@ -574,7 +574,7 @@ }, { "cell_type": "markdown", - "id": "0034070c", + "id": "4210a093", "metadata": {}, "source": [ "### \n", @@ -611,7 +611,7 @@ }, { "cell_type": "markdown", - "id": "476ad5bb", + "id": "0b8e6255", "metadata": {}, "source": [ "## Central limit theorem\n", @@ -624,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "65990481", + "id": "8f990560", "metadata": {}, "source": [ "### Statement of the theorem\n", @@ -636,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "b65f160e", + "id": "13a0c29d", "metadata": {}, "source": [ "### \n", @@ -661,7 +661,7 @@ }, { "cell_type": "markdown", - "id": "a6c70a1a", + "id": "78a11de9", "metadata": {}, "source": [ "### Simulation 1\n", @@ -688,7 +688,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2ace820", + "id": "877d5b76", "metadata": { "hide-output": false }, @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "32e461d3", + "id": "7da92c14", "metadata": {}, "source": [ "(Notice the absence of for loops — every operation is vectorized, meaning that the major calculations are all shifted to fast C code.)\n", @@ -735,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "a51e31a2", + "id": "64fe9b3a", "metadata": {}, "source": [ "## Exercises" @@ -743,7 +743,7 @@ }, { "cell_type": "markdown", - "id": "9bab4ab9", + "id": "25df9bbd", "metadata": {}, "source": [ "## Exercise 19.1\n", @@ -755,7 +755,7 @@ }, { "cell_type": "markdown", - "id": "a4492e57", + "id": "43d6fa5b", "metadata": {}, "source": [ "## Solution to[ Exercise 19.1](https://intro.quantecon.org/#lln_ex1)" @@ -764,7 +764,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73e5d400", + "id": "8c8efc39", "metadata": { "hide-output": false }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "4326b275", + "id": "6254b889", "metadata": {}, "source": [ "## Exercise 19.2\n", @@ -814,7 +814,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cab1df79", + "id": "004d43b2", "metadata": { "hide-output": false }, @@ -827,7 +827,7 @@ }, { "cell_type": "markdown", - "id": "4f04287c", + "id": "3608a099", "metadata": {}, "source": [ "Explain why this provides a random variable $ X $ with the right distribution." @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "11ea0443", + "id": "1abac88b", "metadata": {}, "source": [ "## Solution to[ Exercise 19.2](https://intro.quantecon.org/#lln_ex2)\n", @@ -855,7 +855,7 @@ }, { "cell_type": "markdown", - "id": "c6d4c296", + "id": "1cb79b85", "metadata": {}, "source": [ "## Exercise 19.3\n", @@ -891,7 +891,7 @@ }, { "cell_type": "markdown", - "id": "c86043b8", + "id": "bdc5d076", "metadata": {}, "source": [ "## Solution to[ Exercise 19.3](https://intro.quantecon.org/#lln_ex3)\n", @@ -945,7 +945,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ab767db", + "id": "c610a8b5", "metadata": { "hide-output": false }, @@ -982,7 +982,7 @@ }, { "cell_type": "markdown", - "id": "efc2a6b5", + "id": "e8676b4d", "metadata": {}, "source": [ "We see the convergence of $ \\bar x $ around $ \\mu $ even when the independence assumption is violated." @@ -990,7 +990,7 @@ } ], "metadata": { - "date": 1722488541.9327831, + "date": 1722502938.3736215, "filename": "lln_clt.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/long_run_growth.ipynb b/_notebooks/long_run_growth.ipynb index 9d51f67e..66079525 100644 --- a/_notebooks/long_run_growth.ipynb +++ b/_notebooks/long_run_growth.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e472aeeb", + "id": "4b75872c", "metadata": {}, "source": [ "# Long-Run Growth" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "8a0d8110", + "id": "92fe52fa", "metadata": {}, "source": [ "## Overview\n", @@ -65,7 +65,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe7147ac", + "id": "eb6895a2", "metadata": { "hide-output": false }, @@ -80,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "48caaebf", + "id": "e92d9bfb", "metadata": {}, "source": [ "## Setting up\n", @@ -100,7 +100,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09cb0e83", + "id": "71150f3b", "metadata": { "hide-output": false }, @@ -114,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "6bab009b", + "id": "c36d7ada", "metadata": {}, "source": [ "We can see that this dataset contains GDP per capita (`gdppc`) and population (pop) for many countries and years.\n", @@ -125,7 +125,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d32e5a02", + "id": "b96a4065", "metadata": { "hide-output": false }, @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "75948eda", + "id": "064315a9", "metadata": {}, "source": [ "We can now explore some of the 169 countries that are available.\n", @@ -148,7 +148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a735a87", + "id": "b3e2e7b0", "metadata": { "hide-output": false }, @@ -166,7 +166,7 @@ }, { "cell_type": "markdown", - "id": "f947a0f9", + "id": "ce9033c4", "metadata": {}, "source": [ "Let’s now reshape the original data into some convenient variables to enable quicker access to countries’ time series data.\n", @@ -177,7 +177,7 @@ { "cell_type": "code", "execution_count": null, - "id": "310c6559", + "id": "049c2209", "metadata": { "hide-output": false }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "1d032441", + "id": "c50e91b1", "metadata": {}, "source": [ "Now we can focus on GDP per capita (`gdppc`) and generate a wide data format" @@ -198,7 +198,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ebb18ff8", + "id": "c3f1cc05", "metadata": { "hide-output": false }, @@ -211,7 +211,7 @@ { "cell_type": "code", "execution_count": null, - "id": "521b83d4", + "id": "331fe0c8", "metadata": { "hide-output": false }, @@ -222,7 +222,7 @@ }, { "cell_type": "markdown", - "id": "8f46a09f", + "id": "37f503ef", "metadata": {}, "source": [ "We create a variable `color_mapping` to store a map between country codes and colors for consistency" @@ -231,7 +231,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32a184d5", + "id": "fa29f441", "metadata": { "hide-output": false }, @@ -249,7 +249,7 @@ }, { "cell_type": "markdown", - "id": "f5b0dca6", + "id": "78101973", "metadata": {}, "source": [ "## GDP per capita\n", @@ -259,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "49e63eaa", + "id": "1b852e9d", "metadata": {}, "source": [ "### United Kingdom\n", @@ -270,7 +270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3efd5e16", + "id": "19efbab1", "metadata": { "hide-output": false }, @@ -288,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "9f153f18", + "id": "6835a9d9", "metadata": {}, "source": [ ">**Note**\n", @@ -303,7 +303,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d43f622c", + "id": "7f7df91b", "metadata": { "hide-output": false }, @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "8c735b14", + "id": "47e9ad9b", "metadata": {}, "source": [ "### Comparing the US, UK, and China\n", @@ -339,7 +339,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61054e36", + "id": "1e8bfed6", "metadata": { "hide-output": false }, @@ -386,7 +386,7 @@ }, { "cell_type": "markdown", - "id": "c594b50f", + "id": "16fdfeef", "metadata": {}, "source": [ "As you can see from this chart, economic growth started in earnest in the 18th century and continued for the next two hundred years.\n", @@ -399,7 +399,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69e4405d", + "id": "d0d143c0", "metadata": { "hide-output": false }, @@ -465,7 +465,7 @@ }, { "cell_type": "markdown", - "id": "41d512c5", + "id": "82dd7a98", "metadata": {}, "source": [ "The preceding graph of per capita GDP strikingly reveals how the spread of the Industrial Revolution has over time gradually lifted the living standards of substantial\n", @@ -479,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "f9db136c", + "id": "27d814a7", "metadata": {}, "source": [ "### Focusing on China\n", @@ -499,7 +499,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23c2504e", + "id": "b2979c53", "metadata": { "hide-output": false }, @@ -549,7 +549,7 @@ }, { "cell_type": "markdown", - "id": "2a2577fc", + "id": "db3b24b4", "metadata": {}, "source": [ "### Focusing on the US and UK\n", @@ -568,7 +568,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e5615afe", + "id": "91a6517c", "metadata": { "hide-output": false }, @@ -619,7 +619,7 @@ }, { "cell_type": "markdown", - "id": "504edca3", + "id": "a55df0f1", "metadata": {}, "source": [ "## GDP growth\n", @@ -632,7 +632,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c29d10c", + "id": "2834f45d", "metadata": { "hide-output": false }, @@ -646,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "8c00072f", + "id": "057138f3", "metadata": {}, "source": [ "### Early industrialization (1820 to 1940)\n", @@ -663,7 +663,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c916848", + "id": "a7e4649d", "metadata": { "hide-output": false }, @@ -680,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "c330f2b6", + "id": "70e6ad3a", "metadata": {}, "source": [ "#### Constructing a plot similar to Tooze’s\n", @@ -693,7 +693,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3aea70bf", + "id": "2113b74a", "metadata": { "hide-output": false }, @@ -706,7 +706,7 @@ }, { "cell_type": "markdown", - "id": "db351efe", + "id": "da1fb20d", "metadata": {}, "source": [ "Now let’s assemble our series and get ready to plot them." @@ -715,7 +715,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56493f09", + "id": "25d19a16", "metadata": { "hide-output": false }, @@ -732,7 +732,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75f7dee1", + "id": "94c41e7c", "metadata": { "hide-output": false }, @@ -753,7 +753,7 @@ }, { "cell_type": "markdown", - "id": "e86bec3f", + "id": "916ecd24", "metadata": {}, "source": [ "At the start of this lecture, we noted how US GDP came from “nowhere” at the start of the 19th century to rival and then overtake the GDP of the British Empire\n", @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "3fa97545", + "id": "5c7fb507", "metadata": {}, "source": [ "### The modern era (1950 to 2020)\n", @@ -777,7 +777,7 @@ { "cell_type": "code", "execution_count": null, - "id": "589bb2dd", + "id": "904e6865", "metadata": { "hide-output": false }, @@ -794,7 +794,7 @@ }, { "cell_type": "markdown", - "id": "1ca9a338", + "id": "9b386dd5", "metadata": {}, "source": [ "It is tempting to compare this graph with figure Fig. 2.6 that showed the US overtaking the UK near the start of the “American Century”, a version of the graph featured in chapter 1 of [[Tooze, 2014](https://intro.quantecon.org/zreferences.html#id14)]." @@ -802,7 +802,7 @@ }, { "cell_type": "markdown", - "id": "4d4c307e", + "id": "50adf837", "metadata": {}, "source": [ "## Regional analysis\n", @@ -815,7 +815,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26df6f8d", + "id": "f306af80", "metadata": { "hide-output": false }, @@ -830,7 +830,7 @@ }, { "cell_type": "markdown", - "id": "913a6158", + "id": "4745cb25", "metadata": {}, "source": [ "We can save the raw data in a more convenient format to build a single table of regional GDP per capita" @@ -839,7 +839,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7002afbb", + "id": "c7b2706c", "metadata": { "hide-output": false }, @@ -851,7 +851,7 @@ }, { "cell_type": "markdown", - "id": "0df5abfa", + "id": "3ad81bbe", "metadata": {}, "source": [ "Let’s interpolate based on time to fill in any gaps in the dataset for the purpose of plotting" @@ -860,7 +860,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ca38ad6", + "id": "5e1565ba", "metadata": { "hide-output": false }, @@ -871,7 +871,7 @@ }, { "cell_type": "markdown", - "id": "d6a4003b", + "id": "f94118a9", "metadata": {}, "source": [ "Looking more closely, let’s compare the time series for `Western Offshoots` and `Sub-Saharan Africa` with a number of different regions around the world.\n", @@ -882,7 +882,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac807082", + "id": "bc55b6db", "metadata": { "hide-output": false }, @@ -900,7 +900,7 @@ } ], "metadata": { - "date": 1722488541.963468, + "date": 1722502938.4036283, "filename": "long_run_growth.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/lp_intro.ipynb b/_notebooks/lp_intro.ipynb index a2381140..3705c74c 100644 --- a/_notebooks/lp_intro.ipynb +++ b/_notebooks/lp_intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7a98d8bf", + "id": "e916598c", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "f6774449", + "id": "84f6fa92", "metadata": {}, "source": [ "# Linear Programming\n", @@ -22,7 +22,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41540c94", + "id": "99c52bf7", "metadata": { "hide-output": false }, @@ -33,7 +33,7 @@ }, { "cell_type": "markdown", - "id": "3af796ec", + "id": "62b7b991", "metadata": {}, "source": [ "## Overview\n", @@ -64,7 +64,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e95bc0e9", + "id": "5e5d9742", "metadata": { "hide-output": false }, @@ -79,7 +79,7 @@ }, { "cell_type": "markdown", - "id": "c33e05ae", + "id": "9ed637e7", "metadata": {}, "source": [ "Let’s start with some examples of linear programming problem." @@ -87,7 +87,7 @@ }, { "cell_type": "markdown", - "id": "2a72e787", + "id": "c9a44605", "metadata": {}, "source": [ "## Example 1: production problem\n", @@ -132,7 +132,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81d13a20", + "id": "04d0f969", "metadata": { "hide-output": false }, @@ -167,7 +167,7 @@ }, { "cell_type": "markdown", - "id": "93f3643f", + "id": "89315f1b", "metadata": {}, "source": [ "The blue region is the feasible set within which all constraints are satisfied.\n", @@ -183,7 +183,7 @@ }, { "cell_type": "markdown", - "id": "a73b63a3", + "id": "1e444277", "metadata": {}, "source": [ "### Computation: using OR-Tools\n", @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f7b3984", + "id": "2c2bacfe", "metadata": { "hide-output": false }, @@ -208,7 +208,7 @@ }, { "cell_type": "markdown", - "id": "254cb201", + "id": "daaf3acf", "metadata": {}, "source": [ "Let’s create two variables $ x_1 $ and $ x_2 $ such that they can only have nonnegative values." @@ -217,7 +217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc6a949e", + "id": "d93f7ebc", "metadata": { "hide-output": false }, @@ -230,7 +230,7 @@ }, { "cell_type": "markdown", - "id": "2dc06a5d", + "id": "de8f2355", "metadata": {}, "source": [ "Add the constraints to the problem." @@ -239,7 +239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07492332", + "id": "0bbd3372", "metadata": { "hide-output": false }, @@ -254,7 +254,7 @@ }, { "cell_type": "markdown", - "id": "92c4ccbb", + "id": "e8df7bd6", "metadata": {}, "source": [ "Let’s specify the objective function. We use `solver.Maximize` method in the case when we want to maximize the objective function and in the case of minimization we can use `solver.Minimize`." @@ -263,7 +263,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a95d82a", + "id": "8c81b8c5", "metadata": { "hide-output": false }, @@ -275,7 +275,7 @@ }, { "cell_type": "markdown", - "id": "b8d7d749", + "id": "960cc07b", "metadata": {}, "source": [ "Once we solve the problem, we can check whether the solver was successful in solving the problem using its status. If it’s successful, then the status will be equal to `pywraplp.Solver.OPTIMAL`." @@ -284,7 +284,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a260a1f2", + "id": "c20fd68a", "metadata": { "hide-output": false }, @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "4efa3963", + "id": "64410b34", "metadata": {}, "source": [ "## Example 2: investment problem\n", @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "f0847e48", + "id": "1cb1cc82", "metadata": {}, "source": [ "### Computation: using OR-Tools\n", @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3927422", + "id": "164eb902", "metadata": { "hide-output": false }, @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "96b5b7c1", + "id": "064ef014", "metadata": {}, "source": [ "Let’s create five variables $ x_1, x_2, x_3, x_4, $ and $ x_5 $ such that they can only have the values defined in the above constraints." @@ -416,7 +416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "18a57ccc", + "id": "0773e0ea", "metadata": { "hide-output": false }, @@ -432,7 +432,7 @@ }, { "cell_type": "markdown", - "id": "d8033fe5", + "id": "99166a4a", "metadata": {}, "source": [ "Add the constraints to the problem." @@ -441,7 +441,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef51ba72", + "id": "7f4b6da1", "metadata": { "hide-output": false }, @@ -459,7 +459,7 @@ }, { "cell_type": "markdown", - "id": "22f14bf6", + "id": "4551a853", "metadata": {}, "source": [ "Let’s specify the objective function." @@ -468,7 +468,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bba19efc", + "id": "c91a399c", "metadata": { "hide-output": false }, @@ -480,7 +480,7 @@ }, { "cell_type": "markdown", - "id": "1fef278e", + "id": "d9b283c4", "metadata": {}, "source": [ "Let’s solve the problem and check the status using `pywraplp.Solver.OPTIMAL`." @@ -489,7 +489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85b2ee96", + "id": "168151b0", "metadata": { "hide-output": false }, @@ -512,7 +512,7 @@ }, { "cell_type": "markdown", - "id": "3e5f9ca5", + "id": "daab5517", "metadata": {}, "source": [ "OR-Tools tells us that the best investment strategy is:\n", @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "52624fba", + "id": "ba40bace", "metadata": {}, "source": [ "## Standard form\n", @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "87e13d9c", + "id": "312b15b8", "metadata": {}, "source": [ "### Useful transformations\n", @@ -603,7 +603,7 @@ }, { "cell_type": "markdown", - "id": "0a70142e", + "id": "e865da2e", "metadata": {}, "source": [ "### Example 1: production problem\n", @@ -633,7 +633,7 @@ }, { "cell_type": "markdown", - "id": "390d3613", + "id": "e1c7ceb7", "metadata": {}, "source": [ "### Computation: using SciPy\n", @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f78c04d2", + "id": "d37b1cdc", "metadata": { "hide-output": false }, @@ -678,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "952b26f8", + "id": "1d3c2143", "metadata": {}, "source": [ "Once we solve the problem, we can check whether the solver was successful in solving the problem using the boolean attribute `success`. If it’s successful, then the `success` attribute is set to `True`." @@ -687,7 +687,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab87d3bd", + "id": "34a54a37", "metadata": { "hide-output": false }, @@ -707,7 +707,7 @@ }, { "cell_type": "markdown", - "id": "4a0fd1f9", + "id": "157d079c", "metadata": {}, "source": [ "The optimal plan tells the factory to produce $ 2.5 $ units of Product 1 and $ 5 $ units of Product 2; that generates a maximizing value of revenue of $ 27.5 $.\n", @@ -729,7 +729,7 @@ }, { "cell_type": "markdown", - "id": "a4267561", + "id": "0d637c19", "metadata": {}, "source": [ "### Example 2: investment problem\n", @@ -773,7 +773,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ddc041f2", + "id": "15883c79", "metadata": { "hide-output": false }, @@ -801,7 +801,7 @@ }, { "cell_type": "markdown", - "id": "f46e0484", + "id": "a7a9824b", "metadata": {}, "source": [ "Let’s solve the problem and check the status using `success` attribute." @@ -810,7 +810,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8690e2f9", + "id": "7584b545", "metadata": { "hide-output": false }, @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "1042a11b", + "id": "9c85d259", "metadata": {}, "source": [ "SciPy tells us that the best investment strategy is:\n", @@ -853,7 +853,7 @@ }, { "cell_type": "markdown", - "id": "3ad861f2", + "id": "90d52353", "metadata": {}, "source": [ "## Exercises" @@ -861,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "96c87a31", + "id": "3d5abc6f", "metadata": {}, "source": [ "## Exercise 37.1\n", @@ -871,7 +871,7 @@ }, { "cell_type": "markdown", - "id": "f0d74587", + "id": "7f9d81e7", "metadata": {}, "source": [ "## Solution to[ Exercise 37.1](https://intro.quantecon.org/#lp_intro_ex1)\n", @@ -892,7 +892,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b19c4912", + "id": "61495b0c", "metadata": { "hide-output": false }, @@ -909,7 +909,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35300da2", + "id": "16a862ec", "metadata": { "hide-output": false }, @@ -928,7 +928,7 @@ { "cell_type": "code", "execution_count": null, - "id": "663dc6a8", + "id": "26567291", "metadata": { "hide-output": false }, @@ -941,7 +941,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c71b43f4", + "id": "c24325aa", "metadata": { "hide-output": false }, @@ -961,7 +961,7 @@ }, { "cell_type": "markdown", - "id": "73bc6d66", + "id": "3a199981", "metadata": {}, "source": [ "## Exercise 37.2\n", @@ -979,7 +979,7 @@ }, { "cell_type": "markdown", - "id": "c5fb6da2", + "id": "bb17969d", "metadata": {}, "source": [ "## Solution to[ Exercise 37.2](https://intro.quantecon.org/#lp_intro_ex2)\n", @@ -1000,7 +1000,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aeb8a00c", + "id": "f308913a", "metadata": { "hide-output": false }, @@ -1012,7 +1012,7 @@ }, { "cell_type": "markdown", - "id": "07c151d9", + "id": "445a8f0a", "metadata": {}, "source": [ "Let’s create two variables $ x_1 $ and $ x_2 $ such that they can only have nonnegative values." @@ -1021,7 +1021,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e83f62c9", + "id": "d37b30cf", "metadata": { "hide-output": false }, @@ -1035,7 +1035,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16720790", + "id": "0f051fbd", "metadata": { "hide-output": false }, @@ -1051,7 +1051,7 @@ { "cell_type": "code", "execution_count": null, - "id": "990e4b63", + "id": "0145ca00", "metadata": { "hide-output": false }, @@ -1064,7 +1064,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a567b72d", + "id": "bae12a4f", "metadata": { "hide-output": false }, @@ -1084,7 +1084,7 @@ } ], "metadata": { - "date": 1722488542.0002484, + "date": 1722502938.4382417, "filename": "lp_intro.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/markov_chains_I.ipynb b/_notebooks/markov_chains_I.ipynb index 70c7d168..a82c6271 100644 --- a/_notebooks/markov_chains_I.ipynb +++ b/_notebooks/markov_chains_I.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "988b68e2", + "id": "40d93ee2", "metadata": {}, "source": [ "# Markov Chains: Basic Concepts\n", @@ -15,7 +15,7 @@ { "cell_type": "code", "execution_count": null, - "id": "493e3bba", + "id": "c2e1e167", "metadata": { "hide-output": false }, @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "d7d6aaa0", + "id": "15fd9e3b", "metadata": {}, "source": [ "## Overview\n", @@ -60,7 +60,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c95d45a9", + "id": "dfd30236", "metadata": { "hide-output": false }, @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "d0a8c6da", + "id": "1def94bf", "metadata": {}, "source": [ "## Definitions and examples\n", @@ -94,7 +94,7 @@ }, { "cell_type": "markdown", - "id": "0f15d299", + "id": "d7acf030", "metadata": {}, "source": [ "### Stochastic matrices\n", @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "7780dea6", + "id": "96710a03", "metadata": {}, "source": [ "### Markov chains\n", @@ -135,7 +135,7 @@ }, { "cell_type": "markdown", - "id": "9aaa88c9", + "id": "147f2b27", "metadata": {}, "source": [ "#### Example 1\n", @@ -214,7 +214,7 @@ }, { "cell_type": "markdown", - "id": "cbb5ea94", + "id": "d9d55153", "metadata": {}, "source": [ "#### Example 2\n", @@ -272,7 +272,7 @@ }, { "cell_type": "markdown", - "id": "ba911f04", + "id": "d0504c89", "metadata": {}, "source": [ "#### Example 3\n", @@ -302,7 +302,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6a47459d", + "id": "e150a5b9", "metadata": { "hide-output": false }, @@ -319,7 +319,7 @@ }, { "cell_type": "markdown", - "id": "0b9285d7", + "id": "c24fe441", "metadata": {}, "source": [ "Here is a visualization, with darker colors indicating higher probability." @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8db7991", + "id": "423db28d", "metadata": { "hide-output": false }, @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "9c966426", + "id": "1466fd05", "metadata": {}, "source": [ "Looking at the data, we see that democracies tend to have longer-lasting growth\n", @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "83a828a7", + "id": "2aa6c928", "metadata": {}, "source": [ "### Defining Markov chains\n", @@ -437,7 +437,7 @@ }, { "cell_type": "markdown", - "id": "fe61044b", + "id": "ef056f9f", "metadata": {}, "source": [ "## Simulation\n", @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "21acc0b6", + "id": "d01bc5ce", "metadata": {}, "source": [ "### Writing our own simulation code\n", @@ -487,7 +487,7 @@ { "cell_type": "code", "execution_count": null, - "id": "658ca581", + "id": "8a824d0e", "metadata": { "hide-output": false }, @@ -500,7 +500,7 @@ }, { "cell_type": "markdown", - "id": "24832131", + "id": "a3447544", "metadata": {}, "source": [ "We’ll write our code as a function that accepts the following three arguments\n", @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "129b38d9", + "id": "17076d1b", "metadata": { "hide-output": false }, @@ -544,7 +544,7 @@ }, { "cell_type": "markdown", - "id": "1dc0bf77", + "id": "b36a20a2", "metadata": {}, "source": [ "Let’s see how it works using the small matrix" @@ -553,7 +553,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fe0230c", + "id": "842012f8", "metadata": { "hide-output": false }, @@ -565,7 +565,7 @@ }, { "cell_type": "markdown", - "id": "4fdd7613", + "id": "13e541d7", "metadata": {}, "source": [ "Here’s a short time series." @@ -574,7 +574,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef33883c", + "id": "4e4f8cd0", "metadata": { "hide-output": false }, @@ -585,7 +585,7 @@ }, { "cell_type": "markdown", - "id": "670ea782", + "id": "a65f7c6e", "metadata": {}, "source": [ "It can be shown that for a long series drawn from `P`, the fraction of the\n", @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "888ac480", + "id": "2247e68b", "metadata": { "hide-output": false }, @@ -614,7 +614,7 @@ }, { "cell_type": "markdown", - "id": "ae830c71", + "id": "70a5f6b9", "metadata": {}, "source": [ "You can try changing the initial distribution to confirm that the output is\n", @@ -623,7 +623,7 @@ }, { "cell_type": "markdown", - "id": "40f06f9d", + "id": "feb62837", "metadata": {}, "source": [ "### Using QuantEcon’s routines\n", @@ -636,7 +636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab2a57f5", + "id": "059504fa", "metadata": { "hide-output": false }, @@ -649,7 +649,7 @@ }, { "cell_type": "markdown", - "id": "38a21c3f", + "id": "8efb46e9", "metadata": {}, "source": [ "The `simulate` routine is faster (because it is [JIT compiled](https://python-programming.quantecon.org/numba.html#numba-link))." @@ -658,7 +658,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e08b5c2", + "id": "554b5c84", "metadata": { "hide-output": false }, @@ -670,7 +670,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32b64bcc", + "id": "da15a521", "metadata": { "hide-output": false }, @@ -681,7 +681,7 @@ }, { "cell_type": "markdown", - "id": "945c7a3c", + "id": "3ea44114", "metadata": {}, "source": [ "#### Adding state values and initial conditions\n", @@ -696,7 +696,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f376e515", + "id": "56491d0f", "metadata": { "hide-output": false }, @@ -709,7 +709,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ad3324d", + "id": "5f0fa702", "metadata": { "hide-output": false }, @@ -721,7 +721,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16b9b27b", + "id": "b91838e4", "metadata": { "hide-output": false }, @@ -732,7 +732,7 @@ }, { "cell_type": "markdown", - "id": "153d2393", + "id": "7fc6da0c", "metadata": {}, "source": [ "If we want to see indices rather than state values as outputs as we can use" @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2bd289bb", + "id": "8604ab6e", "metadata": { "hide-output": false }, @@ -752,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "d218a340", + "id": "0fbf5ef2", "metadata": {}, "source": [ "\n", @@ -761,7 +761,7 @@ }, { "cell_type": "markdown", - "id": "60714819", + "id": "cc2af9ef", "metadata": {}, "source": [ "## Distributions over time\n", @@ -843,7 +843,7 @@ }, { "cell_type": "markdown", - "id": "3b2d9695", + "id": "95c3194d", "metadata": {}, "source": [ "### Multiple step transition probabilities\n", @@ -870,7 +870,7 @@ }, { "cell_type": "markdown", - "id": "61dc89c2", + "id": "12cc64b7", "metadata": {}, "source": [ "### Example: probability of recession\n", @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "9c6b6432", + "id": "ff6a8aa6", "metadata": {}, "source": [ "### Example 2: cross-sectional distributions\n", @@ -944,7 +944,7 @@ }, { "cell_type": "markdown", - "id": "733143f5", + "id": "822f826b", "metadata": {}, "source": [ "## Stationary distributions\n", @@ -958,7 +958,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af2cb6d2", + "id": "b03ddb2a", "metadata": { "hide-output": false }, @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "f91ef98b", + "id": "0b817e15", "metadata": {}, "source": [ "Notice that `ψ @ P` is the same as `ψ`.\n", @@ -994,7 +994,7 @@ }, { "cell_type": "markdown", - "id": "3b81fd29", + "id": "65ba52b6", "metadata": {}, "source": [ "## \n", @@ -1015,7 +1015,7 @@ }, { "cell_type": "markdown", - "id": "684e95fc", + "id": "8c90edb0", "metadata": {}, "source": [ "## \n", @@ -1028,7 +1028,7 @@ }, { "cell_type": "markdown", - "id": "295fc779", + "id": "ccd6a0e6", "metadata": {}, "source": [ "### Example\n", @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "8f2d9cfb", + "id": "b8f623c7", "metadata": {}, "source": [ "### Calculating stationary distributions\n", @@ -1066,7 +1066,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b1383d2", + "id": "a8e13e0c", "metadata": { "hide-output": false }, @@ -1081,7 +1081,7 @@ }, { "cell_type": "markdown", - "id": "668f4cfc", + "id": "49f01fd3", "metadata": {}, "source": [ "### Asymptotic stationarity\n", @@ -1098,7 +1098,7 @@ }, { "cell_type": "markdown", - "id": "b267b817", + "id": "b8a1cfa8", "metadata": {}, "source": [ "### \n", @@ -1123,7 +1123,7 @@ }, { "cell_type": "markdown", - "id": "666029fe", + "id": "f7c4b14a", "metadata": {}, "source": [ "#### Example: Hamilton’s chain\n", @@ -1134,7 +1134,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc7e1bab", + "id": "36d42234", "metadata": { "hide-output": false }, @@ -1148,7 +1148,7 @@ }, { "cell_type": "markdown", - "id": "80395903", + "id": "a8df86d0", "metadata": {}, "source": [ "Let’s pick an initial distribution $ \\psi_1, \\psi_2, \\psi_3 $ and trace out the sequence of distributions $ \\psi_i P^t $ for $ t = 0, 1, 2, \\ldots $, for $ i=1, 2, 3 $.\n", @@ -1159,7 +1159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92ca2a6e", + "id": "ff229d62", "metadata": { "hide-output": false }, @@ -1176,7 +1176,7 @@ }, { "cell_type": "markdown", - "id": "df043b97", + "id": "52ac08bb", "metadata": {}, "source": [ "Now we plot the sequence" @@ -1185,7 +1185,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa6a5e7b", + "id": "602e2edd", "metadata": { "hide-output": false }, @@ -1239,7 +1239,7 @@ }, { "cell_type": "markdown", - "id": "6ab8d456", + "id": "cbece212", "metadata": {}, "source": [ "Here\n", @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "a4a3acf0", + "id": "35bce546", "metadata": {}, "source": [ "#### Example: failure of convergence\n", @@ -1291,7 +1291,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c32a8de4", + "id": "a642c9b4", "metadata": { "hide-output": false }, @@ -1349,7 +1349,7 @@ }, { "cell_type": "markdown", - "id": "664df167", + "id": "df5bc2f7", "metadata": {}, "source": [ "This animation demonstrates the behavior of an irreducible and periodic stochastic matrix.\n", @@ -1368,7 +1368,7 @@ }, { "cell_type": "markdown", - "id": "d109a006", + "id": "35ff22a3", "metadata": {}, "source": [ "## Computing expectations\n", @@ -1441,7 +1441,7 @@ }, { "cell_type": "markdown", - "id": "f4a9b2b1", + "id": "8a796d59", "metadata": {}, "source": [ "### Expectations of geometric sums\n", @@ -1471,7 +1471,7 @@ }, { "cell_type": "markdown", - "id": "3c913aaa", + "id": "8724590f", "metadata": {}, "source": [ "### Exercise 34.1\n", @@ -1501,7 +1501,7 @@ }, { "cell_type": "markdown", - "id": "0283d897", + "id": "ce57a471", "metadata": {}, "source": [ "### Solution to[ Exercise 34.1](https://intro.quantecon.org/#mc1_ex_1)\n", @@ -1520,7 +1520,7 @@ { "cell_type": "code", "execution_count": null, - "id": "441d76af", + "id": "d204a12e", "metadata": { "hide-output": false }, @@ -1535,7 +1535,7 @@ }, { "cell_type": "markdown", - "id": "4c47fc95", + "id": "0ea9c34b", "metadata": {}, "source": [ "Note that rows of the transition matrix converge to the stationary distribution." @@ -1544,7 +1544,7 @@ { "cell_type": "code", "execution_count": null, - "id": "967e926a", + "id": "c7a117dd", "metadata": { "hide-output": false }, @@ -1557,7 +1557,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4886c34f", + "id": "ddeb6465", "metadata": { "hide-output": false }, @@ -1570,7 +1570,7 @@ }, { "cell_type": "markdown", - "id": "7da1f2bc", + "id": "bc55ac33", "metadata": {}, "source": [ "### Exercise 34.2\n", @@ -1581,7 +1581,7 @@ { "cell_type": "code", "execution_count": null, - "id": "161e01b7", + "id": "5a94452d", "metadata": { "hide-output": false }, @@ -1598,7 +1598,7 @@ }, { "cell_type": "markdown", - "id": "adaf7f36", + "id": "83e4bb08", "metadata": {}, "source": [ "In this exercise,\n", @@ -1610,7 +1610,7 @@ }, { "cell_type": "markdown", - "id": "f50ec265", + "id": "21117ac0", "metadata": {}, "source": [ "### Solution to[ Exercise 34.2](https://intro.quantecon.org/#mc1_ex_2)\n", @@ -1623,7 +1623,7 @@ { "cell_type": "code", "execution_count": null, - "id": "204f63b4", + "id": "b5ea7d13", "metadata": { "hide-output": false }, @@ -1641,7 +1641,7 @@ }, { "cell_type": "markdown", - "id": "6cec2ef2", + "id": "557a14ab", "metadata": {}, "source": [ "So it satisfies the requirement.\n", @@ -1654,7 +1654,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd945f57", + "id": "2649ba3c", "metadata": { "hide-output": false }, @@ -1688,7 +1688,7 @@ }, { "cell_type": "markdown", - "id": "f4361d7d", + "id": "12f468a2", "metadata": {}, "source": [ "### Exercise 34.3\n", @@ -1699,7 +1699,7 @@ }, { "cell_type": "markdown", - "id": "c31dc61a", + "id": "afc1907c", "metadata": {}, "source": [ "### Solution to[ Exercise 34.3](https://intro.quantecon.org/#mc1_ex_3)\n", @@ -1725,7 +1725,7 @@ } ], "metadata": { - "date": 1722488542.3155077, + "date": 1722502938.892865, "filename": "markov_chains_I.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/markov_chains_II.ipynb b/_notebooks/markov_chains_II.ipynb index 5af7cc4b..b0281ca6 100644 --- a/_notebooks/markov_chains_II.ipynb +++ b/_notebooks/markov_chains_II.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "96438d6d", + "id": "67df9872", "metadata": {}, "source": [ "# Markov Chains: Irreducibility and Ergodicity\n", @@ -15,7 +15,7 @@ { "cell_type": "code", "execution_count": null, - "id": "733337f7", + "id": "1a742f6e", "metadata": { "hide-output": false }, @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "1242594d", + "id": "d0ff4ae5", "metadata": {}, "source": [ "## Overview\n", @@ -54,7 +54,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c192ce1", + "id": "73e4b39c", "metadata": { "hide-output": false }, @@ -67,7 +67,7 @@ }, { "cell_type": "markdown", - "id": "05c1c9de", + "id": "781c2138", "metadata": {}, "source": [ "\n", @@ -76,7 +76,7 @@ }, { "cell_type": "markdown", - "id": "6dd703b6", + "id": "56501d51", "metadata": {}, "source": [ "## Irreducibility\n", @@ -123,7 +123,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97602b30", + "id": "64cba0db", "metadata": { "hide-output": false }, @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "8a7a3060", + "id": "580ab4ac", "metadata": {}, "source": [ "Here’s a more pessimistic scenario in which poor people remain poor forever\n", @@ -155,7 +155,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b1c5d5b", + "id": "f2203727", "metadata": { "hide-output": false }, @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "c8888bed", + "id": "f0bde016", "metadata": {}, "source": [ "It might be clear to you already that irreducibility is going to be important\n", @@ -184,7 +184,7 @@ }, { "cell_type": "markdown", - "id": "7b7fcc39", + "id": "f9beb68b", "metadata": {}, "source": [ "### Irreducibility and stationarity\n", @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "a1a40bdd", + "id": "c518c5a1", "metadata": {}, "source": [ "### \n", @@ -215,7 +215,7 @@ }, { "cell_type": "markdown", - "id": "ea2aed3e", + "id": "86edb5d9", "metadata": {}, "source": [ "## Ergodicity\n", @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "d481d1e1", + "id": "e778a6b9", "metadata": {}, "source": [ "## \n", @@ -268,7 +268,7 @@ }, { "cell_type": "markdown", - "id": "86166a39", + "id": "fdc00c6c", "metadata": {}, "source": [ "### Example: ergodicity and unemployment\n", @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "2d045d33", + "id": "09771cdb", "metadata": {}, "source": [ "### Example: Hamilton dynamics\n", @@ -326,7 +326,7 @@ { "cell_type": "code", "execution_count": null, - "id": "833d25f4", + "id": "33bea2e5", "metadata": { "hide-output": false }, @@ -356,7 +356,7 @@ }, { "cell_type": "markdown", - "id": "3ebfe7cf", + "id": "1862e63d", "metadata": {}, "source": [ "You might like to try changing $ x=1 $ to either $ x=0 $ or $ x=2 $.\n", @@ -366,7 +366,7 @@ }, { "cell_type": "markdown", - "id": "dda25471", + "id": "e65c686c", "metadata": {}, "source": [ "### Example: a periodic chain\n", @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7546aeb0", + "id": "f10d7159", "metadata": { "hide-output": false }, @@ -432,7 +432,7 @@ }, { "cell_type": "markdown", - "id": "375537b6", + "id": "50c23ff1", "metadata": {}, "source": [ "This example helps to emphasize that asymptotic stationarity is about the distribution, while ergodicity is about the sample path.\n", @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "102361cd", + "id": "6382c0ec", "metadata": {}, "source": [ "### Example: political institutions\n", @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e65b109f", + "id": "664aa687", "metadata": { "hide-output": false }, @@ -511,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "8c5c7bdd", + "id": "eba3047b", "metadata": {}, "source": [ "## Exercises" @@ -519,7 +519,7 @@ }, { "cell_type": "markdown", - "id": "5a280409", + "id": "e5fbf96c", "metadata": {}, "source": [ "## Exercise 35.1\n", @@ -552,7 +552,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99d3cedd", + "id": "2b495fc1", "metadata": { "hide-output": false }, @@ -575,7 +575,7 @@ }, { "cell_type": "markdown", - "id": "08d15e94", + "id": "6884a6f1", "metadata": {}, "source": [ "1. Show this process is asymptotically stationary and calculate an approximation to the stationary distribution. \n", @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "b5861c2d", + "id": "a8f22bf2", "metadata": {}, "source": [ "## Solution to[ Exercise 35.1](https://intro.quantecon.org/#mc_ex1)\n", @@ -597,7 +597,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d847d5a0", + "id": "01ead629", "metadata": { "hide-output": false }, @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "88d8c967", + "id": "47e65458", "metadata": {}, "source": [ "For this model, rows of $ P^n $ converge to the stationary distribution as $ n \\to\n", @@ -630,7 +630,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9c2e8e7", + "id": "818ce692", "metadata": { "hide-output": false }, @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "099b100f", + "id": "4e4d8dcc", "metadata": {}, "source": [ "Part 2:" @@ -652,7 +652,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ebf3c350", + "id": "3a1dbb2a", "metadata": { "hide-output": false }, @@ -677,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "37f27244", + "id": "49420fa2", "metadata": {}, "source": [ "Note that the fraction of time spent at each state converges to the probability\n", @@ -686,7 +686,7 @@ }, { "cell_type": "markdown", - "id": "9826a2b3", + "id": "fb64fc8b", "metadata": {}, "source": [ "## Exercise 35.2\n", @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "6acb42d8", + "id": "8e899af6", "metadata": {}, "source": [ "## Solution to[ Exercise 35.2](https://intro.quantecon.org/#mc_ex2)\n", @@ -744,7 +744,7 @@ { "cell_type": "code", "execution_count": null, - "id": "808ca908", + "id": "83f0c8fe", "metadata": { "hide-output": false }, @@ -777,7 +777,7 @@ }, { "cell_type": "markdown", - "id": "fd33fdc0", + "id": "a4ed431f", "metadata": {}, "source": [ "## Exercise 35.3\n", @@ -796,7 +796,7 @@ }, { "cell_type": "markdown", - "id": "311fd011", + "id": "6105e5b5", "metadata": {}, "source": [ "## Solution to[ Exercise 35.3](https://intro.quantecon.org/#mc_ex3)" @@ -805,7 +805,7 @@ { "cell_type": "code", "execution_count": null, - "id": "991aa032", + "id": "5711dc88", "metadata": { "hide-output": false }, @@ -821,7 +821,7 @@ }, { "cell_type": "markdown", - "id": "89ab0b0e", + "id": "862c961e", "metadata": {}, "source": [ "Let’s try it." @@ -830,7 +830,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb597442", + "id": "cc04a0d7", "metadata": { "hide-output": false }, @@ -852,7 +852,7 @@ } ], "metadata": { - "date": 1722488542.3487206, + "date": 1722502938.9279327, "filename": "markov_chains_II.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/mle.ipynb b/_notebooks/mle.ipynb index b85cc297..5f1696bb 100644 --- a/_notebooks/mle.ipynb +++ b/_notebooks/mle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "eb3fe273", + "id": "8ea50dfc", "metadata": {}, "source": [ "# Maximum Likelihood Estimation" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9d0d085", + "id": "e7e865a9", "metadata": { "hide-output": false }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "82017f04", + "id": "2940414c", "metadata": {}, "source": [ "## Introduction\n", @@ -61,7 +61,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5e4e393", + "id": "e2e29aad", "metadata": { "hide-output": false }, @@ -76,7 +76,7 @@ }, { "cell_type": "markdown", - "id": "af2792cc", + "id": "dc4c3076", "metadata": {}, "source": [ "For a population of size $ N $, where individual $ i $ has wealth $ w_i $, total revenue raised by\n", @@ -101,7 +101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "675b5fd2", + "id": "80a68947", "metadata": { "hide-output": false }, @@ -112,7 +112,7 @@ }, { "cell_type": "markdown", - "id": "1e93b678", + "id": "58c9825a", "metadata": {}, "source": [ "The data is derived from the\n", @@ -124,7 +124,7 @@ { "cell_type": "code", "execution_count": null, - "id": "38521f8c", + "id": "b73b5f15", "metadata": { "hide-output": false }, @@ -142,7 +142,7 @@ }, { "cell_type": "markdown", - "id": "79c44bf6", + "id": "8b9d1809", "metadata": {}, "source": [ "Let’s histogram this sample." @@ -151,7 +151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd1153b4", + "id": "9c469f6c", "metadata": { "hide-output": false }, @@ -170,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "42e6264c", + "id": "f20eb3eb", "metadata": {}, "source": [ "The histogram shows that many people have very low wealth and a few people have\n", @@ -182,7 +182,7 @@ { "cell_type": "code", "execution_count": null, - "id": "261a619e", + "id": "a10065db", "metadata": { "hide-output": false }, @@ -193,7 +193,7 @@ }, { "cell_type": "markdown", - "id": "5c3b913b", + "id": "381ffd18", "metadata": {}, "source": [ "How can we estimate total revenue from the full population using only the sample data?\n", @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "9ff03ae6", + "id": "183f7bf1", "metadata": {}, "source": [ "## Maximum likelihood estimation\n", @@ -247,7 +247,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e950f085", + "id": "c42b592b", "metadata": { "hide-output": false }, @@ -261,7 +261,7 @@ }, { "cell_type": "markdown", - "id": "16977d0d", + "id": "e8e83a6c", "metadata": {}, "source": [ "Now our job is to obtain the maximum likelihood estimates of $ \\mu $ and $ \\sigma $, which\n", @@ -332,7 +332,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d0a714f", + "id": "2fcfc7bd", "metadata": { "hide-output": false }, @@ -345,7 +345,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4456c42", + "id": "6716cc3a", "metadata": { "hide-output": false }, @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "9c432573", + "id": "693340fb", "metadata": {}, "source": [ "Let’s plot the log-normal pdf using the estimated parameters against our sample data." @@ -367,7 +367,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82e8b899", + "id": "eceb0f3e", "metadata": { "hide-output": false }, @@ -387,7 +387,7 @@ }, { "cell_type": "markdown", - "id": "e142feb7", + "id": "05ac9608", "metadata": {}, "source": [ "Our estimated lognormal distribution appears to be a reasonable fit for the overall data.\n", @@ -402,7 +402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd0f95ea", + "id": "2d156f88", "metadata": { "hide-output": false }, @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0613e80c", + "id": "d1ddc329", "metadata": { "hide-output": false }, @@ -429,7 +429,7 @@ }, { "cell_type": "markdown", - "id": "592d2b10", + "id": "328a4544", "metadata": {}, "source": [ "(Our unit was 100,000 dollars, so this means that actual revenue is 100,000\n", @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "4cc44542", + "id": "2f891f93", "metadata": {}, "source": [ "## Pareto distribution\n", @@ -466,7 +466,7 @@ { "cell_type": "code", "execution_count": null, - "id": "18ee32cc", + "id": "449b5883", "metadata": { "hide-output": false }, @@ -479,7 +479,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a7917d00", + "id": "1fc3aba0", "metadata": { "hide-output": false }, @@ -492,7 +492,7 @@ }, { "cell_type": "markdown", - "id": "ef42133b", + "id": "8b67980e", "metadata": {}, "source": [ "Now let’s recompute total revenue." @@ -501,7 +501,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f4d7aff", + "id": "b5436fe6", "metadata": { "hide-output": false }, @@ -514,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "dd404743", + "id": "efcacc38", "metadata": {}, "source": [ "The number is very different!" @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3056735", + "id": "b518526e", "metadata": { "hide-output": false }, @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "faa9ed49", + "id": "ea7003dc", "metadata": {}, "source": [ "We see that choosing the right distribution is extremely important.\n", @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "708dc611", + "id": "c9f6cdbe", "metadata": { "hide-output": false }, @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "f9b19d33", + "id": "a1b917af", "metadata": {}, "source": [ "We observe that in this case the fit for the Pareto distribution is not very\n", @@ -573,7 +573,7 @@ }, { "cell_type": "markdown", - "id": "db0179f0", + "id": "a968a216", "metadata": {}, "source": [ "## What is the best distribution?\n", @@ -594,7 +594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9bd5e379", + "id": "d1848d41", "metadata": { "hide-output": false }, @@ -609,7 +609,7 @@ }, { "cell_type": "markdown", - "id": "3bd951f2", + "id": "e9b3afbe", "metadata": {}, "source": [ "Let’s plot this data." @@ -618,7 +618,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ad55a7e", + "id": "a6932215", "metadata": { "hide-output": false }, @@ -632,7 +632,7 @@ }, { "cell_type": "markdown", - "id": "aaa6f26e", + "id": "6a16333f", "metadata": {}, "source": [ "Now let’s try fitting some distributions to this data." @@ -640,7 +640,7 @@ }, { "cell_type": "markdown", - "id": "978c5005", + "id": "e71148b5", "metadata": {}, "source": [ "### Lognormal distribution for the right hand tail\n", @@ -653,7 +653,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad662167", + "id": "ce6314f6", "metadata": { "hide-output": false }, @@ -675,7 +675,7 @@ }, { "cell_type": "markdown", - "id": "34fa5c2a", + "id": "5bb4a3c4", "metadata": {}, "source": [ "While the lognormal distribution was a good fit for the entire dataset,\n", @@ -684,7 +684,7 @@ }, { "cell_type": "markdown", - "id": "9d4a87c0", + "id": "b9b2fa92", "metadata": {}, "source": [ "### Pareto distribution for the right hand tail\n", @@ -697,7 +697,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4a941d4d", + "id": "d64fbc23", "metadata": { "hide-output": false }, @@ -718,7 +718,7 @@ }, { "cell_type": "markdown", - "id": "3e6cef72", + "id": "9f1fa9eb", "metadata": {}, "source": [ "The Pareto distribution is a better fit for the right hand tail of our dataset." @@ -726,7 +726,7 @@ }, { "cell_type": "markdown", - "id": "c663f9e0", + "id": "b943b146", "metadata": {}, "source": [ "### So what is the best distribution?\n", @@ -746,7 +746,7 @@ }, { "cell_type": "markdown", - "id": "938841a3", + "id": "31433295", "metadata": {}, "source": [ "## Exercises" @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "0ecbc548", + "id": "8d4ce8e6", "metadata": {}, "source": [ "## Exercise 46.1\n", @@ -774,7 +774,7 @@ }, { "cell_type": "markdown", - "id": "19dd4efc", + "id": "d210a1a8", "metadata": {}, "source": [ "## Solution to[ Exercise 46.1](https://intro.quantecon.org/#mle_ex1)" @@ -783,7 +783,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbb7702b", + "id": "52b05ba1", "metadata": { "hide-output": false }, @@ -796,7 +796,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8071385", + "id": "3cb09dd3", "metadata": { "hide-output": false }, @@ -809,7 +809,7 @@ }, { "cell_type": "markdown", - "id": "84cbbb8d", + "id": "9daa009b", "metadata": {}, "source": [ "## Exercise 46.2\n", @@ -819,7 +819,7 @@ }, { "cell_type": "markdown", - "id": "4fcaa487", + "id": "f2e1c8c4", "metadata": {}, "source": [ "## Solution to[ Exercise 46.2](https://intro.quantecon.org/#mle_ex2)" @@ -828,7 +828,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dace57b5", + "id": "680a0af2", "metadata": { "hide-output": false }, @@ -846,7 +846,7 @@ }, { "cell_type": "markdown", - "id": "248a2a1b", + "id": "661f407a", "metadata": {}, "source": [ "Clearly, this distribution is not a good fit for our data." @@ -854,7 +854,7 @@ } ], "metadata": { - "date": 1722488542.3762226, + "date": 1722502938.955847, "filename": "mle.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/money_inflation.ipynb b/_notebooks/money_inflation.ipynb index 0cd61b50..8a41415e 100644 --- a/_notebooks/money_inflation.ipynb +++ b/_notebooks/money_inflation.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "16300ce2", + "id": "f723c639", "metadata": {}, "source": [ "# Money Financed Government Deficits and Price Levels" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "5c6b4577", + "id": "048f6af1", "metadata": {}, "source": [ "## Overview\n", @@ -73,7 +73,7 @@ }, { "cell_type": "markdown", - "id": "7f53b880", + "id": "1d553305", "metadata": {}, "source": [ "## Demand for and supply of money\n", @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "b1015344", + "id": "c40314d7", "metadata": {}, "source": [ "## Equilibrium price and money supply sequences\n", @@ -206,7 +206,7 @@ }, { "cell_type": "markdown", - "id": "517cc184", + "id": "b62f426a", "metadata": {}, "source": [ "### Steady states\n", @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "43063f9b", + "id": "10991b92", "metadata": {}, "source": [ "## Some code\n", @@ -301,7 +301,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8eef2b6", + "id": "efbeeeac", "metadata": { "hide-output": false }, @@ -316,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "49e2d476", + "id": "cf062b87", "metadata": {}, "source": [ "Let’s set some parameter values and compute possible steady-state rates of return on currency $ \\bar R $, the seigniorage maximizing rate of return on currency, and an object that we’ll discuss later, namely, an initial price level $ p_0 $ associated with the maximum steady-state rate of return on currency.\n", @@ -327,7 +327,7 @@ { "cell_type": "code", "execution_count": null, - "id": "560d4b24", + "id": "302aa331", "metadata": { "hide-output": false }, @@ -350,7 +350,7 @@ }, { "cell_type": "markdown", - "id": "8c028303", + "id": "312cc600", "metadata": {}, "source": [ "Now we compute the $ \\bar R_{\\rm max} $ and corresponding revenue" @@ -359,7 +359,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f328fcfd", + "id": "10f72795", "metadata": { "hide-output": false }, @@ -383,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "74596560", + "id": "2e051ac3", "metadata": {}, "source": [ "Now let’s plot seigniorage as a function of alternative potential steady-state values of $ R $.\n", @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3714140c", + "id": "f1b83b0e", "metadata": { "hide-output": false }, @@ -423,7 +423,7 @@ }, { "cell_type": "markdown", - "id": "82873168", + "id": "560aa34b", "metadata": {}, "source": [ "Let’s print the two steady-state rates of return $ \\bar R $ and the associated seigniorage revenues that the government collects.\n", @@ -436,7 +436,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dcaa861c", + "id": "a623e746", "metadata": { "hide-output": false }, @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "0202d33d", + "id": "b9bf9d6b", "metadata": {}, "source": [ "Now let’s compute the maximum steady-state amount of seigniorage that could be gathered by printing money and the state state rate of return on money that attains it." @@ -459,7 +459,7 @@ }, { "cell_type": "markdown", - "id": "5babccb8", + "id": "e1890ab9", "metadata": {}, "source": [ "## Two computation strategies\n", @@ -471,7 +471,7 @@ }, { "cell_type": "markdown", - "id": "950421ec", + "id": "96e65a48", "metadata": {}, "source": [ "### Method 1\n", @@ -520,7 +520,7 @@ }, { "cell_type": "markdown", - "id": "edfa1146", + "id": "79ba8e11", "metadata": {}, "source": [ "### Method 2\n", @@ -559,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "3a05cabe", + "id": "d0a874ba", "metadata": {}, "source": [ "## Computation method 1\n", @@ -604,7 +604,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f747f00f", + "id": "300c29cc", "metadata": { "hide-output": false }, @@ -632,7 +632,7 @@ }, { "cell_type": "markdown", - "id": "43d6ebaa", + "id": "aa39f194", "metadata": {}, "source": [ "Let’s write some code to plot outcomes for several possible initial values $ R_0 $." @@ -641,7 +641,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9272348b", + "id": "049e9519", "metadata": { "hide-output": false }, @@ -690,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "2bcece78", + "id": "6d0f0f1a", "metadata": {}, "source": [ "Let’s plot distinct outcomes associated with several $ R_0 \\in [\\frac{\\gamma_2}{\\gamma_1}, R_u] $.\n", @@ -701,7 +701,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41069ea8", + "id": "211ac8d0", "metadata": { "hide-output": false }, @@ -715,7 +715,7 @@ }, { "cell_type": "markdown", - "id": "a1db4edc", + "id": "0648bfc3", "metadata": {}, "source": [ "Notice how sequences that start from $ R_0 $ in the half-open interval $ [R_\\ell, R_u) $ converge to the steady state associated with to $ R_\\ell $." @@ -723,7 +723,7 @@ }, { "cell_type": "markdown", - "id": "a44f1844", + "id": "39807d74", "metadata": {}, "source": [ "## Computation method 2\n", @@ -767,7 +767,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80d164ae", + "id": "c8ccd8ed", "metadata": { "hide-output": false }, @@ -781,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "fc0fe85a", + "id": "14f37221", "metadata": {}, "source": [ "Define\n", @@ -794,7 +794,7 @@ { "cell_type": "code", "execution_count": null, - "id": "168fe326", + "id": "3b36dbbf", "metadata": { "hide-output": false }, @@ -806,7 +806,7 @@ }, { "cell_type": "markdown", - "id": "daf36243", + "id": "e5bd69e3", "metadata": {}, "source": [ "and write the system [(28.13)](#equation-eq-sytem101) as\n", @@ -861,7 +861,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17d84d28", + "id": "8f192300", "metadata": { "hide-output": false }, @@ -875,7 +875,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0eabbb45", + "id": "a51bdd4f", "metadata": { "hide-output": false }, @@ -890,7 +890,7 @@ }, { "cell_type": "markdown", - "id": "9e1e6548", + "id": "43766abe", "metadata": {}, "source": [ "Partition $ Q $ as\n", @@ -946,7 +946,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1614ceb", + "id": "025ce994", "metadata": { "hide-output": false }, @@ -963,7 +963,7 @@ }, { "cell_type": "markdown", - "id": "74ebc76c", + "id": "f0e75fbc", "metadata": {}, "source": [ "For almost all initial vectors $ y_0 $, the gross rate of inflation $ \\frac{p_{t+1}}{p_t} $ eventually converges to the larger eigenvalue $ {R_\\ell}^{-1} $.\n", @@ -1054,7 +1054,7 @@ }, { "cell_type": "markdown", - "id": "a42fffd7", + "id": "9a4f1de9", "metadata": {}, "source": [ "### More convenient formula\n", @@ -1095,7 +1095,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a080ac3e", + "id": "fdedc167", "metadata": { "hide-output": false }, @@ -1108,7 +1108,7 @@ }, { "cell_type": "markdown", - "id": "84fa7969", + "id": "c27c70ac", "metadata": {}, "source": [ "It can be verified that this formula replicates itself over time in the sense that\n", @@ -1127,7 +1127,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6db6233c", + "id": "e8c151e3", "metadata": { "hide-output": false }, @@ -1179,7 +1179,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09e81f0e", + "id": "c5cc86b8", "metadata": { "hide-output": false }, @@ -1192,7 +1192,7 @@ }, { "cell_type": "markdown", - "id": "4c384258", + "id": "1a406c77", "metadata": {}, "source": [ "Please notice that for $ m_t $ and $ p_t $, we have used log scales for the coordinate (i.e., vertical) axes.\n", @@ -1203,7 +1203,7 @@ }, { "cell_type": "markdown", - "id": "ea2490d2", + "id": "f0b0bdf6", "metadata": {}, "source": [ "## Peculiar stationary outcomes\n", @@ -1230,7 +1230,7 @@ }, { "cell_type": "markdown", - "id": "d417e41f", + "id": "02925c92", "metadata": {}, "source": [ "## Equilibrium selection\n", @@ -1260,7 +1260,7 @@ } ], "metadata": { - "date": 1722488542.4392514, + "date": 1722502939.0222955, "filename": "money_inflation.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/money_inflation_nonlinear.ipynb b/_notebooks/money_inflation_nonlinear.ipynb index ff668637..24297fd4 100644 --- a/_notebooks/money_inflation_nonlinear.ipynb +++ b/_notebooks/money_inflation_nonlinear.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "4c50fe47", + "id": "d4f4b16e", "metadata": {}, "source": [ "# Inflation Rate Laffer Curves" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "9548e72e", + "id": "65941c9a", "metadata": {}, "source": [ "## Overview\n", @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "00b46395", + "id": "3dab68e8", "metadata": {}, "source": [ "## The model\n", @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "8bc8ad99", + "id": "3ca800ae", "metadata": {}, "source": [ "## Computing an equilibrium sequence\n", @@ -135,7 +135,7 @@ }, { "cell_type": "markdown", - "id": "ac6cfa2d", + "id": "ae34ca79", "metadata": {}, "source": [ "## Limiting values of inflation rate\n", @@ -183,7 +183,7 @@ { "cell_type": "code", "execution_count": null, - "id": "339f8c9c", + "id": "d25e1975", "metadata": { "hide-output": false }, @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "cf54f486", + "id": "3b39acb0", "metadata": {}, "source": [ "Let’s create a `namedtuple` to store the parameters of the model" @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9baa3d77", + "id": "1d7ff047", "metadata": { "hide-output": false }, @@ -228,7 +228,7 @@ }, { "cell_type": "markdown", - "id": "b78bfe52", + "id": "3f4b4f0a", "metadata": {}, "source": [ "Now we write code that computes steady-state $ \\overline \\pi $s." @@ -237,7 +237,7 @@ { "cell_type": "code", "execution_count": null, - "id": "abad8e24", + "id": "395ceb9e", "metadata": { "hide-output": false }, @@ -259,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "f99b7c64", + "id": "a3ec22ec", "metadata": {}, "source": [ "We find two steady state $ \\overline \\pi $ values." @@ -267,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "a0054a5f", + "id": "f65a5133", "metadata": {}, "source": [ "## Steady state Laffer curve\n", @@ -278,7 +278,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c3fd54d", + "id": "e37b5ad1", "metadata": { "hide-output": false }, @@ -317,7 +317,7 @@ }, { "cell_type": "markdown", - "id": "b7e4d94f", + "id": "ebb3ae33", "metadata": {}, "source": [ "## Associated initial price levels\n", @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1df5309", + "id": "167c5c5f", "metadata": { "hide-output": false }, @@ -356,7 +356,7 @@ }, { "cell_type": "markdown", - "id": "544b3950", + "id": "47d29700", "metadata": {}, "source": [ "### Verification\n", @@ -370,7 +370,7 @@ { "cell_type": "code", "execution_count": null, - "id": "200b8223", + "id": "998da11c", "metadata": { "hide-output": false }, @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0cb9be1", + "id": "12d9882f", "metadata": { "hide-output": false }, @@ -418,7 +418,7 @@ }, { "cell_type": "markdown", - "id": "98084d20", + "id": "5ece151e", "metadata": {}, "source": [ "## Slippery side of Laffer curve dynamics\n", @@ -429,7 +429,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b549093f", + "id": "e0031598", "metadata": { "hide-output": false }, @@ -486,7 +486,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1736ad7", + "id": "5f68bf06", "metadata": { "hide-output": false }, @@ -506,7 +506,7 @@ }, { "cell_type": "markdown", - "id": "0cac1398", + "id": "0138825b", "metadata": {}, "source": [ "Staring at the paths of price levels in Fig. 30.2 reveals that almost all paths converge to the *higher* inflation tax rate displayed in the stationary state Laffer curve. displayed in figure Fig. 30.1.\n", @@ -538,7 +538,7 @@ } ], "metadata": { - "date": 1722488542.4660213, + "date": 1722502939.047687, "filename": "money_inflation_nonlinear.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/monte_carlo.ipynb b/_notebooks/monte_carlo.ipynb index e813283d..d5350bb9 100644 --- a/_notebooks/monte_carlo.ipynb +++ b/_notebooks/monte_carlo.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "255e9eac", + "id": "6b812d69", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "24bf624b", + "id": "c3295db0", "metadata": {}, "source": [ "# Monte Carlo and Option Pricing" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "a83d11d8", + "id": "f6354f30", "metadata": {}, "source": [ "## Overview\n", @@ -55,7 +55,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4ebf56c", + "id": "b2b5f4c0", "metadata": { "hide-output": false }, @@ -68,7 +68,7 @@ }, { "cell_type": "markdown", - "id": "d457c249", + "id": "82c0c16d", "metadata": {}, "source": [ "## An introduction to Monte Carlo\n", @@ -79,7 +79,7 @@ }, { "cell_type": "markdown", - "id": "b6bb0a7b", + "id": "18b68910", "metadata": {}, "source": [ "### Share price with known distribution\n", @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "cc636c90", + "id": "83356097", "metadata": {}, "source": [ "### Share price with unknown distribution\n", @@ -184,7 +184,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9546fe08", + "id": "6aca9c11", "metadata": { "hide-output": false }, @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "996d1a0b", + "id": "03ddb6c8", "metadata": {}, "source": [ "#### A routine using loops in python\n", @@ -214,7 +214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3c662c5", + "id": "ea0453a7", "metadata": { "hide-output": false }, @@ -233,7 +233,7 @@ }, { "cell_type": "markdown", - "id": "c0c81c06", + "id": "9fd621f9", "metadata": {}, "source": [ "We can also construct a function that contains these operations:" @@ -242,7 +242,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2a1a39cb", + "id": "2b55a260", "metadata": { "hide-output": false }, @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "f89cb955", + "id": "9239fbd2", "metadata": {}, "source": [ "Now let’s call it." @@ -269,7 +269,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2a5f3a69", + "id": "b6402f91", "metadata": { "hide-output": false }, @@ -280,7 +280,7 @@ }, { "cell_type": "markdown", - "id": "5f5cc193", + "id": "cd63fb87", "metadata": {}, "source": [ "### A vectorized routine\n", @@ -295,7 +295,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e49c6fcc", + "id": "31801344", "metadata": { "hide-output": false }, @@ -312,7 +312,7 @@ { "cell_type": "code", "execution_count": null, - "id": "503200df", + "id": "82538c39", "metadata": { "hide-output": false }, @@ -325,7 +325,7 @@ }, { "cell_type": "markdown", - "id": "1f409b3c", + "id": "059d93e2", "metadata": {}, "source": [ "Notice that this routine is much faster.\n", @@ -336,7 +336,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d41443e", + "id": "be866e55", "metadata": { "hide-output": false }, @@ -349,7 +349,7 @@ }, { "cell_type": "markdown", - "id": "96c2ed5a", + "id": "7899db30", "metadata": {}, "source": [ "## Pricing a European call option under risk neutrality\n", @@ -361,7 +361,7 @@ }, { "cell_type": "markdown", - "id": "7a809f8b", + "id": "465d69db", "metadata": {}, "source": [ "### Risk-neutral pricing\n", @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "0b54d67b", + "id": "7e096767", "metadata": {}, "source": [ "### A comment on risk\n", @@ -432,7 +432,7 @@ }, { "cell_type": "markdown", - "id": "3b6649ad", + "id": "5495c5ca", "metadata": {}, "source": [ "### Discounting\n", @@ -467,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "5396bdad", + "id": "ad666883", "metadata": {}, "source": [ "### European call options\n", @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cef08c9f", + "id": "c5494232", "metadata": { "hide-output": false }, @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "5ff07f5a", + "id": "68303d2f", "metadata": {}, "source": [ "We set the simulation size to" @@ -542,7 +542,7 @@ { "cell_type": "code", "execution_count": null, - "id": "957efb49", + "id": "29e4f173", "metadata": { "hide-output": false }, @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "7aa3ac2c", + "id": "c3226d4e", "metadata": {}, "source": [ "Here is our code" @@ -562,7 +562,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5aa0ecc1", + "id": "bf3475d3", "metadata": { "hide-output": false }, @@ -576,7 +576,7 @@ }, { "cell_type": "markdown", - "id": "2f4df415", + "id": "35b99539", "metadata": {}, "source": [ "## Pricing via a dynamic model\n", @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "9c44118d", + "id": "9914212d", "metadata": {}, "source": [ "### Simple dynamics\n", @@ -629,7 +629,7 @@ }, { "cell_type": "markdown", - "id": "3e99e074", + "id": "3b911da8", "metadata": {}, "source": [ "### Problems with simple dynamics\n", @@ -647,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "5025f50c", + "id": "34c5db01", "metadata": {}, "source": [ "### More realistic dynamics\n", @@ -671,7 +671,7 @@ }, { "cell_type": "markdown", - "id": "2b21e653", + "id": "4162b927", "metadata": {}, "source": [ "### Default parameters\n", @@ -682,7 +682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ec38b8c", + "id": "eeabd377", "metadata": { "hide-output": false }, @@ -697,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "4bf1a9b4", + "id": "6cd4187b", "metadata": {}, "source": [ "(Here `default_S0` is $ S_0 $ and `default_h0` is $ h_0 $.)