diff --git a/examples/ConsIndShockModel/IndShockConsumerType.ipynb b/examples/ConsIndShockModel/IndShockConsumerType.ipynb index a6a9855a6..12822dfd6 100644 --- a/examples/ConsIndShockModel/IndShockConsumerType.ipynb +++ b/examples/ConsIndShockModel/IndShockConsumerType.ipynb @@ -2,10 +2,11 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "lines_to_next_cell": 2 + }, "source": [ - "# IndShockConsumerType Documentation\n", - "## Consumption-Saving model with Idiosyncratic Income Shocks" + "# IndShockConsumerType: Consumption-saving model with idiosyncratic income shocks" ] }, { @@ -19,12 +20,14 @@ "outputs": [], "source": [ "# Initial imports and notebook setup, click arrow to show\n", - "from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType\n", - "from HARK.utilities import plotFuncsDer, plotFuncs\n", - "from time import clock\n", + "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", - "mystr = lambda number : \"{:.4f}\".format(number)" + "\n", + "from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType\n", + "from HARK.utilities import plotFuncsDer, plotFuncs\n", + "\n", + "mystr = lambda number: \"{:.4f}\".format(number)" ] }, { @@ -33,7 +36,7 @@ "source": [ "The module $\\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks are fully transitory or fully permanent.\n", "\n", - "$\\texttt{ConsIndShockModel}$ includes:\n", + "$\\texttt{ConsIndShockModel}$ currently includes three models:\n", "1. A very basic \"perfect foresight\" model with no uncertainty.\n", "2. A model with risk over transitory and permanent income shocks.\n", "3. The model described in (2), with an interest rate for debt that differs from the interest rate for savings.\n", @@ -52,14 +55,14 @@ "source": [ "## Statement of idiosyncratic income shocks model\n", "\n", - "Suppose we want to solve a model like the one analyzed in [BufferStockTheory](http://econ.jhu.edu/people/ccarroll/papers/BufferStockTheory/), which has all the same features as the perfect foresight consumer, plus idiosyncratic shocks to income each period. Agents with this kind of model are represented by the class $\\texttt{IndShockConsumerType}$.\n", + "Suppose we want to solve a model like the one analyzed in [BufferStockTheory](http://econ.jhu.edu/people/ccarroll/papers/BufferStockTheory/), with all the same features as the perfect foresight consumer, plus idiosyncratic shocks to income each period. Agents with this kind of model are represented by the class $\\texttt{IndShockConsumerType}$.\n", "\n", - "Specifically, this type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\\newcommand{\\tShkEmp}{\\theta}{\\tShkEmp_t}$ and a completely permanent shock $\\newcommand{\\pShk}{\\psi}{\\pShk_t}$. Moreover, the agent is subject to borrowing a borrowing limit: the ratio of end-of-period assets $A_t$ to permanent income $P_t$ must be greater than $\\underline{a}$. As with the perfect foresight problem, this model is stated in terms of *normalized* variables, dividing all real variables by $P_t$:\n", + "Specifically, this type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\\newcommand{\\tShkEmp}{\\theta}{\\tShkEmp_t}$ and a completely permanent shock $\\newcommand{\\pShk}{\\psi}{\\pShk_t}$. Moreover, lenders will not let the agent borrow money such that his ratio of end-of-period assets $A_t$ to permanent income $P_t$ is less than $\\underline{a}$. As with the perfect foresight problem, this model can be framed in terms of *normalized* variables, dividing all real variables by $P_t$:\n", "\n", "\\begin{eqnarray*}\n", - "v_t(m_t) &=& \\max_{c_t} {~} u(c_t) + \\DiscFac (1-\\DiePrb_{t+1}) \\mathbb{E}_{t} \\left[ (\\PermGroFac_{t+1}\\psi_{t+1})^{1-\\CRRA} v_{t+1}(m_{t+1}) \\right], \\\\\n", + "v_t(m_t) &=& \\max_{c_t} {~} U(c_t) + \\DiscFac (1-\\DiePrb_{t+1}) \\mathbb{E}_{t} \\left[ (\\PermGroFac_{t+1}\\psi_{t+1})^{1-\\CRRA} v_{t+1}(m_{t+1}) \\right], \\\\\n", "a_t &=& m_t - c_t, \\\\\n", - "a_t &\\geq& \\text{$\\underline{a}$}, \\\\\n", + "a_t &\\geq& \\underline{a}, \\\\\n", "m_{t+1} &=& \\Rfree/(\\PermGroFac_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1}, \\\\\n", "(\\psi_{t+1},\\theta_{t+1}) &\\sim& F_{t+1}, \\\\\n", "\\mathbb{E}[\\psi]=\\mathbb{E}[\\theta] &=& 1, \\\\\n", @@ -73,21 +76,21 @@ "source": [ "## Solution method for IndShockConsumerType\n", "\n", - "With the introduction of (non-trivial) risk, the idiosyncratic income shocks model has no closed form solution and must be solved numerically. The function $\\texttt{solveConsIndShock}$ solves the one period problem for the $\\texttt{IndShockConsumerType}$ class. To do so, HARK uses the original version of the endogenous grid method (EGM) first described [here](http://www.econ2.jhu.edu/people/ccarroll/EndogenousGridpoints.pdf) ; see also the [SolvingMicroDSOPs](http://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/) lecture notes. \n", + "With the introduction of (non-trivial) risk, the idiosyncratic income shocks model has no closed form solution and must be solved numerically. The function $\\texttt{solveConsIndShock}$ solves the one period problem for the $\\texttt{IndShockConsumerType}$ class. To do so, HARK uses the original version of the endogenous grid method (EGM) first described [here](http://www.econ2.jhu.edu/people/ccarroll/EndogenousGridpoints.pdf); see also the [SolvingMicroDSOPs](http://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/) lecture notes.\n", "\n", - "Briefly, the transition equation for $m_{t+1}$ can be substituted into the problem definition; the second term of the reformulated maximand represents \"end of period value of assets\" $\\mathfrak{v}_t(a_t)$ (\"Gothic v\"):\n", + "Briefly, the transition equation for $m_{t+1}$ can be substituted into the problem definition; the second term of the reformulated maximand represents \"end of period value of assets\" $\\mathfrak{v}_t(a_t)$:\n", "\n", "\\begin{eqnarray*}\n", - "v_t(m_t) &=& \\max_{c_t} {~} u(c_t) + \\underbrace{\\DiscFac (1-\\DiePrb_{t+1}) \\mathbb{E}_{t} \\left[ (\\PermGroFac_{t+1}\\psi_{t+1})^{1-\\CRRA} v_{t+1}(\\Rfree/(\\PermGroFac_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1}) \\right]}_{\\equiv \\mathfrak{v}_t(a_t)}.\n", + "v_t(m_t) &=& \\max_{c_t} {~} U(c_t) + \\underbrace{\\DiscFac (1-\\DiePrb_{t+1}) \\mathbb{E}_{t} \\left[ (\\PermGroFac_{t+1}\\psi_{t+1})^{1-\\CRRA} v_{t+1}(\\Rfree/(\\PermGroFac_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1}) \\right]}_{\\equiv \\mathfrak{v}_t(a_t)}.\n", "\\end{eqnarray*}\n", "\n", "The first order condition with respect to $c_t$ is thus simply:\n", "\n", "\\begin{eqnarray*}\n", - "u^{\\prime}(c_t) - \\mathfrak{v}'_t(a_t) = 0 \\Longrightarrow c_t^{-\\CRRA} = \\mathfrak{v}'_t(a_t) \\Longrightarrow c_t = \\mathfrak{v}'_t(a_t)^{-1/\\CRRA},\n", + "U'(c_t) - \\mathfrak{v}'_t(a_t) = 0 \\Longrightarrow c_t^{-\\CRRA} = \\mathfrak{v}'_t(a_t) \\Longrightarrow c_t = \\mathfrak{v}'_t(a_t)^{-1/\\CRRA}.\n", "\\end{eqnarray*}\n", "\n", - "and the marginal value of end-of-period assets can be computed as:\n", + "Where the marginal value of end-of-period assets can be computed as:\n", "\n", "\\begin{eqnarray*}\n", "\\mathfrak{v}'_t(a_t) = \\DiscFac (1-\\DiePrb_{t+1}) \\mathbb{E}_{t} \\left[ \\Rfree (\\PermGroFac_{t+1}\\psi_{t+1})^{-\\CRRA} v'_{t+1}(\\Rfree/(\\PermGroFac_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1}) \\right].\n", @@ -107,26 +110,26 @@ "| Parameter | Description | Code | Example value | Time-varying? |\n", "| :---: | --- | --- | --- | --- |\n", "| $\\DiscFac$ |Intertemporal discount factor | $\\texttt{DiscFac}$ | $0.96$ | |\n", - "| $\\CRRA$|Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", + "| $\\CRRA $ |Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", "| $\\Rfree$ | Risk free interest factor | $\\texttt{Rfree}$ | $1.03$ | |\n", "| $1 - \\DiePrb_{t+1}$ |Survival probability | $\\texttt{LivPrb}$ | $[0.98]$ | $\\surd$ |\n", "|$\\PermGroFac_{t+1}$|Permanent income growth factor|$\\texttt{PermGroFac}$| $[1.01]$ | $\\surd$ |\n", - "| $\\sigma_\\psi$| Standard deviation of log permanent income shocks | $\\texttt{PermShkStd}$ | $[0.1]$ |$\\surd$ |\n", - "| $N_\\psi$| Number of discrete permanent income shocks | $\\texttt{PermShkCount}$ | $7$ | |\n", - "| $\\sigma_\\theta$| Standard deviation of log transitory income shocks | $\\texttt{TranShkStd}$ | $[0.2]$ | $\\surd$ |\n", - "| $N_\\theta$| Number of discrete transitory income shocks | $\\texttt{TranShkCount}$ | $7$ | |\n", + "| $\\sigma_\\psi $ | Standard deviation of log permanent income shocks | $\\texttt{PermShkStd}$ | $[0.1]$ |$\\surd$ |\n", + "| $N_\\psi $ | Number of discrete permanent income shocks | $\\texttt{PermShkCount}$ | $7$ | |\n", + "| $\\sigma_\\theta $ | Standard deviation of log transitory income shocks | $\\texttt{TranShkStd}$ | $[0.2]$ | $\\surd$ |\n", + "| $N_\\theta $ | Number of discrete transitory income shocks | $\\texttt{TranShkCount}$ | $7$ | |\n", "| $\\mho$ | Probability of being unemployed and getting $\\theta=\\underline{\\theta}$ | $\\texttt{UnempPrb}$ | $0.05$ | |\n", - "| $\\underline{\\theta}$| Transitory shock when unemployed | $\\texttt{IncUnemp}$ | $0.3$ | |\n", + "| $\\underline{\\theta} $ | Transitory shock when unemployed | $\\texttt{IncUnemp}$ | $0.3$ | |\n", "| $\\mho^{Ret}$ | Probability of being \"unemployed\" when retired | $\\texttt{UnempPrb}$ | $0.0005$ | |\n", - "| $\\underline{\\theta}^{Ret}$| Transitory shock when \"unemployed\" and retired | $\\texttt{IncUnemp}$ | $0.0$ | |\n", + "| $\\underline{\\theta}^{Ret} $ | Transitory shock when \"unemployed\" and retired | $\\texttt{IncUnemp}$ | $0.0$ | |\n", "| $(none)$ | Period of the lifecycle model when retirement begins | $\\texttt{T_retire}$ | $0$ | |\n", "| $(none)$ | Minimum value in assets-above-minimum grid | $\\texttt{aXtraMin}$ | $0.001$ | |\n", "| $(none)$ | Maximum value in assets-above-minimum grid | $\\texttt{aXtraMax}$ | $20.0$ | |\n", "| $(none)$ | Number of points in base assets-above-minimum grid | $\\texttt{aXtraCount}$ | $48$ | |\n", "| $(none)$ | Exponential nesting factor for base assets-above-minimum grid | $\\texttt{aXtraNestFac}$ | $3$ | |\n", "| $(none)$ | Additional values to add to assets-above-minimum grid | $\\texttt{aXtraExtra}$ | $None$ | |\n", - "| $\\underline{a}$| Artificial borrowing constraint (normalized) | $\\texttt{BoroCnstArt}$ | $0.0$ | |\n", - "| $(none)$|Indicator for whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | $True$ | |\n", + "| $\\underline{a} $ | Artificial borrowing constraint (normalized) | $\\texttt{BoroCnstArt}$ | $0.0$ | |\n", + "| $(none) $ |Indicator for whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | $True$ | |\n", "| $(none)$ |Indicator for whether $\\texttt{cFunc}$ should use cubic splines | $\\texttt{CubicBool}$ | $False$ | |\n", "|$T$| Number of periods in this type's \"cycle\" |$\\texttt{T_cycle}$| $1$ | |\n", "|(none)| Number of times the \"cycle\" occurs |$\\texttt{cycles}$| $0$ | |" @@ -142,48 +145,44 @@ }, "outputs": [], "source": [ - "IdiosyncDict={\n", + "IdiosyncDict = { # Click the arrow to expand this parameter dictionary\n", " # Parameters shared with the perfect foresight model\n", - " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", - " \"Rfree\": 1.03, # Interest factor on assets\n", - " \"DiscFac\": 0.96, # Intertemporal discount factor\n", - " \"LivPrb\" : [0.98], # Survival probability\n", - " \"PermGroFac\" :[1.01], # Permanent income growth factor\n", - " \n", + " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", + " \"Rfree\": 1.03, # Interest factor on assets\n", + " \"DiscFac\": 0.96, # Intertemporal discount factor\n", + " \"LivPrb\": [0.98], # Survival probability\n", + " \"PermGroFac\": [1.01], # Permanent income growth factor\n", + " \"BoroCnstArt\": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", " # Parameters that specify the income distribution over the lifecycle\n", - " \"PermShkStd\" : [0.1], # Standard deviation of log permanent shocks to income\n", - " \"PermShkCount\" : 7, # Number of points in discrete approximation to permanent income shocks\n", - " \"TranShkStd\" : [0.2], # Standard deviation of log transitory shocks to income\n", - " \"TranShkCount\" : 7, # Number of points in discrete approximation to transitory income shocks\n", - " \"UnempPrb\" : 0.05, # Probability of unemployment while working\n", - " \"IncUnemp\" : 0.3, # Unemployment benefits replacement rate\n", - " \"UnempPrbRet\" : 0.0005, # Probability of \"unemployment\" while retired\n", - " \"IncUnempRet\" : 0.0, # \"Unemployment\" benefits when retired\n", - " \"T_retire\" : 0, # Period of retirement (0 --> no retirement)\n", - " \"tax_rate\" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", - " \n", + " \"PermShkStd\": [0.1], # Standard deviation of log permanent shocks to income\n", + " \"PermShkCount\": 7, # Number of points in discrete approximation to permanent income shocks\n", + " \"TranShkStd\": [0.2], # Standard deviation of log transitory shocks to income\n", + " \"TranShkCount\": 7, # Number of points in discrete approximation to transitory income shocks\n", + " \"UnempPrb\": 0.05, # Probability of unemployment while working\n", + " \"IncUnemp\": 0.3, # Unemployment benefits replacement rate\n", + " \"UnempPrbRet\": 0.0005, # Probability of \"unemployment\" while retired\n", + " \"IncUnempRet\": 0.0, # \"Unemployment\" benefits when retired\n", + " \"T_retire\": 0, # Period of retirement (0 --> no retirement)\n", + " \"tax_rate\": 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", " # Parameters for constructing the \"assets above minimum\" grid\n", - " \"aXtraMin\" : 0.001, # Minimum end-of-period \"assets above minimum\" value\n", - " \"aXtraMax\" : 20, # Maximum end-of-period \"assets above minimum\" value\n", - " \"aXtraCount\" : 48, # Number of points in the base grid of \"assets above minimum\"\n", - " \"aXtraNestFac\" : 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", - " \"aXtraExtra\" : [None], # Additional values to add to aXtraGrid\n", - " \n", + " \"aXtraMin\": 0.001, # Minimum end-of-period \"assets above minimum\" value\n", + " \"aXtraMax\": 20, # Maximum end-of-period \"assets above minimum\" value\n", + " \"aXtraCount\": 48, # Number of points in the base grid of \"assets above minimum\"\n", + " \"aXtraNestFac\": 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", + " \"aXtraExtra\": [None], # Additional values to add to aXtraGrid\n", " # A few other paramaters\n", - " \"BoroCnstArt\" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", - " \"vFuncBool\" : True, # Whether to calculate the value function during solution \n", - " \"CubicBool\" : False, # Preference shocks currently only compatible with linear cFunc\n", - " \"T_cycle\" : 1, # Number of periods in the cycle for this agent type \n", - " \n", + " \"vFuncBool\": True, # Whether to calculate the value function during solution\n", + " \"CubicBool\": False, # Preference shocks currently only compatible with linear cFunc\n", + " \"T_cycle\": 1, # Number of periods in the cycle for this agent type\n", " # Parameters only used in simulation\n", - " \"AgentCount\" : 10000, # Number of agents of this type\n", - " \"T_sim\" : 120, # Number of periods to simulate\n", - " \"aNrmInitMean\" : -6.0, # Mean of log initial assets\n", - " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets\n", - " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income\n", - " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income\n", - " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor\n", - " \"T_age\" : None, # Age after which simulated agents are automatically killed\n", + " \"AgentCount\": 10000, # Number of agents of this type\n", + " \"T_sim\": 120, # Number of periods to simulate\n", + " \"aNrmInitMean\": -6.0, # Mean of log initial assets\n", + " \"aNrmInitStd\": 1.0, # Standard deviation of log initial assets\n", + " \"pLvlInitMean\": 0.0, # Mean of log initial permanent income\n", + " \"pLvlInitStd\": 0.0, # Standard deviation of log initial permanent income\n", + " \"PermGroFacAgg\": 1.0, # Aggregate permanent income growth factor\n", + " \"T_age\": None, # Age after which simulated agents are automatically killed\n", "}" ] }, @@ -204,9 +203,7 @@ }, { "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, + "metadata": {}, "source": [ "## Solving and examining the solution of the idiosyncratic income shocks model\n", "\n", @@ -216,39 +213,88 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "hidden": true, - "lines_to_next_cell": 2 - }, + "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "GIFPF = 0.984539 \n", - "GIFInd = 0.993777 \n", - "GIFAgg = 0.964848 \n", - "Thorn = AIF = 0.994384 \n", - "PermGroFacAdj = 1.000611 \n", - "uInvEpShkuInv = 0.990704 \n", - "FVAF = 0.932054 \n", - "WRIF = 0.213705 \n", - "DiscFacGIFIndMax = 0.972061 \n", - "DiscFacGIFAggMax = 1.010600 \n" + "GPFPF = 0.984539 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "GPFInd = 0.993777 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "GPFAgg = 0.964848 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Thorn = APF = 0.994384 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "PermGroFacAdj = 1.000611 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "uInvEpShkuInv = 0.990704 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "FVAF = 0.932054 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WRPF = 0.213705 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DiscFacGPFIndMax = 0.972061 \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DiscFacGPFAggMax = 1.010600 \n" ] } ], "source": [ "IndShockExample = IndShockConsumerType(**IdiosyncDict)\n", - "IndShockExample.cycles = 0 # Make this type have an infinite horizon\n", + "IndShockExample.cycles = 0 # Make this type have an infinite horizon\n", "IndShockExample.solve()" ] }, { "cell_type": "markdown", - "metadata": { - "hidden": true - }, + "metadata": {}, "source": [ "After solving the model, we can examine an element of this type's $\\texttt{solution}$:" ] @@ -256,15 +302,13 @@ { "cell_type": "code", "execution_count": 4, - "metadata": { - "hidden": true - }, + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'cFunc': , 'vFunc': , 'vPfunc': , 'vPPfunc': , 'mNrmMin': 0.0, 'hNrm': 44.991920196607595, 'MPCmin': 0.044536273404377116, 'MPCmax': 1.0, 'mNrmSS': 1.5488165705077026}\n" + "{'cFunc': , 'vFunc': , 'vPfunc': , 'vPPfunc': , 'mNrmMin': 0.0, 'hNrm': 44.991920196607595, 'MPCmin': 0.044536273404377116, 'MPCmax': 1.0, 'mNrmSS': 1.5488165705077026}\n" ] } ], @@ -274,9 +318,7 @@ }, { "cell_type": "markdown", - "metadata": { - "hidden": true - }, + "metadata": {}, "source": [ "The single-period solution to an idiosyncratic shocks consumer's problem has all of the same attributes as in the perfect foresight model, with a couple additions. The solution can include the marginal marginal value of market resources function $\\texttt{vPPfunc}$, but this is only constructed if $\\texttt{CubicBool}$ is $\\texttt{True}$, so that the MPC can be accurately computed; when it is $\\texttt{False}$, then $\\texttt{vPPfunc}$ merely returns $\\texttt{NaN}$ everywhere.\n", "\n", @@ -288,9 +330,7 @@ { "cell_type": "code", "execution_count": 5, - "metadata": { - "hidden": true - }, + "metadata": {}, "outputs": [ { "name": "stdout", @@ -301,7 +341,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] @@ -332,17 +372,15 @@ } ], "source": [ - "print('Consumption function for an idiosyncratic shocks consumer type:')\n", - "plotFuncs(IndShockExample.solution[0].cFunc,IndShockExample.solution[0].mNrmMin,5)\n", - "print('Marginal propensity to consume for an idiosyncratic shocks consumer type:')\n", - "plotFuncsDer(IndShockExample.solution[0].cFunc,IndShockExample.solution[0].mNrmMin,5)" + "print(\"Consumption function for an idiosyncratic shocks consumer type:\")\n", + "plotFuncs(IndShockExample.solution[0].cFunc, IndShockExample.solution[0].mNrmMin, 5)\n", + "print(\"Marginal propensity to consume for an idiosyncratic shocks consumer type:\")\n", + "plotFuncsDer(IndShockExample.solution[0].cFunc, IndShockExample.solution[0].mNrmMin, 5)" ] }, { "cell_type": "markdown", - "metadata": { - "hidden": true - }, + "metadata": {}, "source": [ "The lower part of the consumption function is linear with a slope of 1, representing the *constrained* part of the consumption function where the consumer *would like* to consume more by borrowing-- his marginal utility of consumption exceeds the marginal value of assets-- but he is prevented from doing so by the artificial borrowing constraint.\n", "\n", @@ -354,9 +392,7 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "hidden": true - }, + "metadata": {}, "outputs": [ { "name": "stdout", @@ -386,19 +422,29 @@ } ], "source": [ - "print('mNrmGrid for unconstrained cFunc is ',IndShockExample.solution[0].cFunc.functions[0].x_list)\n", - "print('cNrmGrid for unconstrained cFunc is ',IndShockExample.solution[0].cFunc.functions[0].y_list)\n", - "print('mNrmGrid for borrowing constrained cFunc is ',IndShockExample.solution[0].cFunc.functions[1].x_list)\n", - "print('cNrmGrid for borrowing constrained cFunc is ',IndShockExample.solution[0].cFunc.functions[1].y_list)" + "print(\n", + " \"mNrmGrid for unconstrained cFunc is \",\n", + " IndShockExample.solution[0].cFunc.functions[0].x_list,\n", + ")\n", + "print(\n", + " \"cNrmGrid for unconstrained cFunc is \",\n", + " IndShockExample.solution[0].cFunc.functions[0].y_list,\n", + ")\n", + "print(\n", + " \"mNrmGrid for borrowing constrained cFunc is \",\n", + " IndShockExample.solution[0].cFunc.functions[1].x_list,\n", + ")\n", + "print(\n", + " \"cNrmGrid for borrowing constrained cFunc is \",\n", + " IndShockExample.solution[0].cFunc.functions[1].y_list,\n", + ")" ] }, { "cell_type": "markdown", - "metadata": { - "hidden": true - }, + "metadata": {}, "source": [ - "The consumption function in this model is an instance of $\\texttt{LowerEnvelope1D}$, a class that takes an arbitrary number of 1D interpolants as arguments to its initialization method. When called, a $\\texttt{LowerEnvelope1D}$ evaluates each of its component functions and returns the lowest value. Here, the two component functions are the *unconstrained* consumption function-- how the agent would consume if the artificial borrowing constraint did not exist for *just this period*-- and the *borrowing constrained* consumption function-- how much he would consume if the artificial borrowing constraint is binding. \n", + "The consumption function in this model is an instance of $\\texttt{LowerEnvelope1D}$, a class that takes an arbitrary number of 1D interpolants as arguments to its initialization method. When called, a $\\texttt{LowerEnvelope1D}$ evaluates each of its component functions and returns the lowest value. Here, the two component functions are the *unconstrained* consumption function-- how the agent would consume if the artificial borrowing constraint did not exist for *just this period*-- and the *borrowing constrained* consumption function-- how much he would consume if the artificial borrowing constraint is binding.\n", "\n", "The *actual* consumption function is the lower of these two functions, pointwise. We can see this by plotting the component functions on the same figure:" ] @@ -406,13 +452,11 @@ { "cell_type": "code", "execution_count": 7, - "metadata": { - "hidden": true - }, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -424,7 +468,7 @@ } ], "source": [ - "plotFuncs(IndShockExample.solution[0].cFunc.functions,-0.25,5.)" + "plotFuncs(IndShockExample.solution[0].cFunc.functions, -0.25, 5.0)" ] }, { @@ -457,7 +501,7 @@ "metadata": {}, "outputs": [], "source": [ - "IndShockExample.track_vars = ['aNrmNow','mNrmNow','cNrmNow','pLvlNow']\n", + "IndShockExample.track_vars = [\"aNrmNow\", \"mNrmNow\", \"cNrmNow\", \"pLvlNow\"]\n", "IndShockExample.initializeSim()\n", "IndShockExample.simulate()" ] @@ -476,7 +520,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -500,14 +544,14 @@ } ], "source": [ - "plt.plot(np.mean(IndShockExample.history['mNrmNow'],axis=1))\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Mean market resources')\n", + "plt.plot(np.mean(IndShockExample.history[\"mNrmNow\"], axis=1))\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Mean market resources\")\n", "plt.show()\n", "\n", - "plt.plot(np.mean(IndShockExample.history['cNrmNow'],axis=1))\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Mean consumption')\n", + "plt.plot(np.mean(IndShockExample.history[\"cNrmNow\"], axis=1))\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Mean consumption\")\n", "plt.show()" ] }, @@ -525,7 +569,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -537,9 +581,9 @@ } ], "source": [ - "plt.plot(IndShockExample.history['cNrmNow'][:,0:5])\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Individual consumption paths')\n", + "plt.plot(IndShockExample.history[\"cNrmNow\"][:, 0:5])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Individual consumption paths\")\n", "plt.show()" ] }, @@ -549,7 +593,7 @@ "source": [ "## Other example specifications of idiosyncratic income shocks consumers\n", "\n", - "$\\texttt{IndShockConsumerType}$-- and $\\texttt{HARK}$ in general-- can also represent models that are not infinite horizon. \n", + "$\\texttt{IndShockConsumerType}$-- and $\\texttt{HARK}$ in general-- can also represent models that are not infinite horizon.\n", "\n", "### Lifecycle example\n", "\n", @@ -568,48 +612,44 @@ }, "outputs": [], "source": [ - "LifecycleDict={ # Click arrow to expand this fairly large parameter dictionary\n", + "LifecycleDict = { # Click arrow to expand this fairly large parameter dictionary\n", " # Parameters shared with the perfect foresight model\n", - " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", - " \"Rfree\": 1.03, # Interest factor on assets\n", - " \"DiscFac\": 0.96, # Intertemporal discount factor\n", - " \"LivPrb\" : [0.99,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1],\n", - " \"PermGroFac\" : [1.01,1.01,1.01,1.02,1.02,1.02,0.7,1.0,1.0,1.0],\n", - " \n", + " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", + " \"Rfree\": 1.03, # Interest factor on assets\n", + " \"DiscFac\": 0.96, # Intertemporal discount factor\n", + " \"LivPrb\": [0.99, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1],\n", + " \"PermGroFac\": [1.01, 1.01, 1.01, 1.02, 1.02, 1.02, 0.7, 1.0, 1.0, 1.0],\n", " # Parameters that specify the income distribution over the lifecycle\n", - " \"PermShkStd\" : [0.1,0.2,0.1,0.2,0.1,0.2,0.1,0,0,0],\n", - " \"PermShkCount\" : 7, # Number of points in discrete approximation to permanent income shocks\n", - " \"TranShkStd\" : [0.3,0.2,0.1,0.3,0.2,0.1,0.3,0,0,0],\n", - " \"TranShkCount\" : 7, # Number of points in discrete approximation to transitory income shocks\n", - " \"UnempPrb\" : 0.05, # Probability of unemployment while working\n", - " \"IncUnemp\" : 0.3, # Unemployment benefits replacement rate\n", - " \"UnempPrbRet\" : 0.0005, # Probability of \"unemployment\" while retired\n", - " \"IncUnempRet\" : 0.0, # \"Unemployment\" benefits when retired\n", - " \"T_retire\" : 7, # Period of retirement (0 --> no retirement)\n", - " \"tax_rate\" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", - " \n", + " \"PermShkStd\": [0.1, 0.2, 0.1, 0.2, 0.1, 0.2, 0.1, 0, 0, 0],\n", + " \"PermShkCount\": 7, # Number of points in discrete approximation to permanent income shocks\n", + " \"TranShkStd\": [0.3, 0.2, 0.1, 0.3, 0.2, 0.1, 0.3, 0, 0, 0],\n", + " \"TranShkCount\": 7, # Number of points in discrete approximation to transitory income shocks\n", + " \"UnempPrb\": 0.05, # Probability of unemployment while working\n", + " \"IncUnemp\": 0.3, # Unemployment benefits replacement rate\n", + " \"UnempPrbRet\": 0.0005, # Probability of \"unemployment\" while retired\n", + " \"IncUnempRet\": 0.0, # \"Unemployment\" benefits when retired\n", + " \"T_retire\": 7, # Period of retirement (0 --> no retirement)\n", + " \"tax_rate\": 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", " # Parameters for constructing the \"assets above minimum\" grid\n", - " \"aXtraMin\" : 0.001, # Minimum end-of-period \"assets above minimum\" value\n", - " \"aXtraMax\" : 20, # Maximum end-of-period \"assets above minimum\" value\n", - " \"aXtraCount\" : 48, # Number of points in the base grid of \"assets above minimum\"\n", - " \"aXtraNestFac\" : 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", - " \"aXtraExtra\" : [None], # Additional values to add to aXtraGrid\n", - " \n", + " \"aXtraMin\": 0.001, # Minimum end-of-period \"assets above minimum\" value\n", + " \"aXtraMax\": 20, # Maximum end-of-period \"assets above minimum\" value\n", + " \"aXtraCount\": 48, # Number of points in the base grid of \"assets above minimum\"\n", + " \"aXtraNestFac\": 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", + " \"aXtraExtra\": [None], # Additional values to add to aXtraGrid\n", " # A few other paramaters\n", - " \"BoroCnstArt\" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", - " \"vFuncBool\" : True, # Whether to calculate the value function during solution \n", - " \"CubicBool\" : False, # Preference shocks currently only compatible with linear cFunc\n", - " \"T_cycle\" : 10, # Number of periods in the cycle for this agent type \n", - " \n", + " \"BoroCnstArt\": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", + " \"vFuncBool\": True, # Whether to calculate the value function during solution\n", + " \"CubicBool\": False, # Preference shocks currently only compatible with linear cFunc\n", + " \"T_cycle\": 10, # Number of periods in the cycle for this agent type\n", " # Parameters only used in simulation\n", - " \"AgentCount\" : 10000, # Number of agents of this type\n", - " \"T_sim\" : 120, # Number of periods to simulate\n", - " \"aNrmInitMean\" : -6.0, # Mean of log initial assets\n", - " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets\n", - " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income\n", - " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income\n", - " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor\n", - " \"T_age\" : 11, # Age after which simulated agents are automatically killed \n", + " \"AgentCount\": 10000, # Number of agents of this type\n", + " \"T_sim\": 120, # Number of periods to simulate\n", + " \"aNrmInitMean\": -6.0, # Mean of log initial assets\n", + " \"aNrmInitStd\": 1.0, # Standard deviation of log initial assets\n", + " \"pLvlInitMean\": 0.0, # Mean of log initial permanent income\n", + " \"pLvlInitStd\": 0.0, # Standard deviation of log initial permanent income\n", + " \"PermGroFacAgg\": 1.0, # Aggregate permanent income growth factor\n", + " \"T_age\": 11, # Age after which simulated agents are automatically killed\n", "}" ] }, @@ -629,17 +669,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "First element of solution is \n", + "First element of solution is \n", "Solution has 11 elements.