\n", @@ -708,7 +708,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5ad977a1", + "id": "5de99021", "metadata": { "hide-output": false }, @@ -721,7 +721,7 @@ }, { "cell_type": "markdown", - "id": "9094e188", + "id": "2bd0611c", "metadata": {}, "source": [ "### Visualizations\n", @@ -738,7 +738,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7241fab4", + "id": "5dedf79a", "metadata": { "hide-output": false }, @@ -758,7 +758,7 @@ }, { "cell_type": "markdown", - "id": "79a63bcc", + "id": "e9a461c7", "metadata": {}, "source": [ "Here we plot the paths and the log of the paths." @@ -767,7 +767,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab904c63", + "id": "e9559e64", "metadata": { "hide-output": false }, @@ -789,7 +789,7 @@ }, { "cell_type": "markdown", - "id": "ae1cab8b", + "id": "1be703ec", "metadata": {}, "source": [ "### Computing the price\n", @@ -814,7 +814,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fce5c35", + "id": "2e732e1c", "metadata": { "hide-output": false }, @@ -847,7 +847,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3ef5837", + "id": "8eb7b8d9", "metadata": { "hide-output": false }, @@ -859,7 +859,7 @@ }, { "cell_type": "markdown", - "id": "0be4e2e3", + "id": "38db58b8", "metadata": {}, "source": [ "## Exercises" @@ -867,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "63889f08", + "id": "89df6df8", "metadata": {}, "source": [ "## Exercise 20.1\n", @@ -882,7 +882,7 @@ }, { "cell_type": "markdown", - "id": "d96e4711", + "id": "c66e6b8c", "metadata": {}, "source": [ "## Solution to[ Exercise 20.1](https://intro.quantecon.org/#monte_carlo_ex1)" @@ -891,7 +891,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29f5397a", + "id": "ba2a302d", "metadata": { "hide-output": false }, @@ -921,7 +921,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7671f1fa", + "id": "65ffd1b4", "metadata": { "hide-output": false }, @@ -933,7 +933,7 @@ }, { "cell_type": "markdown", - "id": "03db1c86", + "id": "977e9e5b", "metadata": {}, "source": [ "Notice that this version is faster than the one using a Python loop.\n", @@ -944,7 +944,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eca0196c", + "id": "7273d627", "metadata": { "hide-output": false }, @@ -956,7 +956,7 @@ }, { "cell_type": "markdown", - "id": "e239f5dc", + "id": "efe96c66", "metadata": {}, "source": [ "## Exercise 20.2\n", @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "99a83a70", + "id": "01d590c5", "metadata": {}, "source": [ "## Solution to[ Exercise 20.2](https://intro.quantecon.org/#monte_carlo_ex2)" @@ -981,7 +981,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88f9fe60", + "id": "4de98d10", "metadata": { "hide-output": false }, @@ -1001,7 +1001,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e426f99", + "id": "150a5926", "metadata": { "hide-output": false }, @@ -1044,7 +1044,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc48d01f", + "id": "c2fb3e4a", "metadata": { "hide-output": false }, @@ -1055,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "ebd80a6c", + "id": "50df5b4d", "metadata": {}, "source": [ "Let’s look at the vectorized version which is faster than using Python loops." @@ -1064,7 +1064,7 @@ { "cell_type": "code", "execution_count": null, - "id": "356274ec", + "id": "10f442a4", "metadata": { "hide-output": false }, @@ -1099,7 +1099,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21e2850f", + "id": "3a32601c", "metadata": { "hide-output": false }, @@ -1110,7 +1110,7 @@ } ], "metadata": { - "date": 1722488542.4994297, + "date": 1722502939.0798125, "filename": "monte_carlo.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/networks.ipynb b/_notebooks/networks.ipynb index dc999655..4632af6b 100644 --- a/_notebooks/networks.ipynb +++ b/_notebooks/networks.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f04f83c4", + "id": "02391e80", "metadata": {}, "source": [ "# Networks" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09ccedbd", + "id": "8e17ff02", "metadata": { "hide-output": false }, @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "87b38dba", + "id": "1540c24a", "metadata": {}, "source": [ "## Outline\n", @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8cc7c99d", + "id": "371a6b76", "metadata": { "hide-output": false }, @@ -80,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "0e61994f", + "id": "15b81236", "metadata": {}, "source": [ "## Economic and financial networks\n", @@ -105,7 +105,7 @@ }, { "cell_type": "markdown", - "id": "2768c9bb", + "id": "c2480cf3", "metadata": {}, "source": [ "### Example: Aircraft Exports\n", @@ -116,7 +116,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7cf5c048", + "id": "3bf1bf6d", "metadata": { "hide-output": false }, @@ -174,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "e4c0f479", + "id": "77363912", "metadata": {}, "source": [ "The circles in the figure are called **nodes** or **vertices** – in this case they represent countries.\n", @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "675867e4", + "id": "00f86fd7", "metadata": {}, "source": [ "### Example: A Markov Chain\n", @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "f102ae8c", + "id": "06da2e33", "metadata": {}, "source": [ "## An introduction to graph theory\n", @@ -254,7 +254,7 @@ }, { "cell_type": "markdown", - "id": "ccb2e03d", + "id": "19178147", "metadata": {}, "source": [ "### Key definitions\n", @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "e3736eee", + "id": "6183e8df", "metadata": {}, "source": [ "### Digraphs in Networkx\n", @@ -323,7 +323,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b11a9287", + "id": "9c161ca3", "metadata": { "hide-output": false }, @@ -334,7 +334,7 @@ }, { "cell_type": "markdown", - "id": "ee7cb5fe", + "id": "e3fefa52", "metadata": {}, "source": [ "Next we populate it with nodes and edges.\n", @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04050516", + "id": "c2a89b95", "metadata": { "hide-output": false }, @@ -359,7 +359,7 @@ }, { "cell_type": "markdown", - "id": "6dcb25af", + "id": "ea797746", "metadata": {}, "source": [ "Finally, we add the edges to our `DiGraph` object:" @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "edb86cd0", + "id": "5e556ff2", "metadata": { "hide-output": false }, @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "9033e479", + "id": "7daaf09f", "metadata": {}, "source": [ "Alternatively, we can use the method `add_edges_from`." @@ -390,7 +390,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdb53488", + "id": "523e0f93", "metadata": { "hide-output": false }, @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "62b07270", + "id": "0a775d64", "metadata": {}, "source": [ "Adding the edges automatically adds the nodes, so `G_p` is now a\n", @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc7d1945", + "id": "3e419542", "metadata": { "hide-output": false }, @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "9f13bfe2", + "id": "e7fcadbb", "metadata": {}, "source": [ "The figure obtained above matches the original directed graph in Fig. 42.3.\n", @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92c83dab", + "id": "9946476e", "metadata": { "hide-output": false }, @@ -453,7 +453,7 @@ }, { "cell_type": "markdown", - "id": "38d7b28a", + "id": "62169aba", "metadata": {}, "source": [ "\n", @@ -462,7 +462,7 @@ }, { "cell_type": "markdown", - "id": "1bb4d0ef", + "id": "7d11a682", "metadata": {}, "source": [ "### Communication\n", @@ -499,7 +499,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5a1663c", + "id": "b7c0dbf9", "metadata": { "hide-output": false }, @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbdb634f", + "id": "3d392378", "metadata": { "hide-output": false }, @@ -530,7 +530,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6cad8222", + "id": "9e922f51", "metadata": { "hide-output": false }, @@ -549,7 +549,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7270d5ce", + "id": "c95032d7", "metadata": { "hide-output": false }, @@ -560,7 +560,7 @@ }, { "cell_type": "markdown", - "id": "2ef29c98", + "id": "ddeb6c34", "metadata": {}, "source": [ "## Weighted graphs\n", @@ -571,7 +571,7 @@ }, { "cell_type": "markdown", - "id": "b7087c93", + "id": "910ea7c0", "metadata": {}, "source": [ "### International private credit flows by country\n", @@ -583,7 +583,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea6efa93", + "id": "ffc46dfb", "metadata": { "hide-output": false }, @@ -645,7 +645,7 @@ }, { "cell_type": "markdown", - "id": "e6a4bfed", + "id": "4e5254db", "metadata": {}, "source": [ "The country codes are given in the following table\n", @@ -681,7 +681,7 @@ }, { "cell_type": "markdown", - "id": "35bd71e4", + "id": "993614e3", "metadata": {}, "source": [ "### Definitions\n", @@ -707,7 +707,7 @@ }, { "cell_type": "markdown", - "id": "ba2d5052", + "id": "1bfe09cd", "metadata": {}, "source": [ "## Adjacency matrices\n", @@ -751,7 +751,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e02edb8e", + "id": "c5af3b86", "metadata": { "hide-output": false }, @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "ca491dc1", + "id": "8dc46aab", "metadata": {}, "source": [ "One of the key points to remember about adjacency matrices is that taking the\n", @@ -780,7 +780,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42488d76", + "id": "53697fbe", "metadata": { "hide-output": false }, @@ -811,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "5eb025bf", + "id": "9a7d245d", "metadata": {}, "source": [ "We see that bank 2 extends a loan of size 200 to bank 3.\n", @@ -850,7 +850,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1ee6f5e", + "id": "5e178946", "metadata": { "hide-output": false }, @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "aa345776", + "id": "2b32ba33", "metadata": {}, "source": [ "In general, every nonnegative $ n \\times n $ matrix $ A = (a_{ij}) $ can be\n", @@ -896,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "c816e546", + "id": "0f9b5680", "metadata": {}, "source": [ "## Properties\n", @@ -910,7 +910,7 @@ }, { "cell_type": "markdown", - "id": "f43fbd67", + "id": "ca5137c0", "metadata": {}, "source": [ "## \n", @@ -935,7 +935,7 @@ }, { "cell_type": "markdown", - "id": "09078c5f", + "id": "08dbbfcf", "metadata": {}, "source": [ "## \n", @@ -958,7 +958,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2a7c7e67", + "id": "f81a91ea", "metadata": { "hide-output": false }, @@ -973,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "8fe04c6b", + "id": "aacfc6cc", "metadata": {}, "source": [ "Then we construct the associated adjacency matrix A." @@ -982,7 +982,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98e0fda8", + "id": "59b75514", "metadata": { "hide-output": false }, @@ -996,7 +996,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31c1a011", + "id": "b031eb18", "metadata": { "hide-output": false }, @@ -1013,7 +1013,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36695d8e", + "id": "e0d12e8e", "metadata": { "hide-output": false }, @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0bde25fb", + "id": "36f0f540", "metadata": { "hide-output": false }, @@ -1036,7 +1036,7 @@ }, { "cell_type": "markdown", - "id": "a363447b", + "id": "e25f14a9", "metadata": {}, "source": [ "## Network centrality\n", @@ -1059,7 +1059,7 @@ }, { "cell_type": "markdown", - "id": "10910b97", + "id": "1dcc1026", "metadata": {}, "source": [ "### Degree centrality\n", @@ -1078,7 +1078,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac44d96e", + "id": "45a92f29", "metadata": { "hide-output": false }, @@ -1106,7 +1106,7 @@ }, { "cell_type": "markdown", - "id": "35bbea92", + "id": "f3b75c85", "metadata": {}, "source": [ "The following code displays the in-degree centrality of all nodes." @@ -1115,7 +1115,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a09e10f1", + "id": "e92c8e00", "metadata": { "hide-output": false }, @@ -1129,7 +1129,7 @@ }, { "cell_type": "markdown", - "id": "183695fe", + "id": "c15f258a", "metadata": {}, "source": [ "Consider the international credit network displayed in Fig. 42.4.\n", @@ -1140,7 +1140,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c58f7212", + "id": "b978c4fe", "metadata": { "hide-output": false }, @@ -1153,7 +1153,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a4589ba3", + "id": "eff090dd", "metadata": { "hide-output": false }, @@ -1170,7 +1170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "469622ec", + "id": "bc0e6b80", "metadata": { "hide-output": false }, @@ -1192,7 +1192,7 @@ }, { "cell_type": "markdown", - "id": "38bf1ea3", + "id": "5ac04bf8", "metadata": {}, "source": [ "Unfortunately, while in-degree and out-degree centrality are simple to\n", @@ -1234,7 +1234,7 @@ }, { "cell_type": "markdown", - "id": "0b1c726c", + "id": "4677b187", "metadata": {}, "source": [ "### Eigenvector centrality\n", @@ -1296,7 +1296,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c499d7a", + "id": "7195ccb8", "metadata": { "hide-output": false }, @@ -1317,7 +1317,7 @@ }, { "cell_type": "markdown", - "id": "7480490d", + "id": "dbed6cc1", "metadata": {}, "source": [ "Let’s compute eigenvector centrality for the graph generated in Fig. 42.6." @@ -1326,7 +1326,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51ec2fd4", + "id": "ec567a1b", "metadata": { "hide-output": false }, @@ -1338,7 +1338,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c84d1f02", + "id": "b8c7567e", "metadata": { "hide-output": false }, @@ -1353,7 +1353,7 @@ }, { "cell_type": "markdown", - "id": "ff81237c", + "id": "2b729b74", "metadata": {}, "source": [ "While nodes $ 2 $ and $ 4 $ had the highest in-degree centrality, we can see that nodes $ 1 $ and $ 2 $ have the\n", @@ -1365,7 +1365,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f2bec6b4", + "id": "ea140583", "metadata": { "hide-output": false }, @@ -1377,7 +1377,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f650c51c", + "id": "be6c23fc", "metadata": { "hide-output": false }, @@ -1397,7 +1397,7 @@ }, { "cell_type": "markdown", - "id": "45cae9ec", + "id": "8c78c8e2", "metadata": {}, "source": [ "Countries that are rated highly according to this rank tend to be important\n", @@ -1416,7 +1416,7 @@ }, { "cell_type": "markdown", - "id": "7e7f2126", + "id": "2e775910", "metadata": {}, "source": [ "### Katz centrality\n", @@ -1472,7 +1472,7 @@ }, { "cell_type": "markdown", - "id": "9449bbbe", + "id": "293b7c3a", "metadata": {}, "source": [ "### Authorities vs hubs\n", @@ -1534,7 +1534,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a7bc2a48", + "id": "b66d547b", "metadata": { "hide-output": false }, @@ -1546,7 +1546,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6345339f", + "id": "d49ece62", "metadata": { "hide-output": false }, @@ -1566,7 +1566,7 @@ }, { "cell_type": "markdown", - "id": "b9baf654", + "id": "318c90fe", "metadata": {}, "source": [ "Highly ranked countries are those that attract large inflows of credit, or\n", @@ -1577,7 +1577,7 @@ }, { "cell_type": "markdown", - "id": "f907c6dc", + "id": "fedd3778", "metadata": {}, "source": [ "## Further reading\n", @@ -1595,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "1144d932", + "id": "03f82113", "metadata": {}, "source": [ "## Exercises" @@ -1603,7 +1603,7 @@ }, { "cell_type": "markdown", - "id": "2ec35385", + "id": "75750617", "metadata": {}, "source": [ "## Exercise 42.1\n", @@ -1617,7 +1617,7 @@ }, { "cell_type": "markdown", - "id": "550952ea", + "id": "294701d5", "metadata": {}, "source": [ "## Solution to[ Exercise 42.1](https://intro.quantecon.org/#networks_ex1)\n", @@ -1648,7 +1648,7 @@ }, { "cell_type": "markdown", - "id": "cd600d1f", + "id": "913257ff", "metadata": {}, "source": [ "## Exercise 42.2\n", @@ -1673,7 +1673,7 @@ }, { "cell_type": "markdown", - "id": "09f2f689", + "id": "5bf33f19", "metadata": {}, "source": [ "## Solution to[ Exercise 42.2](https://intro.quantecon.org/#networks_ex2)" @@ -1682,7 +1682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "780ac9c1", + "id": "8e6a3356", "metadata": { "hide-output": false }, @@ -1711,7 +1711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcf68990", + "id": "132ead58", "metadata": { "hide-output": false }, @@ -1725,7 +1725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1afd4bb5", + "id": "2f6b0ecb", "metadata": { "hide-output": false }, @@ -1740,7 +1740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd0477e0", + "id": "e98d127a", "metadata": { "hide-output": false }, @@ -1755,7 +1755,7 @@ }, { "cell_type": "markdown", - "id": "4217079a", + "id": "284ae57c", "metadata": {}, "source": [ "## Exercise 42.3\n", @@ -1777,7 +1777,7 @@ }, { "cell_type": "markdown", - "id": "9cbe5cac", + "id": "cdc1186c", "metadata": {}, "source": [ "## Solution to[ Exercise 42.3](https://intro.quantecon.org/#networks_ex3)" @@ -1786,7 +1786,7 @@ { "cell_type": "code", "execution_count": null, - "id": "524a1b8a", + "id": "a7c77783", "metadata": { "hide-output": false }, @@ -1807,7 +1807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "568fc67a", + "id": "cb7484dc", "metadata": { "hide-output": false }, @@ -1830,7 +1830,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9782fba", + "id": "6fad864b", "metadata": { "hide-output": false }, @@ -1842,7 +1842,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1166cf8c", + "id": "a7aaaa47", "metadata": { "hide-output": false }, @@ -1853,7 +1853,7 @@ } ], "metadata": { - "date": 1722488543.1917553, + "date": 1722502940.0435827, "filename": "networks.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/olg.ipynb b/_notebooks/olg.ipynb index 64f5d837..f3f878f6 100644 --- a/_notebooks/olg.ipynb +++ b/_notebooks/olg.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "484c98ba", + "id": "1978c6a8", "metadata": {}, "source": [ "# The Overlapping Generations Model\n", @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "d23d8b3c", + "id": "2583ce1f", "metadata": {}, "source": [ "## Overview\n", @@ -66,7 +66,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d75c4c19", + "id": "f9f74187", "metadata": { "hide-output": false }, @@ -80,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "93e578d7", + "id": "22347161", "metadata": {}, "source": [ "## Environment\n", @@ -118,7 +118,7 @@ }, { "cell_type": "markdown", - "id": "6d4d337c", + "id": "8b1fb9bd", "metadata": {}, "source": [ "## Supply of capital\n", @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "f4874cfa", + "id": "04cc4a0a", "metadata": {}, "source": [ "### Consumer’s problem\n", @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "30c0fd78", + "id": "f3996052", "metadata": {}, "source": [ "### Example: log preferences\n", @@ -246,7 +246,7 @@ }, { "cell_type": "markdown", - "id": "4c67fa90", + "id": "4110f7d6", "metadata": {}, "source": [ "### Savings and investment\n", @@ -265,7 +265,7 @@ }, { "cell_type": "markdown", - "id": "22902498", + "id": "f9b72bfb", "metadata": {}, "source": [ "## Demand for capital\n", @@ -276,7 +276,7 @@ }, { "cell_type": "markdown", - "id": "e68abb93", + "id": "52fd6c8a", "metadata": {}, "source": [ "### Firm’s problem\n", @@ -314,7 +314,7 @@ }, { "cell_type": "markdown", - "id": "24f54b48", + "id": "f81b9b8d", "metadata": {}, "source": [ "### Demand\n", @@ -352,7 +352,7 @@ { "cell_type": "code", "execution_count": null, - "id": "03bc29e5", + "id": "f410e4df", "metadata": { "hide-output": false }, @@ -365,7 +365,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f73c905", + "id": "95970528", "metadata": { "hide-output": false }, @@ -378,7 +378,7 @@ }, { "cell_type": "markdown", - "id": "789d1772", + "id": "f4c6899d", "metadata": {}, "source": [ "The next figure plots the supply of capital, as in [(26.6)](#equation-saving-log-2-olg), as well as the demand for capital, as in [(26.11)](#equation-aggregate-demand-capital-olg), as functions of the interest rate $ R_{t+1} $.\n", @@ -388,7 +388,7 @@ }, { "cell_type": "markdown", - "id": "6691035d", + "id": "b30ace74", "metadata": {}, "source": [ "## Equilibrium\n", @@ -398,7 +398,7 @@ }, { "cell_type": "markdown", - "id": "3fec6fa5", + "id": "7798e6bd", "metadata": {}, "source": [ "### Equilibrium conditions\n", @@ -429,7 +429,7 @@ }, { "cell_type": "markdown", - "id": "9c7b53b8", + "id": "4efcf03d", "metadata": {}, "source": [ "### Example: log utility\n", @@ -461,7 +461,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad8b01df", + "id": "673a5dde", "metadata": { "hide-output": false }, @@ -474,7 +474,7 @@ }, { "cell_type": "markdown", - "id": "d9728660", + "id": "3a32cf58", "metadata": {}, "source": [ "In the case of log utility, since capital supply does not depend on the interest rate, the equilibrium quantity is fixed by supply.\n", @@ -493,7 +493,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e7c5138", + "id": "fb34475c", "metadata": { "hide-output": false }, @@ -523,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "7ac31d00", + "id": "a9bede6c", "metadata": {}, "source": [ "## Dynamics\n", @@ -535,7 +535,7 @@ }, { "cell_type": "markdown", - "id": "d5723d72", + "id": "41696278", "metadata": {}, "source": [ "### Evolution of capital\n", @@ -566,7 +566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0c65128", + "id": "1c077f06", "metadata": { "hide-output": false }, @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1455550d", + "id": "59b9dc7b", "metadata": { "hide-output": false }, @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "92459e81", + "id": "5c1fec71", "metadata": {}, "source": [ "### Steady state (log case)\n", @@ -645,7 +645,7 @@ { "cell_type": "code", "execution_count": null, - "id": "883a6af8", + "id": "d778bf34", "metadata": { "hide-output": false }, @@ -657,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "d52366bc", + "id": "0a58ac9b", "metadata": {}, "source": [ "### Time series\n", @@ -670,7 +670,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8529f73", + "id": "1965e70e", "metadata": { "hide-output": false }, @@ -694,7 +694,7 @@ }, { "cell_type": "markdown", - "id": "74f93470", + "id": "32f551f4", "metadata": {}, "source": [ "If you experiment with different positive initial conditions, you will see that the series always converges to $ k^* $.\n", @@ -705,7 +705,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e78ed56f", + "id": "b02840e7", "metadata": { "hide-output": false }, @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "32d30f40", + "id": "7ba453c2", "metadata": {}, "source": [ "The interest rate reflects the marginal product of capital, which is high when capital stock is low." @@ -733,7 +733,7 @@ }, { "cell_type": "markdown", - "id": "2f7b8877", + "id": "abfcc6fa", "metadata": {}, "source": [ "## CRRA preferences\n", @@ -755,7 +755,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f074c883", + "id": "bfe82bd1", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ }, { "cell_type": "markdown", - "id": "67290eeb", + "id": "ddeade47", "metadata": {}, "source": [ "Let’s also redefine the capital demand function to work with this `namedtuple`." @@ -784,7 +784,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35b3ea4e", + "id": "fa2b8a84", "metadata": { "hide-output": false }, @@ -796,7 +796,7 @@ }, { "cell_type": "markdown", - "id": "43cd3aa3", + "id": "95a72554", "metadata": {}, "source": [ "### Supply\n", @@ -827,7 +827,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47b89a8d", + "id": "64ba2015", "metadata": { "hide-output": false }, @@ -841,7 +841,7 @@ { "cell_type": "code", "execution_count": null, - "id": "64a299d0", + "id": "faca2a6e", "metadata": { "hide-output": false }, @@ -865,7 +865,7 @@ }, { "cell_type": "markdown", - "id": "cf6d9a27", + "id": "3e8e20de", "metadata": {}, "source": [ "### Equilibrium\n", @@ -899,7 +899,7 @@ }, { "cell_type": "markdown", - "id": "23c281a3", + "id": "613270ea", "metadata": {}, "source": [ "## Exercises" @@ -907,7 +907,7 @@ }, { "cell_type": "markdown", - "id": "8286e022", + "id": "f1bf2bec", "metadata": {}, "source": [ "## Exercise 26.1\n", @@ -919,7 +919,7 @@ }, { "cell_type": "markdown", - "id": "3d8a0134", + "id": "7644d66a", "metadata": {}, "source": [ "## Solution to[ Exercise 26.1](https://intro.quantecon.org/#olg_ex1)\n", @@ -952,7 +952,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cc2a9c8c", + "id": "b7dfa52f", "metadata": { "hide-output": false }, @@ -969,7 +969,7 @@ }, { "cell_type": "markdown", - "id": "8484c4d0", + "id": "f21e78b4", "metadata": {}, "source": [ "Now let’s define a function that finds the value of $ k_{t+1} $." @@ -978,7 +978,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3af66bad", + "id": "a07ec1b7", "metadata": { "hide-output": false }, @@ -990,7 +990,7 @@ }, { "cell_type": "markdown", - "id": "3a0f7fe4", + "id": "0e53d7b3", "metadata": {}, "source": [ "Finally, here is the 45-degree diagram." @@ -999,7 +999,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9bb06b96", + "id": "b45aa1ac", "metadata": { "hide-output": false }, @@ -1030,7 +1030,7 @@ }, { "cell_type": "markdown", - "id": "ff8e5cfa", + "id": "010eafff", "metadata": {}, "source": [ "## Exercise 26.2\n", @@ -1054,7 +1054,7 @@ }, { "cell_type": "markdown", - "id": "90398990", + "id": "0a255bb9", "metadata": {}, "source": [ "## Solution to[ Exercise 26.2](https://intro.quantecon.org/#olg_ex2)\n", @@ -1077,7 +1077,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc8a4ecf", + "id": "6fc8a5bd", "metadata": { "hide-output": false }, @@ -1094,7 +1094,7 @@ }, { "cell_type": "markdown", - "id": "9f720c8d", + "id": "2faea2b6", "metadata": {}, "source": [ "Let’s apply Newton’s method to find the root:" @@ -1103,7 +1103,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96552ff1", + "id": "e48390b1", "metadata": { "hide-output": false }, @@ -1115,7 +1115,7 @@ }, { "cell_type": "markdown", - "id": "9b6abcae", + "id": "177f7e0f", "metadata": {}, "source": [ "## Exercise 26.3\n", @@ -1128,7 +1128,7 @@ }, { "cell_type": "markdown", - "id": "1aff7e6a", + "id": "fba19a4e", "metadata": {}, "source": [ "## Solution to[ Exercise 26.3](https://intro.quantecon.org/#olg_ex3)\n", @@ -1139,7 +1139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3cbe7dbf", + "id": "6e235bbb", "metadata": { "hide-output": false }, @@ -1152,7 +1152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b81e911", + "id": "5fcde0dd", "metadata": { "hide-output": false }, @@ -1184,7 +1184,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7b8aff5", + "id": "8734c453", "metadata": { "hide-output": false }, @@ -1195,7 +1195,7 @@ } ], "metadata": { - "date": 1722488543.231481, + "date": 1722502940.083072, "filename": "olg.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/prob_dist.ipynb b/_notebooks/prob_dist.ipynb index 3a29dde0..ec4603be 100644 --- a/_notebooks/prob_dist.ipynb +++ b/_notebooks/prob_dist.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "1983ca57", + "id": "b091018e", "metadata": {}, "source": [ "# Distributions and Probabilities\n", @@ -13,7 +13,7 @@ }, { "cell_type": "markdown", - "id": "083a0136", + "id": "f4c8f493", "metadata": {}, "source": [ "## Outline\n", @@ -24,7 +24,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0cc4d49e", + "id": "8ab9297e", "metadata": { "hide-output": false }, @@ -36,7 +36,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8e7997de", + "id": "4dee2aba", "metadata": { "hide-output": false }, @@ -52,7 +52,7 @@ }, { "cell_type": "markdown", - "id": "cd0603e4", + "id": "06d3b637", "metadata": {}, "source": [ "## Common distributions\n", @@ -62,7 +62,7 @@ }, { "cell_type": "markdown", - "id": "ed7e214a", + "id": "a645cff9", "metadata": {}, "source": [ "### Discrete distributions\n", @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "7f7708c4", + "id": "1ceb7133", "metadata": {}, "source": [ "#### Uniform distribution\n", @@ -128,7 +128,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cf4e5ce4", + "id": "94ac4c87", "metadata": { "hide-output": false }, @@ -140,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "f0bf6abb", + "id": "85dd168e", "metadata": {}, "source": [ "Here’s the mean and variance:" @@ -149,7 +149,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb7e223e", + "id": "f6beacfe", "metadata": { "hide-output": false }, @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "a08b1dd8", + "id": "c878c35f", "metadata": {}, "source": [ "The formula for the mean is $ (n+1)/2 $, and the formula for the variance is $ (n^2 - 1)/12 $.\n", @@ -171,7 +171,7 @@ { "cell_type": "code", "execution_count": null, - "id": "680b5374", + "id": "27bd8a56", "metadata": { "hide-output": false }, @@ -183,7 +183,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c7cf973", + "id": "8a342ced", "metadata": { "hide-output": false }, @@ -194,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "0dd139c3", + "id": "c97a8bbf", "metadata": {}, "source": [ "Here’s a plot of the probability mass function:" @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20a1b183", + "id": "00a43678", "metadata": { "hide-output": false }, @@ -221,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "f8cb464d", + "id": "f75e5ff2", "metadata": {}, "source": [ "Here’s a plot of the CDF:" @@ -230,7 +230,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72d70f01", + "id": "b5c04c00", "metadata": { "hide-output": false }, @@ -248,7 +248,7 @@ }, { "cell_type": "markdown", - "id": "2ef68ef3", + "id": "654f55a0", "metadata": {}, "source": [ "The CDF jumps up by $ p(x_i) $ at $ x_i $." @@ -256,7 +256,7 @@ }, { "cell_type": "markdown", - "id": "b1aea099", + "id": "e1a5bc7b", "metadata": {}, "source": [ "#### Exercise 18.1\n", @@ -269,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "b2f9c5a6", + "id": "ba4100f4", "metadata": {}, "source": [ "#### Bernoulli distribution\n", @@ -277,7 +277,8 @@ "Another useful distribution is the Bernoulli distribution on $ S = \\{0,1\\} $, which has PMF:\n", "\n", "$$\n", - "p(i) = \\theta^{i-1} (1 - \\theta)^i\n", + "p(i) = \\theta^i (1 - \\theta)^{1-i}\n", + "\\qquad (i = 0, 1)\n", "$$\n", "\n", "Here $ \\theta \\in [0,1] $ is a parameter.\n", @@ -289,7 +290,7 @@ " probability $ 1-\\theta $ \n", "\n", "\n", - "The formula for the mean is $ p $, and the formula for the variance is $ p(1-p) $.\n", + "The formula for the mean is $ \\theta $, and the formula for the variance is $ \\theta(1-\\theta) $.\n", "\n", "We can import the Bernoulli distribution on $ S = \\{0,1\\} $ from SciPy like so:" ] @@ -297,7 +298,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b038e6f6", + "id": "c8efbd70", "metadata": { "hide-output": false }, @@ -309,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "db2f0b21", + "id": "318ea377", "metadata": {}, "source": [ "Here’s the mean and variance at $ \\theta=0.4 $" @@ -318,7 +319,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d625453f", + "id": "cfc40e86", "metadata": { "hide-output": false }, @@ -329,28 +330,27 @@ }, { "cell_type": "markdown", - "id": "ea6c342c", + "id": "06d25730", "metadata": {}, "source": [ - "Now let’s evaluate the PMF" + "We can evaluate the PMF as follows" ] }, { "cell_type": "code", "execution_count": null, - "id": "463d9012", + "id": "b37bd9a7", "metadata": { "hide-output": false }, "outputs": [], "source": [ - "u.pmf(0)\n", - "u.pmf(1)" + "u.pmf(0), u.pmf(1)" ] }, { "cell_type": "markdown", - "id": "42d6bf35", + "id": "5103a3fe", "metadata": {}, "source": [ "#### Binomial distribution\n", @@ -375,7 +375,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1a2d0d14", + "id": "8d6d529f", "metadata": { "hide-output": false }, @@ -388,7 +388,7 @@ }, { "cell_type": "markdown", - "id": "f6a87b77", + "id": "e9a482aa", "metadata": {}, "source": [ "According to our formulas, the mean and variance are" @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d94e95f1", + "id": "3b0a2f36", "metadata": { "hide-output": false }, @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "fd11cdf7", + "id": "2650669e", "metadata": {}, "source": [ "Let’s see if SciPy gives us the same results:" @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c143df5", + "id": "8d6ecf5c", "metadata": { "hide-output": false }, @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "94f92028", + "id": "adfa9b1d", "metadata": {}, "source": [ "Here’s the PMF:" @@ -437,7 +437,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ee92340", + "id": "8e340f06", "metadata": { "hide-output": false }, @@ -449,7 +449,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c38988b", + "id": "568e6ad9", "metadata": { "hide-output": false }, @@ -467,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "3c56ad41", + "id": "d8eab3f9", "metadata": {}, "source": [ "Here’s the CDF:" @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9742532", + "id": "39d5b73a", "metadata": { "hide-output": false }, @@ -494,7 +494,7 @@ }, { "cell_type": "markdown", - "id": "a12f5b9f", + "id": "432bbcfb", "metadata": {}, "source": [ "#### Exercise 18.2\n", @@ -504,7 +504,7 @@ }, { "cell_type": "markdown", - "id": "3fd99287", + "id": "d8e50684", "metadata": {}, "source": [ "#### Solution to[ Exercise 18.2](https://intro.quantecon.org/#prob_ex3)\n", @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0efc86c9", + "id": "8a32ce31", "metadata": { "hide-output": false }, @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "02ad643a", + "id": "25424f07", "metadata": {}, "source": [ "We can see that the output graph is the same as the one above." @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "24a1d844", + "id": "0fbdc841", "metadata": {}, "source": [ "#### Geometric distribution\n", @@ -569,7 +569,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2f8de7d", + "id": "969e69ee", "metadata": { "hide-output": false }, @@ -582,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "66e2d9e9", + "id": "f7cfac06", "metadata": {}, "source": [ "Here’s part of the PMF:" @@ -591,7 +591,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0467377e", + "id": "bcfd7453", "metadata": { "hide-output": false }, @@ -610,7 +610,7 @@ }, { "cell_type": "markdown", - "id": "85253e59", + "id": "f921cef1", "metadata": {}, "source": [ "#### Poisson distribution\n", @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62ee977f", + "id": "76e8191a", "metadata": { "hide-output": false }, @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "c9c899aa", + "id": "05f7d242", "metadata": {}, "source": [ "Here’s the PMF:" @@ -653,7 +653,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbffadce", + "id": "dc90ccdb", "metadata": { "hide-output": false }, @@ -665,7 +665,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d6ec818", + "id": "60ab6b39", "metadata": { "hide-output": false }, @@ -683,7 +683,7 @@ }, { "cell_type": "markdown", - "id": "b00b6df7", + "id": "66380946", "metadata": {}, "source": [ "### Continuous distributions\n", @@ -720,7 +720,7 @@ }, { "cell_type": "markdown", - "id": "b799bd81", + "id": "b95b8cf8", "metadata": {}, "source": [ "#### Normal distribution\n", @@ -742,7 +742,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4232fa96", + "id": "d59389a1", "metadata": { "hide-output": false }, @@ -755,7 +755,7 @@ { "cell_type": "code", "execution_count": null, - "id": "926ad938", + "id": "4a983e4b", "metadata": { "hide-output": false }, @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "329c9e9f", + "id": "a426d37d", "metadata": {}, "source": [ "Here’s a plot of the density — the famous “bell-shaped curve”:" @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "750d2ec5", + "id": "f98e9ce7", "metadata": { "hide-output": false }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "9ef8fe58", + "id": "2a56ef67", "metadata": {}, "source": [ "Here’s a plot of the CDF:" @@ -808,7 +808,7 @@ { "cell_type": "code", "execution_count": null, - "id": "021a2a15", + "id": "a2752e44", "metadata": { "hide-output": false }, @@ -829,7 +829,7 @@ }, { "cell_type": "markdown", - "id": "ddf453ec", + "id": "0a8023b8", "metadata": {}, "source": [ "#### Lognormal distribution\n", @@ -857,7 +857,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9d1e6328", + "id": "7a84936d", "metadata": { "hide-output": false }, @@ -870,7 +870,7 @@ { "cell_type": "code", "execution_count": null, - "id": "796d3aea", + "id": "09ee4cb3", "metadata": { "hide-output": false }, @@ -882,7 +882,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a892b41", + "id": "fcbb26a4", "metadata": { "hide-output": false }, @@ -907,7 +907,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e644f24", + "id": "12eaae77", "metadata": { "hide-output": false }, @@ -930,7 +930,7 @@ }, { "cell_type": "markdown", - "id": "65b05ba6", + "id": "a4d545ed", "metadata": {}, "source": [ "#### Exponential distribution\n", @@ -954,7 +954,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c29d42fa", + "id": "2eb8a842", "metadata": { "hide-output": false }, @@ -967,7 +967,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9a076cf", + "id": "11ce45f6", "metadata": { "hide-output": false }, @@ -979,7 +979,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e53bbdc7", + "id": "12ebb943", "metadata": { "hide-output": false }, @@ -1003,7 +1003,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82fea7e4", + "id": "f86ed6f6", "metadata": { "hide-output": false }, @@ -1024,7 +1024,7 @@ }, { "cell_type": "markdown", - "id": "942e1004", + "id": "2a43a876", "metadata": {}, "source": [ "#### Beta distribution\n", @@ -1052,7 +1052,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc9b0164", + "id": "2ba67575", "metadata": { "hide-output": false }, @@ -1065,7 +1065,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c99fc28", + "id": "4da26313", "metadata": { "hide-output": false }, @@ -1077,7 +1077,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9aacc33", + "id": "a6863bb2", "metadata": { "hide-output": false }, @@ -1102,7 +1102,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b53de0e", + "id": "edb6bb49", "metadata": { "hide-output": false }, @@ -1123,7 +1123,7 @@ }, { "cell_type": "markdown", - "id": "15409540", + "id": "4266f5bc", "metadata": {}, "source": [ "#### Gamma distribution\n", @@ -1150,7 +1150,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6398c088", + "id": "7487535a", "metadata": { "hide-output": false }, @@ -1163,7 +1163,7 @@ { "cell_type": "code", "execution_count": null, - "id": "deff1161", + "id": "3ea4c495", "metadata": { "hide-output": false }, @@ -1175,7 +1175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "719764db", + "id": "4fac4cae", "metadata": { "hide-output": false }, @@ -1200,7 +1200,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dcac1899", + "id": "7299a465", "metadata": { "hide-output": false }, @@ -1221,7 +1221,7 @@ }, { "cell_type": "markdown", - "id": "91a49186", + "id": "bf5d40d4", "metadata": {}, "source": [ "## Observed distributions\n", @@ -1234,7 +1234,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4206e3b5", + "id": "cf778ea2", "metadata": { "hide-output": false }, @@ -1257,7 +1257,7 @@ }, { "cell_type": "markdown", - "id": "5f82ab69", + "id": "c7934cd7", "metadata": {}, "source": [ "In this situation, we might refer to the set of their incomes as the “income distribution.”\n", @@ -1273,7 +1273,7 @@ }, { "cell_type": "markdown", - "id": "ab7cbccd", + "id": "9877f562", "metadata": {}, "source": [ "### Summary statistics\n", @@ -1298,7 +1298,7 @@ { "cell_type": "code", "execution_count": null, - "id": "53f1ba6e", + "id": "bbf62fb9", "metadata": { "hide-output": false }, @@ -1310,17 +1310,21 @@ }, { "cell_type": "markdown", - "id": "3b7a32ff", + "id": "19273a01", "metadata": {}, "source": [ "### Exercise 18.3\n", "\n", - "Check that the formulas given above produce the same numbers." + "If you try to check that the formulas given above for the sample mean and sample\n", + "variance produce the same numbers, you will see that the variance isn’t quite\n", + "right. This is because SciPy uses $ 1/(n-1) $ instead of $ 1/n $ as the term at the\n", + "front of the variance. (Some books define the sample variance this way.)\n", + "Confirm." ] }, { "cell_type": "markdown", - "id": "b91c0744", + "id": "07bcb550", "metadata": {}, "source": [ "### Visualization\n", @@ -1336,7 +1340,7 @@ }, { "cell_type": "markdown", - "id": "52d30eb9", + "id": "e6c39de5", "metadata": {}, "source": [ "#### Histograms\n", @@ -1347,7 +1351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27ffb26c", + "id": "ccdae993", "metadata": { "hide-output": false }, @@ -1362,7 +1366,7 @@ }, { "cell_type": "markdown", - "id": "fd220971", + "id": "e688740d", "metadata": {}, "source": [ "Let’s look at a distribution from real data.\n", @@ -1377,7 +1381,7 @@ { "cell_type": "code", "execution_count": null, - "id": "121baf26", + "id": "bc23ca03", "metadata": { "hide-output": false }, @@ -1391,7 +1395,7 @@ }, { "cell_type": "markdown", - "id": "9622fd90", + "id": "377472a3", "metadata": {}, "source": [ "The first observation is the monthly return (percent change) over January 2000, which was" @@ -1400,7 +1404,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96cb5952", + "id": "04403633", "metadata": { "hide-output": false }, @@ -1411,7 +1415,7 @@ }, { "cell_type": "markdown", - "id": "a602dc69", + "id": "085938d3", "metadata": {}, "source": [ "Let’s turn the return observations into an array and histogram it." @@ -1420,7 +1424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5308aae7", + "id": "cbd3bbdf", "metadata": { "hide-output": false }, @@ -1435,7 +1439,7 @@ }, { "cell_type": "markdown", - "id": "a9a50c6d", + "id": "67d6d9a4", "metadata": {}, "source": [ "#### Kernel density estimates\n", @@ -1451,7 +1455,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61fe243f", + "id": "8308e67c", "metadata": { "hide-output": false }, @@ -1466,7 +1470,7 @@ }, { "cell_type": "markdown", - "id": "f7cc03f1", + "id": "90d785ae", "metadata": {}, "source": [ "The smoothness of the KDE is dependent on how we choose the bandwidth." @@ -1475,7 +1479,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9837e89e", + "id": "763e951f", "metadata": { "hide-output": false }, @@ -1493,7 +1497,7 @@ }, { "cell_type": "markdown", - "id": "f160a7f2", + "id": "369876b9", "metadata": {}, "source": [ "When we use a larger bandwidth, the KDE is smoother.\n", @@ -1503,7 +1507,7 @@ }, { "cell_type": "markdown", - "id": "75fcdb7e", + "id": "83ccd69e", "metadata": {}, "source": [ "#### Violin plots\n", @@ -1514,7 +1518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bdba80a4", + "id": "c06c767c", "metadata": { "hide-output": false }, @@ -1529,7 +1533,7 @@ }, { "cell_type": "markdown", - "id": "5184ea0e", + "id": "b738b9e8", "metadata": {}, "source": [ "Violin plots are particularly useful when we want to compare different distributions.\n", @@ -1540,7 +1544,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51df2a99", + "id": "78a1dbc7", "metadata": { "hide-output": false }, @@ -1554,7 +1558,7 @@ { "cell_type": "code", "execution_count": null, - "id": "86535fb1", + "id": "07c68abb", "metadata": { "hide-output": false }, @@ -1569,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "b664ce0b", + "id": "d5a39081", "metadata": {}, "source": [ "### Connection to probability distributions\n", @@ -1592,7 +1596,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb9cb408", + "id": "24327c66", "metadata": { "hide-output": false }, @@ -1607,7 +1611,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ffb5ed88", + "id": "bd2cfeac", "metadata": { "hide-output": false }, @@ -1624,7 +1628,7 @@ }, { "cell_type": "markdown", - "id": "94b129d1", + "id": "2d4a4ae7", "metadata": {}, "source": [ "The match between the histogram and the density is not bad but also not very good.\n", @@ -1642,7 +1646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28f207e8", + "id": "09fe6028", "metadata": { "hide-output": false }, @@ -1663,7 +1667,7 @@ }, { "cell_type": "markdown", - "id": "1e3334da", + "id": "807e9dcb", "metadata": {}, "source": [ "Note that if you keep increasing $ N $, which is the number of observations, the fit will get better and better.\n", @@ -1673,7 +1677,7 @@ } ], "metadata": { - "date": 1722488543.2842953, + "date": 1722502940.1342027, "filename": "prob_dist.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/pv.ipynb b/_notebooks/pv.ipynb index b87c0e64..e225eb9b 100644 --- a/_notebooks/pv.ipynb +++ b/_notebooks/pv.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "3f39ef8a", + "id": "d3591581", "metadata": {}, "source": [ "# Present Values" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "390afd29", + "id": "0ddb771e", "metadata": {}, "source": [ "## Overview\n", @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "7b737e52", + "id": "6ffea3bf", "metadata": {}, "source": [ "## Analysis\n", @@ -100,7 +100,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e66d2411", + "id": "3b409778", "metadata": { "hide-output": false }, @@ -112,7 +112,7 @@ }, { "cell_type": "markdown", - "id": "e0e68cf5", + "id": "5eddcf1b", "metadata": {}, "source": [ "## Representing sequences as vectors\n", @@ -155,7 +155,7 @@ }, { "cell_type": "markdown", - "id": "2f7013f5", + "id": "39624778", "metadata": {}, "source": [ "## Exercise 11.1\n", @@ -219,7 +219,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b6dec03", + "id": "0a9b3759", "metadata": { "hide-output": false }, @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "621c69d3", + "id": "0e48a40b", "metadata": {}, "source": [ "Now let’s compute and plot the asset price.\n", @@ -252,7 +252,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10ad4f05", + "id": "95852964", "metadata": { "hide-output": false }, @@ -264,7 +264,7 @@ }, { "cell_type": "markdown", - "id": "0a4abf8f", + "id": "64be175f", "metadata": {}, "source": [ "Let’s build the matrix $ A $" @@ -273,7 +273,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a816bfad", + "id": "2fadbcd1", "metadata": { "hide-output": false }, @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "c223f8bc", + "id": "a7efa0e2", "metadata": {}, "source": [ "Let’s inspect $ A $" @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba191ebc", + "id": "2ea9b902", "metadata": { "hide-output": false }, @@ -310,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "12ef2f0b", + "id": "a4f8305c", "metadata": {}, "source": [ "Now let’s solve for prices using [(11.5)](#equation-eq-apdb-sol)." @@ -319,7 +319,7 @@ { "cell_type": "code", "execution_count": null, - "id": "318f8afd", + "id": "f5b97d99", "metadata": { "hide-output": false }, @@ -337,7 +337,7 @@ }, { "cell_type": "markdown", - "id": "50032bdb", + "id": "8c5a42ca", "metadata": {}, "source": [ "Now let’s consider a cyclically growing dividend sequence:\n", @@ -350,7 +350,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b922bcae", + "id": "e4af2b88", "metadata": { "hide-output": false }, @@ -372,7 +372,7 @@ }, { "cell_type": "markdown", - "id": "de96947f", + "id": "5931c054", "metadata": {}, "source": [ "## Exercise 11.2\n", @@ -383,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "97141916", + "id": "d5a9e2d2", "metadata": {}, "source": [ "## Solution to[ Exercise 11.2](https://intro.quantecon.org/#pv_ex_cyc)\n", @@ -394,7 +394,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23372a49", + "id": "9f13150f", "metadata": { "hide-output": false }, @@ -422,7 +422,7 @@ }, { "cell_type": "markdown", - "id": "e9e5b9b0", + "id": "4a6cf9bb", "metadata": {}, "source": [ "The weighted averaging associated with the present value calculation largely\n", @@ -431,7 +431,7 @@ }, { "cell_type": "markdown", - "id": "5ab1faae", + "id": "6bf688f0", "metadata": {}, "source": [ "## Analytical expressions\n", @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "b01937a2", + "id": "8383a5f1", "metadata": {}, "source": [ "## Exercise 11.3\n", @@ -499,7 +499,7 @@ }, { "cell_type": "markdown", - "id": "ec6a02c5", + "id": "c4037f4f", "metadata": {}, "source": [ "## More about bubbles\n", @@ -561,7 +561,7 @@ }, { "cell_type": "markdown", - "id": "9c424435", + "id": "2b9366a9", "metadata": {}, "source": [ "## Gross rate of return\n", @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "997c6808", + "id": "d0d08557", "metadata": {}, "source": [ "## Exercises" @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "f8b8dbac", + "id": "e1c3eed4", "metadata": {}, "source": [ "## Exercise 11.4\n", @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "7d977a4a", + "id": "3e756f70", "metadata": {}, "source": [ "## Solution to[ Exercise 11.4](https://intro.quantecon.org/#pv_ex_a)\n", @@ -623,7 +623,7 @@ } ], "metadata": { - "date": 1722488543.3125095, + "date": 1722502940.1604893, "filename": "pv.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/scalar_dynam.ipynb b/_notebooks/scalar_dynam.ipynb index 3c2147c0..ff2b8ef8 100644 --- a/_notebooks/scalar_dynam.ipynb +++ b/_notebooks/scalar_dynam.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "928089c7", + "id": "bcc44049", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "fb4711cc", + "id": "af209b3e", "metadata": {}, "source": [ "# Dynamics in One Dimension" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "a45390c1", + "id": "a08ce671", "metadata": {}, "source": [ "## Overview\n", @@ -55,7 +55,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e5489566", + "id": "93eaa8a5", "metadata": { "hide-output": false }, @@ -67,7 +67,7 @@ }, { "cell_type": "markdown", - "id": "37874b09", + "id": "135ffe9d", "metadata": {}, "source": [ "## Some definitions\n", @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "89d80f5c", + "id": "abc2f069", "metadata": {}, "source": [ "### Composition of functions\n", @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "64e7fcf3", + "id": "0495de3d", "metadata": {}, "source": [ "### Dynamic systems\n", @@ -186,7 +186,7 @@ }, { "cell_type": "markdown", - "id": "a28e4ed0", + "id": "9b8c4af2", "metadata": {}, "source": [ "### Example: a linear model\n", @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "ea196820", + "id": "8e63d062", "metadata": {}, "source": [ "### Example: a nonlinear model\n", @@ -271,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "1e47d0bd", + "id": "b0a40ace", "metadata": {}, "source": [ "## Stability\n", @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "7d37bb4a", + "id": "0b432d8c", "metadata": {}, "source": [ "### Steady states\n", @@ -312,7 +312,7 @@ }, { "cell_type": "markdown", - "id": "2579ee4e", + "id": "b056f066", "metadata": {}, "source": [ "### Global stability\n", @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "f6532c7c", + "id": "e77b433a", "metadata": {}, "source": [ "### Local stability\n", @@ -357,7 +357,7 @@ }, { "cell_type": "markdown", - "id": "afeebae1", + "id": "037419f6", "metadata": {}, "source": [ "### \n", @@ -373,7 +373,7 @@ }, { "cell_type": "markdown", - "id": "66e0e719", + "id": "85686ee1", "metadata": {}, "source": [ "## Graphical analysis\n", @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3676d30a", + "id": "f1a046bb", "metadata": { "hide-output": false }, @@ -492,7 +492,7 @@ }, { "cell_type": "markdown", - "id": "e26a636c", + "id": "adc5b1b5", "metadata": {}, "source": [ "Let’s create a 45-degree diagram for the Solow-Swan model with a fixed set of\n", @@ -502,7 +502,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be5cd7d6", + "id": "0a9bf076", "metadata": { "hide-output": false }, @@ -514,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "3b8e8e79", + "id": "6306afe8", "metadata": {}, "source": [ "Here is the 45-degree plot." @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dfab5e19", + "id": "152e57b9", "metadata": { "hide-output": false }, @@ -536,7 +536,7 @@ }, { "cell_type": "markdown", - "id": "5873d0df", + "id": "5198edcf", "metadata": {}, "source": [ "The plot shows the function $ g $ and the 45-degree line.\n", @@ -569,7 +569,7 @@ }, { "cell_type": "markdown", - "id": "515d5a3a", + "id": "fc989299", "metadata": {}, "source": [ "### Trajectories\n", @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d92e6fb7", + "id": "298bda9f", "metadata": { "hide-output": false }, @@ -597,7 +597,7 @@ }, { "cell_type": "markdown", - "id": "b45116e0", + "id": "fa5fc43e", "metadata": {}, "source": [ "We can plot the time series of per capita capital corresponding to the figure above as\n", @@ -607,7 +607,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9cdfe280", + "id": "c57e0826", "metadata": { "hide-output": false }, @@ -618,7 +618,7 @@ }, { "cell_type": "markdown", - "id": "36ec8d7e", + "id": "1929519a", "metadata": {}, "source": [ "Here’s a somewhat longer view:" @@ -627,7 +627,7 @@ { "cell_type": "code", "execution_count": null, - "id": "582374e6", + "id": "a1910ef9", "metadata": { "hide-output": false }, @@ -638,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "7b8f0073", + "id": "9ab344d2", "metadata": {}, "source": [ "When per capita capital stock is higher than the unique positive steady state, we see that\n", @@ -648,7 +648,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95703c0e", + "id": "66942d6f", "metadata": { "hide-output": false }, @@ -661,7 +661,7 @@ }, { "cell_type": "markdown", - "id": "89421b40", + "id": "f58cf218", "metadata": {}, "source": [ "Here is the time series:" @@ -670,7 +670,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23880f07", + "id": "79a077e4", "metadata": { "hide-output": false }, @@ -681,7 +681,7 @@ }, { "cell_type": "markdown", - "id": "a3d83fca", + "id": "8801f156", "metadata": {}, "source": [ "### Complex dynamics\n", @@ -701,7 +701,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27c8f36f", + "id": "ddf522d4", "metadata": { "hide-output": false }, @@ -716,7 +716,7 @@ }, { "cell_type": "markdown", - "id": "fe4c5034", + "id": "d6fcb58e", "metadata": {}, "source": [ "Now let’s look at a typical trajectory." @@ -725,7 +725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82c89520", + "id": "325a94a3", "metadata": { "hide-output": false }, @@ -736,7 +736,7 @@ }, { "cell_type": "markdown", - "id": "ce6bb659", + "id": "30b95f54", "metadata": {}, "source": [ "Notice how irregular it is.\n", @@ -747,7 +747,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2fe15807", + "id": "ac81d297", "metadata": { "hide-output": false }, @@ -758,7 +758,7 @@ }, { "cell_type": "markdown", - "id": "326be2d7", + "id": "44902a16", "metadata": {}, "source": [ "The irregularity is even clearer over a longer time horizon:" @@ -767,7 +767,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7bcfe7ae", + "id": "f5f5a991", "metadata": { "hide-output": false }, @@ -778,7 +778,7 @@ }, { "cell_type": "markdown", - "id": "a2d86aa3", + "id": "97c64d65", "metadata": {}, "source": [ "## Exercises" @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "8f15ef3d", + "id": "d7034458", "metadata": {}, "source": [ "## Exercise 23.1\n", @@ -810,7 +810,7 @@ }, { "cell_type": "markdown", - "id": "021780cc", + "id": "848ca31b", "metadata": {}, "source": [ "## Solution to[ Exercise 23.1](https://intro.quantecon.org/#sd_ex1)\n", @@ -823,7 +823,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3a699cc", + "id": "ca441a33", "metadata": { "hide-output": false }, @@ -836,7 +836,7 @@ }, { "cell_type": "markdown", - "id": "c523b5f1", + "id": "a0388a26", "metadata": {}, "source": [ "Now let’s plot a trajectory:" @@ -845,7 +845,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8175f7a2", + "id": "7d2c7e1e", "metadata": { "hide-output": false }, @@ -857,7 +857,7 @@ }, { "cell_type": "markdown", - "id": "112c87fd", + "id": "e8897d16", "metadata": {}, "source": [ "Here is the corresponding time series, which converges towards the steady\n", @@ -867,7 +867,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a15ab26", + "id": "9ecfa171", "metadata": { "hide-output": false }, @@ -878,7 +878,7 @@ }, { "cell_type": "markdown", - "id": "6dcf0f63", + "id": "f03bd1d7", "metadata": {}, "source": [ "Now let’s try $ a=-0.5 $ and see what differences we observe.\n", @@ -889,7 +889,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4a7ae897", + "id": "f593cfee", "metadata": { "hide-output": false }, @@ -902,7 +902,7 @@ }, { "cell_type": "markdown", - "id": "11d9ccdf", + "id": "de835299", "metadata": {}, "source": [ "Now let’s plot a trajectory:" @@ -911,7 +911,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99b76498", + "id": "98f58a45", "metadata": { "hide-output": false }, @@ -923,7 +923,7 @@ }, { "cell_type": "markdown", - "id": "fdf8b649", + "id": "ebca789e", "metadata": {}, "source": [ "Here is the corresponding time series, which converges towards the steady\n", @@ -933,7 +933,7 @@ { "cell_type": "code", "execution_count": null, - "id": "744f6474", + "id": "73f55cb4", "metadata": { "hide-output": false }, @@ -944,7 +944,7 @@ }, { "cell_type": "markdown", - "id": "d9777b3e", + "id": "29ea652b", "metadata": {}, "source": [ "Once again, we have convergence to the steady state but the nature of\n", @@ -958,7 +958,7 @@ } ], "metadata": { - "date": 1722488543.3474662, + "date": 1722502940.1944335, "filename": "scalar_dynam.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/schelling.ipynb b/_notebooks/schelling.ipynb index 0cc5afe5..8aafe0e4 100644 --- a/_notebooks/schelling.ipynb +++ b/_notebooks/schelling.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "b19dfd09", + "id": "54c8dde1", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "5e33aacf", + "id": "2854590d", "metadata": {}, "source": [ "# Racial Segregation\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "91a65042", + "id": "40e46ea1", "metadata": {}, "source": [ "## Outline\n", @@ -65,7 +65,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3944fe6", + "id": "295d63c0", "metadata": { "hide-output": false }, @@ -79,7 +79,7 @@ }, { "cell_type": "markdown", - "id": "65fcc3ad", + "id": "4c2571a1", "metadata": {}, "source": [ "## The model\n", @@ -89,7 +89,7 @@ }, { "cell_type": "markdown", - "id": "78af7b5b", + "id": "7ae8eaaa", "metadata": {}, "source": [ "### Set-Up\n", @@ -113,7 +113,7 @@ }, { "cell_type": "markdown", - "id": "ec39c237", + "id": "853af23c", "metadata": {}, "source": [ "### Preferences\n", @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "f0d55bc7", + "id": "d4ece3e6", "metadata": {}, "source": [ "### Behavior\n", @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "c1f298e9", + "id": "8ce74fdc", "metadata": {}, "source": [ "### (Jump Chain Algorithm)\n", @@ -178,7 +178,7 @@ }, { "cell_type": "markdown", - "id": "0efe4fc6", + "id": "badf6d61", "metadata": {}, "source": [ "## Results\n", @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "2eba25da", + "id": "71f2ecff", "metadata": { "hide-output": false }, @@ -213,7 +213,7 @@ }, { "cell_type": "markdown", - "id": "6b4cd05a", + "id": "1a46d7a3", "metadata": {}, "source": [ "Let’s build them." @@ -222,7 +222,7 @@ { "cell_type": "code", "execution_count": null, - "id": "169ab672", + "id": "3f456fc1", "metadata": { "hide-output": false }, @@ -279,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "b18a74af", + "id": "fc1a3dbc", "metadata": {}, "source": [ "Here’s some code that takes a list of agents and produces a plot showing their\n", @@ -292,7 +292,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85756433", + "id": "532b3645", "metadata": { "hide-output": false }, @@ -324,7 +324,7 @@ }, { "cell_type": "markdown", - "id": "2c3db882", + "id": "2ab16ffc", "metadata": {}, "source": [ "And here’s some pseudocode for the main loop, where we cycle through the\n", @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "506e344a", + "id": "43703012", "metadata": { "hide-output": false }, @@ -351,7 +351,7 @@ }, { "cell_type": "markdown", - "id": "f2573f2e", + "id": "9f2e2b66", "metadata": {}, "source": [ "The real code is below" @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8da61c6d", + "id": "de886545", "metadata": { "hide-output": false }, @@ -409,7 +409,7 @@ }, { "cell_type": "markdown", - "id": "4efc4aca", + "id": "695cae45", "metadata": {}, "source": [ "Let’s have a look at the results." @@ -418,7 +418,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ee68cb74", + "id": "b5879ba1", "metadata": { "hide-output": false }, @@ -429,7 +429,7 @@ }, { "cell_type": "markdown", - "id": "481ce33f", + "id": "e5997109", "metadata": {}, "source": [ "As discussed above, agents are initially mixed randomly together.\n", @@ -449,7 +449,7 @@ }, { "cell_type": "markdown", - "id": "58878a59", + "id": "52b09401", "metadata": {}, "source": [ "## Exercises" @@ -457,7 +457,7 @@ }, { "cell_type": "markdown", - "id": "588af446", + "id": "4536086c", "metadata": {}, "source": [ "## Exercise 22.1\n", @@ -490,7 +490,7 @@ }, { "cell_type": "markdown", - "id": "791870c9", + "id": "389ac68f", "metadata": {}, "source": [ "## Solution to[ Exercise 22.1](https://intro.quantecon.org/#schelling_ex1)\n", @@ -501,7 +501,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21053aa8", + "id": "5bc82fa5", "metadata": { "hide-output": false }, @@ -610,7 +610,7 @@ }, { "cell_type": "markdown", - "id": "473df3a0", + "id": "11664f10", "metadata": {}, "source": [ "When we run this we again find that mixed neighborhoods break down and segregation emerges.\n", @@ -621,7 +621,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b9e5635", + "id": "89714c38", "metadata": { "hide-output": false }, @@ -632,7 +632,7 @@ } ], "metadata": { - "date": 1722488543.3665826, + "date": 1722502940.2119713, "filename": "schelling.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/short_path.ipynb b/_notebooks/short_path.ipynb index ccb69b08..2ae6be8e 100644 --- a/_notebooks/short_path.ipynb +++ b/_notebooks/short_path.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "471132aa", + "id": "c1e63d95", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "9222a861", + "id": "6b42967e", "metadata": {}, "source": [ "# Shortest Paths\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "bdc4eb3b", + "id": "b94301f4", "metadata": {}, "source": [ "## Overview\n", @@ -52,7 +52,7 @@ { "cell_type": "code", "execution_count": null, - "id": "938f3622", + "id": "fbd6eb38", "metadata": { "hide-output": false }, @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "c8bcd806", + "id": "bf48a4af", "metadata": {}, "source": [ "## Outline of the problem\n", @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "f3276bc3", + "id": "13e00f3d", "metadata": {}, "source": [ "## Finding least-cost paths\n", @@ -163,7 +163,7 @@ }, { "cell_type": "markdown", - "id": "ebc8b90f", + "id": "c867d402", "metadata": {}, "source": [ "## Solving for minimum cost-to-go\n", @@ -174,7 +174,7 @@ }, { "cell_type": "markdown", - "id": "5102950b", + "id": "7aff2c4b", "metadata": {}, "source": [ "### The algorithm\n", @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "d7c1a0a5", + "id": "371c267a", "metadata": {}, "source": [ "### Implementation\n", @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aebb6e46", + "id": "ff51ee44", "metadata": { "hide-output": false }, @@ -262,7 +262,7 @@ }, { "cell_type": "markdown", - "id": "40c053c5", + "id": "58983889", "metadata": {}, "source": [ "Notice that the cost of staying still (on the principle diagonal) is set to\n", @@ -279,7 +279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5951a30", + "id": "74090999", "metadata": { "hide-output": false }, @@ -308,7 +308,7 @@ }, { "cell_type": "markdown", - "id": "1c934e03", + "id": "988c97dc", "metadata": {}, "source": [ "This matches with the numbers we obtained by inspection above.\n", @@ -318,7 +318,7 @@ }, { "cell_type": "markdown", - "id": "4d088807", + "id": "77f9057f", "metadata": {}, "source": [ "## Exercises" @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "a4f30301", + "id": "5d0951c6", "metadata": {}, "source": [ "## Exercise 38.1\n", @@ -355,7 +355,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4250f0f0", + "id": "a4811c42", "metadata": { "hide-output": false }, @@ -466,7 +466,7 @@ }, { "cell_type": "markdown", - "id": "e86d5802", + "id": "9e739aee", "metadata": {}, "source": [ "## Solution to[ Exercise 38.1](https://intro.quantecon.org/#short_path_ex1)\n", @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "885f0869", + "id": "5c60b5d6", "metadata": { "hide-output": false }, @@ -508,7 +508,7 @@ }, { "cell_type": "markdown", - "id": "fdd69edc", + "id": "080aa1ad", "metadata": {}, "source": [ "In addition, let’s write\n", @@ -525,7 +525,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3b029ad", + "id": "baa7965c", "metadata": { "hide-output": false }, @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "be255585", + "id": "04c5a250", "metadata": {}, "source": [ "We used np.allclose() rather than testing exact equality because we are\n", @@ -567,7 +567,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5e62337", + "id": "7273358a", "metadata": { "hide-output": false }, @@ -589,7 +589,7 @@ }, { "cell_type": "markdown", - "id": "d202e973", + "id": "b983a33f", "metadata": {}, "source": [ "Okay, now we have the necessary functions, let’s call them to do the job we were assigned." @@ -598,7 +598,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8121fc21", + "id": "7faca0e9", "metadata": { "hide-output": false }, @@ -611,7 +611,7 @@ }, { "cell_type": "markdown", - "id": "e6859f58", + "id": "3e7d6559", "metadata": {}, "source": [ "The total cost of the path should agree with $ J[0] $ so let’s check this." @@ -620,7 +620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5896c1b1", + "id": "73683676", "metadata": { "hide-output": false }, @@ -631,7 +631,7 @@ } ], "metadata": { - "date": 1722488543.3835995, + "date": 1722502940.229396, "filename": "short_path.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/simple_linear_regression.ipynb b/_notebooks/simple_linear_regression.ipynb index 22171709..219c5238 100644 --- a/_notebooks/simple_linear_regression.ipynb +++ b/_notebooks/simple_linear_regression.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d0426552", + "id": "a2d4c54f", "metadata": {}, "source": [ "# Simple Linear Regression Model" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "168b085d", + "id": "d09e6db6", "metadata": { "hide-output": false }, @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "3ac93a66", + "id": "5bdf7a45", "metadata": {}, "source": [ "The simple regression model estimates the relationship between two variables $ x_i $ and $ y_i $\n", @@ -57,7 +57,7 @@ { "cell_type": "code", "execution_count": null, - "id": "587f666e", + "id": "262b6f29", "metadata": { "hide-output": false }, @@ -72,7 +72,7 @@ }, { "cell_type": "markdown", - "id": "6ae37239", + "id": "335476fb", "metadata": {}, "source": [ "We can use a scatter plot of the data to see the relationship between $ y_i $ (ice-cream sales in dollars (\\$’s)) and $ x_i $ (degrees Celsius)." @@ -81,7 +81,7 @@ { "cell_type": "code", "execution_count": null, - "id": "336eac2c", + "id": "174a17ab", "metadata": { "hide-output": false }, @@ -98,7 +98,7 @@ }, { "cell_type": "markdown", - "id": "9b430476", + "id": "3dd7fb5c", "metadata": {}, "source": [ "as you can see the data suggests that more ice-cream is typically sold on hotter days.\n", @@ -115,7 +115,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ed390fef", + "id": "6838401e", "metadata": { "hide-output": false }, @@ -129,7 +129,7 @@ { "cell_type": "code", "execution_count": null, - "id": "91b916b5", + "id": "61b5fe77", "metadata": { "hide-output": false }, @@ -143,7 +143,7 @@ }, { "cell_type": "markdown", - "id": "a7ccc49c", + "id": "8a86159e", "metadata": {}, "source": [ "We can see that this model does a poor job of estimating the relationship.\n", @@ -154,7 +154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3be76287", + "id": "44bcc07c", "metadata": { "hide-output": false }, @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a85793ce", + "id": "6c20d268", "metadata": { "hide-output": false }, @@ -182,7 +182,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e2d115a2", + "id": "6b11199a", "metadata": { "hide-output": false }, @@ -195,7 +195,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5cee6219", + "id": "1fa65564", "metadata": { "hide-output": false }, @@ -209,7 +209,7 @@ }, { "cell_type": "markdown", - "id": "7b4ddf84", + "id": "bb47e703", "metadata": {}, "source": [ "However we need to think about formalizing this guessing process by thinking of this problem as an optimization problem.\n", @@ -227,7 +227,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0be13144", + "id": "2e7ff31d", "metadata": { "hide-output": false }, @@ -239,7 +239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b0ace8e", + "id": "cf947897", "metadata": { "hide-output": false }, @@ -251,7 +251,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19e4ec76", + "id": "02670a19", "metadata": { "hide-output": false }, @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "f8da3db4", + "id": "bfef8445", "metadata": {}, "source": [ "The Ordinary Least Squares (OLS) method chooses $ \\alpha $ and $ \\beta $ in such a way that **minimizes** the sum of the squared residuals (SSR).\n", @@ -286,7 +286,7 @@ }, { "cell_type": "markdown", - "id": "ea205094", + "id": "5a624e14", "metadata": {}, "source": [ "## How does error change with respect to $ \\alpha $ and $ \\beta $\n", @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "174e42b9", + "id": "3ee1d9fa", "metadata": { "hide-output": false }, @@ -311,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "09d93459", + "id": "77d07580", "metadata": {}, "source": [ "We can then calculate the error for a range of $ \\beta $ values" @@ -320,7 +320,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e33d55f7", + "id": "a102adc7", "metadata": { "hide-output": false }, @@ -333,7 +333,7 @@ }, { "cell_type": "markdown", - "id": "d0deab0b", + "id": "d8e4e0ea", "metadata": {}, "source": [ "Plotting the error" @@ -342,7 +342,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4bf8d4a5", + "id": "1527fcb1", "metadata": { "hide-output": false }, @@ -354,7 +354,7 @@ }, { "cell_type": "markdown", - "id": "44b17cd6", + "id": "3200de7a", "metadata": {}, "source": [ "Now let us vary $ \\alpha $ (holding $ \\beta $ constant)" @@ -363,7 +363,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9e70daa", + "id": "b28b2495", "metadata": { "hide-output": false }, @@ -376,7 +376,7 @@ }, { "cell_type": "markdown", - "id": "993d1177", + "id": "38a75547", "metadata": {}, "source": [ "Plotting the error" @@ -385,7 +385,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5790f055", + "id": "0fc7f8d8", "metadata": { "hide-output": false }, @@ -397,7 +397,7 @@ }, { "cell_type": "markdown", - "id": "f26d09b8", + "id": "0dc4f76f", "metadata": {}, "source": [ "\n", @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "6cc2374e", + "id": "7e54985b", "metadata": {}, "source": [ "## Calculating optimal values\n", @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "905f7d8b", + "id": "147860ce", "metadata": { "hide-output": false }, @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "8d8ac55c", + "id": "b808a3b7", "metadata": {}, "source": [ "Now computing across the 10 observations and then summing the numerator and denominator" @@ -539,7 +539,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c19e58f5", + "id": "a6a94533", "metadata": { "hide-output": false }, @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "f6ad5694", + "id": "ba65d463", "metadata": {}, "source": [ "Calculating $ \\alpha $" @@ -563,7 +563,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3c276bb", + "id": "56585dd3", "metadata": { "hide-output": false }, @@ -575,7 +575,7 @@ }, { "cell_type": "markdown", - "id": "b0f9241c", + "id": "2166b5e5", "metadata": {}, "source": [ "Now we can plot the OLS solution" @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3fa6bc1e", + "id": "982de953", "metadata": { "hide-output": false }, @@ -601,7 +601,7 @@ }, { "cell_type": "markdown", - "id": "9e40bc20", + "id": "d615ba51", "metadata": {}, "source": [ "## Exercise 45.1\n", @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "44b0fb4f", + "id": "fc19dea8", "metadata": {}, "source": [ "## Solution to[ Exercise 45.1](https://intro.quantecon.org/#slr-ex1)\n", @@ -635,7 +635,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5db02bc6", + "id": "de41e960", "metadata": { "hide-output": false }, @@ -648,7 +648,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72a08836", + "id": "b896f276", "metadata": { "hide-output": false }, @@ -659,7 +659,7 @@ }, { "cell_type": "markdown", - "id": "39d91306", + "id": "23c6ec13", "metadata": {}, "source": [ "You can see that the data downloaded from Our World in Data has provided a global set of countries with the GDP per capita and Life Expectancy Data.\n", @@ -674,7 +674,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f800163", + "id": "41d64a7d", "metadata": { "hide-output": false }, @@ -687,7 +687,7 @@ }, { "cell_type": "markdown", - "id": "3264121d", + "id": "8827cd81", "metadata": {}, "source": [ "Sometimes it can be useful to rename your columns to make it easier to work with in the DataFrame" @@ -696,7 +696,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b421716c", + "id": "edcf0b8b", "metadata": { "hide-output": false }, @@ -708,7 +708,7 @@ }, { "cell_type": "markdown", - "id": "236647af", + "id": "d6828d63", "metadata": {}, "source": [ "We can see there are `NaN` values which represents missing data so let us go ahead and drop those" @@ -717,7 +717,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c92a5322", + "id": "23c5e57c", "metadata": { "hide-output": false }, @@ -729,7 +729,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a468e823", + "id": "c13dd39e", "metadata": { "hide-output": false }, @@ -740,7 +740,7 @@ }, { "cell_type": "markdown", - "id": "6bb4cecf", + "id": "a6e75f46", "metadata": {}, "source": [ "We have now dropped the number of rows in our DataFrame from 62156 to 12445 removing a lot of empty data relationships.\n", @@ -757,7 +757,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b64e6b79", + "id": "9339f740", "metadata": { "hide-output": false }, @@ -769,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "bfd2904e", + "id": "605a15c5", "metadata": {}, "source": [ "As you can see there are a lot of countries where data is not available for the Year 1543!\n", @@ -780,7 +780,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de6a7d46", + "id": "b27b5653", "metadata": { "hide-output": false }, @@ -791,7 +791,7 @@ }, { "cell_type": "markdown", - "id": "6c7f8ecb", + "id": "67f8d724", "metadata": {}, "source": [ "You can see that Great Britain (GBR) is the only one available\n", @@ -802,7 +802,7 @@ { "cell_type": "code", "execution_count": null, - "id": "677cf3cd", + "id": "170abeb2", "metadata": { "hide-output": false }, @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "54aa1410", + "id": "318db778", "metadata": {}, "source": [ "In fact we can use pandas to quickly check how many countries are captured in each year" @@ -822,7 +822,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92d699a1", + "id": "c65d426a", "metadata": { "hide-output": false }, @@ -833,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "a9019644", + "id": "40bf3189", "metadata": {}, "source": [ "So it is clear that if you are doing cross-sectional comparisons then more recent data will include a wider set of countries\n", @@ -844,7 +844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b620ef3a", + "id": "e5fd72ff", "metadata": { "hide-output": false }, @@ -856,7 +856,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48f81ea0", + "id": "9222a263", "metadata": { "hide-output": false }, @@ -867,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "4c565f56", + "id": "eb9a751b", "metadata": {}, "source": [ "This data shows a couple of interesting relationships.\n", @@ -884,7 +884,7 @@ { "cell_type": "code", "execution_count": null, - "id": "24683a8a", + "id": "373458b1", "metadata": { "hide-output": false }, @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "eee857af", + "id": "2e1d8282", "metadata": {}, "source": [ "As you can see from this transformation – a linear model fits the shape of the data more closely." @@ -904,7 +904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f158abbb", + "id": "75b51b60", "metadata": { "hide-output": false }, @@ -916,7 +916,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88bdedbe", + "id": "0ba571c2", "metadata": { "hide-output": false }, @@ -927,7 +927,7 @@ }, { "cell_type": "markdown", - "id": "73e0f53f", + "id": "61ecf2b3", "metadata": {}, "source": [ "**Q4:** Use [(45.1)](#equation-eq-optimal-alpha) and [(45.2)](#equation-eq-optimal-beta) to compute optimal values for $ \\alpha $ and $ \\beta $" @@ -936,7 +936,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5f3b7499", + "id": "2ef98f8e", "metadata": { "hide-output": false }, @@ -952,7 +952,7 @@ { "cell_type": "code", "execution_count": null, - "id": "456fed41", + "id": "ceb07f6f", "metadata": { "hide-output": false }, @@ -964,7 +964,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69dd3662", + "id": "08171e19", "metadata": { "hide-output": false }, @@ -980,7 +980,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8b93bed", + "id": "1c51b974", "metadata": { "hide-output": false }, @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "0fc14024", + "id": "a07721d5", "metadata": {}, "source": [ "**Q5:** Plot the line of best fit found using OLS" @@ -1001,7 +1001,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b678979e", + "id": "3707d5ef", "metadata": { "hide-output": false }, @@ -1018,7 +1018,7 @@ }, { "cell_type": "markdown", - "id": "16688db1", + "id": "d6673428", "metadata": {}, "source": [ "## Exercise 45.2\n", @@ -1032,7 +1032,7 @@ } ], "metadata": { - "date": 1722488543.4214602, + "date": 1722502940.2647753, "filename": "simple_linear_regression.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/solow.ipynb b/_notebooks/solow.ipynb index d8af47c9..e21f0646 100644 --- a/_notebooks/solow.ipynb +++ b/_notebooks/solow.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7861f6f1", + "id": "72a61e12", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "e3e8ed15", + "id": "2a3c37ff", "metadata": {}, "source": [ "# The Solow-Swan Growth Model\n", @@ -29,7 +29,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7533dd54", + "id": "e7289c03", "metadata": { "hide-output": false }, @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "7a6517c6", + "id": "4c1e888b", "metadata": {}, "source": [ "## The model\n", @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "a9a5871a", + "id": "a573fb07", "metadata": {}, "source": [ "## A graphical perspective\n", @@ -141,7 +141,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab636a98", + "id": "6f7d18fe", "metadata": { "hide-output": false }, @@ -154,7 +154,7 @@ }, { "cell_type": "markdown", - "id": "8b2d7a9e", + "id": "2c6f9c6d", "metadata": {}, "source": [ "Now, we define the function $ g $." @@ -163,7 +163,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0db4ab49", + "id": "e49711d9", "metadata": { "hide-output": false }, @@ -175,7 +175,7 @@ }, { "cell_type": "markdown", - "id": "e24be199", + "id": "bcad7aaf", "metadata": {}, "source": [ "Let’s plot the 45-degree diagram of $ g $." @@ -184,7 +184,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97889917", + "id": "177870b1", "metadata": { "hide-output": false }, @@ -233,7 +233,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42b4c36c", + "id": "3b100b58", "metadata": { "hide-output": false }, @@ -244,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "4d58b4e8", + "id": "4dac5ad2", "metadata": {}, "source": [ "Suppose, at some $ k_t $, the value $ g(k_t) $ lies strictly above the 45-degree line.\n", @@ -278,7 +278,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0afc13a", + "id": "968db9a4", "metadata": { "hide-output": false }, @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "c4640622", + "id": "2401b047", "metadata": {}, "source": [ "From our graphical analysis, it appears that $ (k_t) $ converges to $ k^* $, regardless of initial capital\n", @@ -309,7 +309,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc00c026", + "id": "ed24ad45", "metadata": { "hide-output": false }, @@ -326,7 +326,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afe90569", + "id": "ca834f55", "metadata": { "hide-output": false }, @@ -361,7 +361,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6739afc", + "id": "799b7bc7", "metadata": { "hide-output": false }, @@ -372,7 +372,7 @@ }, { "cell_type": "markdown", - "id": "8450c4d1", + "id": "1ea23a63", "metadata": {}, "source": [ "As expected, the time paths in the figure all converge to $ k^* $." @@ -380,7 +380,7 @@ }, { "cell_type": "markdown", - "id": "432247ad", + "id": "adfb5132", "metadata": {}, "source": [ "## Growth in continuous time\n", @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92b0d607", + "id": "86f2471a", "metadata": { "hide-output": false }, @@ -454,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "71c31c54", + "id": "28b5683e", "metadata": {}, "source": [ "Next we define the function $ g $ for growth in continuous time" @@ -463,7 +463,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bec6de2", + "id": "a646cdaa", "metadata": { "hide-output": false }, @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60e7230f", + "id": "27fda8ab", "metadata": { "hide-output": false }, @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9622bdd5", + "id": "34a34fc5", "metadata": { "hide-output": false }, @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "15df545b", + "id": "e6ffc40c", "metadata": {}, "source": [ "This shows global stability heuristically for a fixed parameterization, but\n", @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "e4ba4d55", + "id": "175b1101", "metadata": {}, "source": [ "## Exercises" @@ -600,7 +600,7 @@ }, { "cell_type": "markdown", - "id": "68b2d7ce", + "id": "e0c67bcd", "metadata": {}, "source": [ "## Exercise 24.1\n", @@ -616,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "dd781149", + "id": "4cf0717a", "metadata": {}, "source": [ "## Solution to[ Exercise 24.1](https://intro.quantecon.org/#solow_ex1)\n", @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b5df862", + "id": "cde863b5", "metadata": { "hide-output": false }, @@ -645,7 +645,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f0f36ce", + "id": "0784fb79", "metadata": { "hide-output": false }, @@ -658,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "493ce970", + "id": "f18fadc5", "metadata": {}, "source": [ "Let’s find the value of $ s $ that maximizes $ c^* $ using [scipy.optimize.minimize_scalar](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html#scipy.optimize.minimize_scalar).\n", @@ -668,7 +668,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3c17cba", + "id": "46e836cd", "metadata": { "hide-output": false }, @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e83c19d", + "id": "4dcfb4e9", "metadata": { "hide-output": false }, @@ -694,7 +694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "589c936f", + "id": "7b61d52d", "metadata": { "hide-output": false }, @@ -709,7 +709,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca8f0424", + "id": "29efd945", "metadata": { "hide-output": false }, @@ -743,7 +743,7 @@ }, { "cell_type": "markdown", - "id": "f108e08d", + "id": "1310a5ff", "metadata": {}, "source": [ "One can also try to solve this mathematically by differentiating $ c^*(s) $ and solve for $ \\frac{d}{ds}c^*(s)=0 $ using [sympy](https://www.sympy.org/en/index.html)." @@ -752,7 +752,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00aae8d8", + "id": "9e8d6077", "metadata": { "hide-output": false }, @@ -764,7 +764,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c974efa", + "id": "3fd9adae", "metadata": { "hide-output": false }, @@ -777,7 +777,7 @@ }, { "cell_type": "markdown", - "id": "96644e4a", + "id": "b714dfc1", "metadata": {}, "source": [ "Let’s differentiate $ c $ and solve using [sympy.solve](https://docs.sympy.org/latest/modules/solvers/solvers.html#sympy.solvers.solvers.solve)" @@ -786,7 +786,7 @@ { "cell_type": "code", "execution_count": null, - "id": "904ced9d", + "id": "2bd72bdd", "metadata": { "hide-output": false }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "c43093fd", + "id": "a83e444a", "metadata": {}, "source": [ "Incidentally, the rate of savings which maximizes steady state level of per capita consumption is called the [Golden Rule savings rate](https://en.wikipedia.org/wiki/Golden_Rule_savings_rate)." @@ -807,7 +807,7 @@ }, { "cell_type": "markdown", - "id": "52c2d97c", + "id": "d15c7c5d", "metadata": {}, "source": [ "## Exercise 24.2\n", @@ -846,7 +846,7 @@ }, { "cell_type": "markdown", - "id": "b1533909", + "id": "9f680012", "metadata": {}, "source": [ "## Solution to[ Exercise 24.2](https://intro.quantecon.org/#solow_ex2)\n", @@ -857,7 +857,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c3793ea", + "id": "20a62fce", "metadata": { "hide-output": false }, @@ -875,7 +875,7 @@ }, { "cell_type": "markdown", - "id": "2b63be59", + "id": "853b349f", "metadata": {}, "source": [ "Let’s define the function *k_next* to find the next value of $ k $" @@ -884,7 +884,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74dbe535", + "id": "a909abe6", "metadata": { "hide-output": false }, @@ -900,7 +900,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f84b1fcf", + "id": "18b2e573", "metadata": { "hide-output": false }, @@ -930,7 +930,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c38564b3", + "id": "7056d55b", "metadata": { "hide-output": false }, @@ -941,7 +941,7 @@ } ], "metadata": { - "date": 1722488543.4519591, + "date": 1722502940.2947385, "filename": "solow.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/status.ipynb b/_notebooks/status.ipynb index 4796ed8d..3f352c2b 100644 --- a/_notebooks/status.ipynb +++ b/_notebooks/status.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0658744d", + "id": "83646349", "metadata": {}, "source": [ "# Execution Statistics\n", @@ -46,7 +46,7 @@ "|monte_carlo|2024-08-01 04:49|cache|189.5|✅|\n", "|networks|2024-08-01 04:49|cache|8.87|✅|\n", "|olg|2024-08-01 04:49|cache|2.31|✅|\n", - "|prob_dist|2024-08-01 04:49|cache|8.4|✅|\n", + "|prob_dist|2024-08-01 09:00|cache|19.75|✅|\n", "|pv|2024-08-01 04:49|cache|1.73|✅|\n", "|scalar_dynam|2024-08-01 04:49|cache|3.07|✅|\n", "|schelling|2024-08-01 04:50|cache|11.92|✅|\n", @@ -70,7 +70,7 @@ { "cell_type": "code", "execution_count": null, - "id": "989b5a91", + "id": "8972e6e7", "metadata": { "hide-output": false }, @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "b8e3be49", + "id": "8d237249", "metadata": {}, "source": [ "and the following package versions" @@ -90,7 +90,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72c2a842", + "id": "0df6a2b9", "metadata": { "hide-output": false }, @@ -101,7 +101,7 @@ } ], "metadata": { - "date": 1722488543.4756122, + "date": 1722502940.317688, "filename": "status.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/supply_demand_heterogeneity.ipynb b/_notebooks/supply_demand_heterogeneity.ipynb index d2cd7ef4..5ff68555 100644 --- a/_notebooks/supply_demand_heterogeneity.ipynb +++ b/_notebooks/supply_demand_heterogeneity.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5b1cf579", + "id": "57a0acf3", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "c50e50e1", + "id": "e133e15c", "metadata": {}, "source": [ "# Market Equilibrium with Heterogeneity" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "3ed8975c", + "id": "72442f8a", "metadata": {}, "source": [ "## Overview\n", @@ -42,7 +42,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fabe2d3d", + "id": "6e2205a3", "metadata": { "hide-output": false }, @@ -54,7 +54,7 @@ }, { "cell_type": "markdown", - "id": "176af6f9", + "id": "ba55ebc5", "metadata": {}, "source": [ "## An simple example\n", @@ -105,7 +105,7 @@ }, { "cell_type": "markdown", - "id": "1664421a", + "id": "7999148b", "metadata": {}, "source": [ "## Exercise 44.1\n", @@ -131,7 +131,7 @@ }, { "cell_type": "markdown", - "id": "288a7df8", + "id": "0e2df57a", "metadata": {}, "source": [ "## Pure exchange economy\n", @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "6536c57c", + "id": "710128ec", "metadata": {}, "source": [ "### Competitive equilibrium\n", @@ -173,7 +173,7 @@ }, { "cell_type": "markdown", - "id": "688bcc98", + "id": "858a9c7d", "metadata": {}, "source": [ "### Designing some Python code\n", @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "40280cd3", + "id": "30eb1467", "metadata": { "hide-output": false }, @@ -283,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "f8ee1a1e", + "id": "df0ffe02", "metadata": {}, "source": [ "## Implementation\n", @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "22a05111", + "id": "d5fb89d5", "metadata": {}, "source": [ "### Two-person economy without production\n", @@ -308,7 +308,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1d1cadd7", + "id": "4217005a", "metadata": { "hide-output": false }, @@ -332,7 +332,7 @@ }, { "cell_type": "markdown", - "id": "1767bb6e", + "id": "2476baa2", "metadata": {}, "source": [ "What happens if the first consumer likes the first good more and the second consumer likes the second good more?" @@ -341,7 +341,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8ffd01b", + "id": "3d5e5a55", "metadata": { "hide-output": false }, @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "df091320", + "id": "a052f089", "metadata": {}, "source": [ "Let the first consumer be poorer." @@ -367,7 +367,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db141bfd", + "id": "4a68afd9", "metadata": { "hide-output": false }, @@ -384,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "0c3e267e", + "id": "3088b62d", "metadata": {}, "source": [ "Now let’s construct an autarky (i.e., no-trade) equilibrium." @@ -393,7 +393,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca7a566b", + "id": "c2909b7b", "metadata": { "hide-output": false }, @@ -413,7 +413,7 @@ }, { "cell_type": "markdown", - "id": "912b1e3f", + "id": "459f2f1a", "metadata": {}, "source": [ "Now let’s redistribute endowments before trade." @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32b94ae4", + "id": "dd48fc66", "metadata": { "hide-output": false }, @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "dad1b9c5", + "id": "aa08b934", "metadata": {}, "source": [ "### A dynamic economy\n", @@ -455,7 +455,7 @@ { "cell_type": "code", "execution_count": null, - "id": "34c7ed0e", + "id": "607dadca", "metadata": { "hide-output": false }, @@ -479,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "67616cad", + "id": "8269897d", "metadata": {}, "source": [ "### Risk economy with arrow securities\n", @@ -490,7 +490,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a9d2f23d", + "id": "7129b92a", "metadata": { "hide-output": false }, @@ -516,7 +516,7 @@ }, { "cell_type": "markdown", - "id": "35411274", + "id": "2640c06c", "metadata": {}, "source": [ "## Deducing a representative consumer\n", @@ -599,7 +599,7 @@ } ], "metadata": { - "date": 1722488543.491541, + "date": 1722502940.3331583, "filename": "supply_demand_heterogeneity.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/supply_demand_multiple_goods.ipynb b/_notebooks/supply_demand_multiple_goods.ipynb index 13ae40c2..375951f2 100644 --- a/_notebooks/supply_demand_multiple_goods.ipynb +++ b/_notebooks/supply_demand_multiple_goods.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "a2b74c48", + "id": "8f8e76dd", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "d41c9ebd", + "id": "26d7cc1a", "metadata": {}, "source": [ "# Supply and Demand with Many Goods" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "6582d6c9", + "id": "b92ddf54", "metadata": {}, "source": [ "## Overview\n", @@ -68,7 +68,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61d1efe2", + "id": "b2ab09be", "metadata": { "hide-output": false }, @@ -82,7 +82,7 @@ }, { "cell_type": "markdown", - "id": "9a6d5b4f", + "id": "ebb85ac4", "metadata": {}, "source": [ "## Formulas from linear algebra\n", @@ -111,7 +111,7 @@ }, { "cell_type": "markdown", - "id": "51f4be70", + "id": "1c778efb", "metadata": {}, "source": [ "## From utility function to demand curve\n", @@ -173,7 +173,7 @@ }, { "cell_type": "markdown", - "id": "84187bd2", + "id": "17b3cea0", "metadata": {}, "source": [ "### Demand curve implied by constrained utility maximization\n", @@ -230,7 +230,7 @@ }, { "cell_type": "markdown", - "id": "d67dcbbf", + "id": "4db366e0", "metadata": {}, "source": [ "## Endowment economy\n", @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "d6d44032", + "id": "aec67d05", "metadata": {}, "source": [ "## Exercise 43.1\n", @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "3ed2f1fd", + "id": "9faa388a", "metadata": {}, "source": [ "## Exercise 43.2\n", @@ -284,7 +284,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcf06d14", + "id": "29994b2c", "metadata": { "hide-output": false }, @@ -338,7 +338,7 @@ }, { "cell_type": "markdown", - "id": "18ad83b3", + "id": "3dea7797", "metadata": {}, "source": [ "## Digression: Marshallian and Hicksian demand curves\n", @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "727123cc", + "id": "f6966576", "metadata": {}, "source": [ "## Dynamics and risk as special cases\n", @@ -398,7 +398,7 @@ }, { "cell_type": "markdown", - "id": "50187dc4", + "id": "5ff43283", "metadata": {}, "source": [ "### Dynamics\n", @@ -455,7 +455,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e288cbe", + "id": "d825f235", "metadata": { "hide-output": false }, @@ -479,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "40629f06", + "id": "5b30f087", "metadata": {}, "source": [ "### Risk and state-contingent claims\n", @@ -550,7 +550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9a5ef8b2", + "id": "2b77c1db", "metadata": { "hide-output": false }, @@ -574,7 +574,7 @@ }, { "cell_type": "markdown", - "id": "691f5602", + "id": "bd6c31e4", "metadata": {}, "source": [ "### Exercise 43.3\n", @@ -593,7 +593,7 @@ }, { "cell_type": "markdown", - "id": "69302a46", + "id": "16880a9b", "metadata": {}, "source": [ "### Solution to[ Exercise 43.3](https://intro.quantecon.org/#sdm_ex3)\n", @@ -606,7 +606,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c19ab14", + "id": "599f7d4b", "metadata": { "hide-output": false }, @@ -622,7 +622,7 @@ }, { "cell_type": "markdown", - "id": "6440c030", + "id": "1758a308", "metadata": {}, "source": [ "If the consumer likes the first (or second) good more, then we can set a larger bliss value for good 1." @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9350df1b", + "id": "5edea2f4", "metadata": { "hide-output": false }, @@ -646,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "f76b8241", + "id": "285fd6a4", "metadata": {}, "source": [ "Increase the probability that state $ 1 $ occurs." @@ -655,7 +655,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c04d390b", + "id": "d27bf909", "metadata": { "hide-output": false }, @@ -679,7 +679,7 @@ }, { "cell_type": "markdown", - "id": "001e2dc4", + "id": "a38c5ca8", "metadata": {}, "source": [ "## Economies with endogenous supplies of goods\n", @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "bf46d46a", + "id": "1873217f", "metadata": {}, "source": [ "### Supply curve of a competitive firm\n", @@ -741,7 +741,7 @@ }, { "cell_type": "markdown", - "id": "71b7f2c8", + "id": "1eed9cff", "metadata": {}, "source": [ "### Competitive equilibrium\n", @@ -753,7 +753,7 @@ }, { "cell_type": "markdown", - "id": "48744738", + "id": "d06b92c4", "metadata": {}, "source": [ "#### $ \\mu=1 $ warmup\n", @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "3942d138", + "id": "271c28f8", "metadata": {}, "source": [ "#### General $ \\mu\\neq 1 $ case\n", @@ -807,7 +807,7 @@ }, { "cell_type": "markdown", - "id": "4b7a2cac", + "id": "6561d1c4", "metadata": {}, "source": [ "### Implementation\n", @@ -829,7 +829,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c935c2a3", + "id": "bc7b7378", "metadata": { "hide-output": false }, @@ -900,7 +900,7 @@ }, { "cell_type": "markdown", - "id": "ef9e83b8", + "id": "e5bfe046", "metadata": {}, "source": [ "Then define a function that plots demand and supply curves and labels surpluses and equilibrium." @@ -909,7 +909,7 @@ { "cell_type": "code", "execution_count": null, - "id": "57c1f727", + "id": "8d2d530d", "metadata": { "hide-output": false }, @@ -962,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "9e95f4ae", + "id": "554a78c4", "metadata": {}, "source": [ "#### Example: single agent with one good and production\n", @@ -980,7 +980,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f864a1b", + "id": "b296f6ab", "metadata": { "hide-output": false }, @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8063d2b1", + "id": "34528db6", "metadata": { "hide-output": false }, @@ -1019,7 +1019,7 @@ }, { "cell_type": "markdown", - "id": "7688a147", + "id": "3a096d62", "metadata": {}, "source": [ "Let’s give the consumer a lower welfare weight by raising $ \\mu $." @@ -1028,7 +1028,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2718453d", + "id": "7ffb88b3", "metadata": { "hide-output": false }, @@ -1047,7 +1047,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ac7f253", + "id": "6f05ef14", "metadata": { "hide-output": false }, @@ -1061,7 +1061,7 @@ }, { "cell_type": "markdown", - "id": "d252e546", + "id": "8ae75ad7", "metadata": {}, "source": [ "Now we change the bliss point so that the consumer derives more utility from consumption." @@ -1070,7 +1070,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81d6a5e5", + "id": "55e87c14", "metadata": { "hide-output": false }, @@ -1089,7 +1089,7 @@ }, { "cell_type": "markdown", - "id": "032c4578", + "id": "eb0af344", "metadata": {}, "source": [ "This raises both the equilibrium price and quantity." @@ -1097,7 +1097,7 @@ }, { "cell_type": "markdown", - "id": "9783b054", + "id": "c7f86ffb", "metadata": {}, "source": [ "#### Example: single agent two-good economy with production\n", @@ -1109,7 +1109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33fa1b08", + "id": "e564eaeb", "metadata": { "hide-output": false }, @@ -1136,7 +1136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e711e449", + "id": "4e0432e4", "metadata": { "hide-output": false }, @@ -1153,7 +1153,7 @@ { "cell_type": "code", "execution_count": null, - "id": "082e4210", + "id": "738c6101", "metadata": { "hide-output": false }, @@ -1173,7 +1173,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b85cfe6", + "id": "909a954b", "metadata": { "hide-output": false }, @@ -1188,7 +1188,7 @@ }, { "cell_type": "markdown", - "id": "71d195ae", + "id": "e2b8540d", "metadata": {}, "source": [ "### Digression: a supplier who is a monopolist\n", @@ -1229,7 +1229,7 @@ }, { "cell_type": "markdown", - "id": "55399093", + "id": "4fa033f0", "metadata": {}, "source": [ "### Exercise 43.4\n", @@ -1239,7 +1239,7 @@ }, { "cell_type": "markdown", - "id": "3373ede0", + "id": "3f2e727f", "metadata": {}, "source": [ "### A monopolist\n", @@ -1278,7 +1278,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7cb57eaa", + "id": "2b2daa00", "metadata": { "hide-output": false }, @@ -1319,7 +1319,7 @@ }, { "cell_type": "markdown", - "id": "33939150", + "id": "066d3e84", "metadata": {}, "source": [ "Define a function that plots the demand, marginal cost and marginal revenue curves with surpluses and equilibrium labelled." @@ -1328,7 +1328,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd6e119a", + "id": "ff02db68", "metadata": { "hide-output": false }, @@ -1391,7 +1391,7 @@ }, { "cell_type": "markdown", - "id": "30493c0b", + "id": "1b29151e", "metadata": {}, "source": [ "#### A multiple good example\n", @@ -1402,7 +1402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf6e9cde", + "id": "2067576d", "metadata": { "hide-output": false }, @@ -1432,7 +1432,7 @@ }, { "cell_type": "markdown", - "id": "547b2577", + "id": "14edeb77", "metadata": {}, "source": [ "#### A single-good example" @@ -1441,7 +1441,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b04a6300", + "id": "03bd82f7", "metadata": { "hide-output": false }, @@ -1469,7 +1469,7 @@ }, { "cell_type": "markdown", - "id": "36d38dbd", + "id": "495d8ce8", "metadata": {}, "source": [ "## Multi-good welfare maximization problem\n", @@ -1515,7 +1515,7 @@ } ], "metadata": { - "date": 1722488543.5357707, + "date": 1722502940.3755996, "filename": "supply_demand_multiple_goods.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/time_series_with_matrices.ipynb b/_notebooks/time_series_with_matrices.ipynb index 51e57238..75388d42 100644 --- a/_notebooks/time_series_with_matrices.ipynb +++ b/_notebooks/time_series_with_matrices.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "2c184972", + "id": "fa0bedad", "metadata": {}, "source": [ "\n", @@ -16,7 +16,7 @@ }, { "cell_type": "markdown", - "id": "a4c0a7f6", + "id": "2e1fd53e", "metadata": {}, "source": [ "# Univariate Time Series with Matrix Algebra" @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "57ca3566", + "id": "e8a783f8", "metadata": {}, "source": [ "## Overview\n", @@ -54,7 +54,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d12b665", + "id": "ae282b44", "metadata": { "hide-output": false }, @@ -68,7 +68,7 @@ }, { "cell_type": "markdown", - "id": "e64710a1", + "id": "22a17dc3", "metadata": {}, "source": [ "## Samuelson’s model\n", @@ -157,7 +157,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d969e9f8", + "id": "51004bb6", "metadata": { "hide-output": false }, @@ -176,7 +176,7 @@ }, { "cell_type": "markdown", - "id": "31a4f7f9", + "id": "1df161a0", "metadata": {}, "source": [ "Now we construct $ A $ and $ b $." @@ -185,7 +185,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6ee74006", + "id": "75e8eb1e", "metadata": { "hide-output": false }, @@ -208,7 +208,7 @@ }, { "cell_type": "markdown", - "id": "7e012285", + "id": "71f6ea7a", "metadata": {}, "source": [ "Let’s look at the matrix $ A $ and the vector $ b $ for our\n", @@ -218,7 +218,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9c2f573", + "id": "e6057b97", "metadata": { "hide-output": false }, @@ -229,7 +229,7 @@ }, { "cell_type": "markdown", - "id": "506312e4", + "id": "17a4e256", "metadata": {}, "source": [ "Now let’s solve for the path of $ y $.\n", @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "18b0fa6c", + "id": "cdc2f409", "metadata": { "hide-output": false }, @@ -256,7 +256,7 @@ }, { "cell_type": "markdown", - "id": "a6713c9b", + "id": "51934f06", "metadata": {}, "source": [ "or we can use `np.linalg.solve`:" @@ -265,7 +265,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3028c74b", + "id": "aa9839da", "metadata": { "hide-output": false }, @@ -276,7 +276,7 @@ }, { "cell_type": "markdown", - "id": "b2dd4f94", + "id": "f83b65bc", "metadata": {}, "source": [ "Here make sure the two methods give the same result, at least up to floating\n", @@ -286,7 +286,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2389bc6", + "id": "dc7c4cfd", "metadata": { "hide-output": false }, @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "deeb44d5", + "id": "940e1637", "metadata": {}, "source": [ ">**Note**\n", @@ -314,7 +314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "884e70b8", + "id": "f05fa46a", "metadata": { "hide-output": false }, @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "d3f54406", + "id": "944167d7", "metadata": {}, "source": [ "The [*steady state*](https://intro.quantecon.org/scalar_dynam.html#scalar-dynam-steady-state) value $ y^* $ of $ y_t $ is obtained by setting $ y_t = y_{t-1} =\n", @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c25cd97", + "id": "cab4f36b", "metadata": { "hide-output": false }, @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07637812", + "id": "2477158b", "metadata": { "hide-output": false }, @@ -376,7 +376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1246478e", + "id": "8f666c71", "metadata": { "hide-output": false }, @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "83fe9664", + "id": "6536a7ec", "metadata": {}, "source": [ "## Adding a random term\n", @@ -447,7 +447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c461b816", + "id": "ef7ca216", "metadata": { "hide-output": false }, @@ -461,7 +461,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c778ac1", + "id": "d6904ca6", "metadata": { "hide-output": false }, @@ -476,7 +476,7 @@ }, { "cell_type": "markdown", - "id": "9e77cb5d", + "id": "190138eb", "metadata": {}, "source": [ "The above time series looks a lot like (detrended) GDP series for a\n", @@ -488,7 +488,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e5ccb84e", + "id": "cf0a715d", "metadata": { "hide-output": false }, @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "2a07f072", + "id": "04885c8c", "metadata": {}, "source": [ "Also consider the case when $ y_{0} $ and $ y_{-1} $ are at\n", @@ -520,7 +520,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4f92465", + "id": "e200c013", "metadata": { "hide-output": false }, @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "f49b6602", + "id": "a5b87e85", "metadata": {}, "source": [ "## Computing population moments\n", @@ -588,7 +588,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7201ca32", + "id": "a1693ee8", "metadata": { "hide-output": false }, @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "daf2fb36", + "id": "284d0287", "metadata": {}, "source": [ "It is enlightening to study the $ \\mu_y, \\Sigma_y $’s implied by various parameter values.\n", @@ -668,7 +668,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6932b12", + "id": "239cbed6", "metadata": { "hide-output": false }, @@ -691,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "576bbaaf", + "id": "5411975c", "metadata": {}, "source": [ "Visually, notice how the variance across realizations of $ y_t $ decreases as $ t $ increases.\n", @@ -702,7 +702,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25c57bd2", + "id": "798bcb11", "metadata": { "hide-output": false }, @@ -715,7 +715,7 @@ }, { "cell_type": "markdown", - "id": "5cc6d01a", + "id": "a06cfd11", "metadata": {}, "source": [ "Notice how the population variance increases and asymptotes.\n", @@ -726,7 +726,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0377ccee", + "id": "1cb15cf3", "metadata": { "hide-output": false }, @@ -742,7 +742,7 @@ }, { "cell_type": "markdown", - "id": "21ce81e1", + "id": "4d6fd0e1", "metadata": {}, "source": [ "Notice that the covariance between $ y_t $ and $ y_{t-1} $ – the elements on the superdiagonal – are *not* identical.\n", @@ -759,7 +759,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1f519cb", + "id": "27af2504", "metadata": { "hide-output": false }, @@ -773,7 +773,7 @@ }, { "cell_type": "markdown", - "id": "867dab40", + "id": "59f3dc9b", "metadata": {}, "source": [ "Please notice how the subdiagonal and superdiagonal elements seem to have converged.\n", @@ -787,7 +787,7 @@ }, { "cell_type": "markdown", - "id": "a502beb1", + "id": "4b905729", "metadata": {}, "source": [ "## Moving average representation\n", @@ -805,7 +805,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42ad65c5", + "id": "3a1d4604", "metadata": { "hide-output": false }, @@ -817,7 +817,7 @@ }, { "cell_type": "markdown", - "id": "00b3651c", + "id": "8f849d08", "metadata": {}, "source": [ "Evidently, $ A^{-1} $ is a lower triangular matrix.\n", @@ -828,7 +828,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ef908c1", + "id": "ea8121c2", "metadata": { "hide-output": false }, @@ -840,7 +840,7 @@ }, { "cell_type": "markdown", - "id": "f42a53c1", + "id": "24826dce", "metadata": {}, "source": [ "Notice how every row ends with the previous row’s pre-diagonal entries.\n", @@ -867,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "58467b2c", + "id": "7d2767cc", "metadata": {}, "source": [ "## A forward looking model\n", @@ -930,7 +930,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1c5775b", + "id": "f21f4ef9", "metadata": { "hide-output": false }, @@ -942,7 +942,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbc43f3d", + "id": "11acba34", "metadata": { "hide-output": false }, @@ -958,7 +958,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc9f6963", + "id": "14f1391c", "metadata": { "hide-output": false }, @@ -970,7 +970,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7bc168ce", + "id": "3d49d862", "metadata": { "hide-output": false }, @@ -985,7 +985,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ff52d56", + "id": "c12b50a7", "metadata": { "hide-output": false }, @@ -997,7 +997,7 @@ { "cell_type": "code", "execution_count": null, - "id": "03e9cb0d", + "id": "9f956d1d", "metadata": { "hide-output": false }, @@ -1014,7 +1014,7 @@ }, { "cell_type": "markdown", - "id": "7eac53d6", + "id": "c488e472", "metadata": {}, "source": [ "Can you explain why the trend of the price is downward over time?\n", @@ -1026,7 +1026,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1dbf13f1", + "id": "fb67c765", "metadata": { "hide-output": false }, @@ -1045,7 +1045,7 @@ } ], "metadata": { - "date": 1722488543.56873, + "date": 1722502940.8625245, "filename": "time_series_with_matrices.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/troubleshooting.ipynb b/_notebooks/troubleshooting.ipynb index df4dc880..fd2ecc6a 100644 --- a/_notebooks/troubleshooting.ipynb +++ b/_notebooks/troubleshooting.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "47c0e9e0", + "id": "814786a4", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "14f862f4", + "id": "7795e0ac", "metadata": {}, "source": [ "# Troubleshooting\n", @@ -21,7 +21,7 @@ }, { "cell_type": "markdown", - "id": "625245e6", + "id": "0d6537f6", "metadata": {}, "source": [ "## Fixing your local environment\n", @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "b3c41d2d", + "id": "d5431122", "metadata": {}, "source": [ "## Reporting an issue\n", @@ -80,7 +80,7 @@ } ], "metadata": { - "date": 1722488543.5749161, + "date": 1722502940.8690894, "filename": "troubleshooting.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/unpleasant.ipynb b/_notebooks/unpleasant.ipynb index 90f4a0af..6c5c5ea7 100644 --- a/_notebooks/unpleasant.ipynb +++ b/_notebooks/unpleasant.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5a86d736", + "id": "010928df", "metadata": {}, "source": [ "# Some Unpleasant Monetarist Arithmetic" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "1e6d34f5", + "id": "df8cc535", "metadata": {}, "source": [ "## Overview\n", @@ -44,7 +44,7 @@ }, { "cell_type": "markdown", - "id": "c26a8ef6", + "id": "e15e2658", "metadata": {}, "source": [ "## Setup\n", @@ -86,7 +86,7 @@ }, { "cell_type": "markdown", - "id": "a1b14eeb", + "id": "d724bb2b", "metadata": {}, "source": [ "## Monetary-Fiscal Policy\n", @@ -110,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "c6fcfe2b", + "id": "003aeb8f", "metadata": {}, "source": [ "### Open market operations\n", @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "f04065f6", + "id": "d2387662", "metadata": {}, "source": [ "## An open market operation at $ t=0 $\n", @@ -188,7 +188,7 @@ }, { "cell_type": "markdown", - "id": "6159cdf4", + "id": "23414626", "metadata": {}, "source": [ "## Algorithm (basic idea)\n", @@ -234,7 +234,7 @@ }, { "cell_type": "markdown", - "id": "3bcce4a7", + "id": "197254fb", "metadata": {}, "source": [ "## Before time $ T $\n", @@ -287,7 +287,7 @@ }, { "cell_type": "markdown", - "id": "7d846881", + "id": "bcac5123", "metadata": {}, "source": [ "## \n", @@ -298,7 +298,7 @@ }, { "cell_type": "markdown", - "id": "ab4b3b19", + "id": "f8d33b5a", "metadata": {}, "source": [ "## Algorithm (pseudo code)\n", @@ -312,7 +312,7 @@ }, { "cell_type": "markdown", - "id": "ede0171b", + "id": "68911eec", "metadata": {}, "source": [ "## \n", @@ -364,7 +364,7 @@ }, { "cell_type": "markdown", - "id": "667b4ea2", + "id": "49b4e55f", "metadata": {}, "source": [ "## Example Calculations\n", @@ -393,7 +393,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb0246d1", + "id": "28f465c8", "metadata": { "hide-output": false }, @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "e7ac9db6", + "id": "e29a382f", "metadata": {}, "source": [ "Now let’s dive in and implement our pseudo code in Python." @@ -415,7 +415,7 @@ { "cell_type": "code", "execution_count": null, - "id": "154cf5d7", + "id": "0ce5303f", "metadata": { "hide-output": false }, @@ -441,7 +441,7 @@ { "cell_type": "code", "execution_count": null, - "id": "473e59eb", + "id": "4ce88883", "metadata": { "hide-output": false }, @@ -453,7 +453,7 @@ { "cell_type": "code", "execution_count": null, - "id": "460dae20", + "id": "8a0e21b4", "metadata": { "hide-output": false }, @@ -489,7 +489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b5ac5ac", + "id": "7565ea03", "metadata": { "hide-output": false }, @@ -511,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "e3a9c097", + "id": "c86c03c0", "metadata": {}, "source": [ "Let’s look at how price level $ p_0 $ in the stationary $ R_u $ equilibrium depends on the initial\n", @@ -527,7 +527,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5d23308", + "id": "e319f7eb", "metadata": { "hide-output": false }, @@ -539,7 +539,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1a6b7b5", + "id": "c93ac442", "metadata": { "hide-output": false }, @@ -555,7 +555,7 @@ }, { "cell_type": "markdown", - "id": "f859cca2", + "id": "46cca3b8", "metadata": {}, "source": [ "Now let’s write and implement code that lets us experiment with the time $ 0 $ open market operation described earlier." @@ -564,7 +564,7 @@ { "cell_type": "code", "execution_count": null, - "id": "12d954c6", + "id": "cf37667f", "metadata": { "hide-output": false }, @@ -619,7 +619,7 @@ { "cell_type": "code", "execution_count": null, - "id": "38eb995d", + "id": "e93c0711", "metadata": { "hide-output": false }, @@ -644,7 +644,7 @@ { "cell_type": "code", "execution_count": null, - "id": "973b3631", + "id": "be9f7a33", "metadata": { "hide-output": false }, @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "9e05ec49", + "id": "538b2bb9", "metadata": {}, "source": [ "Fig. 29.1 summarizes outcomes of two experiments that convey messages of Sargent and Wallace [[Sargent and Wallace, 1981](https://intro.quantecon.org/zreferences.html#id291)].\n", @@ -668,7 +668,7 @@ } ], "metadata": { - "date": 1722488543.903699, + "date": 1722502940.895821, "filename": "unpleasant.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/zreferences.ipynb b/_notebooks/zreferences.ipynb index 444e1115..0c229735 100644 --- a/_notebooks/zreferences.ipynb +++ b/_notebooks/zreferences.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "b4ec12b2", + "id": "05757b82", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "57fb8fbb", + "id": "aa151b08", "metadata": {}, "source": [ "# References\n", @@ -220,7 +220,7 @@ } ], "metadata": { - "date": 1722488543.9230225, + "date": 1722502940.9149845, "filename": "zreferences.md", "kernelspec": { "display_name": "Python", diff --git a/_pdf/quantecon-python-intro.pdf b/_pdf/quantecon-python-intro.pdf index 94945c3318ddc138b43a63fc0276054fd56dd3ee..beee97b84ed2e81796f44ed9c82b28ba4ce22fed 100644 GIT binary patch delta 74517 zcmZ6x1yEei6E(Vc2p-%Mg1fuB2X}XOwZNKaa(C`bPfz#h(`P6v3`Gv>2}KTuz(8Oja1eM10t69)1bG8NhP;KKKu{rQ5OfFz z1QUV5F!K-hKN8!Az~15hy+9uA_b9# z$UtNvau9il0z?s_1W|^3f~Y`LA!-nHhz3Lxq6N{0=su)e}QfiwB)V4(>GDvi|yp$X$x0b^Lz$=Mk_q zk011$yr*Cf28#sVqpE965%R2wxRoFeOJ|*s2X)UZr>!{z$aZ(kd)07#5J@GsGgec$ z+)k~T2hY{mehsW-;K8I*qzSH6eeRRGEG6NGg}F&(du8*pl zwLIT;TnI6VNcibre{M1P^B;tUeOs#gB}o-Vaxj)Kb@R>lv~T z2T8xN=vv9~OE;P;I2#2k9@lzV2ORKOzy#bM2@n-%B_Pj+!NO{h=#W)@tl3>NH&?G=$#B(XOLtn|l#oUx7^= zqoJQ|`bXJ|_AhM%_PhOmQ%p>zwanO%-M3((2=QRlYRQxqXN53Q%fev#crIPvY{B4z z;BI!~mS0P{_ 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zez*hqcmxA*H-=y!3J@s4P!wZ4M&L1w!WfhyU0y!}lQ02OFd1c-j+0o1*?0jJn1gaG z#8NE6VpQS{RN+t9k`0m(22|V3ZJ73>4x3(ETxC4+f(Eg(${QjKeULU=-4wvm@~Yo1O&}NLR$CE9ujH^XabkbSZqg@jcy^o^D`I zSCgmv(YGVrbKaC(B|l!u-Y7q1S4|iG{EsaE+m#`1YtPdA`7FQ6ZW@oi2eaf==brb& zNxHKjm-Z*Aa8oWF&7}Y4QcIF1Jey0$GpRk74kT%DMJ}Dnq;GTSqf8|I>zA*2Hc9{9 zoJ*}q`sr*gbtLKMewn{uQGQA8!3&x6W-c8}Qt60X>dd6<4)mh(UrzFsOuCdyZAn`8 jefCrS_T4SF{2z598aJQX-yi`X3pOw{HVP#rMNdWw(Pp_d diff --git a/_sources/ak2.ipynb b/_sources/ak2.ipynb index 971990f5..25b718d5 100644 --- a/_sources/ak2.ipynb +++ b/_sources/ak2.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "fd070eb7", + "id": "6253995a", "metadata": {}, "source": [ "# Transitions in an Overlapping Generations Model\n", @@ -13,7 +13,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3fc5f6ab", + "id": "318cf0c1", "metadata": { "tags": [ "hide-output" @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "63a248c6", + "id": "6eaf24d5", "metadata": {}, "source": [ "## Introduction\n", @@ -418,7 +418,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74610b9d", + "id": "92fd7c33", "metadata": {}, "outputs": [], "source": [ @@ -430,7 +430,7 @@ }, { "cell_type": "markdown", - "id": "253a6d9c", + "id": "46c9d16f", "metadata": {}, "source": [ "For parameters $\\alpha = 0.3$ and $\\beta = 0.5$, let's compute $\\hat{K}$:" @@ -439,7 +439,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f184f202", + "id": "4f4590f8", "metadata": {}, "outputs": [], "source": [ @@ -458,7 +458,7 @@ }, { "cell_type": "markdown", - "id": "4e3a11fe", + "id": "ff3084a4", "metadata": {}, "source": [ "Knowing $\\hat K$, we can calculate other equilibrium objects. \n", @@ -469,7 +469,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00a25411", + "id": "a29dc8f2", "metadata": {}, "outputs": [], "source": [ @@ -504,7 +504,7 @@ }, { "cell_type": "markdown", - "id": "c9403b57", + "id": "dab4fb5c", "metadata": {}, "source": [ "We can use these helper functions to obtain steady state values $\\hat{Y}$, $\\hat{r}$, and $\\hat{W}$ associated with steady state values $\\hat{K}$ and $\\hat{r}$." @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00cd3e09", + "id": "4e1f7560", "metadata": {}, "outputs": [], "source": [ @@ -523,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "167c9cc2", + "id": "3c43b8a8", "metadata": {}, "source": [ "Since steady state government debt $\\hat{D}$ is $0$, all taxes are used to pay for government expenditures" @@ -532,7 +532,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a9a8dc9d", + "id": "288dccbc", "metadata": {}, "outputs": [], "source": [ @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "8f2670df", + "id": "ebddf4cc", "metadata": {}, "source": [ "We use the optimal consumption plans to find steady state consumptions for young and old" @@ -551,7 +551,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4182d30", + "id": "b724b571", "metadata": {}, "outputs": [], "source": [ @@ -561,7 +561,7 @@ }, { "cell_type": "markdown", - "id": "e46ea14f", + "id": "5a535c3f", "metadata": {}, "source": [ "Let's store the steady state quantities and prices using an array called `init_ss`" @@ -570,7 +570,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b9e8d55", + "id": "02092c6d", "metadata": {}, "outputs": [], "source": [ @@ -582,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "1b2ffe1f", + "id": "2fc2779e", "metadata": {}, "source": [ "### Transitions\n", @@ -632,7 +632,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d13ff3c9", + "id": "3e5a9620", "metadata": {}, "outputs": [], "source": [ @@ -780,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "d6227883", + "id": "9664e712", "metadata": {}, "source": [ "We can create an instance `closed` for model parameters $\\{\\alpha, \\beta\\}$ and use it for various fiscal policy experiments." @@ -789,7 +789,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8304865", + "id": "d0d7849c", "metadata": {}, "outputs": [], "source": [ @@ -798,7 +798,7 @@ }, { "cell_type": "markdown", - "id": "95dc182f", + "id": "f1aefb78", "metadata": {}, "source": [ "(exp-tax-cut)=\n", @@ -831,7 +831,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92f25598", + "id": "ff0dde87", "metadata": {}, "outputs": [], "source": [ @@ -851,7 +851,7 @@ }, { "cell_type": "markdown", - "id": "cc6c5561", + "id": "39e4edcb", "metadata": {}, "source": [ "Let's use the `simulate` method of `closed` to compute dynamic transitions. \n", @@ -862,7 +862,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8a5ecb5", + "id": "9a162a45", "metadata": {}, "outputs": [], "source": [ @@ -874,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "7614fcb6", + "id": "d2e238f9", "metadata": {}, "source": [ "We can also experiment with a lower tax cut rate, such as $0.2$." @@ -883,7 +883,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3748fe71", + "id": "967ed5be", "metadata": {}, "outputs": [], "source": [ @@ -903,7 +903,7 @@ { "cell_type": "code", "execution_count": null, - "id": "18718fe9", + "id": "df344754", "metadata": {}, "outputs": [], "source": [ @@ -939,7 +939,7 @@ }, { "cell_type": "markdown", - "id": "4e2122c6", + "id": "60ec8ec6", "metadata": {}, "source": [ "The economy with lower tax cut rate at $t=0$ has the same transitional pattern, but is less distorted, and it converges to a new steady state with higher physical capital stock.\n", @@ -959,7 +959,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c8d30d7", + "id": "da15d318", "metadata": {}, "outputs": [], "source": [ @@ -975,7 +975,7 @@ }, { "cell_type": "markdown", - "id": "5f9ee6b6", + "id": "005c3184", "metadata": {}, "source": [ "As the government accumulates the asset and uses it in production, the rental rate on capital falls and private investment falls.\n", @@ -986,7 +986,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c27a3d44", + "id": "796d13d3", "metadata": {}, "outputs": [], "source": [ @@ -997,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "26f4f51f", + "id": "69bb2510", "metadata": {}, "source": [ "We want to know how this policy experiment affects individuals.\n", @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1283b2af", + "id": "4d7114ce", "metadata": {}, "outputs": [], "source": [ @@ -1044,7 +1044,7 @@ }, { "cell_type": "markdown", - "id": "a98a5ca4", + "id": "099112d2", "metadata": {}, "source": [ "The economy quickly converges to a new steady state with higher physical capital stock, lower interest rate, higher wage rate, and higher consumptions for both the young and the old.\n", @@ -1109,7 +1109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e846dac6", + "id": "d7b2a756", "metadata": {}, "outputs": [], "source": [ @@ -1121,7 +1121,7 @@ }, { "cell_type": "markdown", - "id": "7edbfead", + "id": "5d345e00", "metadata": {}, "source": [ "We use `Cy_val` to compute the lifetime value of an arbitrary consumption plan, $C_y$, given the intertemporal budget constraint.\n", @@ -1132,7 +1132,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c0c1058", + "id": "64872f23", "metadata": {}, "outputs": [], "source": [ @@ -1147,7 +1147,7 @@ }, { "cell_type": "markdown", - "id": "44f027a1", + "id": "09cf3e87", "metadata": {}, "source": [ "An optimal consumption plan $C_y^*$ can be found by maximizing `Cy_val`.\n", @@ -1158,7 +1158,7 @@ { "cell_type": "code", "execution_count": null, - "id": "639c8081", + "id": "c96bc926", "metadata": {}, "outputs": [], "source": [ @@ -1175,7 +1175,7 @@ }, { "cell_type": "markdown", - "id": "e89d4440", + "id": "8594fcc3", "metadata": {}, "source": [ "Let's define a Python class `AK2` that computes the transition paths with the fixed-point algorithm.\n", @@ -1186,7 +1186,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32f77182", + "id": "74726fb5", "metadata": {}, "outputs": [], "source": [ @@ -1360,7 +1360,7 @@ }, { "cell_type": "markdown", - "id": "1ef27d27", + "id": "31f3b0ed", "metadata": {}, "source": [ "We can initialize an instance of class `AK2` with model parameters $\\{\\alpha, \\beta\\}$ and then use it to conduct fiscal policy experiments." @@ -1369,7 +1369,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b1e34ef", + "id": "6e40bae1", "metadata": {}, "outputs": [], "source": [ @@ -1378,7 +1378,7 @@ }, { "cell_type": "markdown", - "id": "bffb9ec1", + "id": "670f4c54", "metadata": {}, "source": [ "We first examine that the \"guess and verify\" method leads to the same numerical results as we obtain with the closed form solution when lump sum taxes are muted" @@ -1387,7 +1387,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c8a6eecb", + "id": "f2ab054c", "metadata": {}, "outputs": [], "source": [ @@ -1407,7 +1407,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e01bb855", + "id": "ffa8abe4", "metadata": {}, "outputs": [], "source": [ @@ -1420,7 +1420,7 @@ { "cell_type": "code", "execution_count": null, - "id": "801d19b2", + "id": "9d7e2b8a", "metadata": {}, "outputs": [], "source": [ @@ -1429,7 +1429,7 @@ }, { "cell_type": "markdown", - "id": "071f6de6", + "id": "5c2179ee", "metadata": {}, "source": [ "Next, we activate lump sum taxes. \n", @@ -1440,7 +1440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1baa566f", + "id": "f6795501", "metadata": {}, "outputs": [], "source": [ @@ -1457,7 +1457,7 @@ }, { "cell_type": "markdown", - "id": "0bc9abb7", + "id": "8dc35ccf", "metadata": {}, "source": [ "Note how \"crowding out\" has been mitigated." @@ -1466,7 +1466,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f9437d3", + "id": "06954374", "metadata": {}, "outputs": [], "source": [ @@ -1502,7 +1502,7 @@ }, { "cell_type": "markdown", - "id": "dc52c098", + "id": "38ef0f8a", "metadata": {}, "source": [ "Comparing to {ref}`exp-tax-cut`, the government raises lump-sum taxes to finance the increasing debt interest payment, which is less distortionary comparing to raising the capital income tax rate.\n", @@ -1532,7 +1532,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66ac8730", + "id": "c910266e", "metadata": {}, "outputs": [], "source": [ @@ -1549,7 +1549,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8621ba9a", + "id": "9cdfac4a", "metadata": {}, "outputs": [], "source": [ @@ -1585,7 +1585,7 @@ }, { "cell_type": "markdown", - "id": "4de894db", + "id": "2214805c", "metadata": {}, "source": [ "An initial old person benefits especially when the social security system is launched because he receives a transfer but pays nothing for it.\n", diff --git a/_sources/ar1_processes.ipynb b/_sources/ar1_processes.ipynb index b32610cd..b0702bfb 100644 --- a/_sources/ar1_processes.ipynb +++ b/_sources/ar1_processes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5d6eb644", + "id": "aa8c0a8d", "metadata": {}, "source": [ "(ar1)=\n", @@ -40,7 +40,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c24e63fa", + "id": "cb449f46", "metadata": {}, "outputs": [], "source": [ @@ -51,7 +51,7 @@ }, { "cell_type": "markdown", - "id": "1df053b5", + "id": "337c358a", "metadata": {}, "source": [ "## The AR(1) model\n", @@ -168,7 +168,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b3d1370", + "id": "2c255c58", "metadata": {}, "outputs": [], "source": [ @@ -179,7 +179,7 @@ }, { "cell_type": "markdown", - "id": "f4cafb8a", + "id": "7f7a0e2a", "metadata": {}, "source": [ "Here's the sequence of distributions:" @@ -188,7 +188,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92161815", + "id": "b5a49ba6", "metadata": {}, "outputs": [], "source": [ @@ -213,7 +213,7 @@ }, { "cell_type": "markdown", - "id": "5e997bf3", + "id": "53f0bab7", "metadata": {}, "source": [ "## Stationarity and asymptotic stability\n", @@ -236,7 +236,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b889ff38", + "id": "c0d37b34", "metadata": {}, "outputs": [], "source": [ @@ -256,7 +256,7 @@ }, { "cell_type": "markdown", - "id": "7c12603a", + "id": "783715af", "metadata": {}, "source": [ "Moreover, the limit does not depend on the initial condition.\n", @@ -267,7 +267,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50e47ecf", + "id": "f7255ece", "metadata": {}, "outputs": [], "source": [ @@ -278,7 +278,7 @@ }, { "cell_type": "markdown", - "id": "fdb3c4df", + "id": "b6b02999", "metadata": {}, "source": [ "In fact it's easy to show that such convergence will occur, regardless of the initial condition, whenever $|a| < 1$.\n", @@ -314,7 +314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d374a49", + "id": "1d7aff2e", "metadata": {}, "outputs": [], "source": [ @@ -332,7 +332,7 @@ }, { "cell_type": "markdown", - "id": "b9d59699", + "id": "756e5b78", "metadata": {}, "source": [ "As claimed, the sequence $\\{ \\psi_t \\}$ converges to $\\psi^*$.\n", @@ -469,7 +469,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76463b74", + "id": "b59e4214", "metadata": {}, "outputs": [], "source": [ @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "6730f80a", + "id": "9a4a27cf", "metadata": {}, "source": [ "```{solution-end}\n", @@ -573,7 +573,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ed881f2", + "id": "51d1015e", "metadata": {}, "outputs": [], "source": [ @@ -603,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3df5d63", + "id": "6a00d002", "metadata": {}, "outputs": [], "source": [ @@ -622,7 +622,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf12e08f", + "id": "3c06b8a9", "metadata": {}, "outputs": [], "source": [ @@ -636,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "a7a6ee2d", + "id": "bd9f5b53", "metadata": {}, "source": [ "We see that the kernel density estimator is effective when the underlying\n", @@ -698,7 +698,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0684ca2b", + "id": "3b67498d", "metadata": {}, "outputs": [], "source": [ @@ -712,7 +712,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80649add", + "id": "b4abf107", "metadata": {}, "outputs": [], "source": [ @@ -723,7 +723,7 @@ { "cell_type": "code", "execution_count": null, - "id": "355adb42", + "id": "f5e7ac25", "metadata": {}, "outputs": [], "source": [ @@ -734,7 +734,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8ad6940", + "id": "07bbb4e5", "metadata": {}, "outputs": [], "source": [ @@ -745,7 +745,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5cc6dafa", + "id": "6336f837", "metadata": {}, "outputs": [], "source": [ @@ -767,7 +767,7 @@ }, { "cell_type": "markdown", - "id": "9d1600bc", + "id": "e17b42a0", "metadata": {}, "source": [ "The simulated distribution approximately coincides with the theoretical\n", diff --git a/_sources/business_cycle.ipynb b/_sources/business_cycle.ipynb index ff3b97ed..7ee5bae7 100644 --- a/_sources/business_cycle.ipynb +++ b/_sources/business_cycle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "621b9f06", + "id": "1564a96a", "metadata": {}, "source": [ "# Business Cycles\n", @@ -23,7 +23,7 @@ { "cell_type": "code", "execution_count": null, - "id": "45b4657f", + "id": "f5e3c9f6", "metadata": { "tags": [ "hide-output" @@ -37,7 +37,7 @@ }, { "cell_type": "markdown", - "id": "2c6e1c81", + "id": "4612e75c", "metadata": {}, "source": [ "We use the following imports" @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59df1864", + "id": "4800f99d", "metadata": {}, "outputs": [], "source": [ @@ -59,7 +59,7 @@ }, { "cell_type": "markdown", - "id": "859a7110", + "id": "3a14e377", "metadata": {}, "source": [ "Here's some minor code to help with colors in our plots." @@ -68,7 +68,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c83378e", + "id": "253cb266", "metadata": { "tags": [ "hide-input" @@ -84,7 +84,7 @@ }, { "cell_type": "markdown", - "id": "6b9d8693", + "id": "b5c248ac", "metadata": {}, "source": [ "## Data acquisition\n", @@ -100,7 +100,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef2e7c75", + "id": "c8ebb110", "metadata": {}, "outputs": [], "source": [ @@ -109,7 +109,7 @@ }, { "cell_type": "markdown", - "id": "1e2bbfb3", + "id": "b29cf7af", "metadata": {}, "source": [ "Now we use this series ID to obtain the data." @@ -118,7 +118,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e86fb9b", + "id": "a97d83c1", "metadata": {}, "outputs": [], "source": [ @@ -130,7 +130,7 @@ }, { "cell_type": "markdown", - "id": "47fc1e92", + "id": "66f5b6bc", "metadata": {}, "source": [ "We can look at the series' metadata to learn more about the series (click to expand)." @@ -139,7 +139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a050251", + "id": "9c6742a1", "metadata": { "tags": [ "hide-output" @@ -152,7 +152,7 @@ }, { "cell_type": "markdown", - "id": "99455a04", + "id": "251d47d8", "metadata": {}, "source": [ "(gdp_growth)=\n", @@ -166,7 +166,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b3e6193", + "id": "69233ba0", "metadata": {}, "outputs": [], "source": [ @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "4cbe42e1", + "id": "c4c664bb", "metadata": {}, "source": [ "Here's a first look at the data" @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3712df07", + "id": "0498634f", "metadata": {}, "outputs": [], "source": [ @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "e384b3a4", + "id": "ac1fb40e", "metadata": {}, "source": [ "We write a function to generate plots for individual countries taking into account the recessions." @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4e0fd40", + "id": "2207fafd", "metadata": { "tags": [ "hide-input" @@ -288,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "abc3b338", + "id": "9a386364", "metadata": {}, "source": [ "Let's start with the United States." @@ -297,7 +297,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5a59a42", + "id": "ae83122b", "metadata": { "mystnb": { "figure": { @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "ed5a29a7", + "id": "4f19edf0", "metadata": { "user_expressions": [] }, @@ -334,7 +334,7 @@ }, { "cell_type": "markdown", - "id": "3e368026", + "id": "df73f1d6", "metadata": {}, "source": [ "The United Kingdom (UK) has a similar pattern to the US, with a slow decline\n", @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "367c1802", + "id": "3ace55a2", "metadata": { "mystnb": { "figure": { @@ -368,7 +368,7 @@ }, { "cell_type": "markdown", - "id": "925610d3", + "id": "58ee44fb", "metadata": { "user_expressions": [] }, @@ -383,7 +383,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c166e105", + "id": "17a9c0e0", "metadata": { "mystnb": { "figure": { @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "d2b4c252", + "id": "c41f10f6", "metadata": {}, "source": [ "Now let's study Greece." @@ -414,7 +414,7 @@ { "cell_type": "code", "execution_count": null, - "id": "602d977f", + "id": "353787f9", "metadata": { "mystnb": { "figure": { @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "cc2c6818", + "id": "9fd35644", "metadata": {}, "source": [ "Greece experienced a very large drop in GDP growth around 2010-2011, during the peak\n", @@ -448,7 +448,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa0a6799", + "id": "55fe66bc", "metadata": { "mystnb": { "figure": { @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "493da549", + "id": "47eb939a", "metadata": {}, "source": [ "Notice that Argentina has experienced far more volatile cycles than\n", @@ -490,7 +490,7 @@ { "cell_type": "code", "execution_count": null, - "id": "34c5b1fd", + "id": "eb5bd53c", "metadata": { "tags": [ "hide-input" @@ -515,7 +515,7 @@ }, { "cell_type": "markdown", - "id": "311fef12", + "id": "4d6365e6", "metadata": {}, "source": [ "Let's plot the unemployment rate in the US from 1929 to 2022 with recessions\n", @@ -525,7 +525,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2e975dfe", + "id": "43acdb65", "metadata": { "mystnb": { "figure": { @@ -583,7 +583,7 @@ }, { "cell_type": "markdown", - "id": "a2ec80ab", + "id": "ddae706b", "metadata": {}, "source": [ "The plot shows that \n", @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1e37f4f", + "id": "6f62b571", "metadata": { "tags": [ "hide-input" @@ -698,7 +698,7 @@ }, { "cell_type": "markdown", - "id": "d1d9f16a", + "id": "6f2c2b0c", "metadata": {}, "source": [ "Here we compare the GDP growth rate of developed economies and developing economies." @@ -707,7 +707,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72d072e3", + "id": "dbcf4756", "metadata": { "tags": [ "hide-input" @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "23e8c61d", + "id": "57731736", "metadata": {}, "source": [ "We use the United Kingdom, United States, Germany, and Japan as examples of developed economies." @@ -734,7 +734,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80424a00", + "id": "662ee9b5", "metadata": { "mystnb": { "figure": { @@ -760,7 +760,7 @@ }, { "cell_type": "markdown", - "id": "168e5057", + "id": "513fa1ad", "metadata": {}, "source": [ "We choose Brazil, China, Argentina, and Mexico as representative developing economies." @@ -769,7 +769,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d2e4eaf", + "id": "56005195", "metadata": { "mystnb": { "figure": { @@ -794,7 +794,7 @@ }, { "cell_type": "markdown", - "id": "ad838390", + "id": "aa9c1fa4", "metadata": {}, "source": [ "The comparison of GDP growth rates above suggests that \n", @@ -816,7 +816,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f1abe2b", + "id": "2c433196", "metadata": { "mystnb": { "figure": { @@ -847,7 +847,7 @@ }, { "cell_type": "markdown", - "id": "2d421a84", + "id": "903e1163", "metadata": {}, "source": [ "We see that France, with its strong labor unions, typically experiences\n", @@ -882,7 +882,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6cbe1c88", + "id": "bc6c1a49", "metadata": { "mystnb": { "figure": { @@ -949,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "49d13df2", + "id": "bcccb366", "metadata": {}, "source": [ "We see that \n", @@ -978,7 +978,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3747aba", + "id": "69369f72", "metadata": { "mystnb": { "figure": { @@ -1017,7 +1017,7 @@ }, { "cell_type": "markdown", - "id": "a27677fa", + "id": "4058c3b6", "metadata": {}, "source": [ "We observe the delayed contraction in the plot across recessions.