\n" ] } ], "source": [ "LifecycleExample = IndShockConsumerType(**LifecycleDict)\n", - "LifecycleExample.cycles = 1 # Make this consumer live a sequence of periods -- a lifetime -- exactly once\n", + "# Make this consumer live a sequence of periods -- a lifetime -- exactly once\n", + "LifecycleExample.cycles = 1\n", "LifecycleExample.solve()\n", - "print('First element of solution is',LifecycleExample.solution[0])\n", - "print('Solution has', len(LifecycleExample.solution),'elements.')" + "print(\"First element of solution is\", LifecycleExample.solution[0])\n", + "print(\"Solution has\", len(LifecycleExample.solution), \"elements.\")" ] }, { @@ -665,7 +706,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -677,10 +718,13 @@ } ], "source": [ - "print('Consumption functions across the lifecycle:')\n", - "mMin = np.min([LifecycleExample.solution[t].mNrmMin for t in range(LifecycleExample.T_cycle)])\n", - "LifecycleExample.unpack('cFunc') # This makes all of the cFuncs accessible in the attribute cFunc\n", - "plotFuncs(LifecycleExample.cFunc,mMin,5)" + "print(\"Consumption functions across the lifecycle:\")\n", + "mMin = np.min(\n", + " [LifecycleExample.solution[t].mNrmMin for t in range(LifecycleExample.T_cycle)]\n", + ")\n", + "# This makes all of the cFuncs accessible in the attribute cFunc\n", + "LifecycleExample.unpack(\"cFunc\")\n", + "plotFuncs(LifecycleExample.cFunc, mMin, 5)" ] }, { @@ -704,48 +748,44 @@ }, "outputs": [], "source": [ - "CyclicalDict = { # Click the arrow to expand this parameter dictionary\n", + "CyclicalDict = { # Click the arrow to expand this parameter dictionary\n", " # Parameters shared with the perfect foresight model\n", - " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", - " \"Rfree\": 1.03, # Interest factor on assets\n", - " \"DiscFac\": 0.96, # Intertemporal discount factor\n", - " \"LivPrb\" : 4*[0.98], # Survival probability\n", - " \"PermGroFac\" : [1.082251, 2.8, 0.3, 1.1],\n", - " \n", + " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", + " \"Rfree\": 1.03, # Interest factor on assets\n", + " \"DiscFac\": 0.96, # Intertemporal discount factor\n", + " \"LivPrb\": 4 * [0.98], # Survival probability\n", + " \"PermGroFac\": [1.082251, 2.8, 0.3, 1.1],\n", " # Parameters that specify the income distribution over the lifecycle\n", - " \"PermShkStd\" : [0.1,0.1,0.1,0.1],\n", - " \"PermShkCount\" : 7, # Number of points in discrete approximation to permanent income shocks\n", - " \"TranShkStd\" : [0.2,0.2,0.2,0.2],\n", - " \"TranShkCount\" : 7, # Number of points in discrete approximation to transitory income shocks\n", - " \"UnempPrb\" : 0.05, # Probability of unemployment while working\n", - " \"IncUnemp\" : 0.3, # Unemployment benefits replacement rate\n", - " \"UnempPrbRet\" : 0.0005, # Probability of \"unemployment\" while retired\n", - " \"IncUnempRet\" : 0.0, # \"Unemployment\" benefits when retired\n", - " \"T_retire\" : 0, # Period of retirement (0 --> no retirement)\n", - " \"tax_rate\" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", - " \n", + " \"PermShkStd\": [0.1, 0.1, 0.1, 0.1],\n", + " \"PermShkCount\": 7, # Number of points in discrete approximation to permanent income shocks\n", + " \"TranShkStd\": [0.2, 0.2, 0.2, 0.2],\n", + " \"TranShkCount\": 7, # Number of points in discrete approximation to transitory income shocks\n", + " \"UnempPrb\": 0.05, # Probability of unemployment while working\n", + " \"IncUnemp\": 0.3, # Unemployment benefits replacement rate\n", + " \"UnempPrbRet\": 0.0005, # Probability of \"unemployment\" while retired\n", + " \"IncUnempRet\": 0.0, # \"Unemployment\" benefits when retired\n", + " \"T_retire\": 0, # Period of retirement (0 --> no retirement)\n", + " \"tax_rate\": 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", " # Parameters for constructing the \"assets above minimum\" grid\n", - " \"aXtraMin\" : 0.001, # Minimum end-of-period \"assets above minimum\" value\n", - " \"aXtraMax\" : 20, # Maximum end-of-period \"assets above minimum\" value\n", - " \"aXtraCount\" : 48, # Number of points in the base grid of \"assets above minimum\"\n", - " \"aXtraNestFac\" : 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", - " \"aXtraExtra\" : [None], # Additional values to add to aXtraGrid\n", - " \n", + " \"aXtraMin\": 0.001, # Minimum end-of-period \"assets above minimum\" value\n", + " \"aXtraMax\": 20, # Maximum end-of-period \"assets above minimum\" value\n", + " \"aXtraCount\": 48, # Number of points in the base grid of \"assets above minimum\"\n", + " \"aXtraNestFac\": 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", + " \"aXtraExtra\": [None], # Additional values to add to aXtraGrid\n", " # A few other paramaters\n", - " \"BoroCnstArt\" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", - " \"vFuncBool\" : True, # Whether to calculate the value function during solution \n", - " \"CubicBool\" : False, # Preference shocks currently only compatible with linear cFunc\n", - " \"T_cycle\" : 4, # Number of periods in the cycle for this agent type \n", - " \n", + " \"BoroCnstArt\": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", + " \"vFuncBool\": True, # Whether to calculate the value function during solution\n", + " \"CubicBool\": False, # Preference shocks currently only compatible with linear cFunc\n", + " \"T_cycle\": 4, # Number of periods in the cycle for this agent type\n", " # Parameters only used in simulation\n", - " \"AgentCount\" : 10000, # Number of agents of this type\n", - " \"T_sim\" : 120, # Number of periods to simulate\n", - " \"aNrmInitMean\" : -6.0, # Mean of log initial assets\n", - " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets\n", - " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income\n", - " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income\n", - " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor\n", - " \"T_age\" : None, # Age after which simulated agents are automatically killed \n", + " \"AgentCount\": 10000, # Number of agents of this type\n", + " \"T_sim\": 120, # Number of periods to simulate\n", + " \"aNrmInitMean\": -6.0, # Mean of log initial assets\n", + " \"aNrmInitStd\": 1.0, # Standard deviation of log initial assets\n", + " \"pLvlInitMean\": 0.0, # Mean of log initial permanent income\n", + " \"pLvlInitStd\": 0.0, # Standard deviation of log initial permanent income\n", + " \"PermGroFacAgg\": 1.0, # Aggregate permanent income growth factor\n", + " \"T_age\": None, # Age after which simulated agents are automatically killed\n", "}" ] }, @@ -763,14 +803,6 @@ "execution_count": 15, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ms/dev/HARK/HARK/interpolation.py:1710: RuntimeWarning: All-NaN slice encountered\n", - " y = np.nanmin(fx,axis=1)\n" - ] - }, { "name": "stdout", "output_type": "stream", @@ -780,7 +812,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -793,13 +825,13 @@ ], "source": [ "CyclicalExample = IndShockConsumerType(**CyclicalDict)\n", - "CyclicalExample.cycles = 0 # Make this consumer type have an infinite horizon\n", + "CyclicalExample.cycles = 0 # Make this consumer type have an infinite horizon\n", "CyclicalExample.solve()\n", "\n", - "CyclicalExample.unpack('cFunc')\n", - "print('Quarterly consumption functions:')\n", + "CyclicalExample.unpack(\"cFunc\")\n", + "print(\"Quarterly consumption functions:\")\n", "mMin = min([X.mNrmMin for X in CyclicalExample.solution])\n", - "plotFuncs(CyclicalExample.cFunc,mMin,5)" + "plotFuncs(CyclicalExample.cFunc, mMin, 5)" ] }, { @@ -812,9 +844,8 @@ ], "metadata": { "jupytext": { - "cell_metadata_filter": "collapsed,code_folding,heading_collapsed,hidden", - "formats": "ipynb,py:percent", - "notebook_metadata_filter": "all" + "cell_metadata_filter": "collapsed,code_folding", + "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3", @@ -831,9 +862,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.6" + "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/examples/ConsIndShockModel/IndShockConsumerType.py b/examples/ConsIndShockModel/IndShockConsumerType.py index 4b26caaa9..90b183157 100644 --- a/examples/ConsIndShockModel/IndShockConsumerType.py +++ b/examples/ConsIndShockModel/IndShockConsumerType.py @@ -1,47 +1,38 @@ # --- # jupyter: # jupytext: -# cell_metadata_filter: collapsed,code_folding,heading_collapsed,hidden +# cell_metadata_filter: collapsed,code_folding # formats: ipynb,py:percent -# notebook_metadata_filter: all # text_representation: # extension: .py # format_name: percent -# format_version: '1.2' -# jupytext_version: 1.2.3 +# format_version: '1.3' +# jupytext_version: 1.5.2 # kernelspec: # display_name: Python 3 # language: python # name: python3 -# language_info: -# codemirror_mode: -# name: ipython -# version: 3 -# file_extension: .py -# mimetype: text/x-python -# name: python -# nbconvert_exporter: python -# pygments_lexer: ipython3 -# version: 3.7.6 # --- # %% [markdown] -# # IndShockConsumerType Documentation -# ## Consumption-Saving model with Idiosyncratic Income Shocks +# # IndShockConsumerType: Consumption-saving model with idiosyncratic income shocks -# %% {"code_folding": [0]} + +# %% code_folding=[0] # Initial imports and notebook setup, click arrow to show -from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType -from HARK.utilities import plotFuncsDer, plotFuncs -from time import clock + import matplotlib.pyplot as plt import numpy as np -mystr = lambda number : "{:.4f}".format(number) + +from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType +from HARK.utilities import plotFuncsDer, plotFuncs + +mystr = lambda number: "{:.4f}".format(number) # %% [markdown] # The module $\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks are fully transitory or fully permanent. # -# $\texttt{ConsIndShockModel}$ includes: +# $\texttt{ConsIndShockModel}$ currently includes three models: # 1. A very basic "perfect foresight" model with no uncertainty. # 2. A model with risk over transitory and permanent income shocks. # 3. The model described in (2), with an interest rate for debt that differs from the interest rate for savings. @@ -56,14 +47,14 @@ # %% [markdown] # ## Statement of idiosyncratic income shocks model # -# Suppose we want to solve a model like the one analyzed in [BufferStockTheory](http://econ.jhu.edu/people/ccarroll/papers/BufferStockTheory/), which has all the same features as the perfect foresight consumer, plus idiosyncratic shocks to income each period. Agents with this kind of model are represented by the class $\texttt{IndShockConsumerType}$. +# Suppose we want to solve a model like the one analyzed in [BufferStockTheory](http://econ.jhu.edu/people/ccarroll/papers/BufferStockTheory/), with all the same features as the perfect foresight consumer, plus idiosyncratic shocks to income each period. Agents with this kind of model are represented by the class $\texttt{IndShockConsumerType}$. # -# Specifically, this type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\newcommand{\tShkEmp}{\theta}{\tShkEmp_t}$ and a completely permanent shock $\newcommand{\pShk}{\psi}{\pShk_t}$. Moreover, the agent is subject to borrowing a borrowing limit: the ratio of end-of-period assets $A_t$ to permanent income $P_t$ must be greater than $\underline{a}$. As with the perfect foresight problem, this model is stated in terms of *normalized* variables, dividing all real variables by $P_t$: +# Specifically, this type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\newcommand{\tShkEmp}{\theta}{\tShkEmp_t}$ and a completely permanent shock $\newcommand{\pShk}{\psi}{\pShk_t}$. Moreover, lenders will not let the agent borrow money such that his ratio of end-of-period assets $A_t$ to permanent income $P_t$ is less than $\underline{a}$. As with the perfect foresight problem, this model can be framed in terms of *normalized* variables, dividing all real variables by $P_t$: # # \begin{eqnarray*} -# v_t(m_t) &=& \max_{c_t} {~} u(c_t) + \DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ (\PermGroFac_{t+1}\psi_{t+1})^{1-\CRRA} v_{t+1}(m_{t+1}) \right], \\ +# v_t(m_t) &=& \max_{c_t} {~} U(c_t) + \DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ (\PermGroFac_{t+1}\psi_{t+1})^{1-\CRRA} v_{t+1}(m_{t+1}) \right], \\ # a_t &=& m_t - c_t, \\ -# a_t &\geq& \text{$\underline{a}$}, \\ +# a_t &\geq& \underline{a}, \\ # m_{t+1} &=& \Rfree/(\PermGroFac_{t+1} \psi_{t+1}) a_t + \theta_{t+1}, \\ # (\psi_{t+1},\theta_{t+1}) &\sim& F_{t+1}, \\ # \mathbb{E}[\psi]=\mathbb{E}[\theta] &=& 1, \\ @@ -73,21 +64,21 @@ # %% [markdown] # ## Solution method for IndShockConsumerType # -# With the introduction of (non-trivial) risk, the idiosyncratic income shocks model has no closed form solution and must be solved numerically. The function $\texttt{solveConsIndShock}$ solves the one period problem for the $\texttt{IndShockConsumerType}$ class. To do so, HARK uses the original version of the endogenous grid method (EGM) first described [here](http://www.econ2.jhu.edu/people/ccarroll/EndogenousGridpoints.pdf) ; see also the [SolvingMicroDSOPs](http://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/) lecture notes. +# With the introduction of (non-trivial) risk, the idiosyncratic income shocks model has no closed form solution and must be solved numerically. The function $\texttt{solveConsIndShock}$ solves the one period problem for the $\texttt{IndShockConsumerType}$ class. To do so, HARK uses the original version of the endogenous grid method (EGM) first described [here](http://www.econ2.jhu.edu/people/ccarroll/EndogenousGridpoints.pdf); see also the [SolvingMicroDSOPs](http://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/) lecture notes. # -# Briefly, the transition equation for $m_{t+1}$ can be substituted into the problem definition; the second term of the reformulated maximand represents "end of period value of assets" $\mathfrak{v}_t(a_t)$ ("Gothic v"): +# Briefly, the transition equation for $m_{t+1}$ can be substituted into the problem definition; the second term of the reformulated maximand represents "end of period value of assets" $\mathfrak{v}_t(a_t)$: # # \begin{eqnarray*} -# v_t(m_t) &=& \max_{c_t} {~} u(c_t) + \underbrace{\DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ (\PermGroFac_{t+1}\psi_{t+1})^{1-\CRRA} v_{t+1}(\Rfree/(\PermGroFac_{t+1} \psi_{t+1}) a_t + \theta_{t+1}) \right]}_{\equiv \mathfrak{v}_t(a_t)}. +# v_t(m_t) &=& \max_{c_t} {~} U(c_t) + \underbrace{\DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ (\PermGroFac_{t+1}\psi_{t+1})^{1-\CRRA} v_{t+1}(\Rfree/(\PermGroFac_{t+1} \psi_{t+1}) a_t + \theta_{t+1}) \right]}_{\equiv \mathfrak{v}_t(a_t)}. # \end{eqnarray*} # # The first order condition with respect to $c_t$ is thus simply: # # \begin{eqnarray*} -# u^{\prime}(c_t) - \mathfrak{v}'_t(a_t) = 0 \Longrightarrow c_t^{-\CRRA} = \mathfrak{v}'_t(a_t) \Longrightarrow c_t = \mathfrak{v}'_t(a_t)^{-1/\CRRA}, +# U'(c_t) - \mathfrak{v}'_t(a_t) = 0 \Longrightarrow c_t^{-\CRRA} = \mathfrak{v}'_t(a_t) \Longrightarrow c_t = \mathfrak{v}'_t(a_t)^{-1/\CRRA}. # \end{eqnarray*} # -# and the marginal value of end-of-period assets can be computed as: +# Where the marginal value of end-of-period assets can be computed as: # # \begin{eqnarray*} # \mathfrak{v}'_t(a_t) = \DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ \Rfree (\PermGroFac_{t+1}\psi_{t+1})^{-\CRRA} v'_{t+1}(\Rfree/(\PermGroFac_{t+1} \psi_{t+1}) a_t + \theta_{t+1}) \right]. @@ -103,73 +94,69 @@ # | Parameter | Description | Code | Example value | Time-varying? | # | :---: | --- | --- | --- | --- | # | $\DiscFac$ |Intertemporal discount factor | $\texttt{DiscFac}$ | $0.96$ | | -# | $\CRRA$|Coefficient of relative risk aversion | $\texttt{CRRA}$ | $2.0$ | | +# | $\CRRA $ |Coefficient of relative risk aversion | $\texttt{CRRA}$ | $2.0$ | | # | $\Rfree$ | Risk free interest factor | $\texttt{Rfree}$ | $1.03$ | | # | $1 - \DiePrb_{t+1}$ |Survival probability | $\texttt{LivPrb}$ | $[0.98]$ | $\surd$ | # |$\PermGroFac_{t+1}$|Permanent income growth factor|$\texttt{PermGroFac}$| $[1.01]$ | $\surd$ | -# | $\sigma_\psi$| Standard deviation of log permanent income shocks | $\texttt{PermShkStd}$ | $[0.1]$ |$\surd$ | -# | $N_\psi$| Number of discrete permanent income shocks | $\texttt{PermShkCount}$ | $7$ | | -# | $\sigma_\theta$| Standard deviation of log transitory income shocks | $\texttt{TranShkStd}$ | $[0.2]$ | $\surd$ | -# | $N_\theta$| Number of discrete transitory income shocks | $\texttt{TranShkCount}$ | $7$ | | +# | $\sigma_\psi $ | Standard deviation of log permanent income shocks | $\texttt{PermShkStd}$ | $[0.1]$ |$\surd$ | +# | $N_\psi $ | Number of discrete permanent income shocks | $\texttt{PermShkCount}$ | $7$ | | +# | $\sigma_\theta $ | Standard deviation of log transitory income shocks | $\texttt{TranShkStd}$ | $[0.2]$ | $\surd$ | +# | $N_\theta $ | Number of discrete transitory income shocks | $\texttt{TranShkCount}$ | $7$ | | # | $\mho$ | Probability of being unemployed and getting $\theta=\underline{\theta}$ | $\texttt{UnempPrb}$ | $0.05$ | | -# | $\underline{\theta}$| Transitory shock when unemployed | $\texttt{IncUnemp}$ | $0.3$ | | +# | $\underline{\theta} $ | Transitory shock when unemployed | $\texttt{IncUnemp}$ | $0.3$ | | # | $\mho^{Ret}$ | Probability of being "unemployed" when retired | $\texttt{UnempPrb}$ | $0.0005$ | | -# | $\underline{\theta}^{Ret}$| Transitory shock when "unemployed" and retired | $\texttt{IncUnemp}$ | $0.0$ | | +# | $\underline{\theta}^{Ret} $ | Transitory shock when "unemployed" and retired | $\texttt{IncUnemp}$ | $0.0$ | | # | $(none)$ | Period of the lifecycle model when retirement begins | $\texttt{T_retire}$ | $0$ | | # | $(none)$ | Minimum value in assets-above-minimum grid | $\texttt{aXtraMin}$ | $0.001$ | | # | $(none)$ | Maximum value in assets-above-minimum grid | $\texttt{aXtraMax}$ | $20.0$ | | # | $(none)$ | Number of points in base assets-above-minimum grid | $\texttt{aXtraCount}$ | $48$ | | # | $(none)$ | Exponential nesting factor for base assets-above-minimum grid | $\texttt{aXtraNestFac}$ | $3$ | | # | $(none)$ | Additional values to add to assets-above-minimum grid | $\texttt{aXtraExtra}$ | $None$ | | -# | $\underline{a}$| Artificial borrowing constraint (normalized) | $\texttt{BoroCnstArt}$ | $0.0$ | | -# | $(none)$|Indicator for whether $\texttt{vFunc}$ should be computed | $\texttt{vFuncBool}$ | $True$ | | +# | $\underline{a} $ | Artificial borrowing constraint (normalized) | $\texttt{BoroCnstArt}$ | $0.0$ | | +# | $(none) $ |Indicator for whether $\texttt{vFunc}$ should be computed | $\texttt{vFuncBool}$ | $True$ | | # | $(none)$ |Indicator for whether $\texttt{cFunc}$ should use cubic splines | $\texttt{CubicBool}$ | $False$ | | # |$T$| Number of periods in this type's "cycle" |$\texttt{T_cycle}$| $1$ | | # |(none)| Number of times the "cycle" occurs |$\texttt{cycles}$| $0$ | | -# %% {"code_folding": [0]} -IdiosyncDict={ +# %% code_folding=[0] +IdiosyncDict = { # Click the arrow to expand this parameter dictionary # Parameters shared with the perfect foresight model - "CRRA": 2.0, # Coefficient of relative risk aversion - "Rfree": 1.03, # Interest factor on assets - "DiscFac": 0.96, # Intertemporal discount factor - "LivPrb" : [0.98], # Survival probability - "PermGroFac" :[1.01], # Permanent income growth factor - + "CRRA": 2.0, # Coefficient of relative risk aversion + "Rfree": 1.03, # Interest factor on assets + "DiscFac": 0.96, # Intertemporal discount factor + "LivPrb": [0.98], # Survival probability + "PermGroFac": [1.01], # Permanent income growth factor + "BoroCnstArt": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets # Parameters that specify the income distribution over the lifecycle - "PermShkStd" : [0.1], # Standard deviation of log permanent shocks to income - "PermShkCount" : 7, # Number of points in discrete approximation to permanent income shocks - "TranShkStd" : [0.2], # Standard deviation of log transitory shocks to income - "TranShkCount" : 7, # Number of points in discrete approximation to transitory income shocks - "UnempPrb" : 0.05, # Probability of unemployment while working - "IncUnemp" : 0.3, # Unemployment benefits replacement rate - "UnempPrbRet" : 0.0005, # Probability of "unemployment" while retired - "IncUnempRet" : 0.0, # "Unemployment" benefits when retired - "T_retire" : 0, # Period of retirement (0 --> no retirement) - "tax_rate" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future) - + "PermShkStd": [0.1], # Standard deviation of log permanent shocks to income + "PermShkCount": 7, # Number of points in discrete approximation to permanent income shocks + "TranShkStd": [0.2], # Standard deviation of log transitory shocks to income + "TranShkCount": 7, # Number of points in discrete approximation to transitory income shocks + "UnempPrb": 0.05, # Probability of unemployment while working + "IncUnemp": 0.3, # Unemployment benefits replacement rate + "UnempPrbRet": 0.0005, # Probability of "unemployment" while retired + "IncUnempRet": 0.0, # "Unemployment" benefits when retired + "T_retire": 0, # Period of retirement (0 --> no retirement) + "tax_rate": 0.0, # Flat income tax rate (legacy parameter, will be removed in future) # Parameters for constructing the "assets above minimum" grid - "aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value - "aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value - "aXtraCount" : 48, # Number of points in the base grid of "assets above minimum" - "aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid - "aXtraExtra" : [None], # Additional values to add to aXtraGrid - + "aXtraMin": 0.001, # Minimum end-of-period "assets above minimum" value + "aXtraMax": 20, # Maximum end-of-period "assets above minimum" value + "aXtraCount": 48, # Number of points in the base grid of "assets above minimum" + "aXtraNestFac": 3, # Exponential nesting factor when constructing "assets above minimum" grid + "aXtraExtra": [None], # Additional values to add to aXtraGrid # A few other paramaters - "BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets - "vFuncBool" : True, # Whether to calculate the value function during solution - "CubicBool" : False, # Preference shocks currently only compatible with linear cFunc - "T_cycle" : 1, # Number of periods in the cycle for this agent type - + "vFuncBool": True, # Whether to calculate the value function during solution + "CubicBool": False, # Preference shocks currently only compatible with linear cFunc + "T_cycle": 1, # Number of periods in the cycle for this agent type # Parameters only used in simulation - "AgentCount" : 10000, # Number of agents of this type - "T_sim" : 120, # Number of periods to simulate - "aNrmInitMean" : -6.0, # Mean of log initial assets - "aNrmInitStd" : 1.0, # Standard deviation of log initial assets - "pLvlInitMean" : 0.0, # Mean of log initial permanent income - "pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income - "PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor - "T_age" : None, # Age after which simulated agents are automatically killed + "AgentCount": 10000, # Number of agents of this type + "T_sim": 120, # Number of periods to simulate + "aNrmInitMean": -6.0, # Mean of log initial assets + "aNrmInitStd": 1.0, # Standard deviation of log initial assets + "pLvlInitMean": 0.0, # Mean of log initial permanent income + "pLvlInitStd": 0.0, # Standard deviation of log initial permanent income + "PermGroFacAgg": 1.0, # Aggregate permanent income growth factor + "T_age": None, # Age after which simulated agents are automatically killed } # %% [markdown] @@ -183,56 +170,67 @@ # # It is not necessary to compute the value function in this model, and it is not computationally free to do so. You can choose whether the value function should be calculated and returned as part of the solution of the model with $\texttt{vFuncBool}$. The consumption function will be constructed as a piecewise linear interpolation when $\texttt{CubicBool}$ is \texttt{False}, and will be a piecewise cubic spline interpolator if $\texttt{True}$. -# %% [markdown] {"heading_collapsed": true} +# %% [markdown] # ## Solving and examining the solution of the idiosyncratic income shocks model # # The cell below creates an infinite horizon instance of $\texttt{IndShockConsumerType}$ and solves its model by calling its $\texttt{solve}$ method. -# %% {"hidden": true} +# %% IndShockExample = IndShockConsumerType(**IdiosyncDict) -IndShockExample.cycles = 0 # Make this type have an infinite horizon +IndShockExample.cycles = 0 # Make this type have an infinite horizon IndShockExample.solve() - -# %% [markdown] {"hidden": true} +# %% [markdown] # After solving the model, we can examine an element of this type's $\texttt{solution}$: -# %% {"hidden": true} +# %% print(vars(IndShockExample.solution[0])) -# %% [markdown] {"hidden": true} +# %% [markdown] # The single-period solution to an idiosyncratic shocks consumer's problem has all of the same attributes as in the perfect foresight model, with a couple additions. The solution can include the marginal marginal value of market resources function $\texttt{vPPfunc}$, but this is only constructed if $\texttt{CubicBool}$ is $\texttt{True}$, so that the MPC can be accurately computed; when it is $\texttt{False}$, then $\texttt{vPPfunc}$ merely returns $\texttt{NaN}$ everywhere. # # The $\texttt{solveConsIndShock}$ function calculates steady state market resources and stores it in the attribute $\texttt{mNrmSS}$. This represents the steady state level of $m_t$ if *this period* were to occur indefinitely, but with income shocks turned off. This is relevant in a "one period infinite horizon" model like we've specified here, but is less useful in a lifecycle model. # # Let's take a look at the consumption function by plotting it, along with its derivative (the MPC): -# %% {"hidden": true} -print('Consumption function for an idiosyncratic shocks consumer type:') -plotFuncs(IndShockExample.solution[0].cFunc,IndShockExample.solution[0].mNrmMin,5) -print('Marginal propensity to consume for an idiosyncratic shocks consumer type:') -plotFuncsDer(IndShockExample.solution[0].cFunc,IndShockExample.solution[0].mNrmMin,5) +# %% +print("Consumption function for an idiosyncratic shocks consumer type:") +plotFuncs(IndShockExample.solution[0].cFunc, IndShockExample.solution[0].mNrmMin, 5) +print("Marginal propensity to consume for an idiosyncratic shocks consumer type:") +plotFuncsDer(IndShockExample.solution[0].cFunc, IndShockExample.solution[0].mNrmMin, 5) -# %% [markdown] {"hidden": true} +# %% [markdown] # The lower part of the consumption function is linear with a slope of 1, representing the *constrained* part of the consumption function where the consumer *would like* to consume more by borrowing-- his marginal utility of consumption exceeds the marginal value of assets-- but he is prevented from doing so by the artificial borrowing constraint. # # The MPC is a step function, as the $\texttt{cFunc}$ itself is a piecewise linear function; note the large jump in the MPC where the borrowing constraint begins to bind. # # If you want to look at the interpolation nodes for the consumption function, these can be found by "digging into" attributes of $\texttt{cFunc}$: -# %% {"hidden": true} -print('mNrmGrid for unconstrained cFunc is ',IndShockExample.solution[0].cFunc.functions[0].x_list) -print('cNrmGrid for unconstrained cFunc is ',IndShockExample.solution[0].cFunc.functions[0].y_list) -print('mNrmGrid for borrowing constrained cFunc is ',IndShockExample.solution[0].cFunc.functions[1].x_list) -print('cNrmGrid for borrowing constrained cFunc is ',IndShockExample.solution[0].cFunc.functions[1].y_list) +# %% +print( + "mNrmGrid for unconstrained cFunc is ", + IndShockExample.solution[0].cFunc.functions[0].x_list, +) +print( + "cNrmGrid for unconstrained cFunc is ", + IndShockExample.solution[0].cFunc.functions[0].y_list, +) +print( + "mNrmGrid for borrowing constrained cFunc is ", + IndShockExample.solution[0].cFunc.functions[1].x_list, +) +print( + "cNrmGrid for borrowing constrained cFunc is ", + IndShockExample.solution[0].cFunc.functions[1].y_list, +) -# %% [markdown] {"hidden": true} -# The consumption function in this model is an instance of $\texttt{LowerEnvelope1D}$, a class that takes an arbitrary number of 1D interpolants as arguments to its initialization method. When called, a $\texttt{LowerEnvelope1D}$ evaluates each of its component functions and returns the lowest value. Here, the two component functions are the *unconstrained* consumption function-- how the agent would consume if the artificial borrowing constraint did not exist for *just this period*-- and the *borrowing constrained* consumption function-- how much he would consume if the artificial borrowing constraint is binding. +# %% [markdown] +# The consumption function in this model is an instance of $\texttt{LowerEnvelope1D}$, a class that takes an arbitrary number of 1D interpolants as arguments to its initialization method. When called, a $\texttt{LowerEnvelope1D}$ evaluates each of its component functions and returns the lowest value. Here, the two component functions are the *unconstrained* consumption function-- how the agent would consume if the artificial borrowing constraint did not exist for *just this period*-- and the *borrowing constrained* consumption function-- how much he would consume if the artificial borrowing constraint is binding. # # The *actual* consumption function is the lower of these two functions, pointwise. We can see this by plotting the component functions on the same figure: -# %% {"hidden": true} -plotFuncs(IndShockExample.solution[0].cFunc.functions,-0.25,5.) +# %% +plotFuncs(IndShockExample.solution[0].cFunc.functions, -0.25, 5.0) # %% [markdown] # ## Simulating the idiosyncratic income shocks model @@ -255,7 +253,7 @@ # These example parameter values were already passed as part of the parameter dictionary that we used to create $\texttt{IndShockExample}$, so it is ready to simulate. We need to set the $\texttt{track_vars}$ attribute to indicate the variables for which we want to record a *history*. # %% -IndShockExample.track_vars = ['aNrmNow','mNrmNow','cNrmNow','pLvlNow'] +IndShockExample.track_vars = ["aNrmNow", "mNrmNow", "cNrmNow", "pLvlNow"] IndShockExample.initializeSim() IndShockExample.simulate() @@ -263,29 +261,29 @@ # We can now look at the simulated data in aggregate or at the individual consumer level. Like in the perfect foresight model, we can plot average (normalized) market resources over time, as well as average consumption: # %% -plt.plot(np.mean(IndShockExample.history['mNrmNow'],axis=1)) -plt.xlabel('Time') -plt.ylabel('Mean market resources') +plt.plot(np.mean(IndShockExample.history["mNrmNow"], axis=1)) +plt.xlabel("Time") +plt.ylabel("Mean market resources") plt.show() -plt.plot(np.mean(IndShockExample.history['cNrmNow'],axis=1)) -plt.xlabel('Time') -plt.ylabel('Mean consumption') +plt.plot(np.mean(IndShockExample.history["cNrmNow"], axis=1)) +plt.xlabel("Time") +plt.ylabel("Mean consumption") plt.show() # %% [markdown] # We could also plot individual consumption paths for some of the consumers-- say, the first five: # %% -plt.plot(IndShockExample.history['cNrmNow'][:,0:5]) -plt.xlabel('Time') -plt.ylabel('Individual