\n", @@ -1040,7 +1040,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a38722eb", + "id": "88523b19", "metadata": { "mystnb": { "figure": { @@ -1071,7 +1071,7 @@ }, { "cell_type": "markdown", - "id": "e8d79380", + "id": "a21eff16", "metadata": {}, "source": [ "Note that the credit rises during economic expansions\n", diff --git a/_sources/cagan_adaptive.ipynb b/_sources/cagan_adaptive.ipynb index 52a368ad..38d66d2f 100644 --- a/_sources/cagan_adaptive.ipynb +++ b/_sources/cagan_adaptive.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7f29fd27", + "id": "de997bee", "metadata": {}, "source": [ "# Monetarist Theory of Price Levels with Adaptive Expectations\n", @@ -283,7 +283,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17bcbdec", + "id": "4503e8af", "metadata": {}, "outputs": [], "source": [ @@ -295,7 +295,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a743c5a0", + "id": "233a9247", "metadata": {}, "outputs": [], "source": [ @@ -310,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "6f83ccf3", + "id": "1808256c", "metadata": { "user_expressions": [] }, @@ -321,7 +321,7 @@ { "cell_type": "code", "execution_count": null, - "id": "004d3662", + "id": "e8fff4a1", "metadata": {}, "outputs": [], "source": [ @@ -356,7 +356,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a13ff97", + "id": "438e8340", "metadata": {}, "outputs": [], "source": [ @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "8c4f4cef", + "id": "864d1d53", "metadata": { "user_expressions": [] }, @@ -420,7 +420,7 @@ { "cell_type": "code", "execution_count": null, - "id": "11a4f02c", + "id": "0e41e2c2", "metadata": {}, "outputs": [], "source": [ @@ -429,7 +429,7 @@ }, { "cell_type": "markdown", - "id": "97051ec5", + "id": "93d1f161", "metadata": {}, "source": [ "## Experiments\n", @@ -460,7 +460,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dab44713", + "id": "8f79a6ea", "metadata": {}, "outputs": [], "source": [ @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "0fc17bf3", + "id": "fe15a582", "metadata": {}, "source": [ "We invite the reader to compare outcomes with those under rational expectations studied in {doc}`cagan_ree`.\n", @@ -499,7 +499,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b48c668", + "id": "8c800592", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/cagan_ree.ipynb b/_sources/cagan_ree.ipynb index 0ea74727..a9af0340 100644 --- a/_sources/cagan_ree.ipynb +++ b/_sources/cagan_ree.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "4d040c80", + "id": "ed3f036d", "metadata": {}, "source": [ "# A Monetarist Theory of Price Levels\n", @@ -230,7 +230,7 @@ { "cell_type": "code", "execution_count": null, - "id": "333d0c74", + "id": "88e61da6", "metadata": {}, "outputs": [], "source": [ @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "c30dcf22", + "id": "9d15f09b", "metadata": {}, "source": [ "First, we store parameters in a `namedtuple`:" @@ -250,7 +250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f0c696ba", + "id": "eaddcb97", "metadata": {}, "outputs": [], "source": [ @@ -271,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "b7bf39d6", + "id": "ac0227ed", "metadata": {}, "source": [ "Now we can solve the model to compute $\\pi_t$, $m_t$ and $p_t$ for $t =1, \\ldots, T+1$ using the matrix equation above" @@ -280,7 +280,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e5c893ad", + "id": "fa1626c5", "metadata": {}, "outputs": [], "source": [ @@ -308,7 +308,7 @@ }, { "cell_type": "markdown", - "id": "26e56678", + "id": "3e43a921", "metadata": {}, "source": [ "### Some quantitative experiments\n", @@ -354,7 +354,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e019a30a", + "id": "ed72809f", "metadata": {}, "outputs": [], "source": [ @@ -373,7 +373,7 @@ }, { "cell_type": "markdown", - "id": "e2eb8c1b", + "id": "b2caf1b8", "metadata": {}, "source": [ "Now we use the following function to plot the result" @@ -382,7 +382,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08062c38", + "id": "997c7f2d", "metadata": {}, "outputs": [], "source": [ @@ -402,7 +402,7 @@ }, { "cell_type": "markdown", - "id": "214b5944", + "id": "a0c10160", "metadata": {}, "source": [ "The plot of the money growth rate $\\mu_t$ in the top level panel portrays\n", @@ -543,7 +543,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88509fda", + "id": "041f6010", "metadata": {}, "outputs": [], "source": [ @@ -586,7 +586,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1693a90e", + "id": "b35505dd", "metadata": { "tags": [ "hide-input" @@ -632,7 +632,7 @@ }, { "cell_type": "markdown", - "id": "ba82a885", + "id": "94256cff", "metadata": {}, "source": [ "We invite you to compare these graphs with corresponding ones for the foreseen stabilization analyzed in experiment 1 above.\n", @@ -660,7 +660,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8feea28c", + "id": "c6fd1eea", "metadata": { "tags": [ "hide-input" @@ -690,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "8952e1bb", + "id": "d063712d", "metadata": {}, "source": [ "It is instructive to compare the preceding graphs with graphs of log price levels and inflation rates for data from four big inflations described in\n", @@ -725,7 +725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "397e4477", + "id": "091e5e4b", "metadata": {}, "outputs": [], "source": [ @@ -746,7 +746,7 @@ }, { "cell_type": "markdown", - "id": "d813132a", + "id": "2ca9cfad", "metadata": {}, "source": [ "## Sequel\n", diff --git a/_sources/cobweb.ipynb b/_sources/cobweb.ipynb index 5c3b9f7e..aa1d18f5 100644 --- a/_sources/cobweb.ipynb +++ b/_sources/cobweb.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "13f020fb", + "id": "b5a86746", "metadata": {}, "source": [ "(cobweb)=\n", @@ -55,7 +55,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba8db376", + "id": "4183d54b", "metadata": {}, "outputs": [], "source": [ @@ -65,7 +65,7 @@ }, { "cell_type": "markdown", - "id": "89f57385", + "id": "2934d32f", "metadata": {}, "source": [ "## History\n", @@ -82,7 +82,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a623d299", + "id": "1870850e", "metadata": {}, "outputs": [], "source": [ @@ -101,7 +101,7 @@ }, { "cell_type": "markdown", - "id": "bea0b068", + "id": "ea2b5184", "metadata": {}, "source": [ "## The model\n", @@ -136,7 +136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "204003b6", + "id": "0c73af95", "metadata": {}, "outputs": [], "source": [ @@ -162,7 +162,7 @@ }, { "cell_type": "markdown", - "id": "3c6318a1", + "id": "e786b5a0", "metadata": {}, "source": [ "Now let's plot." @@ -171,7 +171,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e3181f2", + "id": "52be595e", "metadata": {}, "outputs": [], "source": [ @@ -190,7 +190,7 @@ }, { "cell_type": "markdown", - "id": "12a77934", + "id": "646c0b2f", "metadata": {}, "source": [ "Market equilibrium requires that supply equals demand, or\n", @@ -268,7 +268,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a993c13", + "id": "e23a725c", "metadata": {}, "outputs": [], "source": [ @@ -284,7 +284,7 @@ }, { "cell_type": "markdown", - "id": "2761f079", + "id": "dd4b49a1", "metadata": {}, "source": [ "Let's try to understand how prices will evolve using a 45-degree diagram, which is a tool for studying one-dimensional dynamics.\n", @@ -295,7 +295,7 @@ { "cell_type": "code", "execution_count": null, - "id": "873ed943", + "id": "a0aded00", "metadata": { "tags": [ "hide-input" @@ -377,7 +377,7 @@ }, { "cell_type": "markdown", - "id": "f49341c5", + "id": "deb6c759", "metadata": {}, "source": [ "Now we can set up a market and plot the 45-degree diagram." @@ -386,7 +386,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce7707a1", + "id": "5f77252e", "metadata": {}, "outputs": [], "source": [ @@ -396,7 +396,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca57d233", + "id": "acbe3115", "metadata": {}, "outputs": [], "source": [ @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "a2d49ba3", + "id": "8f43bcc4", "metadata": {}, "source": [ "The plot shows the function $g$ defined in {eq}`def_g` and the 45-degree line.\n", @@ -434,7 +434,7 @@ { "cell_type": "code", "execution_count": null, - "id": "242c0dd4", + "id": "43eb751f", "metadata": {}, "outputs": [], "source": [ @@ -468,7 +468,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6859f681", + "id": "113029d8", "metadata": {}, "outputs": [], "source": [ @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "93fb584e", + "id": "9bbfaad7", "metadata": {}, "source": [ "We see that a cycle has formed and the cycle is persistent.\n", @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7aea4d1c", + "id": "0f73bc3e", "metadata": {}, "outputs": [], "source": [ @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "0f145e70", + "id": "943a47d0", "metadata": {}, "source": [ "## Adaptive expectations\n", @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54c30bd4", + "id": "baaa331a", "metadata": {}, "outputs": [], "source": [ @@ -562,7 +562,7 @@ }, { "cell_type": "markdown", - "id": "64d85880", + "id": "a3ca43d1", "metadata": {}, "source": [ "The function below plots price dynamics under adaptive expectations for different values of $\\alpha$." @@ -571,7 +571,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8d37ccc", + "id": "b4550dba", "metadata": {}, "outputs": [], "source": [ @@ -594,7 +594,7 @@ }, { "cell_type": "markdown", - "id": "910f5159", + "id": "4d3e1edb", "metadata": {}, "source": [ "Let's call the function with prices starting at $p_0 = 5$." @@ -603,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e98ab149", + "id": "1219ef1a", "metadata": {}, "outputs": [], "source": [ @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "397eed63", + "id": "d39e46b0", "metadata": {}, "source": [ "Note that if $\\alpha=1$, then adaptive expectations are just naive expectation.\n", @@ -642,7 +642,7 @@ { "cell_type": "code", "execution_count": null, - "id": "13835227", + "id": "0a52ecd1", "metadata": {}, "outputs": [], "source": [ @@ -678,7 +678,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c159831", + "id": "d9401bcd", "metadata": {}, "outputs": [], "source": [ @@ -688,7 +688,7 @@ }, { "cell_type": "markdown", - "id": "3d0e61a6", + "id": "af9b98dc", "metadata": {}, "source": [ "```{solution-end}\n", @@ -724,7 +724,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b1f9cf0", + "id": "058a72ce", "metadata": {}, "outputs": [], "source": [ @@ -739,7 +739,7 @@ { "cell_type": "code", "execution_count": null, - "id": "556d4be5", + "id": "4b30af16", "metadata": {}, "outputs": [], "source": [ @@ -771,7 +771,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ab2ff45", + "id": "e6c2e52b", "metadata": {}, "outputs": [], "source": [ @@ -785,7 +785,7 @@ }, { "cell_type": "markdown", - "id": "83169b44", + "id": "b1f74515", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/commod_price.ipynb b/_sources/commod_price.ipynb index 59d13a81..0893a60e 100644 --- a/_sources/commod_price.ipynb +++ b/_sources/commod_price.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "bb3bb574", + "id": "7e20079c", "metadata": {}, "source": [ "# Commodity Prices\n", @@ -33,7 +33,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3d3722d", + "id": "ee4ca13e", "metadata": { "tags": [ "hide-output" @@ -46,7 +46,7 @@ }, { "cell_type": "markdown", - "id": "ed4c7811", + "id": "dcc67630", "metadata": {}, "source": [ "We will use the following imports" @@ -55,7 +55,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4f17b59", + "id": "334d67ff", "metadata": {}, "outputs": [], "source": [ @@ -69,7 +69,7 @@ }, { "cell_type": "markdown", - "id": "061edf15", + "id": "8d97fbaf", "metadata": {}, "source": [ "## Data\n", @@ -80,7 +80,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21f45960", + "id": "b842e028", "metadata": { "tags": [ "hide-input", @@ -95,7 +95,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54e21531", + "id": "1340efa2", "metadata": { "tags": [ "hide-input" @@ -114,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "98845eb9", + "id": "efcba5dd", "metadata": {}, "source": [ "The figure shows surprisingly large movements in the price of cotton.\n", @@ -394,7 +394,7 @@ { "cell_type": "code", "execution_count": null, - "id": "517f7d33", + "id": "f7d376dc", "metadata": {}, "outputs": [], "source": [ @@ -450,7 +450,7 @@ }, { "cell_type": "markdown", - "id": "074f2bc9", + "id": "308c5e89", "metadata": {}, "source": [ "The figure above shows the inverse demand curve $P$, which is also $p_0$, as\n", @@ -463,7 +463,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e24146b", + "id": "09aad5a9", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/complex_and_trig.ipynb b/_sources/complex_and_trig.ipynb index 06107e80..e3fb67ef 100644 --- a/_sources/complex_and_trig.ipynb +++ b/_sources/complex_and_trig.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "3439bc4b", + "id": "f1a95aae", "metadata": {}, "source": [ "(complex_and_trig)=\n", @@ -93,7 +93,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3635a7e", + "id": "f3441fc8", "metadata": {}, "outputs": [], "source": [ @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "e4f14351", + "id": "464b7981", "metadata": {}, "source": [ "### An Example\n", @@ -125,7 +125,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51e1460f", + "id": "48a20b57", "metadata": {}, "outputs": [], "source": [ @@ -170,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "728be51a", + "id": "25928b0e", "metadata": {}, "source": [ "## De Moivre's Theorem\n", @@ -312,7 +312,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3042cbda", + "id": "738366ee", "metadata": {}, "outputs": [], "source": [ @@ -341,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "08036dba", + "id": "4e8370cf", "metadata": {}, "source": [ "Using the code above, we compute that\n", @@ -354,7 +354,7 @@ { "cell_type": "code", "execution_count": null, - "id": "407382c6", + "id": "c0336fc3", "metadata": {}, "outputs": [], "source": [ @@ -392,7 +392,7 @@ }, { "cell_type": "markdown", - "id": "74fc2594", + "id": "ad990383", "metadata": {}, "source": [ "### Trigonometric Identities\n", @@ -451,7 +451,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85886190", + "id": "9024c033", "metadata": {}, "outputs": [], "source": [ @@ -467,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "1300daf4", + "id": "b3c46030", "metadata": {}, "source": [ "### Trigonometric Integrals\n", @@ -524,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "39b2dd0d", + "id": "4e2a4888", "metadata": {}, "outputs": [], "source": [ @@ -539,7 +539,7 @@ { "cell_type": "code", "execution_count": null, - "id": "daf78789", + "id": "a5ba4787", "metadata": {}, "outputs": [], "source": [ @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "d3e7a0ac", + "id": "6c81b39e", "metadata": {}, "source": [ "### Exercises\n", @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06f65a2c", + "id": "3cf59a68", "metadata": {}, "outputs": [], "source": [ @@ -590,7 +590,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a94f288f", + "id": "fc4c666c", "metadata": {}, "outputs": [], "source": [ @@ -603,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9491cee6", + "id": "91b5f2d5", "metadata": {}, "outputs": [], "source": [ @@ -615,7 +615,7 @@ }, { "cell_type": "markdown", - "id": "7d5fab1f", + "id": "9439059f", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/cons_smooth.ipynb b/_sources/cons_smooth.ipynb index 3a1290ce..315b2256 100644 --- a/_sources/cons_smooth.ipynb +++ b/_sources/cons_smooth.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8a723049", + "id": "e7fc2880", "metadata": {}, "source": [ "# Consumption Smoothing\n", @@ -38,7 +38,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd4839b5", + "id": "03ed3d20", "metadata": {}, "outputs": [], "source": [ @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "c8979026", + "id": "bd6b5eb4", "metadata": {}, "source": [ "The model describes a consumer who lives from time $t=0, 1, \\ldots, T$, receives a stream $\\{y_t\\}_{t=0}^T$ of non-financial income and chooses a consumption stream $\\{c_t\\}_{t=0}^T$.\n", @@ -144,7 +144,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51f676f5", + "id": "510a5fbc", "metadata": {}, "outputs": [], "source": [ @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "0e49cd05", + "id": "06ebc751", "metadata": {}, "source": [ "## Friedman-Hall consumption-smoothing model\n", @@ -280,7 +280,7 @@ { "cell_type": "code", "execution_count": null, - "id": "965f5ae9", + "id": "8059b774", "metadata": {}, "outputs": [], "source": [ @@ -307,7 +307,7 @@ }, { "cell_type": "markdown", - "id": "450dccfd", + "id": "e969df08", "metadata": {}, "source": [ "We use an example where the consumer inherits $a_0<0$.\n", @@ -322,7 +322,7 @@ { "cell_type": "code", "execution_count": null, - "id": "837fff75", + "id": "ed7842fc", "metadata": {}, "outputs": [], "source": [ @@ -341,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "52fa210c", + "id": "a818b535", "metadata": {}, "source": [ "The graphs below show paths of non-financial income, consumption, and financial assets." @@ -350,7 +350,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c4c5c73", + "id": "d8426132", "metadata": {}, "outputs": [], "source": [ @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "8ba062fb", + "id": "5febbc16", "metadata": {}, "source": [ "Note that $a_{T+1} = 0$, as anticipated.\n", @@ -381,7 +381,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09b98d19", + "id": "6b7f75fc", "metadata": {}, "outputs": [], "source": [ @@ -396,7 +396,7 @@ }, { "cell_type": "markdown", - "id": "17bd692f", + "id": "4fdccce2", "metadata": {}, "source": [ "### Experiments\n", @@ -411,7 +411,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d57e3450", + "id": "b7c9f5e9", "metadata": {}, "outputs": [], "source": [ @@ -440,7 +440,7 @@ }, { "cell_type": "markdown", - "id": "b7f5bd74", + "id": "073216b5", "metadata": {}, "source": [ "In the experiments below, please study how consumption and financial asset sequences vary accross different sequences for non-financial income.\n", @@ -455,7 +455,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4e80ddc", + "id": "e47ea979", "metadata": {}, "outputs": [], "source": [ @@ -468,7 +468,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8fbf0c9c", + "id": "59ecfe0f", "metadata": {}, "outputs": [], "source": [ @@ -480,7 +480,7 @@ }, { "cell_type": "markdown", - "id": "edc61c49", + "id": "f056ad01", "metadata": {}, "source": [ "#### Experiment 2: permanent wage gain/loss\n", @@ -493,7 +493,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f05d3fd8", + "id": "3e952d53", "metadata": {}, "outputs": [], "source": [ @@ -507,7 +507,7 @@ { "cell_type": "code", "execution_count": null, - "id": "536be6a7", + "id": "0c9cb83c", "metadata": {}, "outputs": [], "source": [ @@ -520,7 +520,7 @@ }, { "cell_type": "markdown", - "id": "b10beaf0", + "id": "84752d7c", "metadata": {}, "source": [ "#### Experiment 3: a late starter\n", @@ -531,7 +531,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b049a9fe", + "id": "27942faa", "metadata": {}, "outputs": [], "source": [ @@ -544,7 +544,7 @@ }, { "cell_type": "markdown", - "id": "2ea8bbe6", + "id": "2b2deeda", "metadata": {}, "source": [ "#### Experiment 4: geometric earner\n", @@ -557,7 +557,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a90c5eba", + "id": "d05bb9d0", "metadata": {}, "outputs": [], "source": [ @@ -576,7 +576,7 @@ }, { "cell_type": "markdown", - "id": "0463edfc", + "id": "ec66748d", "metadata": {}, "source": [ "Now we show the behavior when $\\lambda = 0.95$" @@ -585,7 +585,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8e773ed0", + "id": "6a18c46b", "metadata": {}, "outputs": [], "source": [ @@ -600,7 +600,7 @@ }, { "cell_type": "markdown", - "id": "e21ee3e8", + "id": "816d1bae", "metadata": {}, "source": [ "What happens when $\\lambda$ is negative" @@ -609,7 +609,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e47476d", + "id": "a1c85712", "metadata": {}, "outputs": [], "source": [ @@ -624,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "899fa00e", + "id": "006800af", "metadata": {}, "source": [ "### Feasible consumption variations\n", @@ -700,7 +700,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de0f99d2", + "id": "90a77af6", "metadata": {}, "outputs": [], "source": [ @@ -721,7 +721,7 @@ }, { "cell_type": "markdown", - "id": "85eb4fb3", + "id": "c0cd2c39", "metadata": {}, "source": [ "We visualize variations for $\\xi_1 \\in \\{.01, .05\\}$ and $\\phi \\in \\{.95, 1.02\\}$" @@ -730,7 +730,7 @@ { "cell_type": "code", "execution_count": null, - "id": "785fb80a", + "id": "10337e7c", "metadata": {}, "outputs": [], "source": [ @@ -769,7 +769,7 @@ }, { "cell_type": "markdown", - "id": "eea5fff4", + "id": "709b5adf", "metadata": {}, "source": [ "We can even use the Python `np.gradient` command to compute derivatives of welfare with respect to our two parameters. \n", @@ -782,7 +782,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a162fa2", + "id": "1edc3c0e", "metadata": {}, "outputs": [], "source": [ @@ -804,7 +804,7 @@ }, { "cell_type": "markdown", - "id": "60ac227e", + "id": "6e849a6a", "metadata": {}, "source": [ "Then we can visualize the relationship between welfare and $\\xi_1$ and compute its derivatives" @@ -813,7 +813,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a9edfb96", + "id": "45e071e9", "metadata": {}, "outputs": [], "source": [ @@ -834,7 +834,7 @@ }, { "cell_type": "markdown", - "id": "3c7d4ff1", + "id": "a45aae01", "metadata": {}, "source": [ "The same can be done on $\\phi$" @@ -843,7 +843,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7e7a7a7", + "id": "00d67000", "metadata": {}, "outputs": [], "source": [ @@ -864,7 +864,7 @@ }, { "cell_type": "markdown", - "id": "6dc1c216", + "id": "c66a005f", "metadata": {}, "source": [ "## Wrapping up the consumption-smoothing model\n", diff --git a/_sources/eigen_I.ipynb b/_sources/eigen_I.ipynb index 4fed010c..8139d889 100644 --- a/_sources/eigen_I.ipynb +++ b/_sources/eigen_I.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d8c7576c", + "id": "e7368b53", "metadata": { "user_expressions": [] }, @@ -36,7 +36,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e04c2da3", + "id": "c6dd67a0", "metadata": {}, "outputs": [], "source": [ @@ -50,7 +50,7 @@ }, { "cell_type": "markdown", - "id": "f98c724c", + "id": "1041c4c4", "metadata": {}, "source": [ "(matrices_as_transformation)=\n", @@ -129,7 +129,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ccb6894", + "id": "bce0ba39", "metadata": {}, "outputs": [], "source": [ @@ -140,7 +140,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d90ad95", + "id": "6fe10e30", "metadata": {}, "outputs": [], "source": [ @@ -185,7 +185,7 @@ }, { "cell_type": "markdown", - "id": "4962592d", + "id": "2b7df47e", "metadata": { "user_expressions": [] }, @@ -217,7 +217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9b97515", + "id": "11b2f42b", "metadata": { "tags": [ "hide-input" @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "4e7e5e34", + "id": "0d10c77d", "metadata": { "user_expressions": [] }, @@ -340,7 +340,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60c81c13", + "id": "58d53f84", "metadata": {}, "outputs": [], "source": [ @@ -352,7 +352,7 @@ }, { "cell_type": "markdown", - "id": "c3baef4b", + "id": "3a02a2c4", "metadata": { "user_expressions": [] }, @@ -375,7 +375,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afa90fb3", + "id": "338ce1ab", "metadata": {}, "outputs": [], "source": [ @@ -387,7 +387,7 @@ }, { "cell_type": "markdown", - "id": "dc5b41c7", + "id": "998eb06b", "metadata": { "user_expressions": [] }, @@ -410,7 +410,7 @@ { "cell_type": "code", "execution_count": null, - "id": "254b0643", + "id": "1e8162f1", "metadata": {}, "outputs": [], "source": [ @@ -422,7 +422,7 @@ }, { "cell_type": "markdown", - "id": "12a7e10c", + "id": "41bda0af", "metadata": { "user_expressions": [] }, @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4ad5800a", + "id": "61242412", "metadata": {}, "outputs": [], "source": [ @@ -453,7 +453,7 @@ }, { "cell_type": "markdown", - "id": "9e4cc06d", + "id": "9c39149f", "metadata": { "user_expressions": [] }, @@ -604,7 +604,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0731ee5", + "id": "d60e7fd3", "metadata": { "tags": [ "hide-input" @@ -651,7 +651,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7dc7702", + "id": "8e124ce3", "metadata": {}, "outputs": [], "source": [ @@ -663,7 +663,7 @@ }, { "cell_type": "markdown", - "id": "cac71f65", + "id": "7b4f8974", "metadata": { "user_expressions": [] }, @@ -674,7 +674,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca923958", + "id": "c3e64682", "metadata": {}, "outputs": [], "source": [ @@ -683,7 +683,7 @@ }, { "cell_type": "markdown", - "id": "39a24e37", + "id": "17fb1bff", "metadata": { "user_expressions": [] }, @@ -694,7 +694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4cfb2ce5", + "id": "596a658d", "metadata": {}, "outputs": [], "source": [ @@ -703,7 +703,7 @@ }, { "cell_type": "markdown", - "id": "f833be2e", + "id": "80c8e4e7", "metadata": { "user_expressions": [] }, @@ -733,7 +733,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21142bab", + "id": "c9365f7b", "metadata": {}, "outputs": [], "source": [ @@ -784,7 +784,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59b8944c", + "id": "e01eff88", "metadata": {}, "outputs": [], "source": [ @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "f9568f32", + "id": "e9b0ab3e", "metadata": { "user_expressions": [] }, @@ -812,7 +812,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0cd8ba9d", + "id": "f3a03b7c", "metadata": {}, "outputs": [], "source": [ @@ -827,7 +827,7 @@ }, { "cell_type": "markdown", - "id": "82958abe", + "id": "b2629d0a", "metadata": { "user_expressions": [] }, @@ -841,7 +841,7 @@ { "cell_type": "code", "execution_count": null, - "id": "482e8cc0", + "id": "334990c4", "metadata": {}, "outputs": [], "source": [ @@ -856,7 +856,7 @@ }, { "cell_type": "markdown", - "id": "0890562f", + "id": "97839023", "metadata": { "user_expressions": [] }, @@ -903,7 +903,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e12c13f5", + "id": "3e8538fa", "metadata": { "tags": [ "output_scroll" @@ -959,7 +959,7 @@ }, { "cell_type": "markdown", - "id": "c51a121f", + "id": "ed02593d", "metadata": { "user_expressions": [] }, @@ -1017,7 +1017,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b893f3d", + "id": "53307a10", "metadata": {}, "outputs": [], "source": [ @@ -1034,7 +1034,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d238bff", + "id": "9054de3e", "metadata": {}, "outputs": [], "source": [ @@ -1043,7 +1043,7 @@ }, { "cell_type": "markdown", - "id": "8551263d", + "id": "bbb8d28a", "metadata": { "user_expressions": [] }, @@ -1133,7 +1133,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1058bbc8", + "id": "6909f261", "metadata": {}, "outputs": [], "source": [ @@ -1148,7 +1148,7 @@ }, { "cell_type": "markdown", - "id": "764af272", + "id": "f4334912", "metadata": {}, "source": [ "The spectral radius $r(A)$ obtained is less than 1.\n", @@ -1159,7 +1159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fca8c590", + "id": "957d0092", "metadata": {}, "outputs": [], "source": [ @@ -1170,7 +1170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c67ed001", + "id": "bee051f3", "metadata": {}, "outputs": [], "source": [ @@ -1180,7 +1180,7 @@ { "cell_type": "code", "execution_count": null, - "id": "187209d7", + "id": "dc69dd31", "metadata": {}, "outputs": [], "source": [ @@ -1193,7 +1193,7 @@ }, { "cell_type": "markdown", - "id": "5cf0d207", + "id": "c18cb710", "metadata": {}, "source": [ "Let's check equality between the sum and the inverse methods." @@ -1202,7 +1202,7 @@ { "cell_type": "code", "execution_count": null, - "id": "681a28b5", + "id": "0b4c6051", "metadata": {}, "outputs": [], "source": [ @@ -1211,7 +1211,7 @@ }, { "cell_type": "markdown", - "id": "2832669d", + "id": "673bc26e", "metadata": {}, "source": [ "Although we truncate the infinite sum at $k = 50$, both methods give us the same\n", @@ -1250,7 +1250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aeb9157b", + "id": "e266e204", "metadata": { "mystnb": { "figure": { @@ -1303,7 +1303,7 @@ }, { "cell_type": "markdown", - "id": "5512eb68", + "id": "b982bef6", "metadata": { "user_expressions": [] }, @@ -1314,7 +1314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0caa2ee", + "id": "58f288c4", "metadata": { "mystnb": { "figure": { @@ -1357,7 +1357,7 @@ }, { "cell_type": "markdown", - "id": "06f65ba2", + "id": "a3d59a72", "metadata": { "user_expressions": [] }, @@ -1384,7 +1384,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9bd325ea", + "id": "3f805371", "metadata": {}, "outputs": [], "source": [ @@ -1404,7 +1404,7 @@ }, { "cell_type": "markdown", - "id": "b6d2a607", + "id": "a10a81df", "metadata": { "user_expressions": [] }, @@ -1419,7 +1419,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21585e9e", + "id": "dae43eac", "metadata": { "mystnb": { "figure": { @@ -1468,7 +1468,7 @@ }, { "cell_type": "markdown", - "id": "a7ec3036", + "id": "63fc27e9", "metadata": { "user_expressions": [] }, @@ -1504,7 +1504,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9eab66f8", + "id": "a6cd5837", "metadata": { "mystnb": { "figure": { @@ -1578,7 +1578,7 @@ }, { "cell_type": "markdown", - "id": "b4ac8a1f", + "id": "00f34d7c", "metadata": { "user_expressions": [] }, @@ -1593,7 +1593,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a07c633f", + "id": "f9ac8b22", "metadata": { "mystnb": { "figure": { @@ -1662,7 +1662,7 @@ }, { "cell_type": "markdown", - "id": "76b5c29d", + "id": "1203c2a4", "metadata": { "user_expressions": [] }, diff --git a/_sources/eigen_II.ipynb b/_sources/eigen_II.ipynb index 3b70dc45..f1ae3d0d 100644 --- a/_sources/eigen_II.ipynb +++ b/_sources/eigen_II.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "edafb566", + "id": "c0c7949f", "metadata": {}, "source": [ "# The Perron-Frobenius Theorem\n", @@ -16,7 +16,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16754135", + "id": "7599e939", "metadata": { "tags": [ "hide-output" @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "17214a32", + "id": "373c8819", "metadata": {}, "source": [ "In this lecture we will begin with the foundational concepts in spectral theory.\n", @@ -42,7 +42,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ee76ad81", + "id": "88e538a3", "metadata": {}, "outputs": [], "source": [ @@ -54,7 +54,7 @@ }, { "cell_type": "markdown", - "id": "cf178a30", + "id": "d0c8607b", "metadata": {}, "source": [ "## Nonnegative matrices\n", @@ -141,7 +141,7 @@ { "cell_type": "code", "execution_count": null, - "id": "67228eb0", + "id": "43635e5f", "metadata": {}, "outputs": [], "source": [ @@ -164,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "0ea59741", + "id": "1b31cb9d", "metadata": {}, "source": [ "We can also use `scipy.linalg.eig` with argument `left=True` to find left eigenvectors directly" @@ -173,7 +173,7 @@ { "cell_type": "code", "execution_count": null, - "id": "492d89b9", + "id": "4a88aa93", "metadata": {}, "outputs": [], "source": [ @@ -186,7 +186,7 @@ }, { "cell_type": "markdown", - "id": "767cad18", + "id": "0303eb05", "metadata": {}, "source": [ "The eigenvalues are the same while the eigenvectors themselves are different.\n", @@ -240,7 +240,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6cc9000", + "id": "042c0e11", "metadata": {}, "outputs": [], "source": [ @@ -251,7 +251,7 @@ }, { "cell_type": "markdown", - "id": "f1dfbc67", + "id": "32098de4", "metadata": {}, "source": [ "We can compute the dominant eigenvalue and the corresponding eigenvector" @@ -260,7 +260,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea719f06", + "id": "a13630ef", "metadata": {}, "outputs": [], "source": [ @@ -269,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "2bcf4f7d", + "id": "9d7e1f10", "metadata": {}, "source": [ "Now we can see the claims of the Perron-Frobenius Theorem holds for the irreducible matrix $A$:\n", @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6467feb3", + "id": "216dbda3", "metadata": {}, "outputs": [], "source": [ @@ -348,7 +348,7 @@ }, { "cell_type": "markdown", - "id": "be98c696", + "id": "2f51cf25", "metadata": {}, "source": [ "We compute the dominant eigenvalue and the corresponding eigenvector" @@ -357,7 +357,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be6ef779", + "id": "99c456d5", "metadata": {}, "outputs": [], "source": [ @@ -366,7 +366,7 @@ }, { "cell_type": "markdown", - "id": "2ffb1367", + "id": "60c2b59d", "metadata": {}, "source": [ "Now let's give some examples to see if the claims of the Perron-Frobenius Theorem hold for the primitive matrix $B$:\n", @@ -384,7 +384,7 @@ { "cell_type": "code", "execution_count": null, - "id": "05608dda", + "id": "b30d58f5", "metadata": {}, "outputs": [], "source": [ @@ -454,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "58d40371", + "id": "71283f23", "metadata": {}, "source": [ "The convergence is not observed in cases of non-primitive matrices.\n", @@ -465,7 +465,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98c6f5b6", + "id": "045abf6c", "metadata": {}, "outputs": [], "source": [ @@ -484,7 +484,7 @@ }, { "cell_type": "markdown", - "id": "2abb2ca2", + "id": "2b82078d", "metadata": {}, "source": [ "The result shows that the matrix is not primitive as it is not everywhere positive.\n", @@ -506,7 +506,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f769652", + "id": "22cb3b6d", "metadata": {}, "outputs": [], "source": [ @@ -520,7 +520,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65ea5335", + "id": "586987ed", "metadata": {}, "outputs": [], "source": [ @@ -532,7 +532,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92153e16", + "id": "5951d4e0", "metadata": {}, "outputs": [], "source": [ @@ -546,7 +546,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6cc6fdc7", + "id": "d1f4eca0", "metadata": {}, "outputs": [], "source": [ @@ -557,7 +557,7 @@ }, { "cell_type": "markdown", - "id": "8cd200ca", + "id": "3831240f", "metadata": {}, "source": [ "We can also verify other properties hinted by Perron-Frobenius in these stochastic matrices." @@ -565,7 +565,7 @@ }, { "cell_type": "markdown", - "id": "a406d9dd", + "id": "4e3155a5", "metadata": {}, "source": [ "Another example is the relationship between convergence gap and convergence rate.\n", @@ -686,7 +686,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b4bb235", + "id": "d8f2ddab", "metadata": {}, "outputs": [], "source": [ @@ -702,7 +702,7 @@ }, { "cell_type": "markdown", - "id": "f1ee5409", + "id": "b288fb26", "metadata": {}, "source": [ "Since we have $r(A) < 1$ we can thus find the solution using the Neumann Series Lemma." @@ -711,7 +711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce7323c7", + "id": "09d220df", "metadata": {}, "outputs": [], "source": [ @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "37a8db65", + "id": "b3009cc0", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/equalizing_difference.ipynb b/_sources/equalizing_difference.ipynb index e2cf85ea..a42e5e95 100644 --- a/_sources/equalizing_difference.ipynb +++ b/_sources/equalizing_difference.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "569056e4", + "id": "b7c422c6", "metadata": {}, "source": [ "# Equalizing Difference Model\n", @@ -45,7 +45,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49535717", + "id": "ddcdffc3", "metadata": {}, "outputs": [], "source": [ @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "1d418d95", + "id": "ee3fe662", "metadata": {}, "source": [ "## The indifference condition\n", @@ -187,7 +187,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6a9945ea", + "id": "a846a9bd", "metadata": {}, "outputs": [], "source": [ @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "3ab90814", + "id": "d3b6b55d", "metadata": {}, "source": [ "Using vectorization instead of loops,\n", @@ -230,7 +230,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d01d609c", + "id": "51d3de70", "metadata": {}, "outputs": [], "source": [ @@ -242,7 +242,7 @@ }, { "cell_type": "markdown", - "id": "4c5b0973", + "id": "dae9fd08", "metadata": {}, "source": [ "Let's not charge for college and recompute $\\phi$.\n", @@ -253,7 +253,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b099ddd", + "id": "53e07b1f", "metadata": {}, "outputs": [], "source": [ @@ -265,7 +265,7 @@ }, { "cell_type": "markdown", - "id": "30dfea8e", + "id": "99532f1c", "metadata": {}, "source": [ "Let us construct some graphs that show us how the initial college-high-school wage ratio $\\phi$ would change if one of its determinants were to change. \n", @@ -276,7 +276,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c672124", + "id": "e4059580", "metadata": {}, "outputs": [], "source": [ @@ -292,7 +292,7 @@ }, { "cell_type": "markdown", - "id": "657339e5", + "id": "d5971d47", "metadata": {}, "source": [ "Evidently, the initial wage ratio $\\phi$ must rise to compensate a prospective high school student for **waiting** to start receiving income -- remember that while she is earning nothing in years $t=0, 1, 2, 3$, the high school worker is earning a salary.\n", @@ -304,7 +304,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46f1d875", + "id": "6d40eefa", "metadata": {}, "outputs": [], "source": [ @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "62177bbb", + "id": "4b20601f", "metadata": {}, "source": [ "Notice how the initial wage gap falls when the rate of growth $\\gamma_c$ of college wages rises. \n", @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a8b8f31", + "id": "301d9165", "metadata": {}, "outputs": [], "source": [ @@ -351,7 +351,7 @@ }, { "cell_type": "markdown", - "id": "d1525ab8", + "id": "634b2f16", "metadata": {}, "source": [ "## Entrepreneur-worker interpretation\n", @@ -384,7 +384,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e44ba1d", + "id": "b959e54c", "metadata": {}, "outputs": [], "source": [ @@ -418,7 +418,7 @@ }, { "cell_type": "markdown", - "id": "58394162", + "id": "1349cd72", "metadata": {}, "source": [ "If the probability that a new business succeeds is $0.2$, let's compute the initial wage premium for successful entrepreneurs." @@ -427,7 +427,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54d89e0d", + "id": "a44c21df", "metadata": {}, "outputs": [], "source": [ @@ -439,7 +439,7 @@ }, { "cell_type": "markdown", - "id": "07e477c8", + "id": "59ba3564", "metadata": {}, "source": [ "Now let's study how the initial wage premium for successful entrepreneurs depend on the success probability." @@ -448,7 +448,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdc08faf", + "id": "5b3e9c12", "metadata": {}, "outputs": [], "source": [ @@ -464,7 +464,7 @@ }, { "cell_type": "markdown", - "id": "f8c84b67", + "id": "f753c114", "metadata": {}, "source": [ "Does the graph make sense to you?\n", @@ -491,7 +491,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db7c790f", + "id": "097464a2", "metadata": {}, "outputs": [], "source": [ @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "389014cd", + "id": "a8982626", "metadata": {}, "source": [ "Define function $A_h$" @@ -510,7 +510,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06580905", + "id": "ac80b36d", "metadata": {}, "outputs": [], "source": [ @@ -520,7 +520,7 @@ }, { "cell_type": "markdown", - "id": "f9718384", + "id": "c4e14214", "metadata": {}, "source": [ "Define function $A_c$" @@ -529,7 +529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0693da1", + "id": "b522d94f", "metadata": {}, "outputs": [], "source": [ @@ -539,7 +539,7 @@ }, { "cell_type": "markdown", - "id": "7db558b7", + "id": "c0535435", "metadata": {}, "source": [ "Now, define $\\phi$" @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "633ee62f", + "id": "3ede560a", "metadata": {}, "outputs": [], "source": [ @@ -558,7 +558,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8da20e88", + "id": "aa252466", "metadata": {}, "outputs": [], "source": [ @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "ae022f76", + "id": "7417d402", "metadata": {}, "source": [ "We begin by setting default parameter values." @@ -576,7 +576,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e24182e", + "id": "85f23812", "metadata": {}, "outputs": [], "source": [ @@ -589,7 +589,7 @@ }, { "cell_type": "markdown", - "id": "65f268de", + "id": "57f236fa", "metadata": {}, "source": [ "Now let's compute $\\frac{\\partial \\phi}{\\partial D}$ and then evaluate it at the default values" @@ -598,7 +598,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32e140a8", + "id": "778e0673", "metadata": {}, "outputs": [], "source": [ @@ -609,7 +609,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66a25b66", + "id": "89d06237", "metadata": {}, "outputs": [], "source": [ @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "d6c133da", + "id": "c121b1e8", "metadata": {}, "source": [ "Thus, as with our earlier graph, we find that raising $R$ increases the initial college wage premium $\\phi$.\n", @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09c984a7", + "id": "ca219f6f", "metadata": {}, "outputs": [], "source": [ @@ -642,7 +642,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0fc7772f", + "id": "d3b3f46e", "metadata": {}, "outputs": [], "source": [ @@ -653,7 +653,7 @@ }, { "cell_type": "markdown", - "id": "ed1a6ce0", + "id": "793db4f9", "metadata": {}, "source": [ "We find that raising $T$ decreases the initial college wage premium $\\phi$. \n", @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "beb58391", + "id": "59083188", "metadata": {}, "outputs": [], "source": [ @@ -677,7 +677,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ddee529f", + "id": "ab5fc887", "metadata": {}, "outputs": [], "source": [ @@ -688,7 +688,7 @@ }, { "cell_type": "markdown", - "id": "b0122bed", + "id": "985088a5", "metadata": {}, "source": [ "We find that raising $\\gamma_h$ increases the initial college wage premium $\\phi$, in line with our earlier graphical analysis.\n", @@ -699,7 +699,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b63a91d2", + "id": "0abf9b40", "metadata": {}, "outputs": [], "source": [ @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5917513", + "id": "7f54e044", "metadata": {}, "outputs": [], "source": [ @@ -721,7 +721,7 @@ }, { "cell_type": "markdown", - "id": "82121cb6", + "id": "017cd510", "metadata": {}, "source": [ "We find that raising $\\gamma_c$ decreases the initial college wage premium $\\phi$, in line with our earlier graphical analysis.\n", @@ -732,7 +732,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5f858f51", + "id": "06d712d6", "metadata": {}, "outputs": [], "source": [ @@ -743,7 +743,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f59a5a7", + "id": "a4aee881", "metadata": {}, "outputs": [], "source": [ @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "c1b53a18", + "id": "b9d234bd", "metadata": {}, "source": [ "We find that raising the gross interest rate $R$ increases the initial college wage premium $\\phi$, in line with our earlier graphical analysis." diff --git a/_sources/french_rev.ipynb b/_sources/french_rev.ipynb index d7843d33..456bc2d3 100644 --- a/_sources/french_rev.ipynb +++ b/_sources/french_rev.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "49083fb2", + "id": "f9c58530", "metadata": {}, "source": [ "# Inflation During French Revolution \n", @@ -65,7 +65,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37c5e665", + "id": "22fbcfa4", "metadata": {}, "outputs": [], "source": [ @@ -84,7 +84,7 @@ }, { "cell_type": "markdown", - "id": "f2dc2704", + "id": "a0740e80", "metadata": {}, "source": [ "## Government Expenditures and Taxes Collected\n", @@ -95,7 +95,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36cd63a5", + "id": "44e55def", "metadata": { "mystnb": { "figure": { @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "90ae60dd", + "id": "4f8a87e5", "metadata": {}, "source": [ "During the 18th century, Britain and France fought four large wars.\n", @@ -157,7 +157,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6559a020", + "id": "924a4f52", "metadata": { "mystnb": { "figure": { @@ -199,7 +199,7 @@ }, { "cell_type": "markdown", - "id": "f01a7b41", + "id": "f86fce24", "metadata": {}, "source": [ "Figures {numref}`fr_fig2` and {numref}`fr_fig3` summarize British and French government fiscal policies during the century before the start the French Revolution in 1789.\n", @@ -245,7 +245,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a197a18", + "id": "f2c2f405", "metadata": { "mystnb": { "figure": { @@ -287,7 +287,7 @@ }, { "cell_type": "markdown", - "id": "12a3ec43", + "id": "d0d383e7", "metadata": {}, "source": [ "Figure {numref}`fr_fig1` shows that interest payments on government debt (i.e., so-called ''debt service'') were high fractions of government tax revenues in both Great Britain and France. \n", @@ -301,7 +301,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bac37dae", + "id": "47dbc5cf", "metadata": {}, "outputs": [], "source": [ @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f58dc67c", + "id": "e62bd06d", "metadata": { "mystnb": { "figure": { @@ -352,7 +352,7 @@ }, { "cell_type": "markdown", - "id": "1db32569", + "id": "0cb8ec47", "metadata": {}, "source": [ "{numref}`fr_fig3` shows that in 1788 on the eve of the French Revolution government expenditures exceeded tax revenues. \n", @@ -478,7 +478,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e0884a6", + "id": "525d2002", "metadata": { "mystnb": { "figure": { @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "fc909fa4", + "id": "2d2cf7fa", "metadata": {}, "source": [ "According to {numref}`fr_fig5`, tax revenues per capita did not rise to their pre 1789 levels\n", @@ -527,7 +527,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb7272b0", + "id": "81b5f556", "metadata": { "mystnb": { "figure": { @@ -574,7 +574,7 @@ }, { "cell_type": "markdown", - "id": "4ace2b0c", + "id": "471a26e0", "metadata": {}, "source": [ "To cover the disrepancies between government expenditures and tax revenues revealed in {numref}`fr_fig11`, the French revolutionaries printed paper money and spent it. \n", @@ -586,7 +586,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d95a4d74", + "id": "c93cb6b6", "metadata": { "mystnb": { "figure": { @@ -624,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "fc0f4cbf", + "id": "79895b07", "metadata": {}, "source": [ "{numref}`fr_fig24` compares the revenues raised by printing money from 1789 to 1796 with tax revenues that the Ancient Regime had raised in 1788.\n", @@ -662,7 +662,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac223a97", + "id": "0b1362fe", "metadata": { "mystnb": { "figure": { @@ -707,7 +707,7 @@ }, { "cell_type": "markdown", - "id": "2907bc38", + "id": "bb1aad2f", "metadata": {}, "source": [ "We have partioned {numref}`fr_fig9` that shows the log of the price level and {numref}`fr_fig8`\n", @@ -743,7 +743,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22dba3b4", + "id": "4883f396", "metadata": { "mystnb": { "figure": { @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "d36c68e2", + "id": "2963a96e", "metadata": {}, "source": [ "The three clouds of points in Figure\n", @@ -817,7 +817,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2f2a7b4", + "id": "15887a82", "metadata": {}, "outputs": [], "source": [ @@ -832,7 +832,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bce34fac", + "id": "9ab2555c", "metadata": {}, "outputs": [], "source": [ @@ -848,7 +848,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da1b2681", + "id": "b8f1b74a", "metadata": {}, "outputs": [], "source": [ @@ -866,7 +866,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4441180f", + "id": "5beed68a", "metadata": { "mystnb": { "figure": { @@ -902,7 +902,7 @@ }, { "cell_type": "markdown", - "id": "26e5844d", + "id": "b0cdf74d", "metadata": {}, "source": [ "The three clouds of points in Figure\n", @@ -923,7 +923,7 @@ { "cell_type": "code", "execution_count": null, - "id": "570af0a5", + "id": "119b8fe8", "metadata": {}, "outputs": [], "source": [ @@ -941,7 +941,7 @@ { "cell_type": "code", "execution_count": null, - "id": "950a7aaf", + "id": "3db3471d", "metadata": { "mystnb": { "figure": { @@ -975,7 +975,7 @@ }, { "cell_type": "markdown", - "id": "2e04cd63", + "id": "c68eb3b4", "metadata": {}, "source": [ "Now let's regress inflation on real balances during the **real bills** period and plot the regression\n", @@ -985,7 +985,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7faf5e30", + "id": "1baa6d9e", "metadata": { "mystnb": { "figure": { @@ -1022,7 +1022,7 @@ }, { "cell_type": "markdown", - "id": "23a9cd6e", + "id": "8e740703", "metadata": {}, "source": [ "The regression line in {numref}`fr_fig104c` shows that large increases in real balances of\n", @@ -1043,7 +1043,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e911c13", + "id": "092ecf0d", "metadata": { "mystnb": { "figure": { @@ -1080,7 +1080,7 @@ }, { "cell_type": "markdown", - "id": "237720ce", + "id": "731dc818", "metadata": {}, "source": [ "The regression line in {numref}`fr_fig104d` shows that large increases in real balances of\n", @@ -1101,7 +1101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3df4321c", + "id": "1f9552f9", "metadata": { "mystnb": { "figure": { @@ -1138,7 +1138,7 @@ }, { "cell_type": "markdown", - "id": "0f2c75b4", + "id": "23c17488", "metadata": {}, "source": [ "{numref}`fr_fig104e` shows the results of regressing inflation on real balances during the\n", @@ -1148,7 +1148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0522691e", + "id": "b1e698b9", "metadata": { "mystnb": { "figure": { @@ -1185,7 +1185,7 @@ }, { "cell_type": "markdown", - "id": "4acbc7d8", + "id": "9dd93a24", "metadata": {}, "source": [ "{numref}`fr_fig104e` shows the results of regressing real balances on inflation during the\n", diff --git a/_sources/geom_series.ipynb b/_sources/geom_series.ipynb index 8ca608a3..b4e6329d 100644 --- a/_sources/geom_series.ipynb +++ b/_sources/geom_series.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "fdf4e4ef", + "id": "794e83da", "metadata": {}, "source": [ "(geom_series)=\n", @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": null, - "id": "928ad17a", + "id": "433c9236", "metadata": {}, "outputs": [], "source": [ @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "88614ae3", + "id": "33b9cf72", "metadata": {}, "source": [ "## Key formulas\n", @@ -658,7 +658,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27ae7f5a", + "id": "83c16a95", "metadata": {}, "outputs": [], "source": [ @@ -686,7 +686,7 @@ }, { "cell_type": "markdown", - "id": "f97fb451", + "id": "741e220e", "metadata": {}, "source": [ "Now that we have defined our functions, we can plot some outcomes.\n", @@ -697,7 +697,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b705ddbb", + "id": "869e1941", "metadata": { "mystnb": { "figure": { @@ -735,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "df19ddeb", + "id": "e3dddbdb", "metadata": {}, "source": [ "Evidently our approximations perform well for small values of $T$.\n", @@ -749,7 +749,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a6036f4", + "id": "f6e93c8f", "metadata": { "mystnb": { "figure": { @@ -776,7 +776,7 @@ }, { "cell_type": "markdown", - "id": "86d6d65c", + "id": "85b7858a", "metadata": {}, "source": [ "The graph above shows how as duration $T \\rightarrow +\\infty$,\n", @@ -790,7 +790,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4c7a561", + "id": "82f6ff5e", "metadata": { "mystnb": { "figure": { @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "7d12d7c2", + "id": "78528616", "metadata": {}, "source": [ "This graph gives a big hint for why the condition $r > g$ is\n", @@ -837,7 +837,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f033436", + "id": "420acef3", "metadata": { "mystnb": { "figure": { @@ -873,7 +873,7 @@ }, { "cell_type": "markdown", - "id": "b281891a", + "id": "f7b977c0", "metadata": {}, "source": [ "We can use a little calculus to study how the present value $p_0$\n", @@ -893,7 +893,7 @@ { "cell_type": "code", "execution_count": null, - "id": "380568d3", + "id": "b86aa5af", "metadata": {}, "outputs": [], "source": [ @@ -910,7 +910,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50b54b8b", + "id": "22db1752", "metadata": {}, "outputs": [], "source": [ @@ -922,7 +922,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca0f30b2", + "id": "3f1c26e6", "metadata": {}, "outputs": [], "source": [ @@ -933,7 +933,7 @@ }, { "cell_type": "markdown", - "id": "6d1030f2", + "id": "048cd1b4", "metadata": {}, "source": [ "We can see that for $\\frac{\\partial p_0}{\\partial r}<0$ as long as\n", @@ -953,7 +953,7 @@ { "cell_type": "code", "execution_count": null, - "id": "621135bc", + "id": "dac85330", "metadata": { "mystnb": { "figure": { @@ -991,7 +991,7 @@ }, { "cell_type": "markdown", - "id": "d2b97971", + "id": "d06780a0", "metadata": {}, "source": [ "In this model, income grows over time, until it gradually converges to\n", @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "453c61c4", + "id": "b3398223", "metadata": { "mystnb": { "figure": { @@ -1031,7 +1031,7 @@ }, { "cell_type": "markdown", - "id": "4fb6ae77", + "id": "259d5062", "metadata": {}, "source": [ "Increasing the marginal propensity to consume $b$ increases the\n", @@ -1043,7 +1043,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27b0e396", + "id": "753cea7a", "metadata": { "mystnb": { "figure": { @@ -1079,7 +1079,7 @@ }, { "cell_type": "markdown", - "id": "d9fb161c", + "id": "ec7c7bdf", "metadata": {}, "source": [ "Notice here, whether government spending increases from 0.3 to 0.4 or\n", diff --git a/_sources/greek_square.ipynb b/_sources/greek_square.ipynb index 103ebd1a..b7a6a410 100644 --- a/_sources/greek_square.ipynb +++ b/_sources/greek_square.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "228ea10c", + "id": "eb32ec5e", "metadata": {}, "source": [ "# Computing Square Roots\n", @@ -324,7 +324,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cac126fb", + "id": "f057f852", "metadata": {}, "outputs": [], "source": [ @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff8be683", + "id": "1630832b", "metadata": {}, "outputs": [], "source": [ @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "d5bbeccf", + "id": "33d6e5cd", "metadata": {}, "source": [ "Now we consider cases where $(\\eta_1, \\eta_2) = (0, 1)$ and $(\\eta_1, \\eta_2) = (1, 0)$" @@ -402,7 +402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc262c51", + "id": "d628eec2", "metadata": {}, "outputs": [], "source": [ @@ -414,7 +414,7 @@ { "cell_type": "code", "execution_count": null, - "id": "785f1c8b", + "id": "18b8fbca", "metadata": {}, "outputs": [], "source": [ @@ -431,7 +431,7 @@ { "cell_type": "code", "execution_count": null, - "id": "966e2c9c", + "id": "98247050", "metadata": {}, "outputs": [], "source": [ @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "77ccd718", + "id": "36856299", "metadata": {}, "source": [ "We find that convergence is immediate.\n", @@ -497,7 +497,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60df720e", + "id": "ea4d0971", "metadata": {}, "outputs": [], "source": [ @@ -536,7 +536,7 @@ }, { "cell_type": "markdown", - "id": "49d9844a", + "id": "2255cf88", "metadata": {}, "source": [ "Let's compare the eigenvalues to the roots {eq}`eq:secretweapon` of equation \n", @@ -546,7 +546,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51a8e740", + "id": "d7cf2e56", "metadata": {}, "outputs": [], "source": [ @@ -556,7 +556,7 @@ }, { "cell_type": "markdown", - "id": "fe9371ae", + "id": "450e0c1e", "metadata": {}, "source": [ "Hence we confirmed {eq}`eq:eigen_sqrt`.\n", @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8d32fed", + "id": "17882036", "metadata": { "tags": [ "hide-input" @@ -616,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "c2da73ca", + "id": "7dea4c3c", "metadata": {}, "source": [ "## Invariant subspace approach \n", @@ -714,7 +714,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a7532fc", + "id": "827bb178", "metadata": {}, "outputs": [], "source": [ @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "aa077352", + "id": "1f38ab31", "metadata": {}, "source": [ "We find $x_{1,0}^* = 0$.\n", @@ -739,7 +739,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0526c8c5", + "id": "56c75b68", "metadata": {}, "outputs": [], "source": [ @@ -753,7 +753,7 @@ }, { "cell_type": "markdown", - "id": "d6bc8324", + "id": "2573a0d9", "metadata": {}, "source": [ "We find $x_{2,0}^* = 0$." @@ -762,7 +762,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ec12cfb", + "id": "acfa7d6d", "metadata": {}, "outputs": [], "source": [ @@ -778,7 +778,7 @@ }, { "cell_type": "markdown", - "id": "14785316", + "id": "7cf81e36", "metadata": {}, "source": [ "The following graph shows the ratios $y_t / y_{t-1}$ for the two cases.\n", @@ -789,7 +789,7 @@ { "cell_type": "code", "execution_count": null, - "id": "45498925", + "id": "bf1af4a5", "metadata": { "tags": [ "hide-input" @@ -828,7 +828,7 @@ }, { "cell_type": "markdown", - "id": "221b0b6a", + "id": "c31ee313", "metadata": {}, "source": [ "## Concluding remarks\n", diff --git a/_sources/heavy_tails.ipynb b/_sources/heavy_tails.ipynb index 48200464..021674de 100644 --- a/_sources/heavy_tails.ipynb +++ b/_sources/heavy_tails.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "1dfb2033", + "id": "a8163beb", "metadata": {}, "source": [ "(heavy_tail)=\n", @@ -14,7 +14,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af0a0478", + "id": "c049a21b", "metadata": { "tags": [ "hide-output" @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "1ee9143f", + "id": "572a09cf", "metadata": {}, "source": [ "We use the following imports." @@ -36,7 +36,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6904ce2", + "id": "6cf5c142", "metadata": {}, "outputs": [], "source": [ @@ -54,7 +54,7 @@ }, { "cell_type": "markdown", - "id": "1b006ce4", + "id": "6a5c4dfd", "metadata": {}, "source": [ "## Overview\n", @@ -101,7 +101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77a00028", + "id": "9663e346", "metadata": { "mystnb": { "figure": { @@ -123,7 +123,7 @@ }, { "cell_type": "markdown", - "id": "4c43da3c", + "id": "225f8b4a", "metadata": {}, "source": [ "Notice how \n", @@ -137,7 +137,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a977146e", + "id": "6610e745", "metadata": {}, "outputs": [], "source": [ @@ -146,7 +146,7 @@ }, { "cell_type": "markdown", - "id": "9aec7875", + "id": "5fd7fbd8", "metadata": {}, "source": [ "Here's another view of draws from the same distribution:" @@ -155,7 +155,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9481135", + "id": "9871b0eb", "metadata": { "mystnb": { "figure": { @@ -179,7 +179,7 @@ }, { "cell_type": "markdown", - "id": "d08168ec", + "id": "c635b07e", "metadata": {}, "source": [ "We have plotted each individual draw $X_i$ against $i$.\n", @@ -242,7 +242,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2265e205", + "id": "c677a999", "metadata": { "tags": [ "hide-output" @@ -256,7 +256,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cee40ef6", + "id": "d75ec33a", "metadata": { "mystnb": { "figure": { @@ -282,7 +282,7 @@ }, { "cell_type": "markdown", - "id": "c15f7571", + "id": "59e2250a", "metadata": {}, "source": [ "This data looks different to the draws from the normal distribution we saw above.\n", @@ -295,7 +295,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f972fd7", + "id": "64b88126", "metadata": { "tags": [ "hide-output" @@ -309,7 +309,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c80aba61", + "id": "d305b683", "metadata": { "mystnb": { "figure": { @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "57a07db3", + "id": "717329d9", "metadata": {}, "source": [ "The histogram also looks different to the histogram of the normal\n", @@ -345,7 +345,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4698a486", + "id": "6795442e", "metadata": { "mystnb": { "figure": { @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "3c4ee5a6", + "id": "a7744c40", "metadata": {}, "source": [ "If we look at higher frequency returns data (e.g., tick-by-tick), we often see \n", @@ -449,7 +449,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20b40877", + "id": "eb24bd9b", "metadata": { "mystnb": { "figure": { @@ -490,7 +490,7 @@ }, { "cell_type": "markdown", - "id": "1d30f330", + "id": "3d2ac719", "metadata": {}, "source": [ "In the top subfigure, the standard deviation of the normal distribution is 2,\n", @@ -521,7 +521,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5976f2eb", + "id": "6cca77eb", "metadata": { "mystnb": { "figure": { @@ -547,7 +547,7 @@ }, { "cell_type": "markdown", - "id": "d4e12020", + "id": "d6905bcc", "metadata": {}, "source": [ "Another nonnegative distribution is the [Pareto distribution](https://en.wikipedia.org/wiki/Pareto_distribution). \n", @@ -591,7 +591,7 @@ { "cell_type": "code", "execution_count": null, - "id": "730b30ca", + "id": "d9da3c69", "metadata": { "mystnb": { "figure": { @@ -617,7 +617,7 @@ }, { "cell_type": "markdown", - "id": "7ea611bf", + "id": "585879c9", "metadata": {}, "source": [ "Notice how extreme outcomes are more common.\n", @@ -685,7 +685,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb84e2a6", + "id": "8c04da83", "metadata": { "mystnb": { "figure": { @@ -709,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "aedbd81b", + "id": "cc3288f5", "metadata": {}, "source": [ "Here's a log-log plot of the same functions, which makes visual comparison\n", @@ -719,7 +719,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97f0a7f6", + "id": "f463677c", "metadata": { "mystnb": { "figure": { @@ -742,7 +742,7 @@ }, { "cell_type": "markdown", - "id": "8525b3e5", + "id": "69843f97", "metadata": {}, "source": [ "In the log-log plot, the Pareto CCDF is linear, while the exponential one is\n", @@ -768,7 +768,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28886680", + "id": "f28d0fb5", "metadata": {}, "outputs": [], "source": [ @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "a478e620", + "id": "bdb729af", "metadata": {}, "source": [ "Here's a figure containing some empirical CCDFs from simulated data." @@ -788,7 +788,7 @@ { "cell_type": "code", "execution_count": null, - "id": "444d7f28", + "id": "1eaee21b", "metadata": { "mystnb": { "figure": { @@ -834,7 +834,7 @@ }, { "cell_type": "markdown", - "id": "073b9873", + "id": "a411eede", "metadata": {}, "source": [ "As with the CCDF, the empirical CCDF from the Pareto distributions is \n", @@ -845,7 +845,7 @@ }, { "cell_type": "markdown", - "id": "dba98207", + "id": "846f767a", "metadata": {}, "source": [ "#### Q-Q Plots\n", @@ -860,7 +860,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09b26700", + "id": "141a1065", "metadata": {}, "outputs": [], "source": [ @@ -871,7 +871,7 @@ }, { "cell_type": "markdown", - "id": "d069d1c2", + "id": "fcfd30a4", "metadata": {}, "source": [ "We can now compare this with the exponential, log-normal, and Pareto distributions" @@ -880,7 +880,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a3e8037", + "id": "3e4b8c96", "metadata": {}, "outputs": [], "source": [ @@ -897,7 +897,7 @@ }, { "cell_type": "markdown", - "id": "37ee100d", + "id": "b4c54925", "metadata": {}, "source": [ "### Power laws \n", @@ -953,7 +953,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0e35ca1d", + "id": "51bf156f", "metadata": { "tags": [ "hide-input" @@ -1021,7 +1021,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c458ea6b", + "id": "beb17b7f", "metadata": { "tags": [ "hide-input" @@ -1052,7 +1052,7 @@ }, { "cell_type": "markdown", - "id": "d455c69f", + "id": "59ba9cd0", "metadata": {}, "source": [ "### Firm size\n", @@ -1063,7 +1063,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79bae940", + "id": "18777bbf", "metadata": { "mystnb": { "figure": { @@ -1091,7 +1091,7 @@ }, { "cell_type": "markdown", - "id": "267c2b0e", + "id": "4f20955a", "metadata": {}, "source": [ "### City size\n", @@ -1104,7 +1104,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f27f6098", + "id": "c3fd5149", "metadata": { "mystnb": { "figure": { @@ -1132,7 +1132,7 @@ }, { "cell_type": "markdown", - "id": "f680e51b", + "id": "3a9beedd", "metadata": {}, "source": [ "### Wealth\n", @@ -1145,7 +1145,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5ce4f4a", + "id": "b9d8c0b5", "metadata": { "mystnb": { "figure": { @@ -1186,7 +1186,7 @@ }, { "cell_type": "markdown", - "id": "b8f174d0", + "id": "90bb56e0", "metadata": {}, "source": [ "### GDP\n", @@ -1199,7 +1199,7 @@ { "cell_type": "code", "execution_count": null, - "id": "932ad1fb", + "id": "54046d4b", "metadata": { "tags": [ "hide-input" @@ -1223,7 +1223,7 @@ { "cell_type": "code", "execution_count": null, - "id": "084e5751", + "id": "bf3c042e", "metadata": { "mystnb": { "figure": { @@ -1247,7 +1247,7 @@ }, { "cell_type": "markdown", - "id": "e47e3b25", + "id": "7275c849", "metadata": {}, "source": [ "The plot is concave rather than linear, so the distribution has light tails.\n", @@ -1289,7 +1289,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcfbf1cb", + "id": "88626490", "metadata": { "mystnb": { "figure": { @@ -1326,7 +1326,7 @@ }, { "cell_type": "markdown", - "id": "a20a276b", + "id": "fb766aa0", "metadata": {}, "source": [ "The sequence shows no sign of converging.\n", @@ -1541,7 +1541,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a58a776", + "id": "c457fe29", "metadata": {}, "outputs": [], "source": [ @@ -1568,7 +1568,7 @@ }, { "cell_type": "markdown", - "id": "c4f5c2df", + "id": "ca85fa6a", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1668,7 +1668,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d21c154", + "id": "d72e63e6", "metadata": {}, "outputs": [], "source": [ @@ -1691,7 +1691,7 @@ }, { "cell_type": "markdown", - "id": "dcedefc1", + "id": "4e49aa7b", "metadata": {}, "source": [ "Let's compute the lognormal parameters:" @@ -1700,7 +1700,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21695e65", + "id": "f779e049", "metadata": {}, "outputs": [], "source": [ @@ -1711,7 +1711,7 @@ }, { "cell_type": "markdown", - "id": "344d3e69", + "id": "7848c724", "metadata": {}, "source": [ "Here's a function to compute a single estimate of tax revenue for a particular\n", @@ -1721,7 +1721,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6b7fe69", + "id": "4b8f7b24", "metadata": {}, "outputs": [], "source": [ @@ -1738,7 +1738,7 @@ }, { "cell_type": "markdown", - "id": "dd27e2c3", + "id": "51b3aa38", "metadata": {}, "source": [ "Now let's generate the violin plot." @@ -1747,7 +1747,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54a7c02f", + "id": "8974feee", "metadata": {}, "outputs": [], "source": [ @@ -1772,7 +1772,7 @@ }, { "cell_type": "markdown", - "id": "f7201dd2", + "id": "ddcaf690", "metadata": {}, "source": [ "Finally, let's print the means and standard deviations." @@ -1781,7 +1781,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36584178", + "id": "3cd9dbb6", "metadata": {}, "outputs": [], "source": [ @@ -1791,7 +1791,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b83b5d83", + "id": "ca4dcb6b", "metadata": {}, "outputs": [], "source": [ @@ -1800,7 +1800,7 @@ }, { "cell_type": "markdown", - "id": "1bce9bdc", + "id": "976c71a2", "metadata": {}, "source": [ "Looking at the output of the code, our main conclusion is that the Pareto\n", diff --git a/_sources/inequality.ipynb b/_sources/inequality.ipynb index 48e37f42..d5ee61da 100644 --- a/_sources/inequality.ipynb +++ b/_sources/inequality.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "51ed370f", + "id": "2ec14bcc", "metadata": {}, "source": [ "# Income and Wealth Inequality\n", @@ -72,7 +72,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dee2a30e", + "id": "2793816e", "metadata": { "tags": [ "hide-output" @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "c338e0ce", + "id": "aaa5d376", "metadata": {}, "source": [ "We will also use the following imports." @@ -94,7 +94,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1106da85", + "id": "6e7351c4", "metadata": {}, "outputs": [], "source": [ @@ -108,7 +108,7 @@ }, { "cell_type": "markdown", - "id": "a61b82bb", + "id": "ecd513dc", "metadata": {}, "source": [ "## The Lorenz curve\n", @@ -173,7 +173,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eb507b34", + "id": "d4bfb40e", "metadata": {}, "outputs": [], "source": [ @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "9467ab87", + "id": "96c2d4db", "metadata": {}, "source": [ "In the next figure, we generate $n=2000$ draws from a lognormal\n", @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea7eb415", + "id": "8dcbccd6", "metadata": { "mystnb": { "figure": { @@ -275,7 +275,7 @@ }, { "cell_type": "markdown", - "id": "b462349b", + "id": "1f7cc162", "metadata": {}, "source": [ "### Lorenz curves for US data\n", @@ -290,7 +290,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b65f9fb8", + "id": "a148498f", "metadata": {}, "outputs": [], "source": [ @@ -302,7 +302,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce604ce1", + "id": "695ea48a", "metadata": {}, "outputs": [], "source": [ @@ -311,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "9fba7474", + "id": "74b6322a", "metadata": {}, "source": [ "The next code block uses data stored in dataframe `df_income_wealth` to generate the Lorenz curves.\n", @@ -323,7 +323,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8631759", + "id": "f8cb3953", "metadata": { "tags": [ "hide-input" @@ -371,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "3533c234", + "id": "586a70ea", "metadata": {}, "source": [ "Now we plot Lorenz curves for net wealth, total income and labor income in the\n", @@ -385,7 +385,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e630afca", + "id": "08d17cd9", "metadata": { "mystnb": { "figure": { @@ -412,7 +412,7 @@ }, { "cell_type": "markdown", - "id": "c05eacd8", + "id": "395c838c", "metadata": {}, "source": [ "One key finding from this figure is that wealth inequality is more extreme than income inequality. \n", @@ -459,7 +459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5e37e43", + "id": "428411a1", "metadata": { "mystnb": { "figure": { @@ -486,7 +486,7 @@ }, { "cell_type": "markdown", - "id": "16d8680e", + "id": "ba0790fa", "metadata": {}, "source": [ "In fact the Gini coefficient can also be expressed as\n", @@ -502,7 +502,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a2f1bfe", + "id": "dadb090b", "metadata": { "mystnb": { "figure": { @@ -531,7 +531,7 @@ }, { "cell_type": "markdown", - "id": "d0d38dbb", + "id": "90956a19", "metadata": {}, "source": [ "```{seealso}\n", @@ -550,7 +550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fd883b7b", + "id": "7885b189", "metadata": {}, "outputs": [], "source": [ @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "194a981e", + "id": "4dd1d6f7", "metadata": {}, "source": [ "Now we can compute the Gini coefficients for five different populations.\n", @@ -606,7 +606,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef137363", + "id": "430673c6", "metadata": {}, "outputs": [], "source": [ @@ -625,7 +625,7 @@ }, { "cell_type": "markdown", - "id": "bc0a0ff6", + "id": "16819c9e", "metadata": {}, "source": [ "Let's build a function that returns a figure (so that we can use it later in the lecture)." @@ -634,7 +634,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7248cc71", + "id": "17a3be1a", "metadata": {}, "outputs": [], "source": [ @@ -650,7 +650,7 @@ { "cell_type": "code", "execution_count": null, - "id": "57672d0c", + "id": "df21e1c6", "metadata": { "mystnb": { "figure": { @@ -671,7 +671,7 @@ }, { "cell_type": "markdown", - "id": "4210a8f4", + "id": "08b03ac9", "metadata": {}, "source": [ "The plots show that inequality rises with $\\sigma$, according to the Gini\n", @@ -689,7 +689,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c9d107b", + "id": "ffd8b512", "metadata": {}, "outputs": [], "source": [ @@ -698,7 +698,7 @@ }, { "cell_type": "markdown", - "id": "d7f9a2a3", + "id": "11826e44", "metadata": {}, "source": [ "We now know the series ID is `SI.POV.GINI`.\n", @@ -711,7 +711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44294d95", + "id": "84a90d04", "metadata": { "mystnb": { "figure": { @@ -739,7 +739,7 @@ }, { "cell_type": "markdown", - "id": "f74ee4f8", + "id": "9c5b1a4f", "metadata": {}, "source": [ "We can see in {numref}`gini_histogram` that across 50 years of data and all countries the measure varies between 20 and 65.\n", @@ -750,7 +750,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c6ba57b4", + "id": "29df75a4", "metadata": {}, "outputs": [], "source": [ @@ -762,7 +762,7 @@ }, { "cell_type": "markdown", - "id": "eaf7a424", + "id": "d1827b64", "metadata": {}, "source": [ "(This package often returns data with year information contained in the columns. This is not always convenient for simple plotting with pandas so it can be useful to transpose the results before plotting.)" @@ -771,7 +771,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e92ef5c9", + "id": "2c4a5b87", "metadata": {}, "outputs": [], "source": [ @@ -781,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "c2c47d58", + "id": "476a9016", "metadata": {}, "source": [ "Let us take a look at the data for the US." @@ -790,7 +790,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76a422b6", + "id": "abf24325", "metadata": { "mystnb": { "figure": { @@ -811,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "282d4add", + "id": "9f4c9971", "metadata": {}, "source": [ "As can be seen in {numref}`gini_usa1`, the income Gini\n", @@ -830,7 +830,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9853bbc5", + "id": "38e5fa60", "metadata": {}, "outputs": [], "source": [ @@ -839,7 +839,7 @@ }, { "cell_type": "markdown", - "id": "5febf838", + "id": "81553311", "metadata": {}, "source": [ "[This notebook](https://github.com/QuantEcon/lecture-python-intro/tree/main/lectures/_static/lecture_specific/inequality/data.ipynb) can be used to compute this information over the full dataset." @@ -848,7 +848,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3dca0343", + "id": "f6982a9d", "metadata": {}, "outputs": [], "source": [ @@ -859,7 +859,7 @@ }, { "cell_type": "markdown", - "id": "3fb81def", + "id": "575c0987", "metadata": {}, "source": [ "Let's plot the Gini coefficients for net wealth." @@ -868,7 +868,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4bc3e8a", + "id": "031c2c1e", "metadata": { "mystnb": { "figure": { @@ -888,7 +888,7 @@ }, { "cell_type": "markdown", - "id": "bafe6c28", + "id": "e8183d83", "metadata": {}, "source": [ "The time series for the wealth Gini exhibits a U-shape, falling until the early\n", @@ -910,7 +910,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1f6ba0a6", + "id": "dc81a29d", "metadata": {}, "outputs": [], "source": [ @@ -920,7 +920,7 @@ }, { "cell_type": "markdown", - "id": "5f1c8a55", + "id": "36819070", "metadata": {}, "source": [ "There are 167 countries represented in this dataset. \n", @@ -931,7 +931,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f08d2a1", + "id": "ff8cb0d7", "metadata": { "mystnb": { "figure": { @@ -951,7 +951,7 @@ }, { "cell_type": "markdown", - "id": "fdde8728", + "id": "9aaceb7b", "metadata": {}, "source": [ "We see that Norway has a shorter time series.\n", @@ -962,7 +962,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6a0dca0d", + "id": "897774ce", "metadata": {}, "outputs": [], "source": [ @@ -971,7 +971,7 @@ }, { "cell_type": "markdown", - "id": "d9530ec9", + "id": "0d2fa4b2", "metadata": {}, "source": [ "The data for Norway in this dataset goes back to 1979 but there are gaps in the time series and matplotlib is not showing those data points. \n", @@ -982,7 +982,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00730442", + "id": "13a5b13d", "metadata": { "mystnb": { "figure": { @@ -1003,7 +1003,7 @@ }, { "cell_type": "markdown", - "id": "0b949e56", + "id": "f7bf0264", "metadata": {}, "source": [ "From this plot we can observe that the US has a higher Gini coefficient (i.e.\n", @@ -1024,7 +1024,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27cd2387", + "id": "1af51e24", "metadata": {}, "outputs": [], "source": [ @@ -1037,7 +1037,7 @@ }, { "cell_type": "markdown", - "id": "de66541e", + "id": "3ff53a25", "metadata": {}, "source": [ "We can rearrange the data so that we can plot GDP per capita and the Gini coefficient across years" @@ -1046,7 +1046,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0775ca82", + "id": "6244e6ed", "metadata": {}, "outputs": [], "source": [ @@ -1057,7 +1057,7 @@ }, { "cell_type": "markdown", - "id": "ee7f0da5", + "id": "1eceb1fa", "metadata": {}, "source": [ "Now we can get the GDP per capita data into a shape that can be merged with `plot_data`" @@ -1066,7 +1066,7 @@ { "cell_type": "code", "execution_count": null, - "id": "462361a6", + "id": "bb2988e9", "metadata": {}, "outputs": [], "source": [ @@ -1079,7 +1079,7 @@ }, { "cell_type": "markdown", - "id": "3c6112e9", + "id": "184183d5", "metadata": {}, "source": [ "Now we use Plotly to build a plot with GDP per capita on the y-axis and the Gini coefficient on the x-axis." @@ -1088,7 +1088,7 @@ { "cell_type": "code", "execution_count": null, - "id": "150223a9", + "id": "97d97ae9", "metadata": {}, "outputs": [], "source": [ @@ -1098,7 +1098,7 @@ }, { "cell_type": "markdown", - "id": "93640282", + "id": "39439edd", "metadata": {}, "source": [ "The time series for all three countries start and stop in different years. We will add a year mask to the data to\n", @@ -1108,7 +1108,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6780f607", + "id": "7dd34f0d", "metadata": {}, "outputs": [], "source": [ @@ -1119,7 +1119,7 @@ }, { "cell_type": "markdown", - "id": "1b15cc0f", + "id": "f5092ddc", "metadata": {}, "source": [ "(fig:plotly-gini-gdppc-years)=" @@ -1128,7 +1128,7 @@ { "cell_type": "code", "execution_count": null, - "id": "24db7a41", + "id": "9a13b4b2", "metadata": {}, "outputs": [], "source": [ @@ -1146,7 +1146,7 @@ }, { "cell_type": "markdown", - "id": "526ca6c1", + "id": "7649835c", "metadata": {}, "source": [ "```{only} latex\n", @@ -1197,7 +1197,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79ad423f", + "id": "209e96f1", "metadata": { "tags": [ "hide-input" @@ -1247,7 +1247,7 @@ }, { "cell_type": "markdown", - "id": "2f632d83", + "id": "a63e6e7c", "metadata": {}, "source": [ "Then let's plot the top shares." @@ -1256,7 +1256,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0e62ee2", + "id": "6db88218", "metadata": { "mystnb": { "figure": { @@ -1282,7 +1282,7 @@ }, { "cell_type": "markdown", - "id": "fe8c7d51", + "id": "0f7a8f16", "metadata": {}, "source": [ "## Exercises\n", @@ -1317,7 +1317,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9df4e51e", + "id": "b4ca1d1b", "metadata": {}, "outputs": [], "source": [ @@ -1332,7 +1332,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c310a46", + "id": "a92d132a", "metadata": {}, "outputs": [], "source": [ @@ -1358,7 +1358,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc7b9109", + "id": "8ac7f269", "metadata": { "mystnb": { "figure": { @@ -1383,7 +1383,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd971950", + "id": "43bc2f48", "metadata": { "mystnb": { "figure": { @@ -1408,7 +1408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f731585b", + "id": "f12edab3", "metadata": { "mystnb": { "figure": { @@ -1432,7 +1432,7 @@ }, { "cell_type": "markdown", - "id": "3d86bdce", + "id": "e45045af", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1460,7 +1460,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37bcf4e2", + "id": "61611c61", "metadata": {}, "outputs": [], "source": [ @@ -1472,7 +1472,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba7fc76e", + "id": "758f57eb", "metadata": {}, "outputs": [], "source": [ @@ -1484,7 +1484,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61788b57", + "id": "66561ebb", "metadata": { "mystnb": { "figure": { @@ -1512,7 +1512,7 @@ }, { "cell_type": "markdown", - "id": "add6ff13", + "id": "f7582f48", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1542,7 +1542,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49afc208", + "id": "55f05ca7", "metadata": {}, "outputs": [], "source": [ @@ -1552,7 +1552,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06bf4144", + "id": "098d6c92", "metadata": {}, "outputs": [], "source": [ @@ -1561,7 +1561,7 @@ }, { "cell_type": "markdown", - "id": "46bd5a7f", + "id": "686e948b", "metadata": {}, "source": [ "We will focus on wealth variable `n_wealth` to compute a Gini coefficient for the year 2016." @@ -1570,7 +1570,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79a0d6dd", + "id": "d82073e8", "metadata": {}, "outputs": [], "source": [ @@ -1580,7 +1580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0d2d9377", + "id": "80558967", "metadata": {}, "outputs": [], "source": [ @@ -1589,7 +1589,7 @@ }, { "cell_type": "markdown", - "id": "40de67aa", + "id": "9e6865bc", "metadata": {}, "source": [ "We can first compute the Gini coefficient using the function defined in the lecture above." @@ -1598,7 +1598,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7187b3a2", + "id": "ffeacb8e", "metadata": {}, "outputs": [], "source": [ @@ -1607,7 +1607,7 @@ }, { "cell_type": "markdown", - "id": "dc904da8", + "id": "818f8561", "metadata": {}, "source": [ "Now we can write a vectorized version using `numpy`" @@ -1616,7 +1616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2110af02", + "id": "868c328f", "metadata": {}, "outputs": [], "source": [ @@ -1631,7 +1631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25b679dd", + "id": "828a24d0", "metadata": {}, "outputs": [], "source": [ @@ -1640,7 +1640,7 @@ }, { "cell_type": "markdown", - "id": "9ad6518c", + "id": "75b84c58", "metadata": {}, "source": [ "Let's simulate five populations by drawing from a lognormal distribution as before" @@ -1649,7 +1649,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08816684", + "id": "015225d1", "metadata": {}, "outputs": [], "source": [ @@ -1663,7 +1663,7 @@ }, { "cell_type": "markdown", - "id": "431b6a78", + "id": "328fa812", "metadata": {}, "source": [ "We can compute the Gini coefficient for these five populations using the vectorized function, the computation time is shown below:" @@ -1672,7 +1672,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d1b1bf1", + "id": "c0c84091", "metadata": {}, "outputs": [], "source": [ @@ -1684,7 +1684,7 @@ }, { "cell_type": "markdown", - "id": "c0589638", + "id": "9ac93ec9", "metadata": {}, "source": [ "This shows the vectorized function is much faster.\n", @@ -1694,7 +1694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5eff1200", + "id": "f57418af", "metadata": {}, "outputs": [], "source": [ @@ -1703,7 +1703,7 @@ }, { "cell_type": "markdown", - "id": "354b81a8", + "id": "342ba1f3", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/inflation_history.ipynb b/_sources/inflation_history.ipynb index f8d1c2d7..2e272d6d 100644 --- a/_sources/inflation_history.ipynb +++ b/_sources/inflation_history.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "202fc1cc", + "id": "51291cc7", "metadata": {}, "source": [ "# Price Level Histories \n", @@ -17,7 +17,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1233ce49", + "id": "3d97dfa8", "metadata": { "tags": [ "hide-output" @@ -30,7 +30,7 @@ }, { "cell_type": "markdown", - "id": "3322ca8b", + "id": "45d1d750", "metadata": {}, "source": [ "" @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b97fa1e2", + "id": "c92ebcee", "metadata": { "tags": [ "hide-cell" @@ -56,7 +56,7 @@ }, { "cell_type": "markdown", - "id": "35e971c3", + "id": "651c9173", "metadata": {}, "source": [ "We can then import the Python modules we will use." @@ -65,7 +65,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59877dfe", + "id": "681c3971", "metadata": {}, "outputs": [], "source": [ @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "5b3965e1", + "id": "966b7455", "metadata": {}, "source": [ "The rate of growth of the price level is called **inflation** in the popular press and in discussions among central bankers and treasury officials.\n", @@ -119,7 +119,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f316c57f", + "id": "cd03f763", "metadata": {}, "outputs": [], "source": [ @@ -134,7 +134,7 @@ }, { "cell_type": "markdown", - "id": "6193e7e3", + "id": "bd2723ab", "metadata": {}, "source": [ "We first plot price levels over the period 1600-1914.\n", @@ -145,7 +145,7 @@ { "cell_type": "code", "execution_count": null, - "id": "292b1bed", + "id": "487ae9c5", "metadata": { "mystnb": { "figure": { @@ -177,7 +177,7 @@ }, { "cell_type": "markdown", - "id": "1816f20f", + "id": "3a161a5a", "metadata": {}, "source": [ "We say \"most years\" because there were temporary lapses from the gold or silver standard.\n", @@ -230,7 +230,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d09e83f6", + "id": "22c0287b", "metadata": { "mystnb": { "figure": { @@ -259,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "57ad112a", + "id": "dc4809ef", "metadata": {}, "source": [ "{numref}`lrpl_lg` shows that paper-money-printing central banks didn't do as well as the gold and standard silver standard in anchoring price levels.\n", @@ -301,7 +301,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e28604ae", + "id": "31754c25", "metadata": { "tags": [ "hide-input" @@ -367,7 +367,7 @@ }, { "cell_type": "markdown", - "id": "56f24c9a", + "id": "9870b03e", "metadata": {}, "source": [ "Now we write plotting functions `pe_plot` and `pr_plot` that will build figures that show the price level, exchange rates, \n", @@ -377,7 +377,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d5f46b4", + "id": "46aa168d", "metadata": { "tags": [ "hide-input" @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "db0bf2d4", + "id": "c6d4e499", "metadata": {}, "source": [ "We prepare the data for each country" @@ -453,7 +453,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07ba80f7", + "id": "00c9feae", "metadata": {}, "outputs": [], "source": [ @@ -494,7 +494,7 @@ }, { "cell_type": "markdown", - "id": "e08066d2", + "id": "959addf5", "metadata": {}, "source": [ "Now let's construct graphs for our four countries.\n", @@ -521,7 +521,7 @@ { "cell_type": "code", "execution_count": null, - "id": "18da28c0", + "id": "2e0b6e9a", "metadata": { "mystnb": { "figure": { @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49ee88b9", + "id": "6a474f2c", "metadata": { "mystnb": { "figure": { @@ -568,7 +568,7 @@ }, { "cell_type": "markdown", - "id": "95f960f8", + "id": "2360e779", "metadata": {}, "source": [ "Staring at {numref}`pi_xrate_austria` and {numref}`inflationrate_austria` conveys the following impressions to the authors of this lecture at QuantEcon.\n", @@ -589,7 +589,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52b386c8", + "id": "5af3704a", "metadata": { "mystnb": { "figure": { @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd44e398", + "id": "4e9b9664", "metadata": { "mystnb": { "figure": { @@ -636,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "c8493595", + "id": "eb74ccaf", "metadata": {}, "source": [ "### Poland\n", @@ -655,7 +655,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3f03949", + "id": "cb810092", "metadata": { "mystnb": { "figure": { @@ -694,7 +694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "63197ca4", + "id": "97a6a039", "metadata": {}, "outputs": [], "source": [ @@ -711,7 +711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c053715a", + "id": "09264798", "metadata": { "mystnb": { "figure": { @@ -731,7 +731,7 @@ }, { "cell_type": "markdown", - "id": "dff369ff", + "id": "67939991", "metadata": {}, "source": [ "### Germany\n", @@ -745,7 +745,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cee75629", + "id": "eca3d7f2", "metadata": { "mystnb": { "figure": { @@ -773,7 +773,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8d63ab8", + "id": "e39d96be", "metadata": { "mystnb": { "figure": { @@ -807,7 +807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74af67c2", + "id": "836ba474", "metadata": { "mystnb": { "figure": { @@ -827,7 +827,7 @@ }, { "cell_type": "markdown", - "id": "c916d8f9", + "id": "1a0e9861", "metadata": {}, "source": [ "## Starting and stopping big inflations\n", diff --git a/_sources/input_output.ipynb b/_sources/input_output.ipynb index ffa420b3..8f867f51 100644 --- a/_sources/input_output.ipynb +++ b/_sources/input_output.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "41a66f93", + "id": "a95c0bee", "metadata": {}, "source": [ "# Input-Output Models\n", @@ -15,7 +15,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42bf201f", + "id": "541966b0", "metadata": { "tags": [ "hide-output" @@ -31,7 +31,7 @@ { "cell_type": "code", "execution_count": null, - "id": "117f8510", + "id": "e136ff67", "metadata": {}, "outputs": [], "source": [ @@ -51,7 +51,7 @@ }, { "cell_type": "markdown", - "id": "59969e5e", + "id": "7558ba1c", "metadata": {}, "source": [ "The following figure illustrates a network of linkages among 15 sectors\n", @@ -62,7 +62,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca01a561", + "id": "ae82dede", "metadata": { "tags": [ "hide-cell" @@ -97,7 +97,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c34eec7", + "id": "ec5d1bc3", "metadata": { "mystnb": { "figure": { @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "943bb8eb", + "id": "3b3242f2", "metadata": {}, "source": [ "|Label| Sector |Label| Sector |Label| Sector |\n", @@ -186,7 +186,7 @@ { "cell_type": "code", "execution_count": null, - "id": "450ffecc", + "id": "727ef8dc", "metadata": { "tags": [ "hide-input" @@ -231,7 +231,7 @@ }, { "cell_type": "markdown", - "id": "84999c25", + "id": "9d184d9f", "metadata": {}, "source": [ "**Feasible allocations must satisfy**\n", @@ -250,7 +250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe1103ed", + "id": "370a522a", "metadata": { "tags": [ "hide-input" @@ -289,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "aa0ffaa4", + "id": "696f0361", "metadata": { "user_expressions": [] }, @@ -348,7 +348,7 @@ { "cell_type": "code", "execution_count": null, - "id": "290cbd69", + "id": "93b3383b", "metadata": {}, "outputs": [], "source": [ @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6857274c", + "id": "5f5a1ed9", "metadata": {}, "outputs": [], "source": [ @@ -371,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "17591d49", + "id": "8f335d01", "metadata": {}, "source": [ "Let's check the **Hawkins-Simon conditions**" @@ -380,7 +380,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c140cb92", + "id": "5d2a39e3", "metadata": {}, "outputs": [], "source": [ @@ -389,7 +389,7 @@ }, { "cell_type": "markdown", - "id": "525a7c53", + "id": "d58d0f7e", "metadata": {}, "source": [ "Now, let's compute the **Leontief inverse** matrix" @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7114da0d", + "id": "8984ac5c", "metadata": {}, "outputs": [], "source": [ @@ -409,7 +409,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b783b2cf", + "id": "5f1d7443", "metadata": {}, "outputs": [], "source": [ @@ -419,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "34449312", + "id": "5c8ff1aa", "metadata": { "user_expressions": [] }, @@ -464,7 +464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf08a62a", + "id": "089653fc", "metadata": {}, "outputs": [], "source": [ @@ -475,7 +475,7 @@ }, { "cell_type": "markdown", - "id": "aa1cccdb", + "id": "562515c3", "metadata": { "user_expressions": [] }, @@ -489,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "f3084c26", + "id": "4ee65bc4", "metadata": { "user_expressions": [] }, @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7667bb09", + "id": "6cd3e826", "metadata": { "tags": [ "hide-input" @@ -618,7 +618,7 @@ }, { "cell_type": "markdown", - "id": "bcc3ff1e", + "id": "b2913ceb", "metadata": { "user_expressions": [] }, @@ -681,7 +681,7 @@ { "cell_type": "code", "execution_count": null, - "id": "224e38d2", + "id": "26df9d00", "metadata": { "tags": [ "hide-input" @@ -697,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "650c2474", + "id": "bfd8241f", "metadata": {}, "source": [ "A higher measure indicates higher importance as a supplier.\n", @@ -742,7 +742,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f48323a1", + "id": "bc7fa2d6", "metadata": { "tags": [ "hide-input" @@ -762,7 +762,7 @@ }, { "cell_type": "markdown", - "id": "3c8d2ab2", + "id": "26648409", "metadata": {}, "source": [ "We observe that manufacturing and agriculture are highest ranking sectors.\n", @@ -839,7 +839,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c258ab7b", + "id": "1412ce61", "metadata": {}, "outputs": [], "source": [ @@ -851,7 +851,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4028b49c", + "id": "7a10ab46", "metadata": {}, "outputs": [], "source": [ @@ -863,7 +863,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0a77485", + "id": "27f73a8d", "metadata": {}, "outputs": [], "source": [ @@ -873,7 +873,7 @@ }, { "cell_type": "markdown", - "id": "c91fe46a", + "id": "185530b1", "metadata": { "user_expressions": [] }, diff --git a/_sources/intro.ipynb b/_sources/intro.ipynb index 77871e1c..903b0d39 100644 --- a/_sources/intro.ipynb +++ b/_sources/intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d7957ec6", + "id": "5353bbd2", "metadata": {}, "source": [ "# A First Course in Quantitative Economics with Python\n", diff --git a/_sources/intro_supply_demand.ipynb b/_sources/intro_supply_demand.ipynb index e8ccc2cb..9efac065 100644 --- a/_sources/intro_supply_demand.ipynb +++ b/_sources/intro_supply_demand.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8e25cfab", + "id": "66e54d70", "metadata": {}, "source": [ "# Introduction to Supply and Demand\n", @@ -52,7 +52,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82a5928d", + "id": "62e2ef5a", "metadata": {}, "outputs": [], "source": [ @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "79ce5d4d", + "id": "72899cee", "metadata": {}, "source": [ "## Consumer surplus\n", @@ -109,7 +109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ba79044", + "id": "6eb080eb", "metadata": { "mystnb": { "figure": { @@ -138,7 +138,7 @@ }, { "cell_type": "markdown", - "id": "725c2edc", + "id": "ca99aabd", "metadata": {}, "source": [ "The total consumer surplus in this market is \n", @@ -182,7 +182,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df17f703", + "id": "af3ce764", "metadata": { "mystnb": { "figure": { @@ -215,7 +215,7 @@ }, { "cell_type": "markdown", - "id": "5adf4a4a", + "id": "a6fc4b7a", "metadata": {}, "source": [ "Reasoning by analogy with the discrete case, the area under the demand curve and above the price is called the **consumer surplus**, and is a measure of total gains from trade on the part of consumers.\n", @@ -226,7 +226,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36fb45c3", + "id": "35a6cf77", "metadata": { "mystnb": { "figure": { @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "2ccc60af", + "id": "582a3581", "metadata": {}, "source": [ "The value $q^*$ is where the inverse demand curve meets price.\n", @@ -277,7 +277,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e03b9a8c", + "id": "42d42747", "metadata": { "mystnb": { "figure": { @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "c5cd85db", + "id": "a5bda22c", "metadata": {}, "source": [ "Let $v_i$ be the price at which producer $i$ is willing to sell the good.\n", @@ -336,7 +336,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0517c72", + "id": "d5cb9263", "metadata": { "mystnb": { "figure": { @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "e21a981d", + "id": "4c7cac87", "metadata": {}, "source": [ "(integration)=\n", @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "70db6cc9", + "id": "83f8de4f", "metadata": { "mystnb": { "figure": { @@ -426,7 +426,7 @@ }, { "cell_type": "markdown", - "id": "1d8b83d0", + "id": "8eefc08b", "metadata": {}, "source": [ "There are many rules for calculating integrals, with different rules applying to different choices of $f$.\n", @@ -483,7 +483,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f0bff520", + "id": "a47164f3", "metadata": {}, "outputs": [], "source": [ @@ -496,7 +496,7 @@ }, { "cell_type": "markdown", - "id": "b285cb90", + "id": "77f0f30d", "metadata": {}, "source": [ "The function below creates an instance of a Market namedtuple with default values." @@ -505,7 +505,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2c270c3", + "id": "e2339617", "metadata": {}, "outputs": [], "source": [ @@ -515,7 +515,7 @@ }, { "cell_type": "markdown", - "id": "40c5d0ed", + "id": "6ec72dac", "metadata": {}, "source": [ "This `market` can then be used by our `inverse_demand` and `inverse_supply` functions." @@ -524,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9899eba", + "id": "8c386be9", "metadata": {}, "outputs": [], "source": [ @@ -537,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "05dcaa82", + "id": "b0caea54", "metadata": {}, "source": [ "Here is a plot of these two functions using `market`." @@ -546,7 +546,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75d6c01a", + "id": "62b47d9f", "metadata": { "mystnb": { "figure": { @@ -578,7 +578,7 @@ }, { "cell_type": "markdown", - "id": "96fc900b", + "id": "5fe9d3b6", "metadata": {}, "source": [ "In the above graph, an **equilibrium** price-quantity pair occurs at the intersection of the supply and demand curves. \n", @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31912329", + "id": "45f6a29b", "metadata": { "mystnb": { "figure": { @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "e41c22c6", + "id": "852c4811", "metadata": {}, "source": [ "Consumer surplus provides a measure of total consumer welfare at quantity $q$.\n", @@ -682,7 +682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be2a9250", + "id": "987ada14", "metadata": { "mystnb": { "figure": { @@ -724,7 +724,7 @@ }, { "cell_type": "markdown", - "id": "4e00b71c", + "id": "ed5fc515", "metadata": {}, "source": [ "Producer surplus measures total producer welfare at quantity $q$ \n", @@ -769,7 +769,7 @@ { "cell_type": "code", "execution_count": null, - "id": "832e655b", + "id": "e60ead07", "metadata": {}, "outputs": [], "source": [ @@ -780,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "33cfdd7a", + "id": "9a4bd4cf", "metadata": {}, "source": [ "The next figure plots welfare as a function of $q$." @@ -789,7 +789,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d969b0f6", + "id": "c7b9a22e", "metadata": { "mystnb": { "figure": { @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "c481e943", + "id": "65d8b00d", "metadata": {}, "source": [ "Let's now give a social planner the task of maximizing social welfare.\n", @@ -917,7 +917,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26664c3b", + "id": "bfaf34cd", "metadata": {}, "outputs": [], "source": [ @@ -930,7 +930,7 @@ }, { "cell_type": "markdown", - "id": "b2b07e5f", + "id": "04113496", "metadata": {}, "source": [ "Here is a plot of inverse supply and demand." @@ -939,7 +939,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba08dbd6", + "id": "a06ba5ab", "metadata": {}, "outputs": [], "source": [ @@ -963,7 +963,7 @@ }, { "cell_type": "markdown", - "id": "769ccece", + "id": "3fa391e2", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1025,7 +1025,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe6215ec", + "id": "ad3de16d", "metadata": {}, "outputs": [], "source": [ @@ -1038,7 +1038,7 @@ }, { "cell_type": "markdown", - "id": "1526aaf5", + "id": "e9f2c1cc", "metadata": {}, "source": [ "The next figure plots welfare as a function of $q$." @@ -1047,7 +1047,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2b73703", + "id": "e5cbcb46", "metadata": {}, "outputs": [], "source": [ @@ -1060,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "5f001668", + "id": "9f96f883", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1092,7 +1092,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c0ac5d5", + "id": "df01a7d3", "metadata": {}, "outputs": [], "source": [ @@ -1108,7 +1108,7 @@ { "cell_type": "code", "execution_count": null, - "id": "779da70c", + "id": "7b74ac6d", "metadata": {}, "outputs": [], "source": [ @@ -1118,7 +1118,7 @@ }, { "cell_type": "markdown", - "id": "b86039f5", + "id": "674d1ba8", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1163,7 +1163,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73ec22b7", + "id": "280cdefc", "metadata": {}, "outputs": [], "source": [ @@ -1178,7 +1178,7 @@ }, { "cell_type": "markdown", - "id": "2b5bb2a5", + "id": "783ed97d", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/laffer_adaptive.ipynb b/_sources/laffer_adaptive.ipynb index 2f5261af..9384424d 100644 --- a/_sources/laffer_adaptive.ipynb +++ b/_sources/laffer_adaptive.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ecd28fdf", + "id": "d879ce75", "metadata": {}, "source": [ "# Laffer Curves with Adaptive Expectations \n", @@ -163,7 +163,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f653ab7", + "id": "dd34e734", "metadata": {}, "outputs": [], "source": [ @@ -179,7 +179,7 @@ }, { "cell_type": "markdown", - "id": "066f3564", + "id": "69981417", "metadata": { "user_expressions": [] }, @@ -190,7 +190,7 @@ { "cell_type": "code", "execution_count": null, - "id": "039c947a", + "id": "9a347ff2", "metadata": {}, "outputs": [], "source": [ @@ -209,7 +209,7 @@ }, { "cell_type": "markdown", - "id": "9a9e86e7", + "id": "e2591a32", "metadata": {}, "source": [ "Now we write code that computes steady-state $\\bar \\pi$s." @@ -218,7 +218,7 @@ { "cell_type": "code", "execution_count": null, - "id": "744f3e59", + "id": "14e001f5", "metadata": {}, "outputs": [], "source": [ @@ -238,7 +238,7 @@ }, { "cell_type": "markdown", - "id": "8d346651", + "id": "8199f064", "metadata": {}, "source": [ "We find two steady state $\\bar \\pi$ values\n", @@ -251,7 +251,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79e176c0", + "id": "285af41b", "metadata": { "mystnb": { "figure": { @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "f000719c", + "id": "b9c22519", "metadata": {}, "source": [ "## Associated Initial Price Levels\n", @@ -314,7 +314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0b1e8b4", + "id": "40ff486c", "metadata": {}, "outputs": [], "source": [ @@ -330,7 +330,7 @@ }, { "cell_type": "markdown", - "id": "c286487d", + "id": "7982fbf6", "metadata": {}, "source": [ "### Verification \n", @@ -343,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96cdcdc9", + "id": "d86190e2", "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "4dc5ee81", + "id": "b8a16d71", "metadata": {}, "source": [ "Compute limiting values starting from $p_{-1}$ associated with $\\pi_l$" @@ -390,7 +390,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77495304", + "id": "356d4406", "metadata": {}, "outputs": [], "source": [ @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "eb1603bd", + "id": "101e33e5", "metadata": {}, "source": [ "Compute limiting values starting from $p_{-1}$ associated with $\\pi_u$" @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04805625", + "id": "92883f0e", "metadata": {}, "outputs": [], "source": [ @@ -435,7 +435,7 @@ }, { "cell_type": "markdown", - "id": "1bbd6c0e", + "id": "a7b0faf7", "metadata": {}, "source": [ "## Slippery Side of Laffer Curve Dynamics\n", @@ -453,7 +453,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4060632", + "id": "982e4e51", "metadata": { "tags": [ "hide-cell" @@ -496,7 +496,7 @@ }, { "cell_type": "markdown", - "id": "dc38c4ee", + "id": "4e174b9c", "metadata": {}, "source": [ "Let's simulate the result generated by varying the initial $\\pi_{-1}$ and corresponding $p_{-1}$" @@ -505,7 +505,7 @@ { "cell_type": "code", "execution_count": null, - "id": "703c1d08", + "id": "ca0fa86a", "metadata": { "mystnb": { "figure": { diff --git a/_sources/lake_model.ipynb b/_sources/lake_model.ipynb index 208ef5ab..2a9add45 100644 --- a/_sources/lake_model.ipynb +++ b/_sources/lake_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6315a3e5", + "id": "db3be6c2", "metadata": {}, "source": [ "# A Lake Model of Employment\n", @@ -15,7 +15,7 @@ { "cell_type": "code", "execution_count": null, - "id": "145b6a70", + "id": "0c9f4c3b", "metadata": {}, "outputs": [], "source": [ @@ -25,7 +25,7 @@ }, { "cell_type": "markdown", - "id": "92cf3afb", + "id": "888feb10", "metadata": {}, "source": [ "## The Lake model\n", @@ -109,7 +109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3fadc5c", + "id": "a5a9ac6a", "metadata": {}, "outputs": [], "source": [ @@ -173,7 +173,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87e94bee", + "id": "55d7959d", "metadata": {}, "outputs": [], "source": [ @@ -208,7 +208,7 @@ }, { "cell_type": "markdown", - "id": "5ba10236", + "id": "4d0bb094", "metadata": {}, "source": [ "Not surprisingly, we observe that labor force $n_t$ increases at a constant rate.\n", @@ -318,7 +318,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fd559d39", + "id": "c36159a8", "metadata": {}, "outputs": [], "source": [ @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c11fd5b5", + "id": "f90153fa", "metadata": {}, "outputs": [], "source": [ @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "0e8c1e24", + "id": "1032fd72", "metadata": {}, "source": [ "Since $\\bar{x}$ is an eigenvector corresponding to the eigenvalue $r(A)$, all the vectors in the set\n", @@ -437,7 +437,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1020edb", + "id": "c486245c", "metadata": {}, "outputs": [], "source": [ @@ -447,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "cc741786", + "id": "81aa5678", "metadata": {}, "source": [ "Thus, while the sequence of iterates still moves towards the dominant eigenvector $\\bar{x}$, in this case\n", @@ -514,7 +514,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b08e431", + "id": "570fcd46", "metadata": {}, "outputs": [], "source": [ @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "a7d42cd3", + "id": "1b8fdb55", "metadata": {}, "source": [ "To provide more intuition for convergence, we further explain the convergence below without the Perron-Frobenius theorem.\n", @@ -620,7 +620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72f0d36a", + "id": "682e7230", "metadata": {}, "outputs": [], "source": [ @@ -641,7 +641,7 @@ }, { "cell_type": "markdown", - "id": "b4bc523b", + "id": "518d3853", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/linear_equations.ipynb b/_sources/linear_equations.ipynb index df9d2022..2ed0a4f7 100644 --- a/_sources/linear_equations.ipynb +++ b/_sources/linear_equations.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d5a42b1f", + "id": "560b4365", "metadata": {}, "source": [ "# Linear Equations and Matrix Algebra\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6605106a", + "id": "59c28274", "metadata": {}, "outputs": [], "source": [ @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "86168f2f", + "id": "012e05da", "metadata": {}, "source": [ "## A two good example\n", @@ -162,7 +162,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3d9796a", + "id": "d5c0fdee", "metadata": { "tags": [ "hide-input" @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "e0ac69dc", + "id": "f18fdc15", "metadata": {}, "source": [ "### Vector operations\n", @@ -263,7 +263,7 @@ { "cell_type": "code", "execution_count": null, - "id": "642d1188", + "id": "e88b770a", "metadata": { "tags": [ "hide-input" @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "3880b93f", + "id": "408d521d", "metadata": {}, "source": [ "Scalar multiplication is an operation that multiplies a vector $x$ with a scalar elementwise.\n", @@ -351,7 +351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c439b28", + "id": "2f2f92fe", "metadata": { "tags": [ "hide-input" @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "e9423037", + "id": "e9ffba82", "metadata": {}, "source": [ "In Python, a vector can be represented as a list or tuple, \n", @@ -407,7 +407,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44267672", + "id": "db053bca", "metadata": {}, "outputs": [], "source": [ @@ -419,7 +419,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72153f84", + "id": "6ed11bed", "metadata": {}, "outputs": [], "source": [ @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "dfaefb33", + "id": "cee69a98", "metadata": {}, "source": [ "### Inner product and norm\n", @@ -471,7 +471,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eb80b55e", + "id": "92b50631", "metadata": {}, "outputs": [], "source": [ @@ -481,7 +481,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e554d1b", + "id": "f53be10a", "metadata": {}, "outputs": [], "source": [ @@ -491,7 +491,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdc201ff", + "id": "ccbad3a8", "metadata": {}, "outputs": [], "source": [ @@ -501,7 +501,7 @@ { "cell_type": "code", "execution_count": null, - "id": "121d8a12", + "id": "2b2a9816", "metadata": {}, "outputs": [], "source": [ @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "f0f39803", + "id": "2bc678e1", "metadata": {}, "source": [ "## Matrix operations\n", @@ -740,7 +740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "14f979a7", + "id": "124388e3", "metadata": {}, "outputs": [], "source": [ @@ -753,7 +753,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f39ee6b9", + "id": "1523fdd0", "metadata": {}, "outputs": [], "source": [ @@ -765,7 +765,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce5c2785", + "id": "600d6092", "metadata": {}, "outputs": [], "source": [ @@ -774,7 +774,7 @@ }, { "cell_type": "markdown", - "id": "f8021be5", + "id": "7d0d1ed2", "metadata": {}, "source": [ "The `shape` attribute is a tuple giving the number of rows and columns ---\n", @@ -792,7 +792,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f8d7bc5", + "id": "87c572ea", "metadata": {}, "outputs": [], "source": [ @@ -804,7 +804,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a68689d", + "id": "501a4034", "metadata": {}, "outputs": [], "source": [ @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "f0db06da", + "id": "f5d37267", "metadata": {}, "source": [ "To multiply matrices we use the `@` symbol.\n", @@ -1052,7 +1052,7 @@ { "cell_type": "code", "execution_count": null, - "id": "448fad0a", + "id": "fa623c75", "metadata": {}, "outputs": [], "source": [ @@ -1066,7 +1066,7 @@ }, { "cell_type": "markdown", - "id": "3a393842", + "id": "43421501", "metadata": { "tags": [] }, @@ -1210,7 +1210,7 @@ { "cell_type": "code", "execution_count": null, - "id": "798bd3e0", + "id": "a8e6fec4", "metadata": {}, "outputs": [], "source": [ @@ -1220,7 +1220,7 @@ }, { "cell_type": "markdown", - "id": "2237169c", + "id": "71046fad", "metadata": {}, "source": [ "Now we change this to a NumPy array." @@ -1229,7 +1229,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e15f3b3f", + "id": "e08721ce", "metadata": {}, "outputs": [], "source": [ @@ -1239,7 +1239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5989834e", + "id": "139ddfb4", "metadata": {}, "outputs": [], "source": [ @@ -1251,7 +1251,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7c13f45", + "id": "50dd61a5", "metadata": {}, "outputs": [], "source": [ @@ -1262,7 +1262,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ed7e035", + "id": "191f738d", "metadata": {}, "outputs": [], "source": [ @@ -1275,7 +1275,7 @@ { "cell_type": "code", "execution_count": null, - "id": "953bf065", + "id": "9e227038", "metadata": {}, "outputs": [], "source": [ @@ -1286,7 +1286,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b851522a", + "id": "3a5e82d3", "metadata": {}, "outputs": [], "source": [ @@ -1297,7 +1297,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f729d047", + "id": "11500cc0", "metadata": {}, "outputs": [], "source": [ @@ -1307,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "cac6e1a8", + "id": "540957dc", "metadata": {}, "source": [ "Notice that we get the same solutions as the pencil and paper case.\n", @@ -1318,7 +1318,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2e3aba4", + "id": "fc899d4e", "metadata": {}, "outputs": [], "source": [ @@ -1330,7 +1330,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bd382ff", + "id": "a73f95c7", "metadata": {}, "outputs": [], "source": [ @@ -1340,7 +1340,7 @@ }, { "cell_type": "markdown", - "id": "ed11ff5f", + "id": "98a101ab", "metadata": {}, "source": [ "Observe how we can solve for $x = A^{-1} y$ by either via `inv(A) @ y`, or using `solve(A, y)`.\n", @@ -1431,7 +1431,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3417a2f2", + "id": "c3b2e1a5", "metadata": {}, "outputs": [], "source": [ @@ -1451,7 +1451,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f135723e", + "id": "2a391852", "metadata": {}, "outputs": [], "source": [ @@ -1467,7 +1467,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8d89157", + "id": "813b64a9", "metadata": {}, "outputs": [], "source": [ @@ -1479,7 +1479,7 @@ }, { "cell_type": "markdown", - "id": "e5f66510", + "id": "7d29fea3", "metadata": {}, "source": [ "The solution is given by:\n", @@ -1583,7 +1583,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba802039", + "id": "5e726e6a", "metadata": {}, "outputs": [], "source": [ @@ -1594,7 +1594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d06eaf73", + "id": "41192871", "metadata": {}, "outputs": [], "source": [ @@ -1615,7 +1615,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1203e81c", + "id": "4ac31489", "metadata": {}, "outputs": [], "source": [ @@ -1626,7 +1626,7 @@ { "cell_type": "code", "execution_count": null, - "id": "982a4271", + "id": "f1f672cd", "metadata": { "tags": [ "hide-input" @@ -1640,7 +1640,7 @@ }, { "cell_type": "markdown", - "id": "f770e200", + "id": "e8b4ed9a", "metadata": {}, "source": [ "Here is a visualization of how the least squares method approximates the equation of a line connecting a set of points.\n", @@ -1651,7 +1651,7 @@ { "cell_type": "code", "execution_count": null, - "id": "579c9ce2", + "id": "4cb07430", "metadata": {}, "outputs": [], "source": [ @@ -1671,7 +1671,7 @@ }, { "cell_type": "markdown", - "id": "f0fcd0a3", + "id": "979b49f1", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/lln_clt.ipynb b/_sources/lln_clt.ipynb index 1f6ca012..9ee1388d 100644 --- a/_sources/lln_clt.ipynb +++ b/_sources/lln_clt.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "67b0f14c", + "id": "4a7f4f5a", "metadata": {}, "source": [ "# LLN and CLT\n", @@ -30,7 +30,7 @@ { "cell_type": "code", "execution_count": null, - "id": "862c5a57", + "id": "9848839f", "metadata": {}, "outputs": [], "source": [ @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "e0735f5c", + "id": "d7fb73a7", "metadata": {}, "source": [ "(lln_mr)=\n", @@ -85,7 +85,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d609c3b2", + "id": "510bd53f", "metadata": {}, "outputs": [], "source": [ @@ -96,7 +96,7 @@ }, { "cell_type": "markdown", - "id": "8a0638d8", + "id": "4757efaa", "metadata": {}, "source": [ "In this setting, the LLN tells us if we flip the coin many times, the fraction\n", @@ -110,7 +110,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66aa8ac6", + "id": "f670d01d", "metadata": {}, "outputs": [], "source": [ @@ -121,7 +121,7 @@ }, { "cell_type": "markdown", - "id": "9c45d913", + "id": "04e07b61", "metadata": {}, "source": [ "If we change $p$ the claim still holds:" @@ -130,7 +130,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c24d4078", + "id": "ea2ccd0b", "metadata": {}, "outputs": [], "source": [ @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "c7d4fbeb", + "id": "8a949803", "metadata": {}, "source": [ "Let's connect this to the discussion above, where we said the sample average\n", @@ -288,7 +288,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48d7cc38", + "id": "9191a62f", "metadata": {}, "outputs": [], "source": [ @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "391911c6", + "id": "68459eb8", "metadata": {}, "source": [ "Now we write a function to generate $m$ sample means and histogram them." @@ -313,7 +313,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3717d70", + "id": "9d3b43e6", "metadata": {}, "outputs": [], "source": [ @@ -342,7 +342,7 @@ }, { "cell_type": "markdown", - "id": "3cbdc56d", + "id": "e08b104a", "metadata": {}, "source": [ "Now we call the function." @@ -351,7 +351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4511ee42", + "id": "e655b0ef", "metadata": {}, "outputs": [], "source": [ @@ -363,7 +363,7 @@ }, { "cell_type": "markdown", - "id": "73518fe1", + "id": "ed38ec30", "metadata": {}, "source": [ "We can see that the distribution of $\\bar X$ is clustered around $\\mathbb E X$\n", @@ -379,7 +379,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c80ac887", + "id": "dfd53137", "metadata": {}, "outputs": [], "source": [ @@ -413,7 +413,7 @@ }, { "cell_type": "markdown", - "id": "54b898e6", + "id": "5bf71321", "metadata": {}, "source": [ "Let's try with a normal distribution." @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe611dd0", + "id": "0fa8dbd8", "metadata": {}, "outputs": [], "source": [ @@ -431,7 +431,7 @@ }, { "cell_type": "markdown", - "id": "1718772c", + "id": "f42e9417", "metadata": {}, "source": [ "As $n$ gets large, more probability mass clusters around the population mean $\\mu$.\n", @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8d3f5e6", + "id": "390632dc", "metadata": {}, "outputs": [], "source": [ @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "8e57fef2", + "id": "3c7d3148", "metadata": {}, "source": [ "We get a similar result." @@ -459,7 +459,7 @@ }, { "cell_type": "markdown", - "id": "7db03b89", + "id": "1745eea3", "metadata": {}, "source": [ "## Breaking the LLN\n", @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "5cc7575f", + "id": "2b98a947", "metadata": {}, "source": [ "### Failure of the IID condition\n", @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "529cac33", + "id": "89ad0ee4", "metadata": {}, "source": [ "## Central limit theorem\n", @@ -599,7 +599,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba72b0d4", + "id": "0008fdb1", "metadata": {}, "outputs": [], "source": [ @@ -634,7 +634,7 @@ }, { "cell_type": "markdown", - "id": "728a99a0", + "id": "40fdddc4", "metadata": {}, "source": [ "(Notice the absence of for loops --- every operation is vectorized, meaning that the major calculations are all shifted to fast C code.)\n", @@ -662,7 +662,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b173e2a", + "id": "440aeab9", "metadata": {}, "outputs": [], "source": [ @@ -695,7 +695,7 @@ }, { "cell_type": "markdown", - "id": "66a2314e", + "id": "cbd9fcd8", "metadata": {}, "source": [ "```{solution-end}\n", @@ -826,7 +826,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bde31d7", + "id": "751bf54c", "metadata": {}, "outputs": [], "source": [ @@ -861,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "ebfbc10f", + "id": "6fe1b068", "metadata": {}, "source": [ "We see the convergence of $\\bar x$ around $\\mu$ even when the independence assumption is violated.\n", diff --git a/_sources/long_run_growth.ipynb b/_sources/long_run_growth.ipynb index c414fe0f..c694d2c3 100644 --- a/_sources/long_run_growth.ipynb +++ b/_sources/long_run_growth.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "13d0559a", + "id": "b8d9e70d", "metadata": {}, "source": [ "# Long-Run Growth\n", @@ -62,7 +62,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5818a27", + "id": "65bf4061", "metadata": {}, "outputs": [], "source": [ @@ -75,7 +75,7 @@ }, { "cell_type": "markdown", - "id": "2a22b217", + "id": "f9fdeebd", "metadata": {}, "source": [ "## Setting up\n", @@ -95,7 +95,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bf0cba8", + "id": "49863d71", "metadata": {}, "outputs": [], "source": [ @@ -107,7 +107,7 @@ }, { "cell_type": "markdown", - "id": "6ebc1453", + "id": "2bf4e435", "metadata": {}, "source": [ "We can see that this dataset contains GDP per capita (`gdppc`) and population (pop) for many countries and years.\n", @@ -118,7 +118,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15ada17e", + "id": "b373afac", "metadata": {}, "outputs": [], "source": [ @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "0209da0e", + "id": "d95f2f0b", "metadata": {}, "source": [ "We can now explore some of the 169 countries that are available. \n", @@ -139,7 +139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74125b67", + "id": "02ef1586", "metadata": {}, "outputs": [], "source": [ @@ -155,7 +155,7 @@ }, { "cell_type": "markdown", - "id": "8ad14928", + "id": "06b345c8", "metadata": {}, "source": [ "Let's now reshape the original data into some convenient variables to enable quicker access to countries' time series data.\n", @@ -166,7 +166,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50949a04", + "id": "9d248428", "metadata": {}, "outputs": [], "source": [ @@ -176,7 +176,7 @@ }, { "cell_type": "markdown", - "id": "38456efa", + "id": "ad3ae1cc", "metadata": {}, "source": [ "Now we can focus on GDP per capita (`gdppc`) and generate a wide data format" @@ -185,7 +185,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f355920", + "id": "fa37da7b", "metadata": {}, "outputs": [], "source": [ @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afcd9e2b", + "id": "a8bbd04d", "metadata": {}, "outputs": [], "source": [ @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "4cc481c7", + "id": "21a227c1", "metadata": {}, "source": [ "We create a variable `color_mapping` to store a map between country codes and colors for consistency" @@ -214,7 +214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3086160", + "id": "efe46bac", "metadata": { "tags": [ "hide-input" @@ -234,7 +234,7 @@ }, { "cell_type": "markdown", - "id": "fd7567ab", + "id": "9d0e13b9", "metadata": {}, "source": [ "## GDP per capita\n", @@ -249,7 +249,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8622152", + "id": "f9339e54", "metadata": { "mystnb": { "figure": { @@ -273,7 +273,7 @@ }, { "cell_type": "markdown", - "id": "61a9ad46", + "id": "da9bf7a0", "metadata": {}, "source": [ ":::{note}\n", @@ -288,7 +288,7 @@ { "cell_type": "code", "execution_count": null, - "id": "283c3d75", + "id": "781276db", "metadata": { "mystnb": { "figure": { @@ -316,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "39cde637", + "id": "856fb431", "metadata": {}, "source": [ "### Comparing the US, UK, and China\n", @@ -329,7 +329,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85a0ed0f", + "id": "9fd15853", "metadata": {}, "outputs": [], "source": [ @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "f1f2aeab", + "id": "bf4e45c8", "metadata": {}, "source": [ "As you can see from this chart, economic growth started in earnest in the 18th century and continued for the next two hundred years. \n", @@ -387,7 +387,7 @@ { "cell_type": "code", "execution_count": null, - "id": "352af113", + "id": "6b8ffdf1", "metadata": { "mystnb": { "figure": { @@ -461,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "8a1917de", + "id": "40d8b989", "metadata": {}, "source": [ "The preceding graph of per capita GDP strikingly reveals how the spread of the Industrial Revolution has over time gradually lifted the living standards of substantial\n", @@ -489,7 +489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "106cc341", + "id": "02f05a88", "metadata": { "mystnb": { "figure": { @@ -547,7 +547,7 @@ }, { "cell_type": "markdown", - "id": "3433def6", + "id": "6deac364", "metadata": {}, "source": [ "### Focusing on the US and UK\n", @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b112413b", + "id": "07d6efb1", "metadata": { "mystnb": { "figure": { @@ -624,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "0348de35", + "id": "4d98478a", "metadata": {}, "source": [ "## GDP growth\n", @@ -637,7 +637,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f09a5b04", + "id": "678681b7", "metadata": {}, "outputs": [], "source": [ @@ -649,7 +649,7 @@ }, { "cell_type": "markdown", - "id": "bf0b0840", + "id": "963647eb", "metadata": {}, "source": [ "### Early industrialization (1820 to 1940)\n", @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d31cebcd", + "id": "e2e50e04", "metadata": { "mystnb": { "figure": { @@ -688,7 +688,7 @@ }, { "cell_type": "markdown", - "id": "d03295d1", + "id": "a220b002", "metadata": {}, "source": [ "#### Constructing a plot similar to Tooze's\n", @@ -701,7 +701,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f6d070f", + "id": "07f6045d", "metadata": {}, "outputs": [], "source": [ @@ -712,7 +712,7 @@ }, { "cell_type": "markdown", - "id": "73aad41f", + "id": "7b37d631", "metadata": {}, "source": [ "Now let's assemble our series and get ready to plot them." @@ -721,7 +721,7 @@ { "cell_type": "code", "execution_count": null, - "id": "54096251", + "id": "e4acffa3", "metadata": {}, "outputs": [], "source": [ @@ -736,7 +736,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0bc8ca6", + "id": "8bedb37a", "metadata": {}, "outputs": [], "source": [ @@ -755,7 +755,7 @@ }, { "cell_type": "markdown", - "id": "8699b834", + "id": "e0819b8c", "metadata": {}, "source": [ "At the start of this lecture, we noted how US GDP came from \"nowhere\" at the start of the 19th century to rival and then overtake the GDP of the British Empire\n", @@ -773,7 +773,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69510131", + "id": "3c73fbc1", "metadata": { "mystnb": { "figure": { @@ -795,7 +795,7 @@ }, { "cell_type": "markdown", - "id": "1ee97de1", + "id": "e173935a", "metadata": {}, "source": [ "It is tempting to compare this graph with figure {numref}`gdp1` that showed the US overtaking the UK near the start of the \"American Century\", a version of the graph featured in chapter 1 of {cite}`Tooze_2014`.\n", @@ -810,7 +810,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0fca1228", + "id": "55499ea8", "metadata": {}, "outputs": [], "source": [ @@ -823,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "8717b03f", + "id": "32c26614", "metadata": {}, "source": [ "We can save the raw data in a more convenient format to build a single table of regional GDP per capita" @@ -832,7 +832,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a23b2ea2", + "id": "403074ec", "metadata": {}, "outputs": [], "source": [ @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "2d51829f", + "id": "41cfbd85", "metadata": {}, "source": [ "Let's interpolate based on time to fill in any gaps in the dataset for the purpose of plotting" @@ -851,7 +851,7 @@ { "cell_type": "code", "execution_count": null, - "id": "189b3bf3", + "id": "d1425fa9", "metadata": {}, "outputs": [], "source": [ @@ -860,7 +860,7 @@ }, { "cell_type": "markdown", - "id": "41a92d2f", + "id": "ee016595", "metadata": {}, "source": [ "Looking more closely, let's compare the time series for `Western Offshoots` and `Sub-Saharan Africa` with a number of different regions around the world.\n", @@ -871,7 +871,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f14d4128", + "id": "1ea24c1f", "metadata": { "mystnb": { "figure": { diff --git a/_sources/lp_intro.ipynb b/_sources/lp_intro.ipynb index a7a8b322..67850f0d 100644 --- a/_sources/lp_intro.ipynb +++ b/_sources/lp_intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "9e18d109", + "id": "c5bbd11f", "metadata": {}, "source": [ "(lp_intro)=\n", @@ -14,7 +14,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bfc89bbf", + "id": "6d7a9725", "metadata": { "tags": [ "hide-output" @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "136819f2", + "id": "c7bafd2a", "metadata": {}, "source": [ "## Overview\n", @@ -60,7 +60,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ed9e5987", + "id": "2e4bffd8", "metadata": {}, "outputs": [], "source": [ @@ -73,7 +73,7 @@ }, { "cell_type": "markdown", - "id": "31cb01aa", + "id": "1cd91168", "metadata": {}, "source": [ "Let's start with some examples of linear programming problem.\n", @@ -123,7 +123,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d72747e", + "id": "c14028a8", "metadata": { "tags": [ "hide-input" @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "98ef5b9b", + "id": "a78ec2b0", "metadata": {}, "source": [ "The blue region is the feasible set within which all constraints are satisfied.