consumption paths') +plt.plot(IndShockExample.history["cNrmNow"][:, 0:5]) +plt.xlabel("Time") +plt.ylabel("Individual consumption paths") plt.show() # %% [markdown] # ## Other example specifications of idiosyncratic income shocks consumers # -# $\texttt{IndShockConsumerType}$-- and $\texttt{HARK}$ in general-- can also represent models that are not infinite horizon. +# $\texttt{IndShockConsumerType}$-- and $\texttt{HARK}$ in general-- can also represent models that are not infinite horizon. # # ### Lifecycle example # @@ -293,49 +291,45 @@ # # In the cell below, we define a parameter dictionary for a rather short ten period lifecycle, with arbitrarily chosen parameters. For a more realistically calibrated (and much longer) lifecycle model, see the [SolvingMicroDSOPs REMARK](https://github.com/econ-ark/REMARK/blob/master/REMARKs/SolvingMicroDSOPs.md). -# %% {"code_folding": [0]} -LifecycleDict={ # Click arrow to expand this fairly large parameter dictionary +# %% code_folding=[0] +LifecycleDict = { # Click arrow to expand this fairly large parameter dictionary # Parameters shared with the perfect foresight model - "CRRA": 2.0, # Coefficient of relative risk aversion - "Rfree": 1.03, # Interest factor on assets - "DiscFac": 0.96, # Intertemporal discount factor - "LivPrb" : [0.99,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1], - "PermGroFac" : [1.01,1.01,1.01,1.02,1.02,1.02,0.7,1.0,1.0,1.0], - + "CRRA": 2.0, # Coefficient of relative risk aversion + "Rfree": 1.03, # Interest factor on assets + "DiscFac": 0.96, # Intertemporal discount factor + "LivPrb": [0.99, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1], + "PermGroFac": [1.01, 1.01, 1.01, 1.02, 1.02, 1.02, 0.7, 1.0, 1.0, 1.0], # Parameters that specify the income distribution over the lifecycle - "PermShkStd" : [0.1,0.2,0.1,0.2,0.1,0.2,0.1,0,0,0], - "PermShkCount" : 7, # Number of points in discrete approximation to permanent income shocks - "TranShkStd" : [0.3,0.2,0.1,0.3,0.2,0.1,0.3,0,0,0], - "TranShkCount" : 7, # Number of points in discrete approximation to transitory income shocks - "UnempPrb" : 0.05, # Probability of unemployment while working - "IncUnemp" : 0.3, # Unemployment benefits replacement rate - "UnempPrbRet" : 0.0005, # Probability of "unemployment" while retired - "IncUnempRet" : 0.0, # "Unemployment" benefits when retired - "T_retire" : 7, # Period of retirement (0 --> no retirement) - "tax_rate" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future) - + "PermShkStd": [0.1, 0.2, 0.1, 0.2, 0.1, 0.2, 0.1, 0, 0, 0], + "PermShkCount": 7, # Number of points in discrete approximation to permanent income shocks + "TranShkStd": [0.3, 0.2, 0.1, 0.3, 0.2, 0.1, 0.3, 0, 0, 0], + "TranShkCount": 7, # Number of points in discrete approximation to transitory income shocks + "UnempPrb": 0.05, # Probability of unemployment while working + "IncUnemp": 0.3, # Unemployment benefits replacement rate + "UnempPrbRet": 0.0005, # Probability of "unemployment" while retired + "IncUnempRet": 0.0, # "Unemployment" benefits when retired + "T_retire": 7, # Period of retirement (0 --> no retirement) + "tax_rate": 0.0, # Flat income tax rate (legacy parameter, will be removed in future) # Parameters for constructing the "assets above minimum" grid - "aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value - "aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value - "aXtraCount" : 48, # Number of points in the base grid of "assets above minimum" - "aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid - "aXtraExtra" : [None], # Additional values to add to aXtraGrid - + "aXtraMin": 0.001, # Minimum end-of-period "assets above minimum" value + "aXtraMax": 20, # Maximum end-of-period "assets above minimum" value + "aXtraCount": 48, # Number of points in the base grid of "assets above minimum" + "aXtraNestFac": 3, # Exponential nesting factor when constructing "assets above minimum" grid + "aXtraExtra": [None], # Additional values to add to aXtraGrid # A few other paramaters - "BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets - "vFuncBool" : True, # Whether to calculate the value function during solution - "CubicBool" : False, # Preference shocks currently only compatible with linear cFunc - "T_cycle" : 10, # Number of periods in the cycle for this agent type - + "BoroCnstArt": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets + "vFuncBool": True, # Whether to calculate the value function during solution + "CubicBool": False, # Preference shocks currently only compatible with linear cFunc + "T_cycle": 10, # Number of periods in the cycle for this agent type # Parameters only used in simulation - "AgentCount" : 10000, # Number of agents of this type - "T_sim" : 120, # Number of periods to simulate - "aNrmInitMean" : -6.0, # Mean of log initial assets - "aNrmInitStd" : 1.0, # Standard deviation of log initial assets - "pLvlInitMean" : 0.0, # Mean of log initial permanent income - "pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income - "PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor - "T_age" : 11, # Age after which simulated agents are automatically killed + "AgentCount": 10000, # Number of agents of this type + "T_sim": 120, # Number of periods to simulate + "aNrmInitMean": -6.0, # Mean of log initial assets + "aNrmInitStd": 1.0, # Standard deviation of log initial assets + "pLvlInitMean": 0.0, # Mean of log initial permanent income + "pLvlInitStd": 0.0, # Standard deviation of log initial permanent income + "PermGroFacAgg": 1.0, # Aggregate permanent income growth factor + "T_age": 11, # Age after which simulated agents are automatically killed } # %% [markdown] @@ -343,10 +337,11 @@ # %% LifecycleExample = IndShockConsumerType(**LifecycleDict) -LifecycleExample.cycles = 1 # Make this consumer live a sequence of periods -- a lifetime -- exactly once +# Make this consumer live a sequence of periods -- a lifetime -- exactly once +LifecycleExample.cycles = 1 LifecycleExample.solve() -print('First element of solution is',LifecycleExample.solution[0]) -print('Solution has', len(LifecycleExample.solution),'elements.') +print("First element of solution is", LifecycleExample.solution[0]) +print("Solution has", len(LifecycleExample.solution), "elements.") # %% [markdown] # This was supposed to be a *ten* period lifecycle model-- why does our consumer type have *eleven* elements in its $\texttt{solution}$? It would be more precise to say that this specification has ten *non-terminal* periods. The solution to the 11th and final period in the model would be the same for every set of parameters: consume $c_t = m_t$, because there is no future. In a lifecycle model, the terminal period is assumed to exist; the $\texttt{LivPrb}$ parameter does not need to end with a $0.0$ in order to guarantee that survivors die. @@ -354,10 +349,13 @@ # We can quickly plot the consumption functions in each period of the model: # %% -print('Consumption functions across the lifecycle:') -mMin = np.min([LifecycleExample.solution[t].mNrmMin for t in range(LifecycleExample.T_cycle)]) -LifecycleExample.unpack('cFunc') # This makes all of the cFuncs accessible in the attribute cFunc -plotFuncs(LifecycleExample.cFunc,mMin,5) +print("Consumption functions across the lifecycle:") +mMin = np.min( + [LifecycleExample.solution[t].mNrmMin for t in range(LifecycleExample.T_cycle)] +) +# This makes all of the cFuncs accessible in the attribute cFunc +LifecycleExample.unpack("cFunc") +plotFuncs(LifecycleExample.cFunc, mMin, 5) # %% [markdown] # ### "Cyclical" example @@ -366,49 +364,45 @@ # # We can represent this type of individual as a four period, infinite horizon model in which expected "permanent" income growth varies greatly across seasons. -# %% {"code_folding": [0]} -CyclicalDict = { # Click the arrow to expand this parameter dictionary +# %% code_folding=[0] +CyclicalDict = { # Click the arrow to expand this parameter dictionary # Parameters shared with the perfect foresight model - "CRRA": 2.0, # Coefficient of relative risk aversion - "Rfree": 1.03, # Interest factor on assets - "DiscFac": 0.96, # Intertemporal discount factor - "LivPrb" : 4*[0.98], # Survival probability - "PermGroFac" : [1.082251, 2.8, 0.3, 1.1], - + "CRRA": 2.0, # Coefficient of relative risk aversion + "Rfree": 1.03, # Interest factor on assets + "DiscFac": 0.96, # Intertemporal discount factor + "LivPrb": 4 * [0.98], # Survival probability + "PermGroFac": [1.082251, 2.8, 0.3, 1.1], # Parameters that specify the income distribution over the lifecycle - "PermShkStd" : [0.1,0.1,0.1,0.1], - "PermShkCount" : 7, # Number of points in discrete approximation to permanent income shocks - "TranShkStd" : [0.2,0.2,0.2,0.2], - "TranShkCount" : 7, # Number of points in discrete approximation to transitory income shocks - "UnempPrb" : 0.05, # Probability of unemployment while working - "IncUnemp" : 0.3, # Unemployment benefits replacement rate - "UnempPrbRet" : 0.0005, # Probability of "unemployment" while retired - "IncUnempRet" : 0.0, # "Unemployment" benefits when retired - "T_retire" : 0, # Period of retirement (0 --> no retirement) - "tax_rate" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future) - + "PermShkStd": [0.1, 0.1, 0.1, 0.1], + "PermShkCount": 7, # Number of points in discrete approximation to permanent income shocks + "TranShkStd": [0.2, 0.2, 0.2, 0.2], + "TranShkCount": 7, # Number of points in discrete approximation to transitory income shocks + "UnempPrb": 0.05, # Probability of unemployment while working + "IncUnemp": 0.3, # Unemployment benefits replacement rate + "UnempPrbRet": 0.0005, # Probability of "unemployment" while retired + "IncUnempRet": 0.0, # "Unemployment" benefits when retired + "T_retire": 0, # Period of retirement (0 --> no retirement) + "tax_rate": 0.0, # Flat income tax rate (legacy parameter, will be removed in future) # Parameters for constructing the "assets above minimum" grid - "aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value - "aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value - "aXtraCount" : 48, # Number of points in the base grid of "assets above minimum" - "aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid - "aXtraExtra" : [None], # Additional values to add to aXtraGrid - + "aXtraMin": 0.001, # Minimum end-of-period "assets above minimum" value + "aXtraMax": 20, # Maximum end-of-period "assets above minimum" value + "aXtraCount": 48, # Number of points in the base grid of "assets above minimum" + "aXtraNestFac": 3, # Exponential nesting factor when constructing "assets above minimum" grid + "aXtraExtra": [None], # Additional values to add to aXtraGrid # A few other paramaters - "BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets - "vFuncBool" : True, # Whether to calculate the value function during solution - "CubicBool" : False, # Preference shocks currently only compatible with linear cFunc - "T_cycle" : 4, # Number of periods in the cycle for this agent type - + "BoroCnstArt": 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets + "vFuncBool": True, # Whether to calculate the value function during solution + "CubicBool": False, # Preference shocks currently only compatible with linear cFunc + "T_cycle": 4, # Number of periods in the cycle for this agent type # Parameters only used in simulation - "AgentCount" : 10000, # Number of agents of this type - "T_sim" : 120, # Number of periods to simulate - "aNrmInitMean" : -6.0, # Mean of log initial assets - "aNrmInitStd" : 1.0, # Standard deviation of log initial assets - "pLvlInitMean" : 0.0, # Mean of log initial permanent income - "pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income - "PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor - "T_age" : None, # Age after which simulated agents are automatically killed + "AgentCount": 10000, # Number of agents of this type + "T_sim": 120, # Number of periods to simulate + "aNrmInitMean": -6.0, # Mean of log initial assets + "aNrmInitStd": 1.0, # Standard deviation of log initial assets + "pLvlInitMean": 0.0, # Mean of log initial permanent income + "pLvlInitStd": 0.0, # Standard deviation of log initial permanent income + "PermGroFacAgg": 1.0, # Aggregate permanent income growth factor + "T_age": None, # Age after which simulated agents are automatically killed } # %% [markdown] @@ -418,13 +412,13 @@ # %% CyclicalExample = IndShockConsumerType(**CyclicalDict) -CyclicalExample.cycles = 0 # Make this consumer type have an infinite horizon +CyclicalExample.cycles = 0 # Make this consumer type have an infinite horizon CyclicalExample.solve() -CyclicalExample.unpack('cFunc') -print('Quarterly consumption functions:') +CyclicalExample.unpack("cFunc") +print("Quarterly consumption functions:") mMin = min([X.mNrmMin for X in CyclicalExample.solution]) -plotFuncs(CyclicalExample.cFunc,mMin,5) +plotFuncs(CyclicalExample.cFunc, mMin, 5) # %% [markdown] # The very low green consumption function corresponds to the quarter in which the ski instructors make most of their income. They know that they are about to experience a 70% drop in "permanent" income, so they do not consume much *relative to their income this quarter*. In the other three quarters, *normalized* consumption is much higher, as current "permanent" income is low relative to future expectations. In *level*, the consumption chosen in each quarter is much more similar diff --git a/examples/ConsIndShockModel/KinkedRconsumerType.ipynb b/examples/ConsIndShockModel/KinkedRconsumerType.ipynb index 0616798d7..b8d0bd739 100644 --- a/examples/ConsIndShockModel/KinkedRconsumerType.ipynb +++ b/examples/ConsIndShockModel/KinkedRconsumerType.ipynb @@ -2,7 +2,9 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "lines_to_next_cell": 2 + }, "source": [ "# KinkedRconsumerType: Consumption-saving model with idiosyncratic income shocks and different interest rates on borrowing and saving" ] @@ -18,12 +20,14 @@ "outputs": [], "source": [ "# Initial imports and notebook setup, click arrow to show\n", - "from HARK.ConsumptionSaving.ConsIndShockModel import KinkedRconsumerType\n", - "from HARK.utilities import plotFuncsDer, plotFuncs\n", - "from time import clock\n", + "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", - "mystr = lambda number : \"{:.4f}\".format(number)" + "\n", + "from HARK.ConsumptionSaving.ConsIndShockModel import KinkedRconsumerType\n", + "from HARK.utilities import plotFuncsDer, plotFuncs\n", + "\n", + "mystr = lambda number: \"{:.4f}\".format(number)" ] }, { @@ -96,27 +100,27 @@ "| Parameter | Description | Code | Example value | Time-varying? |\n", "| :---: | --- | --- | --- | --- |\n", "| $\\DiscFac$ |Intertemporal discount factor | $\\texttt{DiscFac}$ | $0.96$ | |\n", - "| $\\CRRA$ |Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", + "| $\\CRRA $ |Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", "| $\\Rfree_{boro}$ | Risk free interest factor for borrowing | $\\texttt{Rboro}$ | $1.20$ | |\n", "| $\\Rfree_{save}$ | Risk free interest factor for saving | $\\texttt{Rsave}$ | $1.01$ | |\n", "| $1 - \\DiePrb_{t+1}$ |Survival probability | $\\texttt{LivPrb}$ | $[0.98]$ | $\\surd$ |\n", "|$\\PermGroFac_{t+1}$|Permanent income growth factor|$\\texttt{PermGroFac}$| $[1.01]$ | $\\surd$ |\n", - "| $\\sigma_\\psi$ | Standard deviation of log permanent income shocks | $\\texttt{PermShkStd}$ | $[0.1]$ |$\\surd$ |\n", - "| $N_\\psi$ | Number of discrete permanent income shocks | $\\texttt{PermShkCount}$ | $7$ | |\n", - "| $\\sigma_\\theta$ | Standard deviation of log transitory income shocks | $\\texttt{TranShkStd}$ | $[0.2]$ | $\\surd$ |\n", - "| $N_\\theta$ | Number of discrete transitory income shocks | $\\texttt{TranShkCount}$ | $7$ | |\n", + "| $\\sigma_\\psi $ | Standard deviation of log permanent income shocks | $\\texttt{PermShkStd}$ | $[0.1]$ |$\\surd$ |\n", + "| $N_\\psi $ | Number of discrete permanent income shocks | $\\texttt{PermShkCount}$ | $7$ | |\n", + "| $\\sigma_\\theta $ | Standard deviation of log transitory income shocks | $\\texttt{TranShkStd}$ | $[0.2]$ | $\\surd$ |\n", + "| $N_\\theta $ | Number of discrete transitory income shocks | $\\texttt{TranShkCount}$ | $7$ | |\n", "| $\\mho$ | Probability of being unemployed and getting $\\theta=\\underline{\\theta}$ | $\\texttt{UnempPrb}$ | $0.05$ | |\n", - "| $\\underline{\\theta}$ | Transitory shock when unemployed | $\\texttt{IncUnemp}$ | $0.3$ | |\n", + "| $\\underline{\\theta} $ | Transitory shock when unemployed | $\\texttt{IncUnemp}$ | $0.3$ | |\n", "| $\\mho^{Ret}$ | Probability of being \"unemployed\" when retired | $\\texttt{UnempPrb}$ | $0.0005$ | |\n", - "| $\\underline{\\theta}^{Ret}$ | Transitory shock when \"unemployed\" and retired | $\\texttt{IncUnemp}$ | $0.0$ | |\n", + "| $\\underline{\\theta}^{Ret} $ | Transitory shock when \"unemployed\" and retired | $\\texttt{IncUnemp}$ | $0.0$ | |\n", "| $(none)$ | Period of the lifecycle model when retirement begins | $\\texttt{T_retire}$ | $0$ | |\n", "| $(none)$ | Minimum value in assets-above-minimum grid | $\\texttt{aXtraMin}$ | $0.001$ | |\n", "| $(none)$ | Maximum value in assets-above-minimum grid | $\\texttt{aXtraMax}$ | $20.0$ | |\n", "| $(none)$ | Number of points in base assets-above-minimum grid | $\\texttt{aXtraCount}$ | $48$ | |\n", "| $(none)$ | Exponential nesting factor for base assets-above-minimum grid | $\\texttt{aXtraNestFac}$ | $3$ | |\n", "| $(none)$ | Additional values to add to assets-above-minimum grid | $\\texttt{aXtraExtra}$ | $None$ | |\n", - "| $\\underline{a}$ | Artificial borrowing constraint (normalized) | $\\texttt{BoroCnstArt}$ | $None$ | |\n", - "| $(none)$ |Indicator for whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | $True$ | |\n", + "| $\\underline{a} $ | Artificial borrowing constraint (normalized) | $\\texttt{BoroCnstArt}$ | $None$ | |\n", + "| $(none) $ |Indicator for whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | $True$ | |\n", "| $(none)$ |Indicator for whether $\\texttt{cFunc}$ should use cubic splines | $\\texttt{CubicBool}$ | $False$ | |\n", "|$T$| Number of periods in this type's \"cycle\" |$\\texttt{T_cycle}$| $1$ | |\n", "|(none)| Number of times the \"cycle\" occurs |$\\texttt{cycles}$| $0$ | |\n", @@ -134,51 +138,46 @@ }, "outputs": [], "source": [ - "KinkedRdict={ # Click the arrow to expand this parameter dictionary\n", + "KinkedRdict = { # Click the arrow to expand this parameter dictionary\n", " # Parameters shared with the perfect foresight model\n", - " \"CRRA\" : 2.0, # Coefficient of relative risk aversion\n", - " \"DiscFac\": 0.96, # Intertemporal discount factor\n", - " \"LivPrb\" : [0.98], # Survival probability\n", - " \"PermGroFac\" :[1.01], # Permanent income growth factor\n", - " \n", + " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", + " \"DiscFac\": 0.96, # Intertemporal discount factor\n", + " \"LivPrb\": [0.98], # Survival probability\n", + " \"PermGroFac\": [1.01], # Permanent income growth factor\n", + " \"BoroCnstArt\": None, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", " # New parameters unique to the \"kinked R\" model\n", - " \"Rboro\" : 1.20, # Interest factor on borrowing (a < 0)\n", - " \"Rsave\" : 1.01, # Interest factor on saving (a > 0)\n", - " \n", - " # Parameters that specify the income distribution over the lifecycle\n", - " \"PermShkStd\" : [0.1], # Standard deviation of log permanent shocks to income\n", - " \"PermShkCount\" : 7, # Number of points in discrete approximation to permanent income shocks\n", - " \"TranShkStd\" : [0.2], # Standard deviation of log transitory shocks to income\n", - " \"TranShkCount\" : 7, # Number of points in discrete approximation to transitory income shocks\n", - " \"UnempPrb\" : 0.05, # Probability of unemployment while working\n", - " \"IncUnemp\" : 0.3, # Unemployment benefits replacement rate\n", - " \"UnempPrbRet\" : 0.0005, # Probability of \"unemployment\" while retired\n", - " \"IncUnempRet\" : 0.0, # \"Unemployment\" benefits when retired\n", - " \"T_retire\" : 0, # Period of retirement (0 --> no retirement)\n", - " \"tax_rate\" : 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", - " \n", - " # Parameters for constructing the \"assets above minimum\" grid\n", - " \"aXtraMin\" : 0.001, # Minimum end-of-period \"assets above minimum\" value\n", - " \"aXtraMax\" : 20, # Maximum end-of-period \"assets above minimum\" value\n", - " \"aXtraCount\" : 48, # Number of points in the base grid of \"assets above minimum\"\n", - " \"aXtraNestFac\" : 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", - " \"aXtraExtra\" : [None], # Additional values to add to aXtraGrid\n", - " \n", - " # A few other paramaters\n", - " \"BoroCnstArt\" : None, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n", - " \"vFuncBool\" : True, # Whether to calculate the value function during solution \n", - " \"CubicBool\" : False, # Preference shocks currently only compatible with linear cFunc\n", - " \"T_cycle\" : 1, # Number of periods in the cycle for this agent type \n", - " \n", - " # Parameters only used in simulation\n", - " \"AgentCount\" : 10000, # Number of agents of this type\n", - " \"T_sim\" : 500, # Number of periods to simulate\n", - " \"aNrmInitMean\" : -6.0, # Mean of log initial assets\n", - " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets\n", - " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income\n", - " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income\n", - " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor\n", - " \"T_age\" : None, # Age after which simulated agents are automatically killed\n", + " \"Rboro\": 1.20, # Interest factor on borrowing (a < 0)\n", + " \"Rsave\": 1.01, # Interest factor on saving (a > 0)\n", + " # Parameters that specify the income distribution over the lifecycle (shared with IndShockConsumerType)\n", + " \"PermShkStd\": [0.1], # Standard deviation of log permanent shocks to income\n", + " \"PermShkCount\": 7, # Number of points in discrete approximation to permanent income shocks\n", + " \"TranShkStd\": [0.2], # Standard deviation of log transitory shocks to income\n", + " \"TranShkCount\": 7, # Number of points in discrete approximation to transitory income shocks\n", + " \"UnempPrb\": 0.05, # Probability of unemployment while working\n", + " \"IncUnemp\": 0.3, # Unemployment benefits replacement rate\n", + " \"UnempPrbRet\": 0.0005, # Probability of \"unemployment\" while retired\n", + " \"IncUnempRet\": 0.0, # \"Unemployment\" benefits when retired\n", + " \"T_retire\": 0, # Period of retirement (0 --> no retirement)\n", + " \"tax_rate\": 0.0, # Flat income tax rate (legacy parameter, will be removed in future)\n", + " # Parameters for constructing the \"assets above minimum\" grid (shared with IndShockConsumerType)\n", + " \"aXtraMin\": 0.001, # Minimum end-of-period \"assets above minimum\" value\n", + " \"aXtraMax\": 20, # Maximum end-of-period \"assets above minimum\" value\n", + " \"aXtraCount\": 48, # Number of points in the base grid of \"assets above minimum\"\n", + " \"aXtraNestFac\": 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n", + " \"aXtraExtra\": [None], # Additional values to add to aXtraGrid\n", + " # A few other paramaters (shared with IndShockConsumerType)\n", + " \"vFuncBool\": True, # Whether to calculate the value function during solution\n", + " \"CubicBool\": False, # Preference shocks currently only compatible with linear cFunc\n", + " \"T_cycle\": 1, # Number of periods in the cycle for this agent type\n", + " # Parameters only used in simulation (shared with PerfForesightConsumerType)\n", + " \"AgentCount\": 10000, # Number of agents of this type\n", + " \"T_sim\": 500, # Number of periods to simulate\n", + " \"aNrmInitMean\": -6.0, # Mean of log initial assets\n", + " \"aNrmInitStd\": 1.0, # Standard deviation of log initial assets\n", + " \"pLvlInitMean\": 0.0, # Mean of log initial permanent income\n", + " \"pLvlInitStd\": 0.0, # Standard deviation of log initial permanent income\n", + " \"PermGroFacAgg\": 1.0, # Aggregate permanent income growth factor\n", + " \"T_age\": None, # Age after which simulated agents are automatically killed\n", "}" ] }, @@ -198,7 +197,7 @@ "outputs": [], "source": [ "KinkyExample = KinkedRconsumerType(**KinkedRdict)\n", - "KinkyExample.cycles = 0 # Make the example infinite horizon\n", + "KinkyExample.cycles = 0 # Make the example infinite horizon\n", "KinkyExample.solve()" ] }, @@ -225,7 +224,7 @@ }, { "data": { - "image/png": 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WiJwmhXucc2+Zs/6Tv2ynsTnENy/NY+HcUVpPXaSbU7jHsVDIWfjkGl4tPMgFY1P58XWTtPORSIxQuMexFTsqeLXwIN+8NI/bLxqjOesiMUQ7Dsexx97eQ1piH26dO1rBLhJjFO5xaldFLSt2VPCFWTn0TtAfA5FYo7/VceqJd/bSq6exYFZWx41FpNtRuMeh2vom/rCmlKsmp2sOu0iMUrjHoefWlFJb38TN540MuhQR6SQK9zgTCjmPv7OHqVkpnK2lekVilsI9zrxZdIhdFce4eU5O0KWISCdSuMeZx9/eQ+rA3syfnB50KSLSiRTucWTv4WO8vr2cz83K0fICIjFO4R4nisqPcuuTa+ib0JPPz9IuWCKxTssPxDh355l3S7j3pS30753AQ1+cwbAkTX8UiXUK9xhWdbyBu5/bxF+2HOD8Mancd8NUhirYReKCwj1Grdx1mDufXU/F0Xq+c+V4vnLBKHpoJyWRuKFwjzFNzSF++dp7/HpZEblDBvD81+YwJVPz2UXijcI9hhQfPs43nl3HuuIqPjMjkx9eM5EBffRbLBKPwpotY2ZXmNl2Mysys7vbOZ9tZsvMbJ2ZbTSz+ZEvVU7lxfX7mP+rNygqr+X+BdP42fVTFewicazDv/1m1hN4ALgUKAVWm9kSd9/aptn3gMXu/hszmwAsBXI7oV45ydG6Ru55cQsvrNtHfs4gfnHj2WQO6h90WSISsHC6djOBInffBWBmi4Brgbbh7kBS6+tkoCySRUr71hYf4RuL1rHvyAnuvCSPr184moSeenRBRMIL9wygpM1xKTDrpDY/AP7bzP4OGABc0t6FzGwhsBAgO1sP0pyu5pDzm+VF/PzV9xie1JfFt84mP3dw0GWJSBQJp5vX3vw5P+l4AfCYu2cC84EnzexD13b3h909393z09LSPn61QlnVCRb8diU/++8dzJ+czp/vuEDBLiIfEk7PvRRou11PJh8edrkFuALA3d8xs75AKlAeiSKlxdJN+7n7uY00h5x/u34qn56eob1PRaRd4YT7amCsmY0E9gE3Ap87qU0xcDHwmJmdBfQFKiJZaDw73tDEvX/cyqLVJUzNTOaXN04jN3VA0GWJSBTrMNzdvcnMbgdeBnoCj7r7FjO7Fyhw9yXAN4HfmtmdtAzZ3OzuJw/dyGnYWFrFHc+uZ/ehY3z9wtHccUkevXTTVEQ6ENZEaHdfSsv0xrbv3dPm9VbgvMiWFt+amkM8uHwnv3rtPdIS+/DUl2cxZ3Rq0GWJSDehp1yi0O5Dx7jz2fWsL6niurNH8MNrJ5Hcr1fQZYlIN6JwjyLuztPvFvPjlwrp1dO4f8E0Pjl1RNBliUg3pHCPEuVH67j7uU28vq2c88ek8rPrpzI8WcvzisjpUbhHgaWb9vNPL2zieEMzP/jkBL40O1fL84rIGVG4B6jqeAPfX7KFF9eXMSUzmX+7fipjhyUGXZaIxACFe0DeLjrEnYvXc7i2gbsuzeO2eaM1xVFEIkbh3sWamkP86rX3uH9ZEaNSB/C7m85hUkZy0GWJSIxRuHeh/dUn+MYz63l3TyWfmZHJvddOpH9v/RaISOQpWbrIa4UH+Yffb6C+KcTPPzuVT03LDLokEYlhCvdO1tAU4qd/2cYjb+5mQnoSv/7cNEalDQy6LBGJcQr3TlRWdYLbnlrLhpIqvjQ7h+/OP4u+vXoGXZaIxAGFeydZueswX39qLfVNIX7z+elcOTk96JJEJI4o3CPM3fmPt/bw/5YWkjOkPw9/cQZjhmruuoh0LYV7BNU1NvOd5zfxwrp9XDphGPfdMJXEvlrwS0S6nsI9QsqP1vGVJ9awsbSKuy7N4/YLx2gJAREJjMI9AraW1fDlx1dz5HgjD31hBpdPHB50SSIS5xTuZ+j1bQe5/el1JPXtxe+/OltPm4pIVFC4n4HFBSV85/lNnJWeyO9uOodhSVqiV0SiQ1grVZnZFWa23cyKzOzuj2hzg5ltNbMtZvZ0ZMuMPg+t2Mm3/7CR2aOGsGjhbAW7iESVDnvuZtYTeAC4FCgFVpvZktZ9U99vMxb4DnCeux8xs6GdVXDQQiHnX/5cyG/f2M3VU9K574az6Z2g1RxFJLqEk0ozgSJ33+XuDcAi4NqT2nwFeMDdjwC4e3lky4wOoZDzvRc389s3dnPT7Bx+deM0BbuIRKVwkikDKGlzXNr6Xlt5QJ6ZvWVmK83sivYuZGYLzazAzAoqKipOr+KAvB/sT68q5rZ5o/nBNRM11VFEolY44d5egvlJxwnAWGAesAB4xMxSPvSL3B9293x3z09LS/u4tQambbB/bd5ovn35OMwU7CISvcIJ91Igq81xJlDWTpsX3b3R3XcD22kJ+27P3fnBH7d8EOzfUrCLSDcQTrivBsaa2Ugz6w3cCCw5qc1/ARcCmFkqLcM0uyJZaFDuf72IJ97Zy8JPjFKwi0i30WG4u3sTcDvwMlAILHb3LWZ2r5ld09rsZeCwmW0FlgHfcvfDnVV0V1n0bjH3vbKDT0/P4DtXjlewi0i3Ye4nD593jfz8fC8oKAjks8PxytaD3PpkAReMTeORm/K1ebWIRAUzW+Pu+R21U2K1Y/O+av7umbVMzkjmwc9PV7CLSLej1DrJ4dp6bn1yDYP69+aRm85hQB+t0CAi3Y+Sq43G5hC3P72Oitp6/vDV2aQl9gm6JBGR06Keexv/vLSQd3Yd5l8+NZkpmR+api8i0m0o3Fu9uH4f//HWHv72vJH8zYzMoMsRETkjCnegpPI433thMzNyBvHd+eODLkdE5IzFfbg3NYe489n1APzis2eToJkxIhID4v6G6gPLdlKw9wi/vPFssgb3D7ocEZGIiOtu6pq9R/jV6+/xqWkZXHv2yQtdioh0X3Eb7sfqm7jj2XWkJ/flh9dODLocEZGIitthmZ+/soOSyhMsvnU2SX17BV2OiEhExWXPffO+ah59azefm5XNzJGDgy5HRCTi4i7cm5pD3P38RoYM7MM/XqFpjyISm+Iu3B97ew+b99Xw/U9OILmfhmNEJDbFVbiXHjnOfa/s4MJxaVw1OT3ockREOk3chLu7c8+LW3CHH103SRtviEhMi5twf3nLAV7fVs43L8sjc5AeVhKR2BYX4d7QFOKfl24jb9hAbp6TG3Q5IiKdLqxwN7MrzGy7mRWZ2d2naPcZM3Mz63ALqK70xDt7KK48znfnn6W1Y0QkLnSYdGbWE3gAuBKYACwwswnttEsE/h5YFekiz0TV8Qbuf72IC8amMm/c0KDLERHpEuF0Y2cCRe6+y90bgEXAte20+xHwU6AugvWdsftfL6KmrpHvzj8r6FJERLpMOOGeAZS0OS5tfe8DZjYNyHL3l051ITNbaGYFZlZQUVHxsYv9uPYcOsYT7+zhhhlZnJWe1OmfJyISLcIJ9/bmDPoHJ816AD8HvtnRhdz9YXfPd/f8tLS08Ks8TT99eRsJPXpw12V5nf5ZIiLRJJxwLwWy2hxnAmVtjhOBScByM9sDnAssCfqmasGeSpZuOsCtc0cxLKlvkKWIiHS5cMJ9NTDWzEaaWW/gRmDJ+yfdvdrdU909191zgZXANe5e0CkVh8Hd+fGfChma2IeFnxgVVBkiIoHpMNzdvQm4HXgZKAQWu/sWM7vXzK7p7AJPx0sb97O+pIp/uGwc/XvH7arGIhLHwko+d18KLD3pvXs+ou28My/r9NU3NfOTv2xj/PBE/mZGZpCliIgEJuae6FlcUErpkRPcfeV4evbQ+jEiEp9iKtzrm5p5cFkR07NTmJvX+bNxRESiVUyF++LVJeyvruPOS/O06qOIxLWYCff6pmYeWLaTGTmDOH9MatDliIgEKmbCffHqEg7U1HHnJeq1i4jERLjXNbb02vNzBnHemCFBlyMiEriYCPfFBa29do21i4gAMRDuLb32Is7JHcSc0eq1i4hADIT7s6tLOFhTr7F2EZE2unW41zU28+DyImbmDma2eu0iIh/o1uG+6N1iDtbUc8elY9VrFxFpo9uGe0uvfSczRw5m9ij12kVE2uq24f7Mu8WUH9VYu4hIe7pluL/fa581UmPtIiLt6Zbh/vSqYiqO1nPHJdo+T0SkPd0u3Osam3lohXrtIiKn0u3C/bm1pZQfrefvLx4bdCkiIlGrW4V7U3OIh1bsZGpWip5GFRE5hbDC3cyuMLPtZlZkZne3c/4uM9tqZhvN7DUzy4l8qfDHjWWUVJ7g9gvHaIaMiMgpdBjuZtYTeAC4EpgALDCzCSc1Wwfku/sU4A/ATyNdaCjkPLhsJ+OGJXLx+KGRvryISEwJp+c+Eyhy913u3gAsAq5t28Ddl7n78dbDlUDEd6Z+pfAg75XX8rULR9NDe6OKiJxSOOGeAZS0OS5tfe+j3AL8+UyKOpm788CyInKG9OeqyemRvLSISEwKJ9zb6yZ7uw3NvgDkA//6EecXmlmBmRVUVFSEXeSbRYfYWFrNV+eOJqFnt7oHLCISiHCSshTIanOcCZSd3MjMLgH+CbjG3evbu5C7P+zu+e6en5aWFnaRDywrYnhSXz49/VT/wyAiIu8LJ9xXA2PNbKSZ9QZuBJa0bWBm04B/pyXYyyNZ4Jq9lazcVclXPjGKPgk9I3lpEZGY1WG4u3sTcDvwMlAILHb3LWZ2r5ld09rsX4GBwO/NbL2ZLfmIy31sDyzbyaD+vVgwM6vjxiIiAkBCOI3cfSmw9KT37mnz+pII1wXAtgM1vL6tnLsuzaN/77BKFRERovwJ1X9fsYv+vXvypdmd8kyUiEjMitpwL6k8zpINZSyYmU1K/95BlyMi0q1Ebbj/7s3d9DD48gUjgy5FRKTbicpwP1xbz6LVxVx7dgbpyf2CLkdEpNuJynB//J291DWG+OrcUUGXIiLSLUVduB+rb+KJd/Zw6YRhjBmaGHQ5IiLdUtSF+6LVJVQdb+S2eaODLkVEpNuKqnBvaArxuzd2MXPkYKZnDwq6HBGRbiuqwn3JhjLKquvUaxcROUNRE+6hkPPvK3Yyfngi8/LCX1RMREQ+LGrC/bVt5bxXXstX547WFnoiImcoKsLd3fnN8iIyB/Xj6inajENE5ExFRbiv3nOEtcVVfOWCUdqMQ0QkAqIiSR9asZPBA3pzQ76W9RURiYTAw/39ZX1vnpNLv97ajENEJBICD3ct6ysiEnmBhruW9RUR6RyBhruW9RUR6RyBhXtTyLWsr4hIJwkr3M3sCjPbbmZFZnZ3O+f7mNmzredXmVluR9c8XFuvZX1FRDpJh+FuZj2BB4ArgQnAAjObcFKzW4Aj7j4G+Dnwk46ue/hYg5b1FRHpJOH03GcCRe6+y90bgEXAtSe1uRZ4vPX1H4CLrYM1BJpDzlfnaoEwEZHOEE64ZwAlbY5LW99rt427NwHVwJCTL2RmC82swMwK+vUIMSNHy/qKiHSGcMK9vR64n0Yb3P1hd8939/wx6Qp2EZHOEk64lwJt1wXIBMo+qo2ZJQDJQGUkChQRkY8vnHBfDYw1s5Fm1hu4EVhyUpslwE2trz8DvO7uH+q5i4hI10joqIG7N5nZ7cDLQE/gUXffYmb3AgXuvgT4HfCkmRXR0mO/sTOLFhGRU+sw3AHcfSmw9KT37mnzug64PrKliYjI6Qp84TAREYk8hbuISAxSuIuIxCCFu4hIDLKgZiyaWQWwN5APPz2pwKGgi+gC+p6xJ16+a7x8z3Hu3uGiXGHNlukM7p4W1GefDjMrcPf8oOvobPqesSdevms8fc9w2mlYRkQkBincRURikMI9fA8HXUAX0feMPfHyXfU92wjshqqIiHQe9dxFRGKQwl1EJAYp3MPQ0QbhscDMHjWzcjPbHHQtncnMssxsmZkVmtkWM/tG0DV1BjPra2bvmtmG1u/5w6Br6kxm1tPM1pnZS0HX0pnMbI+ZbTKz9R1NidSYewdaNwjfAVxKy6Ykq4EF7r410MIizMw+AdQCT7j7pKDr6Sxmlg6ku/taM0sE1gDXxeDvpwED3L3WzHoBbwLfcPeVAZfWKczsLiAfSHL3q4Oup7OY2R4g3907fFhLPfeOhbNBeLfn7n8lDnbPcvf97r629fVRoJAP7wnc7XmL2tbDXq0/YrInZ2aZwFXAI0HXEk0U7vkb8fkAAAF7SURBVB0LZ4Nw6YbMLBeYBqwKtpLO0TpUsR4oB15x95j8nsAvgG8DoaAL6QIO/LeZrTGzhadqqHDvWFibf0v3YmYDgeeAO9y9Juh6OoO7N7v72bTsezzTzGJuuM3MrgbK3X1N0LV0kfPcfTpwJfD11uHUdincOxbOBuHSjbSOQT8HPOXuzwddT2dz9ypgOXBFwKV0hvOAa1rHohcBF5nZfwZbUudx97LWn8uBF2gZNm6Xwr1j4WwQLt1E643G3wGF7n5f0PV0FjNLM7OU1tf9gEuAbcFWFXnu/h13z3T3XFr+br7u7l8IuKxOYWYDWicBYGYDgMuAj5zdpnDvgLs3Ae9vEF4ILHb3LcFWFXlm9gzwDjDOzErN7Jaga+ok5wFfpKWHt771x/ygi+oE6cAyM9tISwflFXeP6WmCcWAY8KaZbQDeBf7k7n/5qMaaCikiEoPUcxcRiUEKdxGRGKRwFxGJQQp3EZEYpHAXEYlBCncRkRikcBcRiUH/HyO6MiK7RKAsAAAAAElFTkSuQmCC\n", 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\n", 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\n", + "image/png": 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s2bqbp17bHnVJh02Nu0iYSlnn3gJsGPC4HTh94AFm1gJ8ClgAnDrUG5nZ5cDlADNmzBhurZFbMG8qC+ZNBeDkv/stu/dX14hmqO0H1LqLhKeUzr2UOPgRcJ27H3KdoLsvcvc2d29rbm4utcYxqb4mFcS9VbUFsEiYSunc24HpAx63AvkbrLQBd+aCYjLwETPrdvdflaXKMaihJsWuKgt3Z4iNw9S6iwSnlHBfCsw2s1nARuBi4JKBB7j7rL7fm9kdwG9CDnbIhnv1jWUGn1DNLoWMph4RqZyi4e7u3WZ2NdlVMEngdndfaWZX5l6/tcI1jkkN41K8tGkn373/FRIGF586gxmT6qIua9g0lREJU0kbh7n7fcB9ec8VDHV3/9LhlzX2nTx9Ik+9tp3bn1xHV+5mHn9z4byIqzq0Iccy6txFgqNdIUfomnNnc825swE45VsPsmPfgYgrGhndiUkkTNp+oAyaatPsrIJwH6pD1wlVkfAo3MugqTbNzio7udpHM3eRMGksUwZN41K0v7WX+194E4DZUxt575SGiKsaLDtzL7D9gBp3keAo3MugdWIdj6/expd/9kcAjp5cz5K/Oivaogpx14RdJCYU7mXwzU8cx3/64FEA/OTxddy7YlN2TXmVzDzUuIuER+FeBjWpJPOOaAJgztRGOrt72bm/m/G16YgrO1ihpZBmprGMSIAU7mU2pakGgAU/eIREwmisSXHXFR+gubEm4soKq45/W4jIcGm1TJl9eE4zl505k/PnH0HbURNZu20PL258J+qygNyukIVfGeVKRKTS1LmX2YS6DN/4+HwAtu7cz/0vbubZN95m2oRxAExrqmV83dgZ11TJaQERGSaFewVNbqihPpPkpiVruGnJGgDeO6WBh679cCT1OIVP8mrmLhIehXsFJRLGXVd8gA1v7QXg189tYskrWyNbSVNoLKPOXSRMCvcKO75lPMe3jAdg4459PLByMzv3dZd1NLN6yy5Wbdk96PkjJ4zj5BkTi/68GneR8CjcR1HfipkbHlrF+No0ZnDRSS3Mmlxf8nu8sX0v67bvOei5v/q3FXTs6hx0bDJhfPuTx5NOZs+b79h7gGnjxx10jGG45jIiwVG4j6JjpzVRm05yx1Pr+5/r2NXJdz51QsHjt+7az6OvdhzUWX/vgVfZtntwkH/rovmcfvSk/sdbdu7nSz9dylfveeGg4z40e/JhfQcRqQ4K91E0Z2ojL3/rwv7HF9zw2EFB/ermXazb9u545efPbODRVR2D3ucfPn0Cc6Y29j+uSSWYf2TTQXP8OVMbeeZvz2Fv18G3tR3UuZvGMiIhUrhHaFJDhu27u4DsLfAuXvR73t578NbBf/r+Vv7rebP7H9ekkiVfEDWpoYZJxQ/jje17q2q7BBEpTuEeoUkNNTz66lau++XzdHb38PbeA1x73hzOO25q/zFHN9dTk0pWrAYzY+22PTzw4mYWnjCtYp8jIqNLV6hG6EOzJ1Nfk+LRVR08vfYtjp5cz6dObuHYaU39vyoZ7ADf+eTxQHYlj4iEQ517hD7bNp3Ptk2PtIbjpjVhBruq9GYjIlKYOveYSySMhkyKnfvH/m0CRaR0CnfJ3QNWnbtISDSWERrHpXhiTQdX/J9lg147e+4U/vSU1kHPG5BKqjcQGasU7sLHTpzGb55/k9e37z3o+Ve37GLxyi1cn3chFEDC4JYvnMIF848YrTJFZBgU7sLVC2Zz9YLZg57ftruTf1vWTk9v70HPd/c6P3poNWs79gz6GREZGxTuMqTJDTV8+axjBj3fkwv3ru7eAj8lImOBhqYybMmEkUoYnd09xQ8WkUgo3GVEalIJde4iY5jCXUYkk0rQqXAXGbMU7jIiGXXuImOawl1GpCaV1MxdZAxTuMuIZFIJunrUuYuMVQp3GZGaVILOAwp3kbFK4S4jos5dZGwr6SImM7sQuBFIAre5+3fzXv9z4Lrcw93Al919RTkLlbElk0ywtmMPNzy4atBryYTxuVOnM7VpXIGfFJHRUDTczSwJ3AycB7QDS83sXnd/acBh64APu/vbZrYQWAScXomCZWw4dloTf1j3Fjc+vLrg6wb85TmDtzQQkdFRSud+GrDG3dcCmNmdwEVAf7i7+1MDjn8aGLyNoATlm5+Yzzc/Mb/ga/O//sCge8GKyOgqZebeAmwY8Lg999xQ/gK4v9ALZna5mS0zs2UdHR2lVylVpak2rZt/iESslHC3As95wQPNziYb7tcVet3dF7l7m7u3NTc3l16lVJXxtWne2adwF4lSKWOZdmDgjT5bgU35B5nZicBtwEJ3316e8qQaNdWmea1jN3ctfaPg6/OPHM/xLeNHuSqReCkl3JcCs81sFrARuBi4ZOABZjYDuAe41N0HL5+QWJk1qZ5n1r3FdXcPvskHwFGT6nj0r88u+FpXdy+/enYj+4tc/TpnaiNnHD3psGsVCVXRcHf3bjO7GlhMdink7e6+0syuzL1+K/B1YBLwz2YG0O3ubZUrW8ayv//0CVxzbuGVMnc8tZ5/eXwti1duJpUYPPFb9vrb3PLIa0U/Y1J9huVfO++waxUJlbkXHJ9XXFtbmy9bNvienRK2Ja9s4T/fceg/99aJtfzqqjMLnuwBWPT4Wn786FpWf2chad3HVWLGzJaX0jzrTkwyqs6eO4XFX/mTQ246duSEWiY31Az5euvEOgDe3tPFFF0oJVKQwl1GlZkx94jGw3qPSfUZAG5/cj3NjUP/JQBw7rFTOGpS/WF9nkg1UrhL1Zk9pYFUwrj10eKz+ZUb3+GHnztpFKoSGVsU7lJ1Zk9t5IVvXlB047Iv/uQPbNm1f5SqEhlbFO5SlWozSWpJHvKYKU3jeGP73lGqSGRsUbhLsCY31PDoqg4u++kzRY+tSSX52sePo2VC7ShUJlJ5CncJ1gXzp/LSmzvZvqfrkMd19zgvvbmTD82ZzJ+fftQoVSdSWQp3CdZZc6dw1twpRY/r7XXmfe0Bnn1jBye2TCjpvd/TkFGXL2Oawl1iL5Ewjm6u55fL2/nl8vaSfiaTSrD8v59L47h0hasTGRmFuwiw6NI2Vm3ZVdKxL2x8hxsfXs3S9W8x/8jSN0CryyT1l4GMGoW7CDBjUh0zJtWVdOzsqQ3c+PDqotso5BuXTvDkdQuYdIirb0XKReEuMkxHTapn0aWnsG33oU/UDrRxx15u/t1r3PbEOmZPaRj2Zx47rYljpzUN++ckvhTuIiNw/vwjhnX87s5ufvrk+pJ2vCykdWItT1y3YEQ/K/GkcBcZBQ01KZ66fsGI7lB19/J2blqyhs/9+PfYUFtlFlGXSfG9z5x4yA3ZJCwKd5FRMqEuw4S6zLB/7s/apvPshh10dvcykh26u3t6eXrtVm595DVOm/We4b9BnpNnTCy6YZtET/u5iwTO3TnjHx5my87OsrzfucdO4ZYvnFKW9+qTShg20n+WxEyp+7kr3EViYNvuTja/c/ibqC16bC33rhh0C+XDdtFJR3LjxSeX/X1DpJt1iEi/yQ01ZZm3X79wHnOPaKScTeHv127nN8+/yYoNO8r2ngMlzPjrC+ay8IRpFXn/sUqdu4hEav22Pdy0ZDU9vZXJoqde286Bnl5aJ47OdhGZZIIf/Nn7OLp5+EteS6HOXUSqwszJ9fzws5W7ocpvV27mrqUbKvb++R5b3cHnFj3NhNpor0ZWuItI0M6ff8Swr0s4HHc8uY5n1r9Vsfd/qMTjNJYREakipY5lEqNRjIiIjC6Fu4hIgBTuIiIBUriLiARI4S4iEiCFu4hIgBTuIiIBUriLiAQosouYzKwDeD2SDx+ZycC2qIsYBfqe4YnLd43L95zr7o3FDops+wF3b47qs0fCzJaVclVYtdP3DE9cvmucvmcpx2ksIyISIIW7iEiAFO6lWxR1AaNE3zM8cfmu+p4DRHZCVUREKkedu4hIgBTuIiIBUriXwMwuNLNXzWyNmV0fdT2VYGa3m9lWM3sx6loqycymm9nvzOxlM1tpZtdEXVMlmNk4M3vGzFbkvuf/iLqmSjKzpJk9a2a/ibqWSjKz9Wb2gpk9V2xJpGbuRZhZElgFnAe0A0uBz7v7S5EWVmZm9ifAbuBf3f34qOupFDObBkxz9z+aWSOwHPhkgH+eBtS7+24zSwNPANe4+9MRl1YRZnYt0AY0ufvHoq6nUsxsPdDm7kUv1lLnXtxpwBp3X+vuXcCdwEUR11R27v4YULkbP44R7v6mu/8x9/tdwMtAS7RVlZ9n7c49TOd+BdnJmVkr8FHgtqhrGUsU7sW1AANvnd5OgGEQR2Y2EzgZ+EO0lVRGblTxHLAVeNDdg/yewI+AvwF6oy5kFDjwWzNbbmaXH+pAhXtxVuC5IDugODGzBuBu4CvuvjPqeirB3Xvc/SSgFTjNzIIbt5nZx4Ct7r486lpGyZnu/n5gIXBVbpxakMK9uHZg+oDHrcCmiGqRMsjNoO8Gfubu90RdT6W5+w7gEeDCiEuphDOBT+Rm0XcCC8zs/0ZbUuW4+6bc/24F/p3s2LgghXtxS4HZZjbLzDLAxcC9EdckI5Q70fgT4GV3/2HU9VSKmTWb2YTc72uBc4FXoq2q/Nz9q+7e6u4zyf5/c4m7fyHisirCzOpziwAws3rgfGDI1W0K9yLcvRu4GlhM9uTbL9x9ZbRVlZ+Z/Rz4PTDXzNrN7C+irqlCzgQuJdvhPZf79ZGoi6qAacDvzOx5sg3Kg+4e9DLBGJgKPGFmK4BngP9w9weGOlhLIUVEAqTOXUQkQAp3EZEAKdxFRAKkcBcRCZDCXUQkQAp3EZEAKdxFRAL0/wHYx2a0bgWhnQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] @@ -256,11 +255,11 @@ } ], "source": [ - "print('Kinked R consumption function:')\n", - "plotFuncs(KinkyExample.solution[0].cFunc,KinkyExample.solution[0].mNrmMin,5)\n", + "print(\"Kinked R consumption function:\")\n", + "plotFuncs(KinkyExample.solution[0].cFunc, KinkyExample.solution[0].mNrmMin, 5)\n", "\n", - "print('Kinked R marginal propensity to consume:')\n", - "plotFuncsDer(KinkyExample.solution[0].cFunc,KinkyExample.solution[0].mNrmMin,5)" + "print(\"Kinked R marginal propensity to consume:\")\n", + "plotFuncsDer(KinkyExample.solution[0].cFunc, KinkyExample.solution[0].mNrmMin, 5)" ] }, { @@ -293,7 +292,7 @@ "metadata": {}, "outputs": [], "source": [ - "KinkyExample.track_vars = ['mNrmNow','cNrmNow','pLvlNow']\n", + "KinkyExample.track_vars = [\"mNrmNow\", \"cNrmNow\", \"pLvlNow\"]\n", "KinkyExample.initializeSim()\n", "KinkyExample.simulate()" ] @@ -312,7 +311,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -324,9 +323,9 @@ } ], "source": [ - "plt.plot(np.mean(KinkyExample.history['mNrmNow'],axis=1))\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Mean market resources')\n", + "plt.plot(np.mean(KinkyExample.history[\"mNrmNow\"], axis=1))\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Mean market resources\")\n", "plt.show()" ] }, @@ -344,7 +343,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -356,10 +355,10 @@ } ], "source": [ - "plt.plot(np.sort(KinkyExample.aNrmNow),np.linspace(0.,1.,KinkyExample.AgentCount))\n", - "plt.xlabel('End-of-period assets')\n", - "plt.ylabel('Cumulative distribution')\n", - "plt.ylim(-0.01,1.01)\n", + "plt.plot(np.sort(KinkyExample.aNrmNow), np.linspace(0.0, 1.0, KinkyExample.AgentCount))\n", + "plt.xlabel(\"End-of-period assets\")\n", + "plt.ylabel(\"Cumulative distribution\")\n", + "plt.ylim(-0.01, 1.01)\n", "plt.show()" ] }, @@ -371,24 +370,12 @@ "\n", "The smaller point masses in this distribution are due to $\\texttt{HARK}$ drawing simulated income shocks from the discretized distribution, rather than the \"true\" lognormal distributions of shocks. For consumers who ended $t-1$ with $a_{t-1}=0$ in assets, there are only 8 values the transitory shock $\\theta_{t}$ can take on, and thus only 8 values of $m_t$ thus $a_t$ they can achieve; the value of $\\psi_t$ is immaterial to $m_t$ when $a_{t-1}=0$. You can verify this by changing $\\texttt{TranShkCount}$ to some higher value, like 25, in the dictionary above, then running the subsequent cells; the smaller point masses will not be visible to the naked eye." ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { - "@webio": { - "lastCommId": "779f6c5616b04b58baaaa0f6c348270c", - "lastKernelId": "a944b08f-0ae0-4c26-883f-9fab53a82ac3" - }, "jupytext": { "cell_metadata_filter": "collapsed,code_folding", - "formats": "ipynb,py:percent", - "notebook_metadata_filter": "all" + "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3", @@ -405,54 +392,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.9" - }, - "latex_envs": { - "LaTeX_envs_menu_present": true, - "autoclose": false, - "autocomplete": true, - "bibliofile": "biblio.bib", - "cite_by": "apalike", - "current_citInitial": 1, - "eqLabelWithNumbers": true, - "eqNumInitial": 1, - "hotkeys": { - "equation": "Ctrl-E", - "itemize": "Ctrl-I" - }, - "labels_anchors": false, - "latex_user_defs": false, - "report_style_numbering": false, - "user_envs_cfg": false - }, - "varInspector": { - "cols": { - "lenName": 16, - "lenType": 16, - "lenVar": 40 - }, - "kernels_config": { - "python": { - "delete_cmd_postfix": "", - "delete_cmd_prefix": "del ", - "library": "var_list.py", - "varRefreshCmd": "print(var_dic_list())" - }, - "r": { - "delete_cmd_postfix": ") ", - "delete_cmd_prefix": "rm(", - "library": "var_list.r", - "varRefreshCmd": "cat(var_dic_list()) " - } - }, - "types_to_exclude": [ - "module", - "function", - "builtin_function_or_method", - "instance", - "_Feature" - ], - "window_display": false + "version": "3.8.3" } }, "nbformat": 4, diff --git a/examples/ConsIndShockModel/KinkedRconsumerType.py b/examples/ConsIndShockModel/KinkedRconsumerType.py new file mode 100644 index 000000000..6b152264c --- /dev/null +++ b/examples/ConsIndShockModel/KinkedRconsumerType.py @@ -0,0 +1,226 @@ +# --- +# jupyter: +# jupytext: +# cell_metadata_filter: collapsed,code_folding +# formats: ipynb,py:percent +# text_representation: +# extension: .py +# format_name: percent +# format_version: '1.3' +# jupytext_version: 1.5.2 +# kernelspec: +# display_name: Python 3 +# language: python +# name: python3 +# --- + +# %% [markdown] +# # KinkedRconsumerType: Consumption-saving model with idiosyncratic income shocks and different interest rates on borrowing and saving + + +# %% code_folding=[0] +# Initial imports and notebook setup, click arrow to show + +import matplotlib.pyplot as plt +import numpy as np + +from HARK.ConsumptionSaving.ConsIndShockModel import KinkedRconsumerType +from HARK.utilities import plotFuncsDer, plotFuncs + +mystr = lambda number: "{:.4f}".format(number) + +# %% [markdown] +# The module $\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks are fully transitory or fully permanent. +# +# $\texttt{ConsIndShockModel}$ currently includes three models: +# 1. A very basic "perfect foresight" model with no uncertainty. +# 2. A model with risk over transitory and permanent income shocks. +# 3. The model described in (2), with an interest rate for debt that differs from the interest rate for savings. +# +# This notebook provides documentation for the third of these models. +# $\newcommand{\CRRA}{\rho}$ +# $\newcommand{\DiePrb}{\mathsf{D}}$ +# $\newcommand{\PermGroFac}{\Gamma}$ +# $\newcommand{\Rfree}{\mathsf{R}}$ +# $\newcommand{\DiscFac}{\beta}$ + +# %% [markdown] +# ## Statement of "kinked R" model +# +# Consider a small extension to the model faced by $\texttt{IndShockConsumerType}$s: that the interest rate on borrowing $a_t < 0$ is greater than the interest rate on saving $a_t > 0$. Consumers who face this kind of problem are represented by the $\texttt{KinkedRconsumerType}$ class. +# +# For a full theoretical treatment, this model analyzed in [A Theory of the Consumption Function, With +# and Without Liquidity Constraints](http://www.econ2.jhu.edu/people/ccarroll/ATheoryv3JEP.pdf) +# and its [expanded edition](http://www.econ2.jhu.edu/people/ccarroll/ATheoryv3NBER.pdf). +# +# Continuing to work with *normalized* variables (e.g. $m_t$ represents the level of market resources divided by permanent income), the "kinked R" model can be stated as: +# +# \begin{eqnarray*} +# v_t(m_t) &=& \max_{c_t} {~} U(c_t) + \DiscFac (1-\DiePrb_{t+1}) \mathbb{E}_{t} \left[ (\PermGroFac_{t+1}\psi_{t+1})^{1-\CRRA} v_{t+1}(m_{t+1}) \right], \\ +# a_t &=& m_t - c_t, \\ +# a_t &\geq& \underline{a}, \\ +# m_{t+1} &=& \Rfree_t/(\PermGroFac_{t+1} \psi_{t+1}) a_t + \theta_{t+1}, \\ +# \Rfree_t &=& \cases{\Rfree_{boro} \texttt{ if } a_t < 0 \\ +# \Rfree_{save} \texttt{ if } a_t \geq 0},\\ +# \Rfree_{boro} &>& \Rfree_{save}, \\ +# (\psi_{t+1},\theta_{t+1}) &\sim& F_{t+1}, \\ +# \mathbb{E}[\psi]=\mathbb{E}[\theta] &=& 1. +# \end{eqnarray*} + +# %% [markdown] +# ## Solving the "kinked R" model +# +# The solution method for the "kinked R" model is nearly identical to that of the $\texttt{IndShockConsumerType}$ on which it is based, using the endogenous grid method; see the notebook for that model for more information. The only significant difference is that the interest factor varies by $a_t$ across the exogenously chosen grid of end-of-period assets, with a discontinuity in $\Rfree$ at $a_t=0$. +# +# To correctly handle this, the $\texttt{solveConsKinkedR}$ function inserts *two* instances of $a_t=0$ into the grid of $a_t$ values: the first corresponding to $\Rfree_{boro}$ ($a_t = -0$) and the other corresponding to $\Rfree_{save}$ ($a_t = +0$). The two consumption levels (and corresponding endogenous $m_t$ gridpoints) represent points at which the agent's first order condition is satisfied at *exactly* $a_t=0$ at the two different interest factors. In between these two points, the first order condition *does not hold with equality*: the consumer will end the period with exactly $a_t=0$, consuming $c_t=m_t$, but his marginal utility of consumption exceeds the marginal value of saving and is less than the marginal value of borrowing. This generates a consumption function with *two* kinks: two concave portions (for borrowing and saving) with a linear segment of slope 1 in between. + +# %% [markdown] +# ## Example parameter values to construct an instance of KinkedRconsumerType +# +# The parameters required to create an instance of $\texttt{KinkedRconsumerType}$ are nearly identical to those for $\texttt{IndShockConsumerType}$. The only difference is that the parameter $\texttt{Rfree}$ is replaced with $\texttt{Rboro}$ and $\texttt{Rsave}$. +# +# While the parameter $\texttt{CubicBool}$ is required to create a valid $\texttt{KinkedRconsumerType}$ instance, it must be set to $\texttt{False}$; cubic spline interpolation has not yet been implemented for this model. In the future, this restriction will be lifted. +# +# | Parameter | Description | Code | Example value | Time-varying? | +# | :---: | --- | --- | --- | --- | +# | $\DiscFac$ |Intertemporal discount factor | $\texttt{DiscFac}$ | $0.96$ | | +# | $\CRRA $ |Coefficient of relative risk aversion | $\texttt{CRRA}$ | $2.0$ | | +# | $\Rfree_{boro}$ | Risk free interest factor for borrowing | $\texttt{Rboro}$ | $1.20$ | | +# | $\Rfree_{save}$ | Risk free interest factor for saving | $\texttt{Rsave}$ | $1.01$ | | +# | $1 - \DiePrb_{t+1}$ |Survival probability | $\texttt{LivPrb}$ | $[0.98]$ | $\surd$ | +# |$\PermGroFac_{t+1}$|Permanent income growth factor|$\texttt{PermGroFac}$| $[1.01]$ | $\surd$ | +# | $\sigma_\psi $ | Standard deviation of log permanent income shocks | $\texttt{PermShkStd}$ | $[0.1]$ |$\surd$ | +# | $N_\psi $ | Number of discrete permanent income shocks | $\texttt{PermShkCount}$ | $7$ | | +# | $\sigma_\theta $ | Standard deviation of log transitory income shocks | $\texttt{TranShkStd}$ | $[0.2]$ | $\surd$ | +# | $N_\theta $ | Number of discrete transitory income shocks | $\texttt{TranShkCount}$ | $7$ | | +# | $\mho$ | Probability of being unemployed and getting $\theta=\underline{\theta}$ | $\texttt{UnempPrb}$ | $0.05$ | | +# | $\underline{\theta} $ | Transitory shock