\n", @@ -187,7 +187,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e494e6ba", + "id": "6f7d46b4", "metadata": {}, "outputs": [], "source": [ @@ -197,7 +197,7 @@ }, { "cell_type": "markdown", - "id": "f5ffde75", + "id": "7fef58ee", "metadata": {}, "source": [ "Let's create two variables $x_1$ and $x_2$ such that they can only have nonnegative values." @@ -206,7 +206,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a7da3298", + "id": "864019c8", "metadata": {}, "outputs": [], "source": [ @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "f1ad77c9", + "id": "cb10cf0e", "metadata": {}, "source": [ "Add the constraints to the problem." @@ -226,7 +226,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b19e6cd2", + "id": "9737573d", "metadata": {}, "outputs": [], "source": [ @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "4330d439", + "id": "8f65fb6e", "metadata": {}, "source": [ "Let's specify the objective function. We use `solver.Maximize` method in the case when we want to maximize the objective function and in the case of minimization we can use `solver.Minimize`." @@ -248,7 +248,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f4e34a0", + "id": "e8104753", "metadata": {}, "outputs": [], "source": [ @@ -258,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "f562de71", + "id": "3191e8a0", "metadata": {}, "source": [ "Once we solve the problem, we can check whether the solver was successful in solving the problem using its status. If it's successful, then the status will be equal to `pywraplp.Solver.OPTIMAL`." @@ -267,7 +267,7 @@ { "cell_type": "code", "execution_count": null, - "id": "68161ebb", + "id": "37947225", "metadata": {}, "outputs": [], "source": [ @@ -283,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "ad5d8142", + "id": "c7cf024d", "metadata": {}, "source": [ "## Example 2: investment problem\n", @@ -378,7 +378,7 @@ { "cell_type": "code", "execution_count": null, - "id": "885091ee", + "id": "c984c74a", "metadata": {}, "outputs": [], "source": [ @@ -388,7 +388,7 @@ }, { "cell_type": "markdown", - "id": "4e4159c0", + "id": "3823876a", "metadata": {}, "source": [ "Let's create five variables $x_1, x_2, x_3, x_4,$ and $x_5$ such that they can only have the values defined in the above constraints." @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6515a50b", + "id": "19cbb989", "metadata": {}, "outputs": [], "source": [ @@ -411,7 +411,7 @@ }, { "cell_type": "markdown", - "id": "2f246a87", + "id": "da77eb14", "metadata": {}, "source": [ "Add the constraints to the problem." @@ -420,7 +420,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b357781b", + "id": "bdec0f33", "metadata": {}, "outputs": [], "source": [ @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "e3d43080", + "id": "a1c9a2f7", "metadata": {}, "source": [ "Let's specify the objective function." @@ -445,7 +445,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc10be98", + "id": "0447e063", "metadata": {}, "outputs": [], "source": [ @@ -455,7 +455,7 @@ }, { "cell_type": "markdown", - "id": "157a1f29", + "id": "295b3bfc", "metadata": {}, "source": [ "Let's solve the problem and check the status using `pywraplp.Solver.OPTIMAL`." @@ -464,7 +464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76929a33", + "id": "5f0907b9", "metadata": {}, "outputs": [], "source": [ @@ -485,7 +485,7 @@ }, { "cell_type": "markdown", - "id": "4333ef1a", + "id": "b15531ae", "metadata": {}, "source": [ "OR-Tools tells us that the best investment strategy is:\n", @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f23daa0", + "id": "bc5e8ce7", "metadata": {}, "outputs": [], "source": [ @@ -631,7 +631,7 @@ }, { "cell_type": "markdown", - "id": "9ed7aa09", + "id": "24fda8ef", "metadata": {}, "source": [ "Once we solve the problem, we can check whether the solver was successful in solving the problem using the boolean attribute `success`. If it's successful, then the `success` attribute is set to `True`." @@ -640,7 +640,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c166da59", + "id": "f2fefd85", "metadata": {}, "outputs": [], "source": [ @@ -658,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "b0c30ad4", + "id": "8b9b31ee", "metadata": {}, "source": [ "The optimal plan tells the factory to produce $2.5$ units of Product 1 and $5$ units of Product 2; that generates a maximizing value of revenue of $27.5$.\n", @@ -720,7 +720,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ece3df4a", + "id": "cb654617", "metadata": {}, "outputs": [], "source": [ @@ -746,7 +746,7 @@ }, { "cell_type": "markdown", - "id": "585493a6", + "id": "01aa1838", "metadata": {}, "source": [ "Let's solve the problem and check the status using `success` attribute." @@ -755,7 +755,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c4f0744", + "id": "2b08ef5a", "metadata": {}, "outputs": [], "source": [ @@ -778,7 +778,7 @@ }, { "cell_type": "markdown", - "id": "33244e3b", + "id": "7233513e", "metadata": {}, "source": [ "SciPy tells us that the best investment strategy is:\n", @@ -831,7 +831,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3862ff8f", + "id": "3436a37f", "metadata": {}, "outputs": [], "source": [ @@ -846,7 +846,7 @@ { "cell_type": "code", "execution_count": null, - "id": "602a19ea", + "id": "605cc6a8", "metadata": {}, "outputs": [], "source": [ @@ -863,7 +863,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0cc2e545", + "id": "8a730582", "metadata": {}, "outputs": [], "source": [ @@ -874,7 +874,7 @@ { "cell_type": "code", "execution_count": null, - "id": "11f35946", + "id": "0915bfba", "metadata": {}, "outputs": [], "source": [ @@ -892,7 +892,7 @@ }, { "cell_type": "markdown", - "id": "61733a0e", + "id": "b206a064", "metadata": {}, "source": [ "```{solution-end}\n", @@ -937,7 +937,7 @@ { "cell_type": "code", "execution_count": null, - "id": "586c7ecb", + "id": "d7d2e58d", "metadata": {}, "outputs": [], "source": [ @@ -947,7 +947,7 @@ }, { "cell_type": "markdown", - "id": "68735651", + "id": "f149ecb7", "metadata": {}, "source": [ "Let's create two variables $x_1$ and $x_2$ such that they can only have nonnegative values." @@ -956,7 +956,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27bc1435", + "id": "4d7a62d2", "metadata": {}, "outputs": [], "source": [ @@ -968,7 +968,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bec13232", + "id": "24dbb68d", "metadata": {}, "outputs": [], "source": [ @@ -982,7 +982,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db517cc1", + "id": "bc416998", "metadata": {}, "outputs": [], "source": [ @@ -993,7 +993,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06885142", + "id": "cc6c8da0", "metadata": {}, "outputs": [], "source": [ @@ -1011,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": "70cf3302", + "id": "2cfa1608", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/markov_chains_I.ipynb b/_sources/markov_chains_I.ipynb index c6c1e6bf..bdd8ec92 100644 --- a/_sources/markov_chains_I.ipynb +++ b/_sources/markov_chains_I.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "a6ef4105", + "id": "758f1f70", "metadata": {}, "source": [ "# Markov Chains: Basic Concepts \n", @@ -17,7 +17,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6007402d", + "id": "582e7777", "metadata": { "tags": [ "hide-output" @@ -30,7 +30,7 @@ }, { "cell_type": "markdown", - "id": "c776bed0", + "id": "4bb7bb9f", "metadata": {}, "source": [ "## Overview\n", @@ -63,7 +63,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5da578a", + "id": "9791924c", "metadata": {}, "outputs": [], "source": [ @@ -82,7 +82,7 @@ }, { "cell_type": "markdown", - "id": "8acd6c0c", + "id": "e485c246", "metadata": {}, "source": [ "## Definitions and examples\n", @@ -270,7 +270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d9f7402", + "id": "8b32c344", "metadata": {}, "outputs": [], "source": [ @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "68c24e62", + "id": "ce0f9c57", "metadata": {}, "source": [ "Here is a visualization, with darker colors indicating higher probability." @@ -294,7 +294,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f34063b5", + "id": "b3babbff", "metadata": { "tags": [ "hide-input" @@ -330,7 +330,7 @@ }, { "cell_type": "markdown", - "id": "49d45617", + "id": "49000077", "metadata": {}, "source": [ "Looking at the data, we see that democracies tend to have longer-lasting growth\n", @@ -440,7 +440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28b0f433", + "id": "bd5beed0", "metadata": {}, "outputs": [], "source": [ @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "bfea606e", + "id": "f99a201f", "metadata": {}, "source": [ "We'll write our code as a function that accepts the following three arguments\n", @@ -464,7 +464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9170c524", + "id": "e143f058", "metadata": {}, "outputs": [], "source": [ @@ -493,7 +493,7 @@ }, { "cell_type": "markdown", - "id": "147ea437", + "id": "c69ea0fe", "metadata": {}, "source": [ "Let's see how it works using the small matrix" @@ -502,7 +502,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d95e079", + "id": "09b32265", "metadata": {}, "outputs": [], "source": [ @@ -512,7 +512,7 @@ }, { "cell_type": "markdown", - "id": "d6dd3888", + "id": "20ff035f", "metadata": {}, "source": [ "Here's a short time series." @@ -521,7 +521,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ceef3ac0", + "id": "e20969c4", "metadata": {}, "outputs": [], "source": [ @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "d5f1545a", + "id": "64dd496d", "metadata": {}, "source": [ "It can be shown that for a long series drawn from `P`, the fraction of the\n", @@ -547,7 +547,7 @@ { "cell_type": "code", "execution_count": null, - "id": "281fbfb0", + "id": "5b7d80c4", "metadata": {}, "outputs": [], "source": [ @@ -557,7 +557,7 @@ }, { "cell_type": "markdown", - "id": "2b10814d", + "id": "bc2d33fe", "metadata": {}, "source": [ "You can try changing the initial distribution to confirm that the output is\n", @@ -574,7 +574,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8130f651", + "id": "fccc14cf", "metadata": {}, "outputs": [], "source": [ @@ -585,7 +585,7 @@ }, { "cell_type": "markdown", - "id": "93302d8b", + "id": "1ab6e176", "metadata": {}, "source": [ "The `simulate` routine is faster (because it is [JIT compiled](https://python-programming.quantecon.org/numba.html#numba-link))." @@ -594,7 +594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8cf0bc9b", + "id": "1699847e", "metadata": {}, "outputs": [], "source": [ @@ -604,7 +604,7 @@ { "cell_type": "code", "execution_count": null, - "id": "000fee4c", + "id": "3eb1c378", "metadata": {}, "outputs": [], "source": [ @@ -613,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "032b67e1", + "id": "ded4e4e2", "metadata": {}, "source": [ "#### Adding state values and initial conditions\n", @@ -628,7 +628,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3bb3970c", + "id": "20ad46ff", "metadata": {}, "outputs": [], "source": [ @@ -639,7 +639,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7932fde", + "id": "2825c81c", "metadata": {}, "outputs": [], "source": [ @@ -649,7 +649,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2e2e5f93", + "id": "d007aa0a", "metadata": {}, "outputs": [], "source": [ @@ -658,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "191bcde1", + "id": "c35328df", "metadata": {}, "source": [ "If we want to see indices rather than state values as outputs as we can use" @@ -667,7 +667,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94728553", + "id": "f814c589", "metadata": {}, "outputs": [], "source": [ @@ -676,7 +676,7 @@ }, { "cell_type": "markdown", - "id": "7d87ae91", + "id": "5b12a08f", "metadata": {}, "source": [ "(mc_md)=\n", @@ -850,7 +850,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc5c35ef", + "id": "8e0bfd22", "metadata": {}, "outputs": [], "source": [ @@ -862,7 +862,7 @@ }, { "cell_type": "markdown", - "id": "78d7ace5", + "id": "b9cfee07", "metadata": {}, "source": [ "Notice that `ψ @ P` is the same as `ψ`.\n", @@ -944,7 +944,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0917cad", + "id": "cbd6c8c1", "metadata": {}, "outputs": [], "source": [ @@ -957,7 +957,7 @@ }, { "cell_type": "markdown", - "id": "1d7f06a5", + "id": "c61d35be", "metadata": {}, "source": [ "### Asymptotic stationarity\n", @@ -1000,7 +1000,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a896e38a", + "id": "ecfdb092", "metadata": {}, "outputs": [], "source": [ @@ -1012,7 +1012,7 @@ }, { "cell_type": "markdown", - "id": "b22e4f56", + "id": "66149b4a", "metadata": {}, "source": [ "Let's pick an initial distribution $\\psi_1, \\psi_2, \\psi_3$ and trace out the sequence of distributions $\\psi_i P^t$ for $t = 0, 1, 2, \\ldots$, for $i=1, 2, 3$.\n", @@ -1023,7 +1023,7 @@ { "cell_type": "code", "execution_count": null, - "id": "963a1f79", + "id": "87f7e862", "metadata": {}, "outputs": [], "source": [ @@ -1038,7 +1038,7 @@ }, { "cell_type": "markdown", - "id": "c1833687", + "id": "0a52b346", "metadata": {}, "source": [ "Now we plot the sequence" @@ -1047,7 +1047,7 @@ { "cell_type": "code", "execution_count": null, - "id": "728457a4", + "id": "aa81d8ba", "metadata": { "tags": [ "hide-input" @@ -1103,7 +1103,7 @@ }, { "cell_type": "markdown", - "id": "22707126", + "id": "085f37c9", "metadata": {}, "source": [ "Here\n", @@ -1151,7 +1151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3ee8995", + "id": "8c250dca", "metadata": { "tags": [ "hide-input" @@ -1211,7 +1211,7 @@ }, { "cell_type": "markdown", - "id": "6eb4d8b0", + "id": "db70c0f8", "metadata": {}, "source": [ "This animation demonstrates the behavior of an irreducible and periodic stochastic matrix.\n", @@ -1366,7 +1366,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0dbf141", + "id": "c6042932", "metadata": {}, "outputs": [], "source": [ @@ -1379,7 +1379,7 @@ }, { "cell_type": "markdown", - "id": "5176dc48", + "id": "52962c60", "metadata": {}, "source": [ "Note that rows of the transition matrix converge to the stationary distribution." @@ -1388,7 +1388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f8ce1b4", + "id": "0c4273b3", "metadata": {}, "outputs": [], "source": [ @@ -1399,7 +1399,7 @@ { "cell_type": "code", "execution_count": null, - "id": "723910e1", + "id": "fb61b31e", "metadata": {}, "outputs": [], "source": [ @@ -1410,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "feecdfce", + "id": "6374a4b5", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1450,7 +1450,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da48c7f3", + "id": "5d956735", "metadata": {}, "outputs": [], "source": [ @@ -1466,7 +1466,7 @@ }, { "cell_type": "markdown", - "id": "5a0b8c23", + "id": "2fb565f3", "metadata": {}, "source": [ "So it satisfies the requirement.\n", @@ -1479,7 +1479,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3bea4e28", + "id": "1047d260", "metadata": {}, "outputs": [], "source": [ @@ -1511,7 +1511,7 @@ }, { "cell_type": "markdown", - "id": "477c69e1", + "id": "1c60a39d", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/markov_chains_II.ipynb b/_sources/markov_chains_II.ipynb index fe7ecabf..b0b75bca 100644 --- a/_sources/markov_chains_II.ipynb +++ b/_sources/markov_chains_II.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "b36f6c3b", + "id": "237cc41d", "metadata": {}, "source": [ "# Markov Chains: Irreducibility and Ergodicity\n", @@ -16,7 +16,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4acb7073", + "id": "91e51523", "metadata": { "tags": [ "hide-output" @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "a3635895", + "id": "1593becd", "metadata": {}, "source": [ "## Overview\n", @@ -58,7 +58,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2d6c311", + "id": "0eb55302", "metadata": {}, "outputs": [], "source": [ @@ -69,7 +69,7 @@ }, { "cell_type": "markdown", - "id": "115d4f1d", + "id": "000e99bc", "metadata": {}, "source": [ "(mc_irreducible)=\n", @@ -122,7 +122,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62045c7b", + "id": "a6b7ad5a", "metadata": {}, "outputs": [], "source": [ @@ -136,7 +136,7 @@ }, { "cell_type": "markdown", - "id": "0bd69618", + "id": "1b13d725", "metadata": {}, "source": [ "Here's a more pessimistic scenario in which poor people remain poor forever\n", @@ -155,7 +155,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0912e23", + "id": "0e8b3935", "metadata": {}, "outputs": [], "source": [ @@ -169,7 +169,7 @@ }, { "cell_type": "markdown", - "id": "ce64ed12", + "id": "35d207e8", "metadata": {}, "source": [ "It might be clear to you already that irreducibility is going to be important\n", @@ -291,7 +291,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35d676ef", + "id": "27e87534", "metadata": {}, "outputs": [], "source": [ @@ -319,7 +319,7 @@ }, { "cell_type": "markdown", - "id": "4a40e553", + "id": "f223f2c6", "metadata": {}, "source": [ "You might like to try changing $x=1$ to either $x=0$ or $x=2$.\n", @@ -359,7 +359,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21f79318", + "id": "5aca157b", "metadata": {}, "outputs": [], "source": [ @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "47852b16", + "id": "384f0f7a", "metadata": {}, "source": [ "This example helps to emphasize that asymptotic stationarity is about the distribution, while ergodicity is about the sample path.\n", @@ -431,7 +431,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f4f711d", + "id": "65757d56", "metadata": {}, "outputs": [], "source": [ @@ -464,7 +464,7 @@ }, { "cell_type": "markdown", - "id": "34f8c968", + "id": "73e8d062", "metadata": {}, "source": [ "## Exercises\n", @@ -529,7 +529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5cc96419", + "id": "d9ada4e3", "metadata": {}, "outputs": [], "source": [ @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "66a2dc9c", + "id": "639beb04", "metadata": {}, "source": [ "For this model, rows of $P^n$ converge to the stationary distribution as $n \\to\n", @@ -560,7 +560,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1a57ff49", + "id": "00b0ed9f", "metadata": {}, "outputs": [], "source": [ @@ -571,7 +571,7 @@ }, { "cell_type": "markdown", - "id": "f2dd6e12", + "id": "feb1760a", "metadata": {}, "source": [ "Part 2:" @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "039b858f", + "id": "0de6ab60", "metadata": {}, "outputs": [], "source": [ @@ -603,7 +603,7 @@ }, { "cell_type": "markdown", - "id": "04ede8f4", + "id": "883574f3", "metadata": {}, "source": [ "Note that the fraction of time spent at each state converges to the probability\n", @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "30cb5046", + "id": "abbdb442", "metadata": {}, "outputs": [], "source": [ @@ -697,7 +697,7 @@ }, { "cell_type": "markdown", - "id": "e86fe8db", + "id": "bfd5855e", "metadata": {}, "source": [ "```{solution-end}\n", @@ -727,7 +727,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9fa691cf", + "id": "4abd9b9e", "metadata": {}, "outputs": [], "source": [ @@ -741,7 +741,7 @@ }, { "cell_type": "markdown", - "id": "44034663", + "id": "57921e89", "metadata": {}, "source": [ "Let's try it." @@ -750,7 +750,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b796ba2a", + "id": "f25747f0", "metadata": {}, "outputs": [], "source": [ @@ -770,7 +770,7 @@ }, { "cell_type": "markdown", - "id": "69d17f6e", + "id": "8618140b", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/mle.ipynb b/_sources/mle.ipynb index 58d5d868..57c0ad6b 100644 --- a/_sources/mle.ipynb +++ b/_sources/mle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "9fadb3b7", + "id": "36472cc2", "metadata": {}, "source": [ "# Maximum Likelihood Estimation" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7415b743", + "id": "3c926924", "metadata": {}, "outputs": [], "source": [ @@ -25,7 +25,7 @@ }, { "cell_type": "markdown", - "id": "a73278fc", + "id": "86e2eb77", "metadata": {}, "source": [ "## Introduction\n", @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dcb30957", + "id": "b88439f7", "metadata": {}, "outputs": [], "source": [ @@ -72,7 +72,7 @@ }, { "cell_type": "markdown", - "id": "43e7bc16", + "id": "7d86f4c4", "metadata": {}, "source": [ "For a population of size $N$, where individual $i$ has wealth $w_i$, total revenue raised by \n", @@ -97,7 +97,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4558fdd4", + "id": "49e4ce2b", "metadata": {}, "outputs": [], "source": [ @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "ed117268", + "id": "03e51a0c", "metadata": {}, "source": [ "The data is derived from the\n", @@ -119,7 +119,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b7e275c", + "id": "25791b9e", "metadata": { "tags": [ "hide-input" @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "b1344ed6", + "id": "398a6ba6", "metadata": {}, "source": [ "Let's histogram this sample." @@ -148,7 +148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42163ccb", + "id": "ef246151", "metadata": {}, "outputs": [], "source": [ @@ -165,7 +165,7 @@ }, { "cell_type": "markdown", - "id": "66650c78", + "id": "54e969f5", "metadata": {}, "source": [ "The histogram shows that many people have very low wealth and a few people have\n", @@ -178,7 +178,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f064b99", + "id": "f21fc698", "metadata": {}, "outputs": [], "source": [ @@ -187,7 +187,7 @@ }, { "cell_type": "markdown", - "id": "e65665f7", + "id": "8db58e12", "metadata": {}, "source": [ "How can we estimate total revenue from the full population using only the sample data?\n", @@ -233,7 +233,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b74143c", + "id": "2ea72913", "metadata": {}, "outputs": [], "source": [ @@ -245,7 +245,7 @@ }, { "cell_type": "markdown", - "id": "85340c59", + "id": "c9dee8dd", "metadata": {}, "source": [ "Now our job is to obtain the maximum likelihood estimates of $\\mu$ and $\\sigma$, which\n", @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7edb134", + "id": "015c1183", "metadata": {}, "outputs": [], "source": [ @@ -326,7 +326,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f7855f8", + "id": "3b12e3ea", "metadata": {}, "outputs": [], "source": [ @@ -337,7 +337,7 @@ }, { "cell_type": "markdown", - "id": "14c735dd", + "id": "f1c07dae", "metadata": {}, "source": [ "Let's plot the log-normal pdf using the estimated parameters against our sample data." @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f16094a6", + "id": "5278f202", "metadata": {}, "outputs": [], "source": [ @@ -364,7 +364,7 @@ }, { "cell_type": "markdown", - "id": "8d06f06e", + "id": "bcedf9e0", "metadata": {}, "source": [ "Our estimated lognormal distribution appears to be a reasonable fit for the overall data.\n", @@ -379,7 +379,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c32d9c28", + "id": "5f0b8b11", "metadata": {}, "outputs": [], "source": [ @@ -392,7 +392,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31751ff3", + "id": "485217ba", "metadata": {}, "outputs": [], "source": [ @@ -402,7 +402,7 @@ }, { "cell_type": "markdown", - "id": "de1034e4", + "id": "1f85409b", "metadata": {}, "source": [ "(Our unit was 100,000 dollars, so this means that actual revenue is 100,000\n", @@ -434,7 +434,7 @@ { "cell_type": "code", "execution_count": null, - "id": "86c5f6d0", + "id": "2ef1ea5e", "metadata": {}, "outputs": [], "source": [ @@ -445,7 +445,7 @@ { "cell_type": "code", "execution_count": null, - "id": "edfbb0c4", + "id": "236bc156", "metadata": {}, "outputs": [], "source": [ @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "a8228b82", + "id": "3421d282", "metadata": {}, "source": [ "Now let's recompute total revenue." @@ -465,7 +465,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48a1d03f", + "id": "23265ef1", "metadata": {}, "outputs": [], "source": [ @@ -476,7 +476,7 @@ }, { "cell_type": "markdown", - "id": "ed90863d", + "id": "3f4556cc", "metadata": {}, "source": [ "The number is very different!" @@ -485,7 +485,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f50870fb", + "id": "34303566", "metadata": {}, "outputs": [], "source": [ @@ -494,7 +494,7 @@ }, { "cell_type": "markdown", - "id": "843fca79", + "id": "3efc7fa0", "metadata": {}, "source": [ "We see that choosing the right distribution is extremely important.\n", @@ -507,7 +507,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f87a15b", + "id": "eb2a3b24", "metadata": {}, "outputs": [], "source": [ @@ -524,7 +524,7 @@ }, { "cell_type": "markdown", - "id": "35087a96", + "id": "73b9e9e3", "metadata": {}, "source": [ "We observe that in this case the fit for the Pareto distribution is not very\n", @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aa067676", + "id": "6ae54f04", "metadata": { "tags": [ "hide-input" @@ -565,7 +565,7 @@ }, { "cell_type": "markdown", - "id": "e20ee38e", + "id": "54b44681", "metadata": {}, "source": [ "Let's plot this data." @@ -574,7 +574,7 @@ { "cell_type": "code", "execution_count": null, - "id": "39bed884", + "id": "25c976f4", "metadata": {}, "outputs": [], "source": [ @@ -586,7 +586,7 @@ }, { "cell_type": "markdown", - "id": "500fb3c7", + "id": "43becd8a", "metadata": {}, "source": [ "Now let's try fitting some distributions to this data.\n", @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5b528bd", + "id": "188c891c", "metadata": {}, "outputs": [], "source": [ @@ -622,7 +622,7 @@ }, { "cell_type": "markdown", - "id": "0f054e48", + "id": "34765367", "metadata": {}, "source": [ "While the lognormal distribution was a good fit for the entire dataset,\n", @@ -639,7 +639,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2fdd1ba", + "id": "bcc7a305", "metadata": {}, "outputs": [], "source": [ @@ -658,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "90f466fc", + "id": "6fa9cbf4", "metadata": {}, "source": [ "The Pareto distribution is a better fit for the right hand tail of our dataset.\n", @@ -705,7 +705,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21afb1a0", + "id": "8eb878f5", "metadata": {}, "outputs": [], "source": [ @@ -716,7 +716,7 @@ { "cell_type": "code", "execution_count": null, - "id": "934261eb", + "id": "e13ae95d", "metadata": {}, "outputs": [], "source": [ @@ -727,7 +727,7 @@ }, { "cell_type": "markdown", - "id": "a6546c40", + "id": "cdd13b26", "metadata": {}, "source": [ "```{solution-end}\n", @@ -750,7 +750,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84216c8b", + "id": "f496716f", "metadata": {}, "outputs": [], "source": [ @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "e1b28672", + "id": "c8a8c1bd", "metadata": {}, "source": [ "Clearly, this distribution is not a good fit for our data.\n", diff --git a/_sources/money_inflation.ipynb b/_sources/money_inflation.ipynb index 461366aa..145d049d 100644 --- a/_sources/money_inflation.ipynb +++ b/_sources/money_inflation.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d12bea96", + "id": "d2f23b7e", "metadata": {}, "source": [ "# Money Financed Government Deficits and Price Levels\n", @@ -253,7 +253,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f228d090", + "id": "60983147", "metadata": {}, "outputs": [], "source": [ @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "7b6ed87a", + "id": "1a431c7d", "metadata": {}, "source": [ "Let's set some parameter values and compute possible steady-state rates of return on currency $\\bar R$, the seigniorage maximizing rate of return on currency, and an object that we'll discuss later, namely, an initial price level $p_0$ associated with the maximum steady-state rate of return on currency.\n", @@ -277,7 +277,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c52fb9da", + "id": "c4334995", "metadata": {}, "outputs": [], "source": [ @@ -298,7 +298,7 @@ }, { "cell_type": "markdown", - "id": "3e23215d", + "id": "f9a1445d", "metadata": {}, "source": [ "Now we compute the $\\bar R_{\\rm max}$ and corresponding revenue" @@ -307,7 +307,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0831f575", + "id": "c2be2d4e", "metadata": {}, "outputs": [], "source": [ @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "c87b70df", + "id": "4788eae6", "metadata": {}, "source": [ "Now let's plot seigniorage as a function of alternative potential steady-state values of $R$.\n", @@ -344,7 +344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4cb2f38c", + "id": "942d2cb9", "metadata": { "mystnb": { "figure": { @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "ba6248c6", + "id": "3694597c", "metadata": {}, "source": [ "Let's print the two steady-state rates of return $\\bar R$ and the associated seigniorage revenues that the government collects.\n", @@ -388,7 +388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fab68193", + "id": "adb5595f", "metadata": {}, "outputs": [], "source": [ @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "1c89fc18", + "id": "e3ad4757", "metadata": {}, "source": [ "Now let's compute the maximum steady-state amount of seigniorage that could be gathered by printing money and the state state rate of return on money that attains it.\n", @@ -527,7 +527,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afc60a14", + "id": "a2a43aa7", "metadata": {}, "outputs": [], "source": [ @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "2575878d", + "id": "5a833951", "metadata": {}, "source": [ "Let's write some code to plot outcomes for several possible initial values $R_0$." @@ -562,7 +562,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d79af9c", + "id": "c531674e", "metadata": { "tags": [ "hide-cell" @@ -613,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "4579a689", + "id": "340979f5", "metadata": {}, "source": [ "Let's plot distinct outcomes associated with several $R_0 \\in [\\frac{\\gamma_2}{\\gamma_1}, R_u]$.\n", @@ -624,7 +624,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cab6a7a1", + "id": "5355d8b2", "metadata": { "mystnb": { "figure": { @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "689084b9", + "id": "93e7b79b", "metadata": {}, "source": [ "Notice how sequences that start from $R_0$ in the half-open interval $[R_\\ell, R_u)$ converge to the steady state associated with to $ R_\\ell$.\n", @@ -688,7 +688,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95f8c560", + "id": "aa0d0edf", "metadata": {}, "outputs": [], "source": [ @@ -700,7 +700,7 @@ }, { "cell_type": "markdown", - "id": "253d1977", + "id": "b759a8ae", "metadata": {}, "source": [ "Define\n", @@ -713,7 +713,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2886c5e", + "id": "bf4b8635", "metadata": {}, "outputs": [], "source": [ @@ -723,7 +723,7 @@ }, { "cell_type": "markdown", - "id": "67b46ed4", + "id": "3b4a2aef", "metadata": {}, "source": [ "and write the system {eq}`eq:sytem101` as\n", @@ -774,7 +774,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b50f06b8", + "id": "354bf624", "metadata": {}, "outputs": [], "source": [ @@ -786,7 +786,7 @@ { "cell_type": "code", "execution_count": null, - "id": "329451ac", + "id": "55d6bf95", "metadata": {}, "outputs": [], "source": [ @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "8bf7d5d1", + "id": "f904fdfe", "metadata": {}, "source": [ "Partition $Q$ as\n", @@ -857,7 +857,7 @@ { "cell_type": "code", "execution_count": null, - "id": "21c4ec12", + "id": "854f27c3", "metadata": {}, "outputs": [], "source": [ @@ -872,7 +872,7 @@ }, { "cell_type": "markdown", - "id": "4c8ff25a", + "id": "5e9f4f9c", "metadata": {}, "source": [ "For almost all initial vectors $y_0$, the gross rate of inflation $\\frac{p_{t+1}}{p_t}$ eventually converges to the larger eigenvalue ${R_\\ell}^{-1}$.\n", @@ -999,7 +999,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0a6c67a", + "id": "c4482d44", "metadata": {}, "outputs": [], "source": [ @@ -1010,7 +1010,7 @@ }, { "cell_type": "markdown", - "id": "8184ac93", + "id": "1c4fa77d", "metadata": {}, "source": [ "It can be verified that this formula replicates itself over time in the sense that\n", @@ -1029,7 +1029,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50b7b33d", + "id": "f2415526", "metadata": { "tags": [ "hide-cell" @@ -1083,7 +1083,7 @@ { "cell_type": "code", "execution_count": null, - "id": "196026a2", + "id": "aa643e8f", "metadata": { "mystnb": { "figure": { @@ -1102,7 +1102,7 @@ }, { "cell_type": "markdown", - "id": "babb8b18", + "id": "21e17f12", "metadata": {}, "source": [ "Please notice that for $m_t$ and $p_t$, we have used log scales for the coordinate (i.e., vertical) axes. \n", diff --git a/_sources/money_inflation_nonlinear.ipynb b/_sources/money_inflation_nonlinear.ipynb index 3e759162..451e5fa6 100644 --- a/_sources/money_inflation_nonlinear.ipynb +++ b/_sources/money_inflation_nonlinear.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e5f6dab6", + "id": "cdcb4d84", "metadata": {}, "source": [ "# Inflation Rate Laffer Curves \n", @@ -154,7 +154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec8aa92e", + "id": "b63576fb", "metadata": {}, "outputs": [], "source": [ @@ -167,7 +167,7 @@ }, { "cell_type": "markdown", - "id": "5d756c4c", + "id": "8aecb67e", "metadata": { "user_expressions": [] }, @@ -178,7 +178,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3624faad", + "id": "163262f0", "metadata": {}, "outputs": [], "source": [ @@ -197,7 +197,7 @@ }, { "cell_type": "markdown", - "id": "2296e1b0", + "id": "fd262706", "metadata": { "user_expressions": [] }, @@ -208,7 +208,7 @@ { "cell_type": "code", "execution_count": null, - "id": "401a8c36", + "id": "67fb3ba1", "metadata": {}, "outputs": [], "source": [ @@ -228,7 +228,7 @@ }, { "cell_type": "markdown", - "id": "0bb5f87f", + "id": "516463cd", "metadata": {}, "source": [ "We find two steady state $\\overline \\pi$ values.\n", @@ -241,7 +241,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15220cc5", + "id": "ec4af664", "metadata": { "mystnb": { "figure": { @@ -286,7 +286,7 @@ }, { "cell_type": "markdown", - "id": "ac3ebe81", + "id": "09cb2553", "metadata": {}, "source": [ "## Associated initial price levels\n", @@ -297,7 +297,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4139a60d", + "id": "215fa306", "metadata": {}, "outputs": [], "source": [ @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "8f47eaa0", + "id": "e0ac6d2e", "metadata": {}, "source": [ "### Verification \n", @@ -337,7 +337,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16242d61", + "id": "4e1fb642", "metadata": {}, "outputs": [], "source": [ @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1f1795e7", + "id": "f9900452", "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "c462a4cf", + "id": "0d00c034", "metadata": {}, "source": [ "## Slippery side of Laffer curve dynamics\n", @@ -392,7 +392,7 @@ { "cell_type": "code", "execution_count": null, - "id": "003186d6", + "id": "77c3a504", "metadata": { "tags": [ "hide-cell" @@ -451,7 +451,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99cc7702", + "id": "3c53ad72", "metadata": { "mystnb": { "figure": { @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "6e05c762", + "id": "2659c81b", "metadata": {}, "source": [ "Staring at the paths of price levels in {numref}`p0_path_nonlin` reveals that almost all paths converge to the *higher* inflation tax rate displayed in the stationary state Laffer curve. displayed in figure {numref}`laffer_curve_nonlinear`. \n", diff --git a/_sources/monte_carlo.ipynb b/_sources/monte_carlo.ipynb index 29438227..25da9120 100644 --- a/_sources/monte_carlo.ipynb +++ b/_sources/monte_carlo.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6ffd196d", + "id": "c31f427b", "metadata": {}, "source": [ "(monte-carlo)=\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d968fd96", + "id": "fc67427d", "metadata": {}, "outputs": [], "source": [ @@ -50,7 +50,7 @@ }, { "cell_type": "markdown", - "id": "bb7ec245", + "id": "fab50842", "metadata": {}, "source": [ "## An introduction to Monte Carlo\n", @@ -152,7 +152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb829d9e", + "id": "037c4afa", "metadata": {}, "outputs": [], "source": [ @@ -164,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "3f58000b", + "id": "84317b03", "metadata": {}, "source": [ "#### A routine using loops in python\n", @@ -181,7 +181,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ee65d33", + "id": "9fbba712", "metadata": {}, "outputs": [], "source": [ @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "5d56daed", + "id": "740a85a0", "metadata": {}, "source": [ "We can also construct a function that contains these operations:" @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df1df28b", + "id": "ba6f7ddc", "metadata": {}, "outputs": [], "source": [ @@ -223,7 +223,7 @@ }, { "cell_type": "markdown", - "id": "9a3b2c71", + "id": "b635e548", "metadata": {}, "source": [ "Now let's call it." @@ -232,7 +232,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e83f576b", + "id": "436f9261", "metadata": {}, "outputs": [], "source": [ @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "bdd6f748", + "id": "35f1d131", "metadata": {}, "source": [ "### A vectorized routine\n", @@ -256,7 +256,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad13839a", + "id": "ce3144b5", "metadata": {}, "outputs": [], "source": [ @@ -271,7 +271,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3caadc7", + "id": "1af899e8", "metadata": {}, "outputs": [], "source": [ @@ -282,7 +282,7 @@ }, { "cell_type": "markdown", - "id": "6e0b8ef5", + "id": "4115fdac", "metadata": {}, "source": [ "Notice that this routine is much faster.\n", @@ -293,7 +293,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df5c6970", + "id": "26d529a1", "metadata": {}, "outputs": [], "source": [ @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "270cd977", + "id": "b17c7e11", "metadata": {}, "source": [ "## Pricing a European call option under risk neutrality\n", @@ -452,7 +452,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79c449f3", + "id": "30aeaf44", "metadata": {}, "outputs": [], "source": [ @@ -465,7 +465,7 @@ }, { "cell_type": "markdown", - "id": "0a166b83", + "id": "59c6fc57", "metadata": {}, "source": [ "We set the simulation size to" @@ -474,7 +474,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f79c7370", + "id": "5cd09d8d", "metadata": {}, "outputs": [], "source": [ @@ -483,7 +483,7 @@ }, { "cell_type": "markdown", - "id": "51d2b93c", + "id": "f9585529", "metadata": {}, "source": [ "Here is our code" @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aaeeb25b", + "id": "ca33c75e", "metadata": {}, "outputs": [], "source": [ @@ -504,7 +504,7 @@ }, { "cell_type": "markdown", - "id": "703d5255", + "id": "4b675cc3", "metadata": {}, "source": [ "## Pricing via a dynamic model\n", @@ -587,7 +587,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b2a9352", + "id": "06cc0cfc", "metadata": {}, "outputs": [], "source": [ @@ -600,7 +600,7 @@ }, { "cell_type": "markdown", - "id": "6ea6289d", + "id": "699087ee", "metadata": {}, "source": [ "(Here `default_S0` is $S_0$ and `default_h0` is $h_0$.)\n", @@ -611,7 +611,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ae2e8b5d", + "id": "caab1c86", "metadata": {}, "outputs": [], "source": [ @@ -622,7 +622,7 @@ }, { "cell_type": "markdown", - "id": "e7b9f9ce", + "id": "983769ca", "metadata": {}, "source": [ "### Visualizations\n", @@ -637,7 +637,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41b022a9", + "id": "0b3eb077", "metadata": {}, "outputs": [], "source": [ @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "2b9bae9b", + "id": "176964ff", "metadata": {}, "source": [ "Here we plot the paths and the log of the paths." @@ -664,7 +664,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81c51fd0", + "id": "26f4a554", "metadata": {}, "outputs": [], "source": [ @@ -684,7 +684,7 @@ }, { "cell_type": "markdown", - "id": "39919d0d", + "id": "c61e8f16", "metadata": {}, "source": [ "### Computing the price\n", @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5cddc0f3", + "id": "75844e6d", "metadata": {}, "outputs": [], "source": [ @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d005193", + "id": "7607440b", "metadata": {}, "outputs": [], "source": [ @@ -751,7 +751,7 @@ }, { "cell_type": "markdown", - "id": "26ade99e", + "id": "f4a4f2b6", "metadata": {}, "source": [ "## Exercises\n", @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9d46687", + "id": "c3a660df", "metadata": {}, "outputs": [], "source": [ @@ -803,7 +803,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72393553", + "id": "efd9117e", "metadata": {}, "outputs": [], "source": [ @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "c3cedc27", + "id": "e2e7a637", "metadata": {}, "source": [ "Notice that this version is faster than the one using a Python loop.\n", @@ -824,7 +824,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50109b5f", + "id": "34e9b1d8", "metadata": {}, "outputs": [], "source": [ @@ -834,7 +834,7 @@ }, { "cell_type": "markdown", - "id": "299b6a49", + "id": "a7da0d56", "metadata": {}, "source": [ "```{solution-end}\n", @@ -860,7 +860,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3200bd5d", + "id": "f5195c14", "metadata": {}, "outputs": [], "source": [ @@ -878,7 +878,7 @@ { "cell_type": "code", "execution_count": null, - "id": "78f3e949", + "id": "8d1675f5", "metadata": {}, "outputs": [], "source": [ @@ -919,7 +919,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8df84555", + "id": "5e33b88a", "metadata": {}, "outputs": [], "source": [ @@ -928,7 +928,7 @@ }, { "cell_type": "markdown", - "id": "8dc4d972", + "id": "8e256083", "metadata": {}, "source": [ "Let's look at the vectorized version which is faster than using Python loops." @@ -937,7 +937,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af9101da", + "id": "4d5fcb4c", "metadata": {}, "outputs": [], "source": [ @@ -970,7 +970,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5abaf8eb", + "id": "2e8ecd17", "metadata": {}, "outputs": [], "source": [ @@ -979,7 +979,7 @@ }, { "cell_type": "markdown", - "id": "7adf368f", + "id": "1f0c01c0", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/networks.ipynb b/_sources/networks.ipynb index 2f7564b9..1e56a216 100644 --- a/_sources/networks.ipynb +++ b/_sources/networks.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e2dca0d6", + "id": "1affc17d", "metadata": {}, "source": [ "# Networks" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cfcc0625", + "id": "2a1bffca", "metadata": { "tags": [ "hide-output" @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "3f0a3a1d", + "id": "c86e1129", "metadata": {}, "source": [ "## Outline\n", @@ -61,7 +61,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3be67690", + "id": "29d16691", "metadata": {}, "outputs": [], "source": [ @@ -80,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "dcc71b18", + "id": "e5d90159", "metadata": {}, "source": [ "## Economic and financial networks\n", @@ -110,7 +110,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23a577ab", + "id": "357b28da", "metadata": { "mystnb": { "figure": { @@ -176,7 +176,7 @@ }, { "cell_type": "markdown", - "id": "d12e8151", + "id": "9c4547ba", "metadata": {}, "source": [ "The circles in the figure are called **nodes** or **vertices** -- in this case they represent countries.\n", @@ -279,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "ee5fbd47", + "id": "917fcebd", "metadata": {}, "source": [ "We now construct a graph with the same nodes but different edges.\n", @@ -293,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "71977e92", + "id": "d399ca0e", "metadata": {}, "source": [ "For these graphs, the arrows (edges) can be thought of as representing\n", @@ -322,7 +322,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2709a75a", + "id": "f9ea3d4a", "metadata": {}, "outputs": [], "source": [ @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "217bd483", + "id": "db06c4a1", "metadata": {}, "source": [ "Next we populate it with nodes and edges.\n", @@ -343,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4653076", + "id": "a5eda3bc", "metadata": {}, "outputs": [], "source": [ @@ -354,7 +354,7 @@ }, { "cell_type": "markdown", - "id": "bc16035c", + "id": "adc17cff", "metadata": {}, "source": [ "Finally, we add the edges to our `DiGraph` object:" @@ -363,7 +363,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c2ee531", + "id": "4a766f80", "metadata": {}, "outputs": [], "source": [ @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "bb9e27fd", + "id": "5dd0fe34", "metadata": {}, "source": [ "Alternatively, we can use the method `add_edges_from`." @@ -383,7 +383,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bbe2061d", + "id": "932d52eb", "metadata": {}, "outputs": [], "source": [ @@ -392,7 +392,7 @@ }, { "cell_type": "markdown", - "id": "ff480307", + "id": "c21a2e2d", "metadata": {}, "source": [ "Adding the edges automatically adds the nodes, so `G_p` is now a\n", @@ -404,7 +404,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16447e06", + "id": "543445bb", "metadata": {}, "outputs": [], "source": [ @@ -417,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "cab1a570", + "id": "24803b85", "metadata": {}, "source": [ "The figure obtained above matches the original directed graph in {numref}`poverty_trap_2`.\n", @@ -432,7 +432,7 @@ { "cell_type": "code", "execution_count": null, - "id": "725fa449", + "id": "5477377c", "metadata": {}, "outputs": [], "source": [ @@ -441,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "88114ac6", + "id": "81afdf4b", "metadata": {}, "source": [ "(strongly_connected)=\n", @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ff604db", + "id": "a2f84596", "metadata": {}, "outputs": [], "source": [ @@ -494,7 +494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "02097152", + "id": "89349d09", "metadata": {}, "outputs": [], "source": [ @@ -504,7 +504,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eb4d1112", + "id": "644cb935", "metadata": {}, "outputs": [], "source": [ @@ -521,7 +521,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55af1745", + "id": "7a999259", "metadata": {}, "outputs": [], "source": [ @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "8874deda", + "id": "43faf72b", "metadata": {}, "source": [ "## Weighted graphs\n", @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6553f6c0", + "id": "bfcd84fa", "metadata": { "mystnb": { "figure": { @@ -618,7 +618,7 @@ }, { "cell_type": "markdown", - "id": "a625dd57", + "id": "97259c05", "metadata": {}, "source": [ "The country codes are given in the following table\n", @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "6fdbd1aa", + "id": "557b8bdf", "metadata": {}, "source": [ "### Definitions\n", @@ -725,7 +725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd3dfa7b", + "id": "b95107be", "metadata": {}, "outputs": [], "source": [ @@ -738,7 +738,7 @@ }, { "cell_type": "markdown", - "id": "24d3a1b6", + "id": "15edd491", "metadata": {}, "source": [ "One of the key points to remember about adjacency matrices is that taking the\n", @@ -753,7 +753,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1275dddc", + "id": "69e8b308", "metadata": {}, "outputs": [], "source": [ @@ -782,7 +782,7 @@ }, { "cell_type": "markdown", - "id": "a794fb69", + "id": "979a433c", "metadata": {}, "source": [ "We see that bank 2 extends a loan of size 200 to bank 3.\n", @@ -821,7 +821,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73a56914", + "id": "df2b9152", "metadata": {}, "outputs": [], "source": [ @@ -849,7 +849,7 @@ }, { "cell_type": "markdown", - "id": "e9e64a4f", + "id": "9b55d663", "metadata": {}, "source": [ "In general, every nonnegative $n \\times n$ matrix $A = (a_{ij})$ can be\n", @@ -887,7 +887,7 @@ }, { "cell_type": "markdown", - "id": "681c8942", + "id": "9ba7daad", "metadata": {}, "source": [ "The above result is obvious when $k=1$ and a proof of the general case can be\n", @@ -912,7 +912,7 @@ }, { "cell_type": "markdown", - "id": "1b980a7a", + "id": "74dcf1f3", "metadata": {}, "source": [ "We illustrate the above theorem with a simple example.\n", @@ -928,7 +928,7 @@ }, { "cell_type": "markdown", - "id": "2f9afcb1", + "id": "4219d2df", "metadata": {}, "source": [ "We first create the above network as a Networkx `DiGraph` object." @@ -937,7 +937,7 @@ { "cell_type": "code", "execution_count": null, - "id": "24f69009", + "id": "36ba69e8", "metadata": {}, "outputs": [], "source": [ @@ -950,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "d1aa3cd2", + "id": "014efe90", "metadata": {}, "source": [ "Then we construct the associated adjacency matrix A." @@ -959,7 +959,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e8ad1fe", + "id": "a2ad960a", "metadata": {}, "outputs": [], "source": [ @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fdb58557", + "id": "c1224e19", "metadata": { "tags": [ "hide-input" @@ -990,7 +990,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8e6ebd4", + "id": "6c85decf", "metadata": {}, "outputs": [], "source": [ @@ -1000,7 +1000,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d11cbbd", + "id": "be2aa30f", "metadata": {}, "outputs": [], "source": [ @@ -1009,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "c091beea", + "id": "1423307b", "metadata": {}, "source": [ "## Network centrality\n", @@ -1044,7 +1044,7 @@ { "cell_type": "code", "execution_count": null, - "id": "242871c7", + "id": "3ee8a00d", "metadata": { "mystnb": { "figure": { @@ -1077,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "812621e7", + "id": "3c36032e", "metadata": {}, "source": [ "The following code displays the in-degree centrality of all nodes." @@ -1086,7 +1086,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ad38711", + "id": "d709b703", "metadata": {}, "outputs": [], "source": [ @@ -1098,7 +1098,7 @@ }, { "cell_type": "markdown", - "id": "4ac3c909", + "id": "08c32913", "metadata": {}, "source": [ "Consider the international credit network displayed in {numref}`financial_network`.\n", @@ -1109,7 +1109,7 @@ { "cell_type": "code", "execution_count": null, - "id": "703e181b", + "id": "8337c2ec", "metadata": {}, "outputs": [], "source": [ @@ -1120,7 +1120,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f28ad2d", + "id": "2038f809", "metadata": {}, "outputs": [], "source": [ @@ -1135,7 +1135,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6f05871", + "id": "8ecd085b", "metadata": {}, "outputs": [], "source": [ @@ -1155,7 +1155,7 @@ }, { "cell_type": "markdown", - "id": "3d195668", + "id": "98d423e4", "metadata": {}, "source": [ "Unfortunately, while in-degree and out-degree centrality are simple to\n", @@ -1249,7 +1249,7 @@ { "cell_type": "code", "execution_count": null, - "id": "533886ef", + "id": "9009bbc2", "metadata": {}, "outputs": [], "source": [ @@ -1268,7 +1268,7 @@ }, { "cell_type": "markdown", - "id": "c31c4610", + "id": "583621cc", "metadata": {}, "source": [ "Let's compute eigenvector centrality for the graph generated in {numref}`sample_gph_1`." @@ -1277,7 +1277,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17d6a1b5", + "id": "e6b38bd9", "metadata": {}, "outputs": [], "source": [ @@ -1287,7 +1287,7 @@ { "cell_type": "code", "execution_count": null, - "id": "384100e5", + "id": "82c08ef2", "metadata": {}, "outputs": [], "source": [ @@ -1300,7 +1300,7 @@ }, { "cell_type": "markdown", - "id": "816d9413", + "id": "d47282c2", "metadata": {}, "source": [ "While nodes $2$ and $4$ had the highest in-degree centrality, we can see that nodes $1$ and $2$ have the\n", @@ -1312,7 +1312,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9d0a54cc", + "id": "21fe51f4", "metadata": {}, "outputs": [], "source": [ @@ -1322,7 +1322,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c18400b2", + "id": "1e5cc9fc", "metadata": { "mystnb": { "figure": { @@ -1347,7 +1347,7 @@ }, { "cell_type": "markdown", - "id": "b3588968", + "id": "9bdda96d", "metadata": {}, "source": [ "Countries that are rated highly according to this rank tend to be important\n", @@ -1467,7 +1467,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5f99a068", + "id": "6e3fa6e1", "metadata": {}, "outputs": [], "source": [ @@ -1477,7 +1477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4b976cc", + "id": "dad21981", "metadata": { "mystnb": { "figure": { @@ -1502,7 +1502,7 @@ }, { "cell_type": "markdown", - "id": "623f293d", + "id": "c8d4cd53", "metadata": {}, "source": [ "Highly ranked countries are those that attract large inflows of credit, or\n", @@ -1604,7 +1604,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f35d73e8", + "id": "7182c60b", "metadata": {}, "outputs": [], "source": [ @@ -1631,7 +1631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3750433", + "id": "e8caeb0e", "metadata": {}, "outputs": [], "source": [ @@ -1643,7 +1643,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e3955ff", + "id": "5f182a7d", "metadata": {}, "outputs": [], "source": [ @@ -1656,7 +1656,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56c25f84", + "id": "8d1fd7c6", "metadata": {}, "outputs": [], "source": [ @@ -1669,7 +1669,7 @@ }, { "cell_type": "markdown", - "id": "10f295d5", + "id": "f7cf8feb", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1704,7 +1704,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c666fa4f", + "id": "4a6c1bc1", "metadata": {}, "outputs": [], "source": [ @@ -1723,7 +1723,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19b613e1", + "id": "7942d4c5", "metadata": {}, "outputs": [], "source": [ @@ -1744,7 +1744,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9fb6d467", + "id": "a0904521", "metadata": {}, "outputs": [], "source": [ @@ -1754,7 +1754,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e5ba016", + "id": "7c190c81", "metadata": {}, "outputs": [], "source": [ @@ -1763,7 +1763,7 @@ }, { "cell_type": "markdown", - "id": "f5c69373", + "id": "42d2eaa9", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/olg.ipynb b/_sources/olg.ipynb index 28ac2240..68c2fb30 100644 --- a/_sources/olg.ipynb +++ b/_sources/olg.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "a096c8b0", + "id": "354d3f3a", "metadata": {}, "source": [ "# The Overlapping Generations Model\n", @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e3de3ce", + "id": "73ef6c42", "metadata": {}, "outputs": [], "source": [ @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "8db9ff4c", + "id": "0a5de4d9", "metadata": {}, "source": [ "## Environment\n", @@ -298,7 +298,7 @@ { "cell_type": "code", "execution_count": null, - "id": "13a78664", + "id": "ab12dd84", "metadata": {}, "outputs": [], "source": [ @@ -309,7 +309,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81eac5d2", + "id": "3168889b", "metadata": {}, "outputs": [], "source": [ @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "fd83e5e9", + "id": "6a891307", "metadata": {}, "source": [ "The next figure plots the supply of capital, as in [](saving_log_2_olg), as well as the demand for capital, as in [](aggregate_demand_capital_olg), as functions of the interest rate $R_{t+1}$.\n", @@ -387,7 +387,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6924786", + "id": "83042a6d", "metadata": {}, "outputs": [], "source": [ @@ -398,7 +398,7 @@ }, { "cell_type": "markdown", - "id": "a1ca4b5e", + "id": "93c431c0", "metadata": {}, "source": [ "In the case of log utility, since capital supply does not depend on the interest rate, the equilibrium quantity is fixed by supply.\n", @@ -416,7 +416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "623f9052", + "id": "aa52f0d2", "metadata": {}, "outputs": [], "source": [ @@ -444,7 +444,7 @@ }, { "cell_type": "markdown", - "id": "d4ddd507", + "id": "539db0c0", "metadata": {}, "source": [ "## Dynamics \n", @@ -481,7 +481,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a1cb85a2", + "id": "63222ff5", "metadata": {}, "outputs": [], "source": [ @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04bdbbba", + "id": "8b61cfba", "metadata": {}, "outputs": [], "source": [ @@ -519,7 +519,7 @@ }, { "cell_type": "markdown", - "id": "8ff49ef0", + "id": "b63880fa", "metadata": {}, "source": [ "### Steady state (log case)\n", @@ -554,7 +554,7 @@ { "cell_type": "code", "execution_count": null, - "id": "791b4689", + "id": "c7904388", "metadata": {}, "outputs": [], "source": [ @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "3a0b61dc", + "id": "23a32002", "metadata": {}, "source": [ "### Time series\n", @@ -577,7 +577,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3968b004", + "id": "b8a55f2c", "metadata": {}, "outputs": [], "source": [ @@ -599,7 +599,7 @@ }, { "cell_type": "markdown", - "id": "223deee7", + "id": "c841012c", "metadata": {}, "source": [ "If you experiment with different positive initial conditions, you will see that the series always converges to $k^*$." @@ -607,7 +607,7 @@ }, { "cell_type": "markdown", - "id": "6efd3e91", + "id": "fc863d26", "metadata": {}, "source": [ "Below we also plot the gross interest rate over time." @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a74fb35", + "id": "9cf4e32e", "metadata": {}, "outputs": [], "source": [ @@ -634,7 +634,7 @@ }, { "cell_type": "markdown", - "id": "4f4a4c20", + "id": "fcbd62bb", "metadata": {}, "source": [ "The interest rate reflects the marginal product of capital, which is high when capital stock is low." @@ -642,7 +642,7 @@ }, { "cell_type": "markdown", - "id": "d068dd76", + "id": "b34c7aa4", "metadata": {}, "source": [ "## CRRA preferences\n", @@ -664,7 +664,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6417c5ca", + "id": "86a5525d", "metadata": {}, "outputs": [], "source": [ @@ -682,7 +682,7 @@ }, { "cell_type": "markdown", - "id": "b2dc55c8", + "id": "b4d11e51", "metadata": {}, "source": [ "Let's also redefine the capital demand function to work with this `namedtuple`." @@ -691,7 +691,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1a0a4eee", + "id": "e56494d0", "metadata": {}, "outputs": [], "source": [ @@ -701,7 +701,7 @@ }, { "cell_type": "markdown", - "id": "a7fa1154", + "id": "b4698a3d", "metadata": {}, "source": [ "### Supply\n", @@ -732,7 +732,7 @@ { "cell_type": "code", "execution_count": null, - "id": "964a8a1b", + "id": "45e0bb70", "metadata": {}, "outputs": [], "source": [ @@ -744,7 +744,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59887897", + "id": "206b475c", "metadata": {}, "outputs": [], "source": [ @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "b891d024", + "id": "cf21a262", "metadata": {}, "source": [ "### Equilibrium\n", @@ -801,7 +801,7 @@ }, { "cell_type": "markdown", - "id": "4ffeeab9", + "id": "a9219e54", "metadata": {}, "source": [ "## Exercises\n", @@ -849,7 +849,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dfa16efc", + "id": "d9c03427", "metadata": {}, "outputs": [], "source": [ @@ -864,7 +864,7 @@ }, { "cell_type": "markdown", - "id": "07a7141d", + "id": "852fb640", "metadata": {}, "source": [ "Now let's define a function that finds the value of $k_{t+1}$." @@ -873,7 +873,7 @@ { "cell_type": "code", "execution_count": null, - "id": "740e2e53", + "id": "92f66e9e", "metadata": {}, "outputs": [], "source": [ @@ -883,7 +883,7 @@ }, { "cell_type": "markdown", - "id": "46596c06", + "id": "c825c5bf", "metadata": {}, "source": [ "Finally, here is the 45-degree diagram." @@ -892,7 +892,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f85f55f8", + "id": "d788ed0c", "metadata": {}, "outputs": [], "source": [ @@ -921,7 +921,7 @@ }, { "cell_type": "markdown", - "id": "5ff03941", + "id": "02d0ecbc", "metadata": {}, "source": [ "```{solution-end}\n", @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1cc7c633", + "id": "5fea58a1", "metadata": {}, "outputs": [], "source": [ @@ -986,7 +986,7 @@ }, { "cell_type": "markdown", - "id": "6f10ccbc", + "id": "9590e574", "metadata": {}, "source": [ "Let's apply Newton's method to find the root:" @@ -995,7 +995,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92f38c6d", + "id": "25ddf9af", "metadata": {}, "outputs": [], "source": [ @@ -1005,7 +1005,7 @@ }, { "cell_type": "markdown", - "id": "4bc6f0e4", + "id": "80a7fdb9", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1036,7 +1036,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87245aac", + "id": "ee194411", "metadata": {}, "outputs": [], "source": [ @@ -1047,7 +1047,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2aa3389", + "id": "64950252", "metadata": {}, "outputs": [], "source": [ @@ -1077,7 +1077,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d90726e5", + "id": "224e3a5c", "metadata": {}, "outputs": [], "source": [ @@ -1086,7 +1086,7 @@ }, { "cell_type": "markdown", - "id": "ed3b9560", + "id": "56ea13cf", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/prob_dist.ipynb b/_sources/prob_dist.ipynb index d443775c..1eba7ef6 100644 --- a/_sources/prob_dist.ipynb +++ b/_sources/prob_dist.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "42802ff9", + "id": "9c3393ad", "metadata": {}, "source": [ "# Distributions and Probabilities\n", @@ -18,7 +18,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a50d78fa", + "id": "16485fee", "metadata": { "tags": [ "hide-output" @@ -32,7 +32,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2419ec13", + "id": "472053d1", "metadata": {}, "outputs": [], "source": [ @@ -46,7 +46,7 @@ }, { "cell_type": "markdown", - "id": "c38120e9", + "id": "d747cbb7", "metadata": {}, "source": [ "## Common distributions\n", @@ -111,7 +111,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec329630", + "id": "6837774a", "metadata": {}, "outputs": [], "source": [ @@ -121,7 +121,7 @@ }, { "cell_type": "markdown", - "id": "d2921096", + "id": "d7709bfa", "metadata": {}, "source": [ "Here's the mean and variance:" @@ -130,7 +130,7 @@ { "cell_type": "code", "execution_count": null, - "id": "005137f3", + "id": "1982fe89", "metadata": {}, "outputs": [], "source": [ @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "c07d4d92", + "id": "33e28087", "metadata": {}, "source": [ "The formula for the mean is $(n+1)/2$, and the formula for the variance is $(n^2 - 1)/12$.\n", @@ -151,7 +151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a897310a", + "id": "78ab4b4c", "metadata": {}, "outputs": [], "source": [ @@ -161,7 +161,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f01ff1be", + "id": "869537bb", "metadata": {}, "outputs": [], "source": [ @@ -170,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "3bc7fcac", + "id": "75434c6a", "metadata": {}, "source": [ "Here's a plot of the probability mass function:" @@ -179,7 +179,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fedf278a", + "id": "4e278bb2", "metadata": {}, "outputs": [], "source": [ @@ -195,7 +195,7 @@ }, { "cell_type": "markdown", - "id": "d785e214", + "id": "7a5c2239", "metadata": {}, "source": [ "Here's a plot of the CDF:" @@ -204,7 +204,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3e656ab", + "id": "953c8176", "metadata": {}, "outputs": [], "source": [ @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "078c5a3c", + "id": "c7b6a6d6", "metadata": {}, "source": [ "The CDF jumps up by $p(x_i)$ at $x_i$.\n", @@ -240,7 +240,8 @@ "Another useful distribution is the Bernoulli distribution on $S = \\{0,1\\}$, which has PMF:\n", "\n", "$$\n", - "p(i) = \\theta^{i-1} (1 - \\theta)^i\n", + "p(i) = \\theta^i (1 - \\theta)^{1-i}\n", + "\\qquad (i = 0, 1)\n", "$$\n", "\n", "Here $\\theta \\in [0,1]$ is a parameter.\n", @@ -251,7 +252,7 @@ "* $p(0) = 1 - \\theta$ means that the trial fails (takes value 0) with\n", " probability $1-\\theta$\n", "\n", - "The formula for the mean is $p$, and the formula for the variance is $p(1-p)$.\n", + "The formula for the mean is $\\theta$, and the formula for the variance is $\\theta(1-\\theta)$.\n", "\n", "We can import the Bernoulli distribution on $S = \\{0,1\\}$ from SciPy like so:" ] @@ -259,7 +260,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7733a26e", + "id": "dd23510e", "metadata": {}, "outputs": [], "source": [ @@ -269,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "135255aa", + "id": "5d5e5f97", "metadata": {}, "source": [ "Here's the mean and variance at $\\theta=0.4$" @@ -278,7 +279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2b12234", + "id": "ad2d38ef", "metadata": {}, "outputs": [], "source": [ @@ -287,26 +288,25 @@ }, { "cell_type": "markdown", - "id": "aeb460fb", + "id": "8a2d37ae", "metadata": {}, "source": [ - "Now let's evaluate the PMF" + "We can evaluate the PMF as follows" ] }, { "cell_type": "code", "execution_count": null, - "id": "11530a1d", + "id": "8f082a07", "metadata": {}, "outputs": [], "source": [ - "u.pmf(0)\n", - "u.pmf(1)" + "u.pmf(0), u.pmf(1)" ] }, { "cell_type": "markdown", - "id": "6c52673c", + "id": "1e999933", "metadata": {}, "source": [ "#### Binomial distribution\n", @@ -331,7 +331,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9a619d9f", + "id": "8be28ad5", "metadata": {}, "outputs": [], "source": [ @@ -342,7 +342,7 @@ }, { "cell_type": "markdown", - "id": "670b5851", + "id": "63ca2b80", "metadata": {}, "source": [ "According to our formulas, the mean and variance are" @@ -351,7 +351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b74960d", + "id": "d5532b0d", "metadata": {}, "outputs": [], "source": [ @@ -360,7 +360,7 @@ }, { "cell_type": "markdown", - "id": "4d7426de", + "id": "0018a56d", "metadata": {}, "source": [ "Let's see if SciPy gives us the same results:" @@ -369,7 +369,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20e41ebe", + "id": "b0695c3f", "metadata": {}, "outputs": [], "source": [ @@ -378,7 +378,7 @@ }, { "cell_type": "markdown", - "id": "515f211b", + "id": "06f5c155", "metadata": {}, "source": [ "Here's the PMF:" @@ -387,7 +387,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e132ed90", + "id": "ef5c3c2f", "metadata": {}, "outputs": [], "source": [ @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b72a2002", + "id": "63be82d8", "metadata": {}, "outputs": [], "source": [ @@ -413,7 +413,7 @@ }, { "cell_type": "markdown", - "id": "6d1682d0", + "id": "f71eb196", "metadata": {}, "source": [ "Here's the CDF:" @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "430046e8", + "id": "44c2a0ec", "metadata": {}, "outputs": [], "source": [ @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "ea280cdc", + "id": "8c24ed62", "metadata": {}, "source": [ "```{exercise}\n", @@ -457,7 +457,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b715cf3", + "id": "74418bd4", "metadata": {}, "outputs": [], "source": [ @@ -474,7 +474,7 @@ }, { "cell_type": "markdown", - "id": "bae66036", + "id": "c5b99bcb", "metadata": {}, "source": [ "We can see that the output graph is the same as the one above.\n", @@ -506,7 +506,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da10609c", + "id": "e9f02836", "metadata": {}, "outputs": [], "source": [ @@ -517,7 +517,7 @@ }, { "cell_type": "markdown", - "id": "af34e96e", + "id": "19dbe22e", "metadata": {}, "source": [ "Here's part of the PMF:" @@ -526,7 +526,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65cd0669", + "id": "66de1328", "metadata": {}, "outputs": [], "source": [ @@ -543,7 +543,7 @@ }, { "cell_type": "markdown", - "id": "2688959a", + "id": "6ce34806", "metadata": {}, "source": [ "#### Poisson distribution\n", @@ -564,7 +564,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc25a8b8", + "id": "b4ccafac", "metadata": {}, "outputs": [], "source": [ @@ -575,7 +575,7 @@ }, { "cell_type": "markdown", - "id": "5cd4538e", + "id": "94a4d7d0", "metadata": {}, "source": [ "Here's the PMF:" @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98d65752", + "id": "a33036dc", "metadata": {}, "outputs": [], "source": [ @@ -594,7 +594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a69b7fbf", + "id": "5d7953ba", "metadata": {}, "outputs": [], "source": [ @@ -610,7 +610,7 @@ }, { "cell_type": "markdown", - "id": "c54a3489", + "id": "32794ee4", "metadata": {}, "source": [ "### Continuous distributions\n", @@ -665,7 +665,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd19d649", + "id": "60e68cf7", "metadata": {}, "outputs": [], "source": [ @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1eec81af", + "id": "b7e8601f", "metadata": {}, "outputs": [], "source": [ @@ -685,7 +685,7 @@ }, { "cell_type": "markdown", - "id": "601986d9", + "id": "8c3dfceb", "metadata": {}, "source": [ "Here's a plot of the density --- the famous \"bell-shaped curve\":" @@ -694,7 +694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "342cb94b", + "id": "e6a104b0", "metadata": {}, "outputs": [], "source": [ @@ -716,7 +716,7 @@ }, { "cell_type": "markdown", - "id": "a58af010", + "id": "18530ed4", "metadata": {}, "source": [ "Here's a plot of the CDF:" @@ -725,7 +725,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7ecb72c", + "id": "6c28152c", "metadata": {}, "outputs": [], "source": [ @@ -744,7 +744,7 @@ }, { "cell_type": "markdown", - "id": "7d4d09aa", + "id": "3b85580c", "metadata": {}, "source": [ "#### Lognormal distribution\n", @@ -771,7 +771,7 @@ { "cell_type": "code", "execution_count": null, - "id": "116c2d36", + "id": "26a36828", "metadata": {}, "outputs": [], "source": [ @@ -782,7 +782,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b6bcf305", + "id": "645c5c39", "metadata": {}, "outputs": [], "source": [ @@ -792,7 +792,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d640815c", + "id": "39dbc054", "metadata": {}, "outputs": [], "source": [ @@ -815,7 +815,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4a7bbb1", + "id": "27467f10", "metadata": {}, "outputs": [], "source": [ @@ -836,7 +836,7 @@ }, { "cell_type": "markdown", - "id": "0ffd366c", + "id": "4759463e", "metadata": {}, "source": [ "#### Exponential distribution\n", @@ -860,7 +860,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbac4e42", + "id": "08a19db1", "metadata": {}, "outputs": [], "source": [ @@ -871,7 +871,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c6fcd12", + "id": "75a7bab3", "metadata": {}, "outputs": [], "source": [ @@ -881,7 +881,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c01efa0", + "id": "e02ca5f7", "metadata": {}, "outputs": [], "source": [ @@ -903,7 +903,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2b0e1cd", + "id": "3075ac88", "metadata": {}, "outputs": [], "source": [ @@ -922,7 +922,7 @@ }, { "cell_type": "markdown", - "id": "93b50747", + "id": "ac1eec6e", "metadata": {}, "source": [ "#### Beta distribution\n", @@ -950,7 +950,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5648759a", + "id": "c6eeaddf", "metadata": {}, "outputs": [], "source": [ @@ -961,7 +961,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3702e4e", + "id": "5179213f", "metadata": {}, "outputs": [], "source": [ @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6816484", + "id": "12f4ca8c", "metadata": {}, "outputs": [], "source": [ @@ -994,7 +994,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c613e76", + "id": "e66598f7", "metadata": {}, "outputs": [], "source": [ @@ -1013,7 +1013,7 @@ }, { "cell_type": "markdown", - "id": "9a02f4a5", + "id": "23d8af39", "metadata": {}, "source": [ "#### Gamma distribution\n", @@ -1040,7 +1040,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4a97a25", + "id": "2bffc3c4", "metadata": {}, "outputs": [], "source": [ @@ -1051,7 +1051,7 @@ { "cell_type": "code", "execution_count": null, - "id": "067a18ba", + "id": "b5d2e530", "metadata": {}, "outputs": [], "source": [ @@ -1061,7 +1061,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4e6b4a4", + "id": "b7092ef8", "metadata": {}, "outputs": [], "source": [ @@ -1084,7 +1084,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3749b64d", + "id": "f8b8d4c9", "metadata": {}, "outputs": [], "source": [ @@ -1103,7 +1103,7 @@ }, { "cell_type": "markdown", - "id": "71315fc4", + "id": "b92c1692", "metadata": {}, "source": [ "## Observed distributions\n", @@ -1117,7 +1117,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fafa3f9f", + "id": "c0a795a6", "metadata": {}, "outputs": [], "source": [ @@ -1138,7 +1138,7 @@ }, { "cell_type": "markdown", - "id": "75346138", + "id": "7e6d56e3", "metadata": {}, "source": [ "In this situation, we might refer to the set of their incomes as the \"income distribution.\"\n", @@ -1174,7 +1174,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8889c8e3", + "id": "204e599d", "metadata": {}, "outputs": [], "source": [ @@ -1184,13 +1184,17 @@ }, { "cell_type": "markdown", - "id": "8ccde198", + "id": "afe33f58", "metadata": {}, "source": [ "```{exercise}\n", ":label: prob_ex4\n", "\n", - "Check that the formulas given above produce the same numbers.\n", + "If you try to check that the formulas given above for the sample mean and sample\n", + "variance produce the same numbers, you will see that the variance isn't quite\n", + "right. This is because SciPy uses $1/(n-1)$ instead of $1/n$ as the term at the\n", + "front of the variance. (Some books define the sample variance this way.)\n", + "Confirm.\n", "```\n", "\n", "\n", @@ -1213,7 +1217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a7d294e", + "id": "0d695579", "metadata": {}, "outputs": [], "source": [ @@ -1226,7 +1230,7 @@ }, { "cell_type": "markdown", - "id": "fc3121b6", + "id": "c1ab0375", "metadata": {}, "source": [ "Let's look at a distribution from real data.\n", @@ -1241,7 +1245,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f7271d7", + "id": "e20da05e", "metadata": { "tags": [ "hide-output" @@ -1257,7 +1261,7 @@ }, { "cell_type": "markdown", - "id": "7d555eb3", + "id": "a652eea8", "metadata": {}, "source": [ "The first observation is the monthly return (percent change) over January 2000, which was" @@ -1266,7 +1270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf719785", + "id": "232c4743", "metadata": {}, "outputs": [], "source": [ @@ -1275,7 +1279,7 @@ }, { "cell_type": "markdown", - "id": "2bdf6134", + "id": "28830f88", "metadata": {}, "source": [ "Let's turn the return observations into an array and histogram it." @@ -1284,7 +1288,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2290dacf", + "id": "cd054af0", "metadata": {}, "outputs": [], "source": [ @@ -1297,7 +1301,7 @@ }, { "cell_type": "markdown", - "id": "b02b0c58", + "id": "f0ae1095", "metadata": {}, "source": [ "#### Kernel density estimates\n", @@ -1313,7 +1317,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c393e9ba", + "id": "fde7ded7", "metadata": {}, "outputs": [], "source": [ @@ -1326,7 +1330,7 @@ }, { "cell_type": "markdown", - "id": "97cec8b5", + "id": "9ac4e24e", "metadata": {}, "source": [ "The smoothness of the KDE is dependent on how we choose the bandwidth." @@ -1335,7 +1339,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b328dd22", + "id": "66f68d8f", "metadata": {}, "outputs": [], "source": [ @@ -1351,7 +1355,7 @@ }, { "cell_type": "markdown", - "id": "5c784f85", + "id": "72fe4cf1", "metadata": {}, "source": [ "When we use a larger bandwidth, the KDE is smoother.\n", @@ -1368,7 +1372,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c83c4e4a", + "id": "6877f2d5", "metadata": {}, "outputs": [], "source": [ @@ -1381,7 +1385,7 @@ }, { "cell_type": "markdown", - "id": "efb44360", + "id": "fe5550fb", "metadata": {}, "source": [ "Violin plots are particularly useful when we want to compare different distributions.\n", @@ -1392,7 +1396,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2631a8e6", + "id": "9a43d348", "metadata": { "tags": [ "hide-output" @@ -1408,7 +1412,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b008e2c", + "id": "4ecaeef8", "metadata": {}, "outputs": [], "source": [ @@ -1421,7 +1425,7 @@ }, { "cell_type": "markdown", - "id": "2b832cf4", + "id": "7d629b06", "metadata": {}, "source": [ "### Connection to probability distributions\n", @@ -1444,7 +1448,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be0540c9", + "id": "5162305b", "metadata": {}, "outputs": [], "source": [ @@ -1457,7 +1461,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9403738", + "id": "6584a931", "metadata": {}, "outputs": [], "source": [ @@ -1472,7 +1476,7 @@ }, { "cell_type": "markdown", - "id": "a4f32615", + "id": "900415b9", "metadata": {}, "source": [ "The match between the histogram and the density is not bad but also not very good.\n", @@ -1490,7 +1494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "205030cd", + "id": "11b62ec3", "metadata": {}, "outputs": [], "source": [ @@ -1509,7 +1513,7 @@ }, { "cell_type": "markdown", - "id": "21675b36", + "id": "86d0f31b", "metadata": {}, "source": [ "Note that if you keep increasing $N$, which is the number of observations, the fit will get better and better.\n", @@ -1548,11 +1552,11 @@ 131, 135, 144, - 178, - 181, - 185, - 187, - 191, + 179, + 182, + 186, + 188, + 192, 194, 214, 218, @@ -1607,28 +1611,28 @@ 720, 751, 754, - 778, - 784, - 794, - 801, + 782, + 788, + 798, 805, - 807, + 809, 811, - 817, - 828, - 834, + 815, + 821, + 832, 838, - 847, - 859, - 865, - 871, - 879, - 885, - 903, - 910, - 918, - 931, - 943 + 842, + 851, + 863, + 869, + 875, + 883, + 889, + 907, + 914, + 922, + 935, + 947 ] }, "nbformat": 4, diff --git a/_sources/prob_dist.md b/_sources/prob_dist.md index 2b619724..6976b665 100644 --- a/_sources/prob_dist.md +++ b/_sources/prob_dist.md @@ -160,7 +160,8 @@ Check that your answers agree with `u.mean()` and `u.var()`. Another useful distribution is the Bernoulli distribution on $S = \{0,1\}$, which has PMF: $$ -p(i) = \theta^{i-1} (1 - \theta)^i +p(i) = \theta^i (1 - \theta)^{1-i} +\qquad (i = 0, 1) $$ Here $\theta \in [0,1]$ is a parameter. @@ -171,7 +172,7 @@ We can think of this distribution as modeling probabilities for a random trial w * $p(0) = 1 - \theta$ means that the trial fails (takes value 0) with probability $1-\theta$ -The formula for the mean is $p$, and the formula for the variance is $p(1-p)$. +The formula for the mean is $\theta$, and the formula for the variance is $\theta(1-\theta)$. We can import the Bernoulli distribution on $S = \{0,1\}$ from SciPy like so: @@ -186,11 +187,10 @@ Here's the mean and variance at $\theta=0.4$ u.mean(), u.var() ``` -Now let's evaluate the PMF +We can evaluate the PMF as follows ```{code-cell} ipython3 -u.pmf(0) -u.pmf(1) +u.pmf(0), u.pmf(1) ``` #### Binomial distribution @@ -756,7 +756,11 @@ x.mean(), x.var() ```{exercise} :label: prob_ex4 -Check that the formulas given above produce the same numbers. +If you try to check that the formulas given above for the sample mean and sample +variance produce the same numbers, you will see that the variance isn't quite +right. This is because SciPy uses $1/(n-1)$ instead of $1/n$ as the term at the +front of the variance. (Some books define the sample variance this way.) +Confirm. ``` diff --git a/_sources/pv.ipynb b/_sources/pv.ipynb index 20146e44..e4876f74 100644 --- a/_sources/pv.ipynb +++ b/_sources/pv.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "aac5c59c", + "id": "84287fdf", "metadata": {}, "source": [ "# Present Values\n", @@ -86,7 +86,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e0a116e", + "id": "b3fbbc2f", "metadata": {}, "outputs": [], "source": [ @@ -96,7 +96,7 @@ }, { "cell_type": "markdown", - "id": "0735fc09", + "id": "0a0ccca2", "metadata": {}, "source": [ "## Representing sequences as vectors\n", @@ -135,7 +135,7 @@ }, { "cell_type": "markdown", - "id": "5ebff0e3", + "id": "9c597a8b", "metadata": {}, "source": [ "```{exercise-start} \n", @@ -201,7 +201,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47cd72cd", + "id": "87f5e313", "metadata": {}, "outputs": [], "source": [ @@ -221,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "592106bc", + "id": "975e3fd0", "metadata": {}, "source": [ "Now let's compute and plot the asset price.\n", @@ -232,7 +232,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce39576c", + "id": "c55326e5", "metadata": {}, "outputs": [], "source": [ @@ -242,7 +242,7 @@ }, { "cell_type": "markdown", - "id": "fa6c1d66", + "id": "9f2dacf5", "metadata": {}, "source": [ "Let's build the matrix $A$" @@ -251,7 +251,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6087ab07", + "id": "917bc56f", "metadata": {}, "outputs": [], "source": [ @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "7700b81b", + "id": "8bc8d874", "metadata": {}, "source": [ "Let's inspect $A$" @@ -275,7 +275,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b05c83b4", + "id": "a150188a", "metadata": {}, "outputs": [], "source": [ @@ -284,7 +284,7 @@ }, { "cell_type": "markdown", - "id": "e88ea781", + "id": "965e02dc", "metadata": {}, "source": [ "Now let's solve for prices using {eq}`eq:apdb_sol`." @@ -293,7 +293,7 @@ { "cell_type": "code", "execution_count": null, - "id": "efd22d1d", + "id": "1b4a55d2", "metadata": {}, "outputs": [], "source": [ @@ -309,7 +309,7 @@ }, { "cell_type": "markdown", - "id": "5610b802", + "id": "d6a35cf3", "metadata": {}, "source": [ "Now let's consider a cyclically growing dividend sequence:\n", @@ -322,7 +322,7 @@ { "cell_type": "code", "execution_count": null, - "id": "654c18ec", + "id": "d586abdd", "metadata": {}, "outputs": [], "source": [ @@ -342,7 +342,7 @@ }, { "cell_type": "markdown", - "id": "36f072af", + "id": "8c61b5f3", "metadata": {}, "source": [ "```{exercise-start} \n", @@ -365,7 +365,7 @@ { "cell_type": "code", "execution_count": null, - "id": "895c74e5", + "id": "b887ca7a", "metadata": {}, "outputs": [], "source": [ @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "93d91c2a", + "id": "c71d47b8", "metadata": {}, "source": [ "The weighted averaging associated with the present value calculation largely\n", @@ -466,7 +466,7 @@ }, { "cell_type": "markdown", - "id": "d0f43f57", + "id": "2aa8d37f", "metadata": {}, "source": [ "## More about bubbles\n", @@ -485,7 +485,7 @@ }, { "cell_type": "markdown", - "id": "4ef6f818", + "id": "d175ab97", "metadata": {}, "source": [ "In this case system {eq}`eq:Euler1` of our $T+1$ asset pricing equations takes the\n", diff --git a/_sources/scalar_dynam.ipynb b/_sources/scalar_dynam.ipynb index 5f87f81e..42724207 100644 --- a/_sources/scalar_dynam.ipynb +++ b/_sources/scalar_dynam.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c5e3ed1b", + "id": "6400a6c2", "metadata": {}, "source": [ "```{raw} html\n", @@ -48,7 +48,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb2368e1", + "id": "d113f68f", "metadata": {}, "outputs": [], "source": [ @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "41153a1e", + "id": "37c66d49", "metadata": {}, "source": [ "## Some definitions\n", @@ -336,7 +336,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ce5e835", + "id": "cef03c93", "metadata": { "tags": [ "hide-input", @@ -433,7 +433,7 @@ }, { "cell_type": "markdown", - "id": "9bb524f7", + "id": "eac3f119", "metadata": {}, "source": [ "Let's create a 45-degree diagram for the Solow-Swan model with a fixed set of\n", @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "036b9096", + "id": "2ddd7d6e", "metadata": {}, "outputs": [], "source": [ @@ -453,7 +453,7 @@ }, { "cell_type": "markdown", - "id": "905e143b", + "id": "109b7b6b", "metadata": {}, "source": [ "Here is the 45-degree plot." @@ -462,7 +462,7 @@ { "cell_type": "code", "execution_count": null, - "id": "239e16f9", + "id": "85cb81c6", "metadata": {}, "outputs": [], "source": [ @@ -473,7 +473,7 @@ }, { "cell_type": "markdown", - "id": "d1e28e4a", + "id": "beb8e786", "metadata": {}, "source": [ "The plot shows the function $g$ and the 45-degree line.\n", @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "484338eb", + "id": "72d6fac8", "metadata": {}, "outputs": [], "source": [ @@ -524,7 +524,7 @@ }, { "cell_type": "markdown", - "id": "6f922f27", + "id": "cb54cc51", "metadata": {}, "source": [ "We can plot the time series of per capita capital corresponding to the figure above as\n", @@ -534,7 +534,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c881670a", + "id": "36956d26", "metadata": {}, "outputs": [], "source": [ @@ -543,7 +543,7 @@ }, { "cell_type": "markdown", - "id": "a014e621", + "id": "430164a1", "metadata": {}, "source": [ "Here's a somewhat longer view:" @@ -552,7 +552,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac480d9a", + "id": "a4617de7", "metadata": {}, "outputs": [], "source": [ @@ -561,7 +561,7 @@ }, { "cell_type": "markdown", - "id": "cec0cbe5", + "id": "8b14adb1", "metadata": {}, "source": [ "When per capita capital stock is higher than the unique positive steady state, we see that\n", @@ -571,7 +571,7 @@ { "cell_type": "code", "execution_count": null, - "id": "690bc90c", + "id": "e5198d75", "metadata": {}, "outputs": [], "source": [ @@ -582,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "0c6b6709", + "id": "dc551e4a", "metadata": {}, "source": [ "Here is the time series:" @@ -591,7 +591,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d16acdf1", + "id": "f334e5db", "metadata": {}, "outputs": [], "source": [ @@ -600,7 +600,7 @@ }, { "cell_type": "markdown", - "id": "5b3ce01e", + "id": "70c464e3", "metadata": {}, "source": [ "### Complex dynamics\n", @@ -620,7 +620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "911cdcc0", + "id": "ebeb6244", "metadata": {}, "outputs": [], "source": [ @@ -633,7 +633,7 @@ }, { "cell_type": "markdown", - "id": "93118695", + "id": "36f14a80", "metadata": {}, "source": [ "Now let's look at a typical trajectory." @@ -642,7 +642,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d34ac65", + "id": "5ce26d78", "metadata": {}, "outputs": [], "source": [ @@ -651,7 +651,7 @@ }, { "cell_type": "markdown", - "id": "c119f067", + "id": "dd732910", "metadata": {}, "source": [ "Notice how irregular it is.\n", @@ -662,7 +662,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83aba17a", + "id": "cbe41444", "metadata": {}, "outputs": [], "source": [ @@ -671,7 +671,7 @@ }, { "cell_type": "markdown", - "id": "6fdbccbf", + "id": "a3686a34", "metadata": {}, "source": [ "The irregularity is even clearer over a longer time horizon:" @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06d2431c", + "id": "676fd961", "metadata": {}, "outputs": [], "source": [ @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "afe9e567", + "id": "1b39441d", "metadata": {}, "source": [ "## Exercises\n", @@ -726,7 +726,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6cf472a4", + "id": "1198bebd", "metadata": {}, "outputs": [], "source": [ @@ -737,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "6d441f9d", + "id": "5a38155a", "metadata": {}, "source": [ "Now let's plot a trajectory:" @@ -746,7 +746,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1775f62", + "id": "66e96571", "metadata": {}, "outputs": [], "source": [ @@ -756,7 +756,7 @@ }, { "cell_type": "markdown", - "id": "21374d1c", + "id": "0da07cb4", "metadata": {}, "source": [ "Here is the corresponding time series, which converges towards the steady\n", @@ -766,7 +766,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8940213", + "id": "1b09b9a6", "metadata": {}, "outputs": [], "source": [ @@ -775,7 +775,7 @@ }, { "cell_type": "markdown", - "id": "66a17dbe", + "id": "7c1ace7f", "metadata": {}, "source": [ "Now let's try $a=-0.5$ and see what differences we observe.\n", @@ -786,7 +786,7 @@ { "cell_type": "code", "execution_count": null, - "id": "581682db", + "id": "a010575c", "metadata": {}, "outputs": [], "source": [ @@ -797,7 +797,7 @@ }, { "cell_type": "markdown", - "id": "50b4e111", + "id": "f1771744", "metadata": {}, "source": [ "Now let's plot a trajectory:" @@ -806,7 +806,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcf8f4e6", + "id": "c5ddef3e", "metadata": {}, "outputs": [], "source": [ @@ -816,7 +816,7 @@ }, { "cell_type": "markdown", - "id": "08005624", + "id": "1dd15030", "metadata": {}, "source": [ "Here is the corresponding time series, which converges towards the steady\n", @@ -826,7 +826,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aabba128", + "id": "60995304", "metadata": {}, "outputs": [], "source": [ @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "2f65f17d", + "id": "29d33277", "metadata": {}, "source": [ "Once again, we have convergence to the steady state but the nature of\n", diff --git a/_sources/schelling.ipynb b/_sources/schelling.ipynb index ef878705..3fbfe6d3 100644 --- a/_sources/schelling.ipynb +++ b/_sources/schelling.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "1c461bc8", + "id": "70e3d464", "metadata": {}, "source": [ "(schelling)=\n", @@ -63,7 +63,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5484e240", + "id": "23e4f73a", "metadata": {}, "outputs": [], "source": [ @@ -75,7 +75,7 @@ }, { "cell_type": "markdown", - "id": "8923076e", + "id": "d46b6103", "metadata": {}, "source": [ "## The model\n", @@ -103,7 +103,7 @@ }, { "cell_type": "markdown", - "id": "d90e6213", + "id": "f96610d7", "metadata": {}, "source": [ "### Preferences\n", @@ -126,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "440a2b2b", + "id": "11111e21", "metadata": {}, "source": [ "### Behavior\n", @@ -162,7 +162,7 @@ }, { "cell_type": "markdown", - "id": "b56eca6a", + "id": "b556132f", "metadata": {}, "source": [ "## Results\n", @@ -192,7 +192,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eaa6e099", + "id": "f57b8053", "metadata": {}, "outputs": [], "source": [ @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "b5566679", + "id": "8e3f7adb", "metadata": {}, "source": [ "Here's some code that takes a list of agents and produces a plot showing their\n", @@ -260,7 +260,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a469ca32", + "id": "2bed36d1", "metadata": {}, "outputs": [], "source": [ @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "671546d5", + "id": "bce4a916", "metadata": {}, "source": [ "And here's some pseudocode for the main loop, where we cycle through the\n", @@ -312,7 +312,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2202f807", + "id": "b76d9999", "metadata": {}, "outputs": [], "source": [ @@ -359,7 +359,7 @@ }, { "cell_type": "markdown", - "id": "dbdb7a11", + "id": "d4cba2bc", "metadata": {}, "source": [ "Let's have a look at the results." @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "326539c6", + "id": "3fde8595", "metadata": {}, "outputs": [], "source": [ @@ -377,7 +377,7 @@ }, { "cell_type": "markdown", - "id": "6f0b676f", + "id": "cc93fabe", "metadata": {}, "source": [ "As discussed above, agents are initially mixed randomly together.\n", @@ -437,7 +437,7 @@ { "cell_type": "code", "execution_count": null, - "id": "91fbda57", + "id": "792bb388", "metadata": {}, "outputs": [], "source": [ @@ -544,7 +544,7 @@ }, { "cell_type": "markdown", - "id": "734bbcba", + "id": "77b93d75", "metadata": {}, "source": [ "```{solution-end}\n", @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "0160e440", + "id": "a768eedd", "metadata": {}, "source": [ "When we run this we again find that mixed neighborhoods break down and segregation emerges.\n", @@ -564,7 +564,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c71da41", + "id": "ba50f938", "metadata": {}, "outputs": [], "source": [ @@ -574,7 +574,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b0f9037", + "id": "4c52d2d0", "metadata": {}, "outputs": [], "source": [] diff --git a/_sources/short_path.ipynb b/_sources/short_path.ipynb index c63de84c..89d05d6e 100644 --- a/_sources/short_path.ipynb +++ b/_sources/short_path.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "548df6e3", + "id": "5ed78548", "metadata": {}, "source": [ "(short_path)=\n", @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66f20712", + "id": "20891de7", "metadata": {}, "outputs": [], "source": [ @@ -53,7 +53,7 @@ }, { "cell_type": "markdown", - "id": "3753eb75", + "id": "b20569c2", "metadata": {}, "source": [ "## Outline of the problem\n", @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44eb7df6", + "id": "3a4bff87", "metadata": {}, "outputs": [], "source": [ @@ -224,7 +224,7 @@ }, { "cell_type": "markdown", - "id": "5f038766", + "id": "50e08f3a", "metadata": {}, "source": [ "Notice that the cost of staying still (on the principle diagonal) is set to\n", @@ -240,7 +240,7 @@ { "cell_type": "code", "execution_count": null, - "id": "344305b8", + "id": "fbde8934", "metadata": {}, "outputs": [], "source": [ @@ -267,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "7650a21a", + "id": "35e694e2", "metadata": {}, "source": [ "This matches with the numbers we obtained by inspection above.\n", @@ -304,7 +304,7 @@ { "cell_type": "code", "execution_count": null, - "id": "382a6279", + "id": "1abf7424", "metadata": {}, "outputs": [], "source": [ @@ -413,7 +413,7 @@ }, { "cell_type": "markdown", - "id": "10b2bff7", + "id": "0bcfbe00", "metadata": {}, "source": [ "```{exercise-end}\n", @@ -429,7 +429,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e948747", + "id": "35641ba8", "metadata": {}, "outputs": [], "source": [ @@ -458,7 +458,7 @@ }, { "cell_type": "markdown", - "id": "ff44a7d3", + "id": "de202dc2", "metadata": {}, "source": [ "In addition, let's write\n", @@ -474,7 +474,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1621690", + "id": "a7a863e3", "metadata": {}, "outputs": [], "source": [ @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "f4885417", + "id": "b6f667e3", "metadata": {}, "source": [ "We used np.allclose() rather than testing exact equality because we are\n", @@ -514,7 +514,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c68ef31", + "id": "6ebd8ae1", "metadata": {}, "outputs": [], "source": [ @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "2bc0de29", + "id": "6946ffc7", "metadata": {}, "source": [ "Okay, now we have the necessary functions, let's call them to do the job we were assigned." @@ -543,7 +543,7 @@ { "cell_type": "code", "execution_count": null, - "id": "322598ca", + "id": "56bff1ba", "metadata": {}, "outputs": [], "source": [ @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "cab072dc", + "id": "8ea633fa", "metadata": {}, "source": [ "The total cost of the path should agree with $J[0]$ so let's check this." @@ -563,7 +563,7 @@ { "cell_type": "code", "execution_count": null, - "id": "58d4ef0c", + "id": "98f3c5ac", "metadata": {}, "outputs": [], "source": [ @@ -572,7 +572,7 @@ }, { "cell_type": "markdown", - "id": "63222c02", + "id": "4ac7bf3d", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/simple_linear_regression.ipynb b/_sources/simple_linear_regression.ipynb index 248a275d..611d8dd7 100644 --- a/_sources/simple_linear_regression.ipynb +++ b/_sources/simple_linear_regression.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8b11bdb2", + "id": "a8d68d33", "metadata": {}, "source": [ "# Simple Linear Regression Model" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7ace984", + "id": "c36916de", "metadata": {}, "outputs": [], "source": [ @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "354c2f47", + "id": "76c07b3b", "metadata": {}, "source": [ "The simple regression model estimates the relationship between two variables $x_i$ and $y_i$\n", @@ -56,7 +56,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df4b8313", + "id": "db3c6f36", "metadata": {}, "outputs": [], "source": [ @@ -69,7 +69,7 @@ }, { "cell_type": "markdown", - "id": "c46a5c13", + "id": "8713fbcc", "metadata": {}, "source": [ "We can use a scatter plot of the data to see the relationship between $y_i$ (ice-cream sales in dollars (\\$\\'s)) and $x_i$ (degrees Celsius)." @@ -78,7 +78,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44f803b1", + "id": "58fcbbf7", "metadata": { "mystnb": { "figure": { @@ -100,7 +100,7 @@ }, { "cell_type": "markdown", - "id": "5ca42322", + "id": "8c5bb680", "metadata": {}, "source": [ "as you can see the data suggests that more ice-cream is typically sold on hotter days. \n", @@ -117,7 +117,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43596e29", + "id": "f0a0c96b", "metadata": {}, "outputs": [], "source": [ @@ -129,7 +129,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d37b0442", + "id": "a38e3904", "metadata": { "mystnb": { "figure": { @@ -148,7 +148,7 @@ }, { "cell_type": "markdown", - "id": "dc8a4887", + "id": "186e01b3", "metadata": {}, "source": [ "We can see that this model does a poor job of estimating the relationship.\n", @@ -159,7 +159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b396a9bc", + "id": "ca40ae28", "metadata": {}, "outputs": [], "source": [ @@ -170,7 +170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55838291", + "id": "9686a751", "metadata": { "mystnb": { "figure": { @@ -190,7 +190,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9515aa9b", + "id": "6fc27e89", "metadata": {}, "outputs": [], "source": [ @@ -201,7 +201,7 @@ { "cell_type": "code", "execution_count": null, - "id": "044aa539", + "id": "1fddec2e", "metadata": { "mystnb": { "figure": { @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "4f7fd3a6", + "id": "2e7a06b8", "metadata": {}, "source": [ "However we need to think about formalizing this guessing process by thinking of this problem as an optimization problem. \n", @@ -238,7 +238,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c8ed1bd9", + "id": "d5a598c8", "metadata": {}, "outputs": [], "source": [ @@ -248,7 +248,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55faea8a", + "id": "5c9d0f82", "metadata": {}, "outputs": [], "source": [ @@ -258,7 +258,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dcd0b9d9", + "id": "ed159e42", "metadata": { "mystnb": { "figure": { @@ -278,7 +278,7 @@ }, { "cell_type": "markdown", - "id": "6e64f467", + "id": "d4257c3f", "metadata": {}, "source": [ "The Ordinary Least Squares (OLS) method chooses $\\alpha$ and $\\beta$ in such a way that **minimizes** the sum of the squared residuals (SSR). \n", @@ -305,7 +305,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73b82ec2", + "id": "4ef402b6", "metadata": {}, "outputs": [], "source": [ @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "4ee63cc2", + "id": "b77d6ef1", "metadata": {}, "source": [ "We can then calculate the error for a range of $\\beta$ values" @@ -324,7 +324,7 @@ { "cell_type": "code", "execution_count": null, - "id": "57204e7a", + "id": "bc96ff3b", "metadata": {}, "outputs": [], "source": [ @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "194bbed7", + "id": "c184d8df", "metadata": {}, "source": [ "Plotting the error" @@ -344,7 +344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3bc47be", + "id": "aef5cc66", "metadata": { "mystnb": { "figure": { @@ -361,7 +361,7 @@ }, { "cell_type": "markdown", - "id": "3c8f0ac7", + "id": "d2d6cc35", "metadata": {}, "source": [ "Now let us vary $\\alpha$ (holding $\\beta$ constant)" @@ -370,7 +370,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e238a9a", + "id": "c1574a97", "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "66978ece", + "id": "001b1990", "metadata": {}, "source": [ "Plotting the error" @@ -390,7 +390,7 @@ { "cell_type": "code", "execution_count": null, - "id": "082b44a7", + "id": "0d0584a4", "metadata": { "mystnb": { "figure": { @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "45135b53", + "id": "d88429e1", "metadata": {}, "source": [ "(slr:optimal-values)=\n", @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "243fdf6f", + "id": "93da2964", "metadata": {}, "outputs": [], "source": [ @@ -526,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "28081e4d", + "id": "5ba2174a", "metadata": {}, "source": [ "Now computing across the 10 observations and then summing the numerator and denominator" @@ -535,7 +535,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6da27b45", + "id": "6034586b", "metadata": {}, "outputs": [], "source": [ @@ -548,7 +548,7 @@ }, { "cell_type": "markdown", - "id": "01ef392c", + "id": "abe7d832", "metadata": {}, "source": [ "Calculating $\\alpha$" @@ -557,7 +557,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42ef83c5", + "id": "2e652ff7", "metadata": {}, "outputs": [], "source": [ @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "b1c82e71", + "id": "5dabb8ce", "metadata": {}, "source": [ "Now we can plot the OLS solution" @@ -576,7 +576,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90da0c32", + "id": "15c565b0", "metadata": { "mystnb": { "figure": { @@ -598,7 +598,7 @@ }, { "cell_type": "markdown", - "id": "5e0e5135", + "id": "893c9ca9", "metadata": {}, "source": [ ":::{exercise}\n", @@ -634,7 +634,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcf91ad2", + "id": "77b933c3", "metadata": {}, "outputs": [], "source": [ @@ -645,7 +645,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc7befaa", + "id": "0d622e7d", "metadata": {}, "outputs": [], "source": [ @@ -654,7 +654,7 @@ }, { "cell_type": "markdown", - "id": "fb8b03f8", + "id": "37e36e1b", "metadata": {}, "source": [ "You can see that the data downloaded from Our World in Data has provided a global set of countries with the GDP per capita and Life Expectancy Data.\n", @@ -669,7 +669,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f9793fb", + "id": "b2043ebd", "metadata": {}, "outputs": [], "source": [ @@ -680,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "70b91975", + "id": "5d6d3b1f", "metadata": {}, "source": [ "Sometimes it can be useful to rename your columns to make it easier to work with in the DataFrame" @@ -689,7 +689,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60686bcf", + "id": "09ee8df6", "metadata": {}, "outputs": [], "source": [ @@ -699,7 +699,7 @@ }, { "cell_type": "markdown", - "id": "0cfa64cb", + "id": "7065aac5", "metadata": {}, "source": [ "We can see there are `NaN` values which represents missing data so let us go ahead and drop those" @@ -708,7 +708,7 @@ { "cell_type": "code", "execution_count": null, - "id": "114b9eb1", + "id": "b7a7e4da", "metadata": {}, "outputs": [], "source": [ @@ -718,7 +718,7 @@ { "cell_type": "code", "execution_count": null, - "id": "13a81512", + "id": "acc28e34", "metadata": {}, "outputs": [], "source": [ @@ -727,7 +727,7 @@ }, { "cell_type": "markdown", - "id": "6adf76ce", + "id": "174fe119", "metadata": {}, "source": [ "We have now dropped the number of rows in our DataFrame from 62156 to 12445 removing a lot of empty data relationships.\n", @@ -744,7 +744,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3911a1e", + "id": "0298caf4", "metadata": {}, "outputs": [], "source": [ @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "16a72be8", + "id": "d4d9cdef", "metadata": {}, "source": [ "As you can see there are a lot of countries where data is not available for the Year 1543!\n", @@ -765,7 +765,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b6446e72", + "id": "367d7311", "metadata": {}, "outputs": [], "source": [ @@ -774,7 +774,7 @@ }, { "cell_type": "markdown", - "id": "a15bd738", + "id": "4856f283", "metadata": {}, "source": [ "You can see that Great Britain (GBR) is the only one available\n", @@ -785,7 +785,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6fea37a", + "id": "ef62c72e", "metadata": {}, "outputs": [], "source": [ @@ -794,7 +794,7 @@ }, { "cell_type": "markdown", - "id": "4cf7f07e", + "id": "64bd0487", "metadata": {}, "source": [ "In fact we can use pandas to quickly check how many countries are captured in each year" @@ -803,7 +803,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48e17530", + "id": "71b2b8b2", "metadata": {}, "outputs": [], "source": [ @@ -812,7 +812,7 @@ }, { "cell_type": "markdown", - "id": "17db9f44", + "id": "a789150b", "metadata": {}, "source": [ "So it is clear that if you are doing cross-sectional comparisons then more recent data will include a wider set of countries\n", @@ -823,7 +823,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26ba17ff", + "id": "cc1c25bb", "metadata": {}, "outputs": [], "source": [ @@ -833,7 +833,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c14bccc6", + "id": "3de9e96b", "metadata": {}, "outputs": [], "source": [ @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "813a5497", + "id": "9b1ba0b8", "metadata": {}, "source": [ "This data shows a couple of interesting relationships.\n", @@ -858,7 +858,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6d37d73", + "id": "6216c165", "metadata": {}, "outputs": [], "source": [ @@ -867,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "82e16281", + "id": "8fc0be77", "metadata": {}, "source": [ "As you can see from this transformation -- a linear model fits the shape of the data more closely." @@ -876,7 +876,7 @@ { "cell_type": "code", "execution_count": null, - "id": "516e1233", + "id": "920c2a81", "metadata": {}, "outputs": [], "source": [ @@ -886,7 +886,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab5fb4af", + "id": "b63dd854", "metadata": {}, "outputs": [], "source": [ @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "a5e100b2", + "id": "79344d33", "metadata": {}, "source": [ "**Q4:** Use {eq}`eq:optimal-alpha` and {eq}`eq:optimal-beta` to compute optimal values for $\\alpha$ and $\\beta$" @@ -904,7 +904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd899b3d", + "id": "cb5af6f0", "metadata": {}, "outputs": [], "source": [ @@ -918,7 +918,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2411aae", + "id": "2b79cb72", "metadata": {}, "outputs": [], "source": [ @@ -928,7 +928,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef258c10", + "id": "d9c8517f", "metadata": {}, "outputs": [], "source": [ @@ -942,7 +942,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2812be33", + "id": "867140b8", "metadata": {}, "outputs": [], "source": [ @@ -952,7 +952,7 @@ }, { "cell_type": "markdown", - "id": "24a0a9a1", + "id": "3aa71841", "metadata": {}, "source": [ "**Q5:** Plot the line of best fit found using OLS" @@ -961,7 +961,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3daedbc", + "id": "98619aeb", "metadata": {}, "outputs": [], "source": [ @@ -976,7 +976,7 @@ }, { "cell_type": "markdown", - "id": "3669a3e7", + "id": "612e50b0", "metadata": {}, "source": [ ":::{solution-end}\n", diff --git a/_sources/solow.ipynb b/_sources/solow.ipynb index 93bdd4ba..3b8a6e87 100644 --- a/_sources/solow.ipynb +++ b/_sources/solow.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ea78cc36", + "id": "0fd60c26", "metadata": {}, "source": [ "(solow)=\n", @@ -22,7 +22,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6ce3938", + "id": "cb0c5267", "metadata": {}, "outputs": [], "source": [ @@ -32,7 +32,7 @@ }, { "cell_type": "markdown", - "id": "94770897", + "id": "cd3f21ac", "metadata": {}, "source": [ "## The model\n", @@ -128,7 +128,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0fa34e54", + "id": "91fa87a7", "metadata": {}, "outputs": [], "source": [ @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "8c10322d", + "id": "e627b9b6", "metadata": {}, "source": [ "Now, we define the function $g$." @@ -148,7 +148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "adb1aa7a", + "id": "a268b755", "metadata": {}, "outputs": [], "source": [ @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "2e1d871e", + "id": "63ccb621", "metadata": {}, "source": [ "Let's plot the 45-degree diagram of $g$." @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3cdeacd", + "id": "2c6188ed", "metadata": {}, "outputs": [], "source": [ @@ -214,7 +214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b381c1c", + "id": "578805e4", "metadata": {}, "outputs": [], "source": [ @@ -223,7 +223,7 @@ }, { "cell_type": "markdown", - "id": "fd2666a9", + "id": "8d5c74e3", "metadata": {}, "source": [ "Suppose, at some $k_t$, the value $g(k_t)$ lies strictly above the 45-degree line.\n", @@ -255,7 +255,7 @@ { "cell_type": "code", "execution_count": null, - "id": "668d9d81", + "id": "65d12a6a", "metadata": {}, "outputs": [], "source": [ @@ -265,7 +265,7 @@ }, { "cell_type": "markdown", - "id": "adab9ec0", + "id": "3586ba85", "metadata": {}, "source": [ "From our graphical analysis, it appears that $(k_t)$ converges to $k^*$, regardless of initial capital\n", @@ -285,7 +285,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10f1b8c0", + "id": "6481ba6a", "metadata": {}, "outputs": [], "source": [ @@ -300,7 +300,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ec5de66", + "id": "f26da4bf", "metadata": {}, "outputs": [], "source": [ @@ -333,7 +333,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50c1ef22", + "id": "46e9c176", "metadata": {}, "outputs": [], "source": [ @@ -342,7 +342,7 @@ }, { "cell_type": "markdown", - "id": "f9f434f8", + "id": "87e33f02", "metadata": {}, "source": [ "As expected, the time paths in the figure all converge to $k^*$.\n", @@ -407,7 +407,7 @@ { "cell_type": "code", "execution_count": null, - "id": "246f2da2", + "id": "94735047", "metadata": {}, "outputs": [], "source": [ @@ -416,7 +416,7 @@ }, { "cell_type": "markdown", - "id": "9b8a59bc", + "id": "9acce40b", "metadata": {}, "source": [ "Next we define the function $g$ for growth in continuous time" @@ -425,7 +425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3bd15b76", + "id": "6c3970a1", "metadata": {}, "outputs": [], "source": [ @@ -436,7 +436,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6fb6de82", + "id": "f04508bf", "metadata": {}, "outputs": [], "source": [ @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f456afd3", + "id": "9e17c045", "metadata": {}, "outputs": [], "source": [ @@ -486,7 +486,7 @@ }, { "cell_type": "markdown", - "id": "134f2c00", + "id": "d02d993f", "metadata": {}, "source": [ "This shows global stability heuristically for a fixed parameterization, but\n", @@ -573,7 +573,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f70cadd", + "id": "d850f6cc", "metadata": {}, "outputs": [], "source": [ @@ -585,7 +585,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3707b0d6", + "id": "b185b355", "metadata": {}, "outputs": [], "source": [ @@ -596,7 +596,7 @@ }, { "cell_type": "markdown", - "id": "2a0f13c5", + "id": "dae092cc", "metadata": {}, "source": [ "Let's find the value of $s$ that maximizes $c^*$ using [scipy.optimize.minimize_scalar](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html#scipy.optimize.minimize_scalar).\n", @@ -606,7 +606,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f419cf4", + "id": "9c25511b", "metadata": {}, "outputs": [], "source": [ @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "440f9b1e", + "id": "b26baa27", "metadata": {}, "outputs": [], "source": [ @@ -628,7 +628,7 @@ { "cell_type": "code", "execution_count": null, - "id": "089412c2", + "id": "fac0e8f3", "metadata": {}, "outputs": [], "source": [ @@ -641,7 +641,7 @@ { "cell_type": "code", "execution_count": null, - "id": "93c87210", + "id": "af9b16bb", "metadata": {}, "outputs": [], "source": [ @@ -673,7 +673,7 @@ }, { "cell_type": "markdown", - "id": "f760d296", + "id": "fd8d5be8", "metadata": {}, "source": [ "One can also try to solve this mathematically by differentiating $c^*(s)$ and solve for $\\frac{d}{ds}c^*(s)=0$ using [sympy](https://www.sympy.org/en/index.html)." @@ -682,7 +682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8e2b253e", + "id": "e5c245d1", "metadata": {}, "outputs": [], "source": [ @@ -692,7 +692,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f6ee130", + "id": "10a136e7", "metadata": {}, "outputs": [], "source": [ @@ -703,7 +703,7 @@ }, { "cell_type": "markdown", - "id": "099b99bd", + "id": "098362ca", "metadata": {}, "source": [ "Let's differentiate $c$ and solve using [sympy.solve](https://docs.sympy.org/latest/modules/solvers/solvers.html#sympy.solvers.solvers.solve)" @@ -712,7 +712,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f8d848a", + "id": "e641b806", "metadata": {}, "outputs": [], "source": [ @@ -723,7 +723,7 @@ }, { "cell_type": "markdown", - "id": "e15ca918", + "id": "45aeb66a", "metadata": {}, "source": [ "Incidentally, the rate of savings which maximizes steady state level of per capita consumption is called the [Golden Rule savings rate](https://en.wikipedia.org/wiki/Golden_Rule_savings_rate).\n", @@ -777,7 +777,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4b07777", + "id": "311a9df5", "metadata": {}, "outputs": [], "source": [ @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "b9c8cf72", + "id": "5516d635", "metadata": {}, "source": [ "Let's define the function *k_next* to find the next value of $k$" @@ -802,7 +802,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0e11d8ba", + "id": "a1582d55", "metadata": {}, "outputs": [], "source": [ @@ -816,7 +816,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d0a69ff9", + "id": "c7290905", "metadata": {}, "outputs": [], "source": [ @@ -844,7 +844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d65e14d3", + "id": "2fe48ba8", "metadata": {}, "outputs": [], "source": [ @@ -853,7 +853,7 @@ }, { "cell_type": "markdown", - "id": "4894fced", + "id": "6ee8f7ef", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/status.ipynb b/_sources/status.ipynb index a7a0586b..8593ed61 100644 --- a/_sources/status.ipynb +++ b/_sources/status.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8fbb614b", + "id": "14bd9dd3", "metadata": {}, "source": [ "# Execution Statistics\n", @@ -22,7 +22,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c56de135", + "id": "454f978b", "metadata": {}, "outputs": [], "source": [ @@ -31,7 +31,7 @@ }, { "cell_type": "markdown", - "id": "a8545a7e", + "id": "c61df0ab", "metadata": {}, "source": [ "and the following package versions" @@ -40,7 +40,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc3a0961", + "id": "71293ac1", "metadata": { "tags": [ "hide-output" diff --git a/_sources/supply_demand_heterogeneity.ipynb b/_sources/supply_demand_heterogeneity.ipynb index e31c80b2..dcbbaf55 100644 --- a/_sources/supply_demand_heterogeneity.ipynb +++ b/_sources/supply_demand_heterogeneity.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "de38a141", + "id": "af02aa16", "metadata": {}, "source": [ "(supply_demand_heterogeneity)=\n", @@ -29,7 +29,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea81d7fd", + "id": "66b8afa7", "metadata": {}, "outputs": [], "source": [ @@ -39,7 +39,7 @@ }, { "cell_type": "markdown", - "id": "3d77468e", + "id": "30f8ae1e", "metadata": {}, "source": [ "## An simple example\n", @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e7db085", + "id": "64fd757e", "metadata": {}, "outputs": [], "source": [ @@ -249,7 +249,7 @@ }, { "cell_type": "markdown", - "id": "1f55662e", + "id": "770ad661", "metadata": {}, "source": [ "## Implementation\n", @@ -268,7 +268,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8413da53", + "id": "dc0b57e6", "metadata": {}, "outputs": [], "source": [ @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "37641ac9", + "id": "7049d032", "metadata": {}, "source": [ "What happens if the first consumer likes the first good more and the second consumer likes the second good more?" @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcae34d7", + "id": "48ae44d8", "metadata": {}, "outputs": [], "source": [ @@ -314,7 +314,7 @@ }, { "cell_type": "markdown", - "id": "2abbd24c", + "id": "bf684288", "metadata": {}, "source": [ "Let the first consumer be poorer." @@ -323,7 +323,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df48260d", + "id": "64b52486", "metadata": {}, "outputs": [], "source": [ @@ -338,7 +338,7 @@ }, { "cell_type": "markdown", - "id": "c8075738", + "id": "ef0bd57f", "metadata": {}, "source": [ "Now let's construct an autarky (i.e., no-trade) equilibrium." @@ -347,7 +347,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c23d48aa", + "id": "d0037940", "metadata": {}, "outputs": [], "source": [ @@ -365,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "5cd94310", + "id": "ec75fa82", "metadata": {}, "source": [ "Now let's redistribute endowments before trade." @@ -374,7 +374,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db096aa5", + "id": "0d7c042b", "metadata": {}, "outputs": [], "source": [ @@ -394,7 +394,7 @@ }, { "cell_type": "markdown", - "id": "bb0497c6", + "id": "3e530b3c", "metadata": {}, "source": [ "### A dynamic economy\n", @@ -405,7 +405,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f8abcb9", + "id": "2ab9000c", "metadata": {}, "outputs": [], "source": [ @@ -427,7 +427,7 @@ }, { "cell_type": "markdown", - "id": "2a0af42c", + "id": "7dbd858d", "metadata": {}, "source": [ "### Risk economy with arrow securities\n", @@ -438,7 +438,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec25c4cc", + "id": "6a3a74f5", "metadata": {}, "outputs": [], "source": [ @@ -462,7 +462,7 @@ }, { "cell_type": "markdown", - "id": "3c37c562", + "id": "a4c1f230", "metadata": {}, "source": [ "## Deducing a representative consumer\n", diff --git a/_sources/supply_demand_multiple_goods.ipynb b/_sources/supply_demand_multiple_goods.ipynb index 3528014e..b631a179 100644 --- a/_sources/supply_demand_multiple_goods.ipynb +++ b/_sources/supply_demand_multiple_goods.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e906d090", + "id": "1f1f30cd", "metadata": {}, "source": [ "(supply_demand_multiple_goods)=\n", @@ -53,7 +53,7 @@ { "cell_type": "code", "execution_count": null, - "id": "193ad217", + "id": "9cb16084", "metadata": {}, "outputs": [], "source": [ @@ -65,7 +65,7 @@ }, { "cell_type": "markdown", - "id": "6c806a62", + "id": "a3646782", "metadata": {}, "source": [ "## Formulas from linear algebra\n", @@ -101,7 +101,7 @@ }, { "cell_type": "markdown", - "id": "1b156cd0", + "id": "32ccdcda", "metadata": {}, "source": [ "We will analyze endogenous objects $c$ and $p$, where\n", @@ -112,7 +112,7 @@ }, { "cell_type": "markdown", - "id": "cc4c6c6e", + "id": "a7d79359", "metadata": {}, "source": [ "The matrix $\\Pi$ describes a consumer's willingness to substitute one good for every other good.\n", @@ -152,7 +152,7 @@ }, { "cell_type": "markdown", - "id": "93ffb711", + "id": "748f8625", "metadata": {}, "source": [ "### Demand curve implied by constrained utility maximization\n", @@ -245,7 +245,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9798dfe", + "id": "4e14fbc5", "metadata": {}, "outputs": [], "source": [ @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "eb76e561", + "id": "837b622d", "metadata": {}, "source": [ "## Digression: Marshallian and Hicksian demand curves\n", @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "6d20bfd4", + "id": "22552cd1", "metadata": {}, "source": [ "## Dynamics and risk as special cases\n", @@ -402,7 +402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0910c673", + "id": "005edb65", "metadata": {}, "outputs": [], "source": [ @@ -424,7 +424,7 @@ }, { "cell_type": "markdown", - "id": "4e43668c", + "id": "cd049792", "metadata": {}, "source": [ "### Risk and state-contingent claims\n", @@ -466,7 +466,7 @@ }, { "cell_type": "markdown", - "id": "af297bc1", + "id": "89d5281e", "metadata": {}, "source": [ "$$\n", @@ -496,7 +496,7 @@ }, { "cell_type": "markdown", - "id": "bb3563e7", + "id": "9a6f75f7", "metadata": {}, "source": [ "We use the tricks described above to interpret $c_1, c_2$ as \"Arrow securities\" that are state-contingent claims to consumption goods." @@ -504,7 +504,7 @@ }, { "cell_type": "markdown", - "id": "9580aa94", + "id": "900c9a70", "metadata": {}, "source": [ "Here is an instance of the risk economy:" @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33c66267", + "id": "49e31974", "metadata": {}, "outputs": [], "source": [ @@ -535,7 +535,7 @@ }, { "cell_type": "markdown", - "id": "bbc034e6", + "id": "3e81b98e", "metadata": {}, "source": [ "```{exercise}\n", @@ -556,7 +556,7 @@ }, { "cell_type": "markdown", - "id": "c336853e", + "id": "c98b5fcb", "metadata": {}, "source": [ "```{solution-start} sdm_ex3\n", @@ -571,7 +571,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f0aea6ec", + "id": "85c29c85", "metadata": {}, "outputs": [], "source": [ @@ -585,7 +585,7 @@ }, { "cell_type": "markdown", - "id": "be5e10b7", + "id": "624c9654", "metadata": {}, "source": [ "If the consumer likes the first (or second) good more, then we can set a larger bliss value for good 1." @@ -594,7 +594,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a10c3ee6", + "id": "a599b214", "metadata": {}, "outputs": [], "source": [ @@ -607,7 +607,7 @@ }, { "cell_type": "markdown", - "id": "36940e30", + "id": "176752de", "metadata": {}, "source": [ "Increase the probability that state $1$ occurs." @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d8c8315", + "id": "704a5e7f", "metadata": {}, "outputs": [], "source": [ @@ -638,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "58b0c744", + "id": "066e38f7", "metadata": {}, "source": [ "```{solution-end}\n", @@ -647,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "20310508", + "id": "a16372a6", "metadata": {}, "source": [ "## Economies with endogenous supplies of goods\n", @@ -752,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "6ed02678", + "id": "63350d52", "metadata": {}, "source": [ "### Implementation\n", @@ -773,7 +773,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9531e59b", + "id": "9f07c12e", "metadata": {}, "outputs": [], "source": [ @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "567775f0", + "id": "d7de3168", "metadata": {}, "source": [ "Then define a function that plots demand and supply curves and labels surpluses and equilibrium." @@ -851,7 +851,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28e1d89f", + "id": "64733d77", "metadata": { "tags": [ "hide-input" @@ -906,7 +906,7 @@ }, { "cell_type": "markdown", - "id": "1ac64684", + "id": "5b93e841", "metadata": {}, "source": [ "#### Example: single agent with one good and production\n", @@ -927,7 +927,7 @@ { "cell_type": "code", "execution_count": null, - "id": "241eabb7", + "id": "6ee76b59", "metadata": {}, "outputs": [], "source": [ @@ -950,7 +950,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cc27ab29", + "id": "dfbe2547", "metadata": {}, "outputs": [], "source": [ @@ -962,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "43233aff", + "id": "e7769b5c", "metadata": {}, "source": [ "Let's give the consumer a lower welfare weight by raising $\\mu$." @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83380176", + "id": "2e7829af", "metadata": {}, "outputs": [], "source": [ @@ -988,7 +988,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a98391d", + "id": "64b46f92", "metadata": {}, "outputs": [], "source": [ @@ -1000,7 +1000,7 @@ }, { "cell_type": "markdown", - "id": "eba6c893", + "id": "0996515c", "metadata": {}, "source": [ "Now we change the bliss point so that the consumer derives more utility from consumption." @@ -1009,7 +1009,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4121008f", + "id": "693894a4", "metadata": {}, "outputs": [], "source": [ @@ -1026,7 +1026,7 @@ }, { "cell_type": "markdown", - "id": "9b9a57b1", + "id": "333309bf", "metadata": {}, "source": [ "This raises both the equilibrium price and quantity.\n", @@ -1042,7 +1042,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4ea7e2b0", + "id": "791d8e86", "metadata": {}, "outputs": [], "source": [ @@ -1067,7 +1067,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66f80cb7", + "id": "9471bea5", "metadata": {}, "outputs": [], "source": [ @@ -1082,7 +1082,7 @@ { "cell_type": "code", "execution_count": null, - "id": "878010a6", + "id": "a060131a", "metadata": {}, "outputs": [], "source": [ @@ -1100,7 +1100,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69eeb40e", + "id": "6fd938ce", "metadata": {}, "outputs": [], "source": [ @@ -1113,7 +1113,7 @@ }, { "cell_type": "markdown", - "id": "cc6bfadb", + "id": "01dd7139", "metadata": {}, "source": [ "### Digression: a supplier who is a monopolist\n", @@ -1160,7 +1160,7 @@ }, { "cell_type": "markdown", - "id": "0418033c", + "id": "7137d61a", "metadata": {}, "source": [ "### A monopolist\n", @@ -1198,7 +1198,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2acfa40", + "id": "2ed5e80d", "metadata": {}, "outputs": [], "source": [ @@ -1237,7 +1237,7 @@ }, { "cell_type": "markdown", - "id": "eb928c30", + "id": "d4a8f170", "metadata": {}, "source": [ "Define a function that plots the demand, marginal cost and marginal revenue curves with surpluses and equilibrium labelled." @@ -1246,7 +1246,7 @@ { "cell_type": "code", "execution_count": null, - "id": "71b2c5d6", + "id": "3611733c", "metadata": { "tags": [ "hide-input" @@ -1311,7 +1311,7 @@ }, { "cell_type": "markdown", - "id": "044e93cc", + "id": "ac9289e8", "metadata": {}, "source": [ "#### A multiple good example\n", @@ -1322,7 +1322,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f88507d6", + "id": "9f7676b4", "metadata": {}, "outputs": [], "source": [ @@ -1350,7 +1350,7 @@ }, { "cell_type": "markdown", - "id": "330ead0a", + "id": "deec1ed8", "metadata": {}, "source": [ "#### A single-good example" @@ -1359,7 +1359,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60e8ed2b", + "id": "ebafa6c8", "metadata": {}, "outputs": [], "source": [ @@ -1385,7 +1385,7 @@ }, { "cell_type": "markdown", - "id": "a6118647", + "id": "f11dd644", "metadata": {}, "source": [ "## Multi-good welfare maximization problem\n", diff --git a/_sources/time_series_with_matrices.ipynb b/_sources/time_series_with_matrices.ipynb index e547e96f..c4bceed5 100644 --- a/_sources/time_series_with_matrices.ipynb +++ b/_sources/time_series_with_matrices.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "26091b17", + "id": "5a1e8d27", "metadata": {}, "source": [ "(time_series_with_matrices)=\n", @@ -43,7 +43,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8546befd", + "id": "9f7db766", "metadata": {}, "outputs": [], "source": [ @@ -55,7 +55,7 @@ }, { "cell_type": "markdown", - "id": "0c5c1805", + "id": "047919d1", "metadata": {}, "source": [ "## Samuelson's model\n", @@ -144,7 +144,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d57c528", + "id": "179430c4", "metadata": {}, "outputs": [], "source": [ @@ -161,7 +161,7 @@ }, { "cell_type": "markdown", - "id": "85d4aef9", + "id": "abb95145", "metadata": {}, "source": [ "Now we construct $A$ and $b$." @@ -170,7 +170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e106f024", + "id": "c897aeff", "metadata": {}, "outputs": [], "source": [ @@ -191,7 +191,7 @@ }, { "cell_type": "markdown", - "id": "958cd157", + "id": "18334a82", "metadata": {}, "source": [ "Let’s look at the matrix $A$ and the vector $b$ for our\n", @@ -201,7 +201,7 @@ { "cell_type": "code", "execution_count": null, - "id": "53452317", + "id": "25524d79", "metadata": {}, "outputs": [], "source": [ @@ -210,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "62eebf17", + "id": "578fee1c", "metadata": {}, "source": [ "Now let’s solve for the path of $y$.\n", @@ -224,7 +224,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c076c772", + "id": "9296de07", "metadata": {}, "outputs": [], "source": [ @@ -235,7 +235,7 @@ }, { "cell_type": "markdown", - "id": "7cf70d38", + "id": "071472fd", "metadata": {}, "source": [ "or we can use `np.linalg.solve`:" @@ -244,7 +244,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb1a0d6d", + "id": "4513415d", "metadata": {}, "outputs": [], "source": [ @@ -253,7 +253,7 @@ }, { "cell_type": "markdown", - "id": "5fb7f219", + "id": "93b618d6", "metadata": {}, "source": [ "Here make sure the two methods give the same result, at least up to floating\n", @@ -263,7 +263,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9e09ded", + "id": "a7ecca3e", "metadata": {}, "outputs": [], "source": [ @@ -272,7 +272,7 @@ }, { "cell_type": "markdown", - "id": "1571282b", + "id": "05a3c35a", "metadata": {}, "source": [ "```{note}\n", @@ -289,7 +289,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f3bdfe7", + "id": "c93b6eca", "metadata": {}, "outputs": [], "source": [ @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "dd9640c7", + "id": "1b0abd3b", "metadata": {}, "source": [ "The {ref}`*steady state*` value $y^*$ of $y_t$ is obtained by setting $y_t = y_{t-1} =\n", @@ -319,7 +319,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25d55a29", + "id": "434d1a6c", "metadata": {}, "outputs": [], "source": [ @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2b541863", + "id": "e3abdd36", "metadata": {}, "outputs": [], "source": [ @@ -345,7 +345,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9a709881", + "id": "443b9114", "metadata": {}, "outputs": [], "source": [ @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "79aa9fbe", + "id": "a5e904fa", "metadata": {}, "source": [ "## Adding a random term\n", @@ -410,7 +410,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6f81edf", + "id": "cd810b23", "metadata": {}, "outputs": [], "source": [ @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "907b2262", + "id": "3fd4aaa7", "metadata": {}, "outputs": [], "source": [ @@ -435,7 +435,7 @@ }, { "cell_type": "markdown", - "id": "949e30af", + "id": "56742aff", "metadata": {}, "source": [ "The above time series looks a lot like (detrended) GDP series for a\n", @@ -447,7 +447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a49308f4", + "id": "bf8663dd", "metadata": {}, "outputs": [], "source": [ @@ -467,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "3bc0489d", + "id": "d554fbcb", "metadata": {}, "source": [ "Also consider the case when $y_{0}$ and $y_{-1}$ are at\n", @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29017ee1", + "id": "a09ab246", "metadata": {}, "outputs": [], "source": [ @@ -497,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "81cf6745", + "id": "69812271", "metadata": {}, "source": [ "## Computing population moments\n", @@ -544,7 +544,7 @@ { "cell_type": "code", "execution_count": null, - "id": "122ee861", + "id": "f07557b7", "metadata": {}, "outputs": [], "source": [ @@ -609,7 +609,7 @@ }, { "cell_type": "markdown", - "id": "94f95004", + "id": "d766f986", "metadata": {}, "source": [ "It is enlightening to study the $\\mu_y, \\Sigma_y$'s implied by various parameter values.\n", @@ -622,7 +622,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b8e1b01", + "id": "fb3b5c06", "metadata": {}, "outputs": [], "source": [ @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "aa9cc57b", + "id": "40fbee04", "metadata": {}, "source": [ "Visually, notice how the variance across realizations of $y_t$ decreases as $t$ increases.\n", @@ -654,7 +654,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d5b1b2b", + "id": "664b8595", "metadata": {}, "outputs": [], "source": [ @@ -665,7 +665,7 @@ }, { "cell_type": "markdown", - "id": "58ec57bc", + "id": "c6d9c4a0", "metadata": {}, "source": [ "Notice how the population variance increases and asymptotes." @@ -673,7 +673,7 @@ }, { "cell_type": "markdown", - "id": "a23d8dc3", + "id": "c4c93f98", "metadata": {}, "source": [ "Let's print out the covariance matrix $\\Sigma_y$ for a time series $y$." @@ -682,7 +682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa4db0fd", + "id": "04f98027", "metadata": {}, "outputs": [], "source": [ @@ -696,7 +696,7 @@ }, { "cell_type": "markdown", - "id": "2d0c690d", + "id": "7a983f69", "metadata": {}, "source": [ "Notice that the covariance between $y_t$ and $y_{t-1}$ -- the elements on the superdiagonal -- are *not* identical.\n", @@ -713,7 +713,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2b6311a", + "id": "161517d9", "metadata": {}, "outputs": [], "source": [ @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "b8fa09a4", + "id": "d951f016", "metadata": {}, "source": [ "Please notice how the subdiagonal and superdiagonal elements seem to have converged.\n", @@ -739,7 +739,7 @@ }, { "cell_type": "markdown", - "id": "07fdb7ff", + "id": "d10908be", "metadata": {}, "source": [ "## Moving average representation\n", @@ -756,7 +756,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1fc5bc61", + "id": "4cdb13a1", "metadata": {}, "outputs": [], "source": [ @@ -766,7 +766,7 @@ }, { "cell_type": "markdown", - "id": "4797023d", + "id": "1584a55a", "metadata": {}, "source": [ "Evidently, $A^{-1}$ is a lower triangular matrix. \n", @@ -778,7 +778,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fb35412", + "id": "9f921053", "metadata": {}, "outputs": [], "source": [ @@ -788,7 +788,7 @@ }, { "cell_type": "markdown", - "id": "11e54863", + "id": "e40e7404", "metadata": {}, "source": [ "Notice how every row ends with the previous row's pre-diagonal entries.\n", @@ -877,7 +877,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b4636f1", + "id": "bdf711f5", "metadata": {}, "outputs": [], "source": [ @@ -887,7 +887,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5597a72c", + "id": "0ff9eeb5", "metadata": {}, "outputs": [], "source": [ @@ -901,7 +901,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f852186", + "id": "fdb3c812", "metadata": {}, "outputs": [], "source": [ @@ -911,7 +911,7 @@ { "cell_type": "code", "execution_count": null, - "id": "528823fd", + "id": "c09ccc09", "metadata": {}, "outputs": [], "source": [ @@ -924,7 +924,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72de662c", + "id": "51a20a15", "metadata": {}, "outputs": [], "source": [ @@ -934,7 +934,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff9658c7", + "id": "9ba90db2", "metadata": {}, "outputs": [], "source": [ @@ -949,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "b7555d62", + "id": "3fd91f10", "metadata": {}, "source": [ "Can you explain why the trend of the price is downward over time?\n", @@ -961,7 +961,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5403d678", + "id": "44cff0aa", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/troubleshooting.ipynb b/_sources/troubleshooting.ipynb index fb65fa0b..2f146386 100644 --- a/_sources/troubleshooting.ipynb +++ b/_sources/troubleshooting.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ed1e5c86", + "id": "7ffe5883", "metadata": {}, "source": [ "(troubleshooting)=\n", diff --git a/_sources/unpleasant.ipynb b/_sources/unpleasant.ipynb index 6d3b1e58..47f29d05 100644 --- a/_sources/unpleasant.ipynb +++ b/_sources/unpleasant.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e1c89fe7", + "id": "9e6f1f84", "metadata": {}, "source": [ "# Some Unpleasant Monetarist Arithmetic \n", @@ -320,7 +320,7 @@ { "cell_type": "code", "execution_count": null, - "id": "012ad6bd", + "id": "078f60d0", "metadata": {}, "outputs": [], "source": [ @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "7553463c", + "id": "983d7291", "metadata": {}, "source": [ "Now let's dive in and implement our pseudo code in Python." @@ -340,7 +340,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d46a70a5", + "id": "ff5f04df", "metadata": {}, "outputs": [], "source": [ @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f2a40b25", + "id": "b2b4aaa1", "metadata": {}, "outputs": [], "source": [ @@ -374,7 +374,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f2fab23b", + "id": "b7348580", "metadata": {}, "outputs": [], "source": [ @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d76542e7", + "id": "8824ad72", "metadata": {}, "outputs": [], "source": [ @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "aa8315bd", + "id": "8bafdc68", "metadata": {}, "source": [ "Let's look at how price level $p_0$ in the stationary $R_u$ equilibrium depends on the initial\n", @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99a52a4f", + "id": "0a4d9932", "metadata": {}, "outputs": [], "source": [ @@ -454,7 +454,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01ffe698", + "id": "446b8f69", "metadata": {}, "outputs": [], "source": [ @@ -468,7 +468,7 @@ }, { "cell_type": "markdown", - "id": "97c8773e", + "id": "4bbf42ab", "metadata": {}, "source": [ "Now let's write and implement code that lets us experiment with the time $0$ open market operation described earlier." @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea958b0e", + "id": "1503fcc3", "metadata": {}, "outputs": [], "source": [ @@ -530,7 +530,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd6be279", + "id": "e21f6d1a", "metadata": {}, "outputs": [], "source": [ @@ -553,7 +553,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe702ddb", + "id": "ba5657d7", "metadata": { "mystnb": { "figure": { @@ -569,7 +569,7 @@ }, { "cell_type": "markdown", - "id": "b163d68c", + "id": "74dab40d", "metadata": {}, "source": [ "{numref}`fig:unpl1` summarizes outcomes of two experiments that convey messages of Sargent and Wallace {cite}`sargent1981`.\n", diff --git a/_sources/zreferences.ipynb b/_sources/zreferences.ipynb index c2c2aa1f..9c6a14b4 100644 --- a/_sources/zreferences.ipynb +++ b/_sources/zreferences.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "bd443e1b", + "id": "6cca6fd9", "metadata": {}, "source": [ "(references)=\n", diff --git a/prob_dist.html b/prob_dist.html index 5d9b2421..2a66b84d 100644 --- a/prob_dist.html +++ b/prob_dist.html @@ -278,20 +278,62 @@

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@@ -462,7 +538,8 @@

18.2.1.2. Bernoulli distributionAnother useful distribution is the Bernoulli distribution on \(S = \{0,1\}\), which has PMF:

\[ -p(i) = \theta^{i-1} (1 - \theta)^i +p(i) = \theta^i (1 - \theta)^{1-i} +\qquad (i = 0, 1) \]

Here \(\theta \in [0,1]\) is a parameter.

We can think of this distribution as modeling probabilities for a random trial with success probability \(\theta\).

@@ -471,7 +548,7 @@

18.2.1.2. Bernoulli distribution

\(p(0) = 1 - \theta\) means that the trial fails (takes value 0) with probability \(1-\theta\)

-

The formula for the mean is \(p\), and the formula for the variance is \(p(1-p)\).

+

The formula for the mean is \(\theta\), and the formula for the variance is \(\theta(1-\theta)\).

We can import the Bernoulli distribution on \(S = \{0,1\}\) from SciPy like so:

@@ -494,16 +571,15 @@

18.2.1.2. Bernoulli distribution

-

Now let’s evaluate the PMF

+

We can evaluate the PMF as follows

-
u.pmf(0)
-u.pmf(1)
+
u.pmf(0), u.pmf(1)
-
0.4
+
(0.6, 0.4)
@@ -1297,7 +1373,11 @@

18.3.1. Summary statisticsExercise 18.3

-

Check that the formulas given above produce the same numbers.

+

If you try to check that the formulas given above for the sample mean and sample +variance produce the same numbers, you will see that the variance isn’t quite +right. This is because SciPy uses \(1/(n-1)\) instead of \(1/n\) as the term at the +front of the variance. (Some books define the sample variance this way.) +Confirm.

@@ -1487,7 +1567,7 @@

18.3.2.3. Violin plots -_images/b67d232574f21006ee69f6c2a450b10678180003ad64d5b6473a52226b0c9db4.png +_images/bd73ac2896c6cc1426c86c0b7d201aecba0b087ae02d3ea76159e77927e3c34b.png

@@ -1553,7 +1633,7 @@

18.3.3. Connection to probability distri

-_images/2cbc1733feab965e74554d59c2db6a620560a7df01153bb7166c872281b6df70.png +_images/3e7588d04d69e84b68d662349b1e955a84c2a250cfb2b37759f09c73dae9532e.png

Note that if you keep increasing \(N\), which is the number of observations, the fit will get better and better.

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29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 46], "save": [1, 14, 17, 26, 38, 42], "consum": [1, 3, 7, 9, 11, 14, 17, 24, 30, 34, 45], "dissav": 1, "doe": [1, 2, 3, 4, 9, 12, 13, 16, 17, 24, 25, 26, 27, 28, 29, 33, 34, 35, 38, 44, 45], "i": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 44, 45, 46, 48], "spend": [1, 4, 5, 13, 14, 27, 29, 41], "borrow": [1, 3, 9, 13, 14, 27], "outsid": [1, 9, 14, 26, 31, 37, 41, 45, 48], "k_0": [1, 35, 38, 42], "stock": [1, 13, 16, 23, 31, 35, 37, 38, 42, 46, 48], "brought": [1, 5, 10, 21, 26, 31], "d_0": [1, 14, 19, 21, 37], "fall": [1, 3, 4, 5, 12, 13, 17, 25, 33, 42], "due": [1, 3, 21, 31, 33, 42, 48], "own": [1, 2, 8, 13, 17, 24, 27, 37, 41, 48], "measur": [1, 3, 13, 16, 18, 19, 21, 25, 28, 31, 33, 34, 36, 45, 46, 48], "unit": [1, 3, 6, 7, 10, 11, 13, 14, 16, 17, 18, 19, 21, 27, 28, 30, 31, 34, 35, 39, 42, 45, 46, 48], "five": [1, 16, 17, 27, 33], "g_t": [1, 14, 48], "d_t": [1, 37], "tau_t": 1, "delta_": 1, "ot": [1, 19], "yt": 1, "_": [1, 4, 5, 7, 8, 9, 10, 11, 12, 15, 18, 19, 23, 24, 25, 30, 31, 34, 35, 37, 38, 42, 46, 48], "infti": [1, 2, 5, 7, 8, 10, 11, 14, 15, 16, 19, 23, 25, 28, 29, 30, 31, 36, 38, 40, 42, 48], "whose": [1, 7, 8, 28, 37, 44, 45], "compon": [1, 3, 4, 13, 14, 15, 19, 29, 31, 37, 41, 45, 48], "flat": [1, 39, 48], "rate": [1, 4, 5, 7, 9, 11, 12, 16, 18, 20, 27, 28, 31, 33, 34, 35, 36, 38, 42, 45, 48], "wage": [1, 3, 12, 19, 35, 38], "earn": [1, 9, 12, 13, 17, 35, 37], "bond": [1, 12, 13, 27, 48], "princip": [1, 4, 10, 11, 14, 24, 26], "per": [1, 13, 14, 16, 18, 19, 27, 31, 38, 41, 42, 45], "capita": [1, 13, 16, 38, 41, 42], "purchas": [1, 3, 7, 13, 18, 21, 26, 37, 45], "alloc": [1, 19, 28, 44, 45], "c_": [1, 35, 44], "k_": [1, 34, 35, 38, 42], "l_t": [1, 42], "y_t": [1, 9, 14, 15, 31, 32, 35, 42, 46], "constitu": [1, 13], "k_t": [1, 35, 38, 42], "physic": 1, "labor": [1, 2, 3, 9, 12, 14, 17, 19, 23, 27, 35, 37, 42], "output": [1, 3, 4, 10, 14, 16, 17, 20, 28, 35, 36, 42, 45, 49], "consumpt": [1, 4, 5, 8, 14, 17, 18, 19, 20, 21, 35, 37, 42, 44, 45, 49], "equiv": [1, 5, 9, 12, 15, 19, 31, 32, 37, 46, 48], "i_t": [1, 7, 14], "invest": [1, 8, 14, 16, 42], "nation": [1, 3, 12, 14, 26, 46, 49], "incom": [1, 2, 3, 9, 12, 13, 14, 16, 20, 34, 35, 36, 42, 45, 46, 49], "account": [1, 3, 7, 14, 16, 19, 26, 27, 28, 37], "equal": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 45, 46], "quad": [1, 2, 4, 5, 7, 8, 9, 10, 11, 15, 16, 17, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 46, 48], "price": [1, 3, 6, 9, 13, 15, 16, 20, 21, 24, 35, 36, 37, 38, 44, 45, 46, 48, 49], "pair": [1, 8, 9, 15, 19, 21, 22, 24, 27, 31, 34, 37, 39, 44], "w_t": [1, 2, 12, 35], "r_t": [1, 23, 31, 35, 37, 48], "rental": [1, 35], "There": [1, 6, 10, 11, 14, 15, 16, 17, 21, 24, 28, 29, 30, 31, 37, 38, 44, 46], "depreci": [1, 3, 7, 18, 38, 42], "rent": 1, "net": [1, 3, 4, 5, 12, 14, 17, 19, 27, 30, 35, 45, 48], "emerg": [1, 3, 5, 21, 22, 31, 32, 39], "cumul": [1, 17, 28, 36], "past": [1, 3, 4, 5, 6, 26, 28, 38, 46], "sum_": [1, 2, 4, 5, 9, 10, 11, 12, 14, 16, 17, 19, 21, 24, 25, 27, 28, 29, 30, 33, 34, 36, 37, 41, 44, 46, 48], "i_": [1, 7, 21, 46], "cobb": [1, 35, 42], "dougla": [1, 35, 42], "technolog": [1, 17, 19, 26, 35], "convert": [1, 3, 9, 14, 17, 18, 24, 28, 40, 42], "alpha": [1, 2, 3, 4, 5, 6, 7, 10, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 42, 45], "risk": [1, 7, 16], "free": [1, 4, 5, 7, 9, 12, 14, 15, 21, 26, 27, 45], "promis": [1, 9, 13, 14, 18, 31, 33], "pai": [1, 5, 12, 13, 14, 18, 21, 25, 27, 31, 33, 37, 49], "d_": [1, 14, 19, 37], "bear": [1, 48], "befor": [1, 3, 10, 11, 13, 14, 15, 17, 18, 19, 21, 24, 25, 28, 29, 33, 36, 44, 45], "r_": [1, 7, 16, 23, 31, 35, 38, 48], "budget": [1, 9, 13, 21, 31, 44, 45, 48], "constraint": [1, 9, 13, 19, 21, 27, 31, 35, 44, 45, 48], "t_t": 1, "total": [1, 3, 7, 11, 13, 14, 17, 19, 21, 23, 26, 27, 28, 30, 33, 34, 35, 38, 40, 41, 44, 45], "bring": [1, 5, 12, 13, 17, 18, 21, 31, 42, 48], "its": [1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 30, 31, 33, 34, 36, 38, 40, 41, 45, 46, 48, 49], "sell": [1, 6, 13, 14, 21, 27, 33, 45, 48], "gover": [1, 5], "acquir": [1, 5, 18], "neg": [1, 3, 9, 11, 14, 27, 38, 44, 45, 48], "a_": [1, 9, 11, 19, 24, 27, 34, 42], "If": [1, 2, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 19, 21, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 45, 46, 47], "hire": [1, 12, 13], "competit": [1, 12, 49], "numerair": [1, 44, 45], "so": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48], "profit": [1, 7, 16, 21, 27, 33, 35, 45], "To": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 41, 42, 44, 45, 46, 48], "maxim": [1, 7, 9, 19, 21, 27, 30, 31, 35, 42], "margin": [1, 2, 8, 9, 14, 28, 35, 42, 44, 45], "begin": [1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 41, 45, 46, 48], "align": [1, 4, 5, 8, 14, 15, 16, 19, 23, 24, 25, 27, 28, 30, 31, 34, 37, 41, 48], "end": [1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 37, 40, 41, 45, 46, 48, 49], "either": [1, 2, 3, 5, 11, 12, 14, 15, 16, 21, 22, 24, 27, 28, 29, 33, 34, 45, 46, 47, 48], "sold": [1, 13, 21, 41], "augment": 1, "util": [1, 9, 19, 21, 44], "thrown": 1, "ocean": 1, "thu": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 39, 42, 44, 45, 46, 48], "endow": [1, 44], "r_0": [1, 23, 31], "tau_0": 1, "a_0": [1, 9, 19], "It": [1, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 21, 22, 24, 26, 27, 28, 29, 31, 32, 36, 37, 39, 41, 42, 46, 48], "must": [1, 5, 7, 9, 12, 14, 15, 17, 19, 23, 24, 25, 27, 31, 39, 40, 48], "posit": [1, 3, 6, 7, 8, 9, 11, 14, 15, 16, 19, 21, 23, 28, 29, 31, 33, 34, 35, 36, 37, 38, 41, 44, 45, 48], "receiv": [1, 9, 12, 14, 27, 33, 34, 48], "o0": 1, "optim": [1, 7, 9, 19, 21, 22, 24, 27, 30, 32, 35, 39, 40, 42, 45, 49], "plan": [1, 13, 19, 27, 30, 33, 45], "inelast": 1, "suppli": [1, 4, 5, 6, 7, 9, 13, 14, 17, 18, 20, 22, 24, 32, 34, 37, 48], "return": [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48], "pre": [1, 13, 17, 18, 19, 24, 31, 32, 46], "post": [1, 3, 13, 18, 29, 48], "choos": [1, 3, 7, 8, 9, 12, 15, 16, 18, 19, 21, 24, 25, 26, 27, 30, 34, 36, 38, 39, 41, 42, 45, 46, 48], "u_t": [1, 23, 35, 46], "beta": [1, 2, 7, 9, 10, 19, 25, 28, 29, 33, 34, 35, 44, 45, 46], "o": [1, 6, 7, 8, 9, 10, 11, 13, 16, 17, 22, 24, 31, 32, 35, 36, 37, 39, 42, 49], "subject": [1, 19, 21, 27, 35, 45, 48], "tau_": 1, "second": [1, 2, 5, 6, 7, 8, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 24, 25, 27, 29, 31, 32, 33, 35, 36, 38, 39, 44, 45, 46, 47], "substitut": [1, 14, 27, 35, 37, 41, 42, 44, 45], "impli": [1, 2, 4, 5, 7, 9, 10, 11, 14, 17, 19, 22, 23, 28, 30, 31, 32, 34, 38, 42, 44, 46, 48], "frac": [1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 44, 45, 46, 48], "choic": [1, 6, 7, 10, 16, 19, 21, 25, 29, 30, 31, 34, 35, 37, 40, 44], "lagrangian": [1, 45], "mathcal": [1, 15, 46, 48], "l": [1, 13, 17, 19, 27, 30, 38, 42, 45, 49], "lambda": [1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 22, 23, 25, 29, 30, 31, 32, 33, 35, 36, 38, 42, 45, 48], "bigl": [1, 4], "bigr": [1, 4], "where": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48], "lagrang": [1, 45], "multipli": [1, 4, 5, 8, 9, 10, 15, 16, 24, 33, 37, 45, 46, 49], "intertempor": [1, 9, 35], "after": [1, 3, 5, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 26, 33, 34, 36, 37, 39, 40, 44, 45, 48], "sever": [1, 5, 11, 13, 16, 17, 26, 28, 31, 34, 39], "line": [1, 3, 4, 5, 6, 8, 10, 12, 13, 14, 16, 17, 19, 21, 22, 23, 24, 26, 27, 31, 32, 38, 40, 41, 42, 44, 47], "order": [1, 2, 5, 8, 10, 11, 17, 21, 22, 24, 27, 31, 34, 35, 38, 45, 46, 49], "respect": [1, 2, 8, 9, 12, 13, 16, 17, 21, 23, 31, 32, 34, 35, 42, 45], "0t": 1, "minim": [1, 19, 27, 40, 41, 45], "8": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 45, 46, 48, 49], "multipl": [1, 3, 4, 5, 9, 11, 12, 14, 15, 21, 31, 37, 44], "recov": [1, 3, 15, 26, 37], "which": [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 44, 45, 46, 48], "definit": [1, 11, 13, 16, 21, 24, 33, 36, 44, 45], "equilibrium": [1, 4, 5, 6, 12, 24, 48], "properti": [1, 2, 10, 11, 12, 13, 17, 24, 25, 28, 29, 31, 36, 38, 42, 45], "all": [1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45], "outcom": [1, 4, 5, 8, 9, 12, 13, 14, 16, 21, 22, 26, 28, 29, 32, 33, 35, 39, 41, 45, 48], "special": [1, 2, 11, 12, 15, 24, 28, 31, 34, 35, 37, 44, 46], "case": [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 23, 24, 25, 27, 28, 29, 30, 34, 36, 37, 38, 40, 42, 46], "began": [1, 13, 26, 45], "shall": [1, 4, 5, 9, 14, 15, 18, 22, 31, 32, 37, 44, 45, 46], "deriv": [1, 9, 12, 14, 16, 17, 19, 21, 30, 35, 41, 45], "pretend": 1, "don": [1, 12, 14, 16, 18, 31, 39, 47], "know": [1, 2, 4, 7, 11, 12, 13, 16, 17, 21, 27, 28, 33, 38, 40, 41, 45, 46], "formul": [1, 12, 19, 27, 31, 45], "fix": [1, 2, 3, 6, 9, 12, 14, 16, 17, 21, 22, 23, 25, 29, 34, 35, 36, 38, 42, 45, 46, 48], "map": [1, 12, 17, 18, 22, 26, 34, 38, 40, 42, 48], "iter": [1, 2, 7, 9, 15, 23, 26, 28, 31, 32, 35, 38, 39, 40, 41, 48], "converg": [1, 2, 6, 7, 10, 11, 14, 15, 16, 22, 23, 25, 26, 29, 31, 32, 35, 36, 38, 39, 40, 42, 46, 48], "get": [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 38, 39, 41, 45, 47], "zero": [1, 2, 4, 5, 7, 8, 9, 10, 11, 14, 15, 16, 17, 21, 23, 24, 25, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 46], "As": [1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 38, 39, 41, 42, 45, 46, 48], "a_t": [1, 9, 24, 42], "obtain": [1, 2, 3, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 19, 21, 22, 23, 24, 29, 30, 34, 35, 36, 38, 39, 40, 42, 45, 46], "law": [1, 2, 13, 22, 28, 29, 30, 31, 32, 33, 36, 49], "left": [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 44, 45, 46, 48], "right": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 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28, 34, 44, 46], "autoregress": [2, 46], "form": [2, 3, 6, 8, 9, 10, 13, 14, 15, 16, 17, 19, 21, 22, 23, 28, 29, 31, 34, 35, 36, 37, 38, 42, 44, 45, 46, 48], "x_": [2, 7, 8, 14, 15, 23, 24, 25, 28, 38], "x_t": [2, 7, 14, 15, 23, 25, 28, 29, 38, 42], "b": [2, 4, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 27, 30, 31, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 46], "w_": [2, 17, 44], "scalar": [2, 11, 14, 15, 21, 23, 31, 44, 45], "sometim": [2, 5, 14, 15, 19, 21, 23, 24, 25, 28, 29, 31, 33, 35, 36, 37, 38, 41, 45], "log": [2, 4, 12, 13, 16, 17, 18, 21, 22, 26, 30, 31, 32, 33, 36, 41, 42], "household": [2, 3, 17, 29, 30, 34, 35, 39, 44], "monei": [2, 4, 5, 13, 15, 17, 18, 20, 22, 32, 33, 34, 37, 48, 49], "demand": [2, 4, 5, 6, 7, 11, 13, 14, 18, 20, 22, 24, 32, 34, 37, 38, 44, 48], "show": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48], "evolv": [2, 6, 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7, 10, 11, 13, 14, 16, 17, 18, 19, 21, 27, 28, 30, 31, 34, 35, 39, 42, 45, 46, 48], "five": [1, 16, 17, 27, 33], "g_t": [1, 14, 48], "d_t": [1, 37], "tau_t": 1, "delta_": 1, "ot": [1, 19], "yt": 1, "_": [1, 4, 5, 7, 8, 9, 10, 11, 12, 15, 18, 19, 23, 24, 25, 30, 31, 34, 35, 37, 38, 42, 46, 48], "infti": [1, 2, 5, 7, 8, 10, 11, 14, 15, 16, 19, 23, 25, 28, 29, 30, 31, 36, 38, 40, 42, 48], "whose": [1, 7, 8, 28, 37, 44, 45], "compon": [1, 3, 4, 13, 14, 15, 19, 29, 31, 37, 41, 45, 48], "flat": [1, 39, 48], "rate": [1, 4, 5, 7, 9, 11, 12, 16, 18, 20, 27, 28, 31, 33, 34, 35, 36, 38, 42, 45, 48], "wage": [1, 3, 12, 19, 35, 38], "earn": [1, 9, 12, 13, 17, 35, 37], "bond": [1, 12, 13, 27, 48], "princip": [1, 4, 10, 11, 14, 24, 26], "per": [1, 13, 14, 16, 18, 19, 27, 31, 38, 41, 42, 45], "capita": [1, 13, 16, 38, 41, 42], "purchas": [1, 3, 7, 13, 18, 21, 26, 37, 45], "alloc": [1, 19, 28, 44, 45], "c_": [1, 35, 44], "k_": [1, 34, 35, 38, 42], "l_t": [1, 42], "y_t": [1, 9, 14, 15, 31, 32, 35, 42, 46], "constitu": [1, 13], "k_t": [1, 35, 38, 42], "physic": 1, "labor": [1, 2, 3, 9, 12, 14, 17, 19, 23, 27, 35, 37, 42], "output": [1, 3, 4, 10, 14, 16, 17, 20, 28, 35, 36, 42, 45, 49], "consumpt": [1, 4, 5, 8, 14, 17, 18, 19, 20, 21, 35, 37, 42, 44, 45, 49], "equiv": [1, 5, 9, 12, 15, 19, 31, 32, 37, 46, 48], "i_t": [1, 7, 14], "invest": [1, 8, 14, 16, 42], "nation": [1, 3, 12, 14, 26, 46, 49], "incom": [1, 2, 3, 9, 12, 13, 14, 16, 20, 34, 35, 36, 42, 45, 46, 49], "account": [1, 3, 7, 14, 16, 19, 26, 27, 28, 37], "equal": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 45, 46], "quad": [1, 2, 4, 5, 7, 8, 9, 10, 11, 15, 16, 17, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 46, 48], "price": [1, 3, 6, 9, 13, 15, 16, 20, 21, 24, 35, 36, 37, 38, 44, 45, 46, 48, 49], "pair": [1, 8, 9, 15, 19, 21, 22, 24, 27, 31, 34, 37, 39, 44], "w_t": [1, 2, 12, 35], "r_t": [1, 23, 31, 35, 37, 48], 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45], "r_": [1, 7, 16, 23, 31, 35, 38, 48], "budget": [1, 9, 13, 21, 31, 44, 45, 48], "constraint": [1, 9, 13, 19, 21, 27, 31, 35, 44, 45, 48], "t_t": 1, "total": [1, 3, 7, 11, 13, 14, 17, 19, 21, 23, 26, 27, 28, 30, 33, 34, 35, 38, 40, 41, 44, 45], "bring": [1, 5, 12, 13, 17, 18, 21, 31, 42, 48], "its": [1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 30, 31, 33, 34, 36, 38, 40, 41, 45, 46, 48, 49], "sell": [1, 6, 13, 14, 21, 27, 33, 45, 48], "gover": [1, 5], "acquir": [1, 5, 18], "neg": [1, 3, 9, 11, 14, 27, 38, 44, 45, 48], "a_": [1, 9, 11, 19, 24, 27, 34, 42], "If": [1, 2, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 19, 21, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 45, 46, 47], "hire": [1, 12, 13], "competit": [1, 12, 49], "numerair": [1, 44, 45], "so": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48], "profit": [1, 7, 16, 21, 27, 33, 35, 45], "To": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 41, 42, 44, 45, 46, 48], "maxim": [1, 7, 9, 19, 21, 27, 30, 31, 35, 42], "margin": [1, 2, 8, 9, 14, 28, 35, 42, 44, 45], "begin": [1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 38, 40, 41, 45, 46, 48], "align": [1, 4, 5, 8, 14, 15, 16, 19, 23, 24, 25, 27, 28, 30, 31, 34, 37, 41, 48], "end": [1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 37, 40, 41, 45, 46, 48, 49], "either": [1, 2, 3, 5, 11, 12, 14, 15, 16, 21, 22, 24, 27, 28, 29, 33, 34, 45, 46, 47, 48], "sold": [1, 13, 21, 41], "augment": 1, "util": [1, 9, 19, 21, 44], "thrown": 1, "ocean": 1, "thu": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 39, 42, 44, 45, 46, 48], "endow": [1, 44], "r_0": 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26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48], "lagrang": [1, 45], "multipli": [1, 4, 5, 8, 9, 10, 15, 16, 24, 33, 37, 45, 46, 49], "intertempor": [1, 9, 35], "after": [1, 3, 5, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 26, 33, 34, 36, 37, 39, 40, 44, 45, 48], "sever": [1, 5, 11, 13, 16, 17, 26, 28, 31, 34, 39], "line": [1, 3, 4, 5, 6, 8, 10, 12, 13, 14, 16, 17, 19, 21, 22, 23, 24, 26, 27, 31, 32, 38, 40, 41, 42, 44, 47], "order": [1, 2, 5, 8, 10, 11, 17, 21, 22, 24, 27, 31, 34, 35, 38, 45, 46, 49], "respect": [1, 2, 8, 9, 12, 13, 16, 17, 21, 23, 31, 32, 34, 35, 42, 45], "0t": 1, "minim": [1, 19, 27, 40, 41, 45], "8": [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 45, 46, 48, 49], "multipl": [1, 3, 4, 5, 9, 11, 12, 14, 15, 21, 31, 37, 44], "recov": [1, 3, 15, 26, 37], "which": [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 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24, 25, 26, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 44, 45, 46, 48], "right": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 28, 31, 32, 33, 35, 36, 37, 38, 42, 44, 45, 46, 48], "invari": [1, 28, 31, 48], "hat": [1, 4, 16, 23, 24, 29, 30, 41], "k": [1, 2, 4, 5, 6, 7, 9, 10, 11, 13, 16, 17, 21, 23, 24, 25, 27, 28, 29, 30, 33, 34, 35, 38, 39, 42, 49], "d": [1, 4, 5, 6, 7, 8, 11, 12, 13, 14, 16, 18, 19, 21, 23, 24, 25, 28, 31, 34, 35, 37, 39, 40, 42, 44, 46, 49], "tau": 1, "r": [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 23, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 38, 41, 42, 45, 48, 49], "y": [1, 2, 3, 6, 8, 9, 10, 13, 14, 15, 16, 17, 18, 22, 24, 25, 26, 27, 28, 29, 31, 32, 38, 39, 41, 42, 45, 46, 47, 49], "These": [1, 2, 3, 7, 11, 13, 14, 15, 17, 18, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 39, 43, 48], "let": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 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a/status.html b/status.html index 84c78820..7649dbb7 100644 --- a/status.html +++ b/status.html @@ -447,9 +447,9 @@

49. Execution Statistics

prob_dist

-

2024-08-01 04:49

+

2024-08-01 09:00

cache

-

8.4

+

19.75

✅

pv