when unemployed | $\texttt{IncUnemp}$ | $0.3$ | | +# | $\mho^{Ret}$ | Probability of being "unemployed" when retired | $\texttt{UnempPrb}$ | $0.0005$ | | +# | $\underline{\theta}^{Ret} $ | Transitory shock when "unemployed" and retired | $\texttt{IncUnemp}$ | $0.0$ | | +# | $(none)$ | Period of the lifecycle model when retirement begins | $\texttt{T_retire}$ | $0$ | | +# | $(none)$ | Minimum value in assets-above-minimum grid | $\texttt{aXtraMin}$ | $0.001$ | | +# | $(none)$ | Maximum value in assets-above-minimum grid | $\texttt{aXtraMax}$ | $20.0$ | | +# | $(none)$ | Number of points in base assets-above-minimum grid | $\texttt{aXtraCount}$ | $48$ | | +# | $(none)$ | Exponential nesting factor for base assets-above-minimum grid | $\texttt{aXtraNestFac}$ | $3$ | | +# | $(none)$ | Additional values to add to assets-above-minimum grid | $\texttt{aXtraExtra}$ | $None$ | | +# | $\underline{a} $ | Artificial borrowing constraint (normalized) | $\texttt{BoroCnstArt}$ | $None$ | | +# | $(none) $ |Indicator for whether $\texttt{vFunc}$ should be computed | $\texttt{vFuncBool}$ | $True$ | | +# | $(none)$ |Indicator for whether $\texttt{cFunc}$ should use cubic splines | $\texttt{CubicBool}$ | $False$ | | +# |$T$| Number of periods in this type's "cycle" |$\texttt{T_cycle}$| $1$ | | +# |(none)| Number of times the "cycle" occurs |$\texttt{cycles}$| $0$ | | +# +# These example parameters are almostidentical to those used for $\texttt{IndShockExample}$ in the prior notebook, except that the interest rate on borrowing is 20% (like a credit card), and the interest rate on saving is 1%. Moreover, the artificial borrowing constraint has been set to $\texttt{None}$. The cell below defines a parameter dictionary with these example values. + +# %% code_folding=[0] +KinkedRdict = { # Click the arrow to expand this parameter dictionary + # Parameters shared with the perfect foresight model + "CRRA": 2.0, # Coefficient of relative risk aversion + "DiscFac": 0.96, # Intertemporal discount factor + "LivPrb": [0.98], # Survival probability + "PermGroFac": [1.01], # Permanent income growth factor + "BoroCnstArt": None, # Artificial borrowing constraint; imposed minimum level of end-of period assets + # New parameters unique to the "kinked R" model + "Rboro": 1.20, # Interest factor on borrowing (a < 0) + "Rsave": 1.01, # Interest factor on saving (a > 0) + # Parameters that specify the income distribution over the lifecycle (shared with IndShockConsumerType) + "PermShkStd": [0.1], # Standard deviation of log permanent shocks to income + "PermShkCount": 7, # Number of points in discrete approximation to permanent income shocks + "TranShkStd": [0.2], # Standard deviation of log transitory shocks to income + "TranShkCount": 7, # Number of points in discrete approximation to transitory income shocks + "UnempPrb": 0.05, # Probability of unemployment while working + "IncUnemp": 0.3, # Unemployment benefits replacement rate + "UnempPrbRet": 0.0005, # Probability of "unemployment" while retired + "IncUnempRet": 0.0, # "Unemployment" benefits when retired + "T_retire": 0, # Period of retirement (0 --> no retirement) + "tax_rate": 0.0, # Flat income tax rate (legacy parameter, will be removed in future) + # Parameters for constructing the "assets above minimum" grid (shared with IndShockConsumerType) + "aXtraMin": 0.001, # Minimum end-of-period "assets above minimum" value + "aXtraMax": 20, # Maximum end-of-period "assets above minimum" value + "aXtraCount": 48, # Number of points in the base grid of "assets above minimum" + "aXtraNestFac": 3, # Exponential nesting factor when constructing "assets above minimum" grid + "aXtraExtra": [None], # Additional values to add to aXtraGrid + # A few other paramaters (shared with IndShockConsumerType) + "vFuncBool": True, # Whether to calculate the value function during solution + "CubicBool": False, # Preference shocks currently only compatible with linear cFunc + "T_cycle": 1, # Number of periods in the cycle for this agent type + # Parameters only used in simulation (shared with PerfForesightConsumerType) + "AgentCount": 10000, # Number of agents of this type + "T_sim": 500, # Number of periods to simulate + "aNrmInitMean": -6.0, # Mean of log initial assets + "aNrmInitStd": 1.0, # Standard deviation of log initial assets + "pLvlInitMean": 0.0, # Mean of log initial permanent income + "pLvlInitStd": 0.0, # Standard deviation of log initial permanent income + "PermGroFacAgg": 1.0, # Aggregate permanent income growth factor + "T_age": None, # Age after which simulated agents are automatically killed +} + +# %% [markdown] +# ## Solving and examining the solution of the "kinked R" model +# +# The cell below creates an infinite horizon instance of $\texttt{KinkedRconsumerType}$ and solves its model by calling its $\texttt{solve}$ method. + +# %% +KinkyExample = KinkedRconsumerType(**KinkedRdict) +KinkyExample.cycles = 0 # Make the example infinite horizon +KinkyExample.solve() + +# %% [markdown] +# An element of a $\texttt{KinkedRconsumerType}$'s solution will have all the same attributes as that of a $\texttt{IndShockConsumerType}$; see that notebook for details. +# +# We can plot the consumption function of our "kinked R" example, as well as the MPC: + +# %% +print("Kinked R consumption function:") +plotFuncs(KinkyExample.solution[0].cFunc, KinkyExample.solution[0].mNrmMin, 5) + +print("Kinked R marginal propensity to consume:") +plotFuncsDer(KinkyExample.solution[0].cFunc, KinkyExample.solution[0].mNrmMin, 5) + +# %% [markdown] +# ## Simulating the "kinked R" model +# +# In order to generate simulated data, an instance of $\texttt{KinkedRconsumerType}$ needs to know how many agents there are that share these particular parameters (and are thus *ex ante* homogeneous), the distribution of states for newly "born" agents, and how many periods to simulated. These simulation parameters are described in the table below, along with example values. +# +# | Description | Code | Example value | +# | :---: | --- | --- | +# | Number of consumers of this type | $\texttt{AgentCount}$ | $10000$ | +# | Number of periods to simulate | $\texttt{T_sim}$ | $500$ | +# | Mean of initial log (normalized) assets | $\texttt{aNrmInitMean}$ | $-6.0$ | +# | Stdev of initial log (normalized) assets | $\texttt{aNrmInitStd}$ | $1.0$ | +# | Mean of initial log permanent income | $\texttt{pLvlInitMean}$ | $0.0$ | +# | Stdev of initial log permanent income | $\texttt{pLvlInitStd}$ | $0.0$ | +# | Aggregrate productivity growth factor | $\texttt{PermGroFacAgg}$ | $1.0$ | +# | Age after which consumers are automatically killed | $\texttt{T_age}$ | $None$ | +# +# Here, we will simulate 10,000 consumers for 500 periods. All newly born agents will start with permanent income of exactly $P_t = 1.0 = \exp(\texttt{pLvlInitMean})$, as $\texttt{pLvlInitStd}$ has been set to zero; they will have essentially zero assets at birth, as $\texttt{aNrmInitMean}$ is $-6.0$; assets will be less than $1\%$ of permanent income at birth. +# +# These example parameter values were already passed as part of the parameter dictionary that we used to create $\texttt{KinkyExample}$, so it is ready to simulate. We need to set the $\texttt{track_vars}$ attribute to indicate the variables for which we want to record a *history*. + +# %% +KinkyExample.track_vars = ["mNrmNow", "cNrmNow", "pLvlNow"] +KinkyExample.initializeSim() +KinkyExample.simulate() + +# %% [markdown] +# We can plot the average (normalized) market resources in each simulated period: + +# %% +plt.plot(np.mean(KinkyExample.history["mNrmNow"], axis=1)) +plt.xlabel("Time") +plt.ylabel("Mean market resources") +plt.show() + +# %% [markdown] +# Now let's plot the distribution of (normalized) assets $a_t$ for the current population, after simulating for $500$ periods; this should be fairly close to the long run distribution: + +# %% +plt.plot(np.sort(KinkyExample.aNrmNow), np.linspace(0.0, 1.0, KinkyExample.AgentCount)) +plt.xlabel("End-of-period assets") +plt.ylabel("Cumulative distribution") +plt.ylim(-0.01, 1.01) +plt.show() + +# %% [markdown] +# We can see there's a significant point mass of consumers with *exactly* $a_t=0$; these are consumers who do not find it worthwhile to give up a bit of consumption to begin saving (because $\Rfree_{save}$ is too low), and also are not willing to finance additional consumption by borrowing (because $\Rfree_{boro}$ is too high). +# +# The smaller point masses in this distribution are due to $\texttt{HARK}$ drawing simulated income shocks from the discretized distribution, rather than the "true" lognormal distributions of shocks. For consumers who ended $t-1$ with $a_{t-1}=0$ in assets, there are only 8 values the transitory shock $\theta_{t}$ can take on, and thus only 8 values of $m_t$ thus $a_t$ they can achieve; the value of $\psi_t$ is immaterial to $m_t$ when $a_{t-1}=0$. You can verify this by changing $\texttt{TranShkCount}$ to some higher value, like 25, in the dictionary above, then running the subsequent cells; the smaller point masses will not be visible to the naked eye. diff --git a/examples/ConsIndShockModel/PerfForesightConsumerType.ipynb b/examples/ConsIndShockModel/PerfForesightConsumerType.ipynb index 459a127a6..e897103d6 100644 --- a/examples/ConsIndShockModel/PerfForesightConsumerType.ipynb +++ b/examples/ConsIndShockModel/PerfForesightConsumerType.ipynb @@ -2,9 +2,11 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "lines_to_next_cell": 2 + }, "source": [ - "# PerfForesightConsumerType" + "# PerfForesightConsumerType: Perfect foresight consumption-saving" ] }, { @@ -18,22 +20,26 @@ "outputs": [], "source": [ "# Initial imports and notebook setup, click arrow to show\n", - "from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType\n", - "from HARK.utilities import plotFuncs\n", - "from time import clock\n", + "\n", + "from copy import copy\n", + "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", - "mystr = lambda number : \"{:.4f}\".format(number)" + "\n", + "from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType\n", + "from HARK.utilities import plotFuncs\n", + "\n", + "mystr = lambda number: \"{:.4f}\".format(number)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The module $\\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks that are either fully transitory or fully permanent.\n", + "The module $\\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks are fully transitory or fully permanent.\n", "\n", "$\\texttt{ConsIndShockModel}$ currently includes three models:\n", - "1. A very basic \"perfect foresight\" model with no uncertainty (shocks are zero).\n", + "1. A very basic \"perfect foresight\" model with no uncertainty.\n", "2. A model with risk over transitory and permanent income shocks.\n", "3. The model described in (2), with an interest rate for debt that differs from the interest rate for savings.\n", "\n", @@ -49,35 +55,41 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Statement of the model\n", + "## Statement of perfect foresight consumption-saving model\n", "\n", - "The $\\texttt{PerfForesightConsumerType}$ class solves the problem of a consumer with Constant Relative Risk Aversion utility \n", + "The $\\texttt{PerfForesightConsumerType}$ class the problem of a consumer with Constant Relative Risk Aversion utility\n", "${\\CRRA}$\n", "\\begin{equation}\n", "U(C) = \\frac{C^{1-\\CRRA}}{1-\\rho},\n", "\\end{equation}\n", - "who has perfect foresight about everything except whether he will die between the end of period $t$ and the beginning of period $t+1$. Permanent labor income $P_t$ grows from period $t$ to period $t+1$ by factor $\\PermGroFac_{t+1}$. The consumer faces no artificial borrowing constraint: He is able to borrow against his entire future stream of income.\n", + "has perfect foresight about everything except whether he will die between the end of period $t$ and the beginning of period $t+1$, which occurs with probability $\\DiePrb_{t+1}$. Permanent labor income $P_t$ grows from period $t$ to period $t+1$ by factor $\\PermGroFac_{t+1}$.\n", "\n", - "At the beginning of period $t$, the consumer has market resources $M_t$ (which includes both market wealth and currrent income) and must choose how much to consume $C_t$ and how much to retain in a riskless asset $A_t$, which will earn return factor $\\Rfree$. The agent's flow of future utility $U(C_{t+n})$ from consumption is geometrically discounted by factor $\\DiscFac$ per period. The consumer only experiences future value if he survives, which occurs with probability $1-\\DiePrb_{t+1}$.\n", + "At the beginning of period $t$, the consumer has an amount of market resources $M_t$ (which includes both market wealth and currrent income) and must choose how much of those resources to consume $C_t$ and how much to retain in a riskless asset $A_t$, which will earn return factor $\\Rfree$. The consumer cannot necessarily borrow arbitarily; instead, he might be constrained to have a wealth-to-income ratio at least as great as some \"artificial borrowing constraint\" $\\underline{a} \\leq 0$.\n", "\n", - "For parallelism with the treatment of more complicated problems, we write the problem rather elaborately in Bellman form as:\n", + "The agent's flow of future utility $U(C_{t+n})$ from consumption is geometrically discounted by factor $\\DiscFac$ per period. If the consumer dies, he receives zero utility flow for the rest of time.\n", + "\n", + "The agent's problem can be written in Bellman form as:\n", "\n", "\\begin{eqnarray*}\n", "V_t(M_t,P_t) &=& \\max_{C_t}~U(C_t) ~+ \\DiscFac (1 - \\DiePrb_{t+1}) V_{t+1}(M_{t+1},P_{t+1}), \\\\\n", "& s.t. & \\\\\n", "A_t &=& M_t - C_t, \\\\\n", + "A_t/P_t &\\geq& \\underline{a}, \\\\\n", "M_{t+1} &=& \\Rfree A_t + Y_{t+1}, \\\\\n", - "Y_{t+1} &=& P_{t+1}, \\\\ \n", + "Y_{t+1} &=& P_{t+1}, \\\\\n", "P_{t+1} &=& \\PermGroFac_{t+1} P_t.\n", "\\end{eqnarray*}\n", "\n", - "The parameters of the consumer's problem are the coefficient of relative risk aversion $\\CRRA$, the intertemporal discount factor $\\DiscFac$, an interest factor $\\Rfree$, and age-varying sequences of the permanent income growth factor $\\PermGroFac_t$ and survival probability $(1 - \\DiePrb_t)$. [These lecture notes](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA) show that under these assumptions the problem can be transformed into an equivalent problem stated in terms of *normalized* variables (represented in lower case); all real variables are divided by permanent income $P_t$ and value is divided by $P_t^{1-\\CRRA}$. The Bellman form of the normalized model (see the lecture notes for details) is:\n", + "The consumer's problem is characterized by a coefficient of relative risk aversion $\\CRRA$, an intertemporal discount factor $\\DiscFac$, an interest factor $\\Rfree$, and age-varying sequences of the permanent income growth factor $\\PermGroFac_t$ and survival probability $(1 - \\DiePrb_t)$.\n", + "\n", + "While it does not reduce the computational complexity of the problem (as permanent income is deterministic, given its initial condition $P_0$), HARK represents this problem with *normalized* variables (represented in lower case), dividing all real variables by permanent income $P_t$ and utility levels by $P_t^{1-\\CRRA}$. The Bellman form of the model thus reduces to:\n", "\n", "\\begin{eqnarray*}\n", "v_t(m_t) &=& \\max_{c_t}~U(c_t) ~+ \\DiscFac (1 - \\DiePrb_{t+1}) \\PermGroFac_{t+1}^{1-\\CRRA} v_{t+1}(m_{t+1}), \\\\\n", "& s.t. & \\\\\n", "a_t &=& m_t - c_t, \\\\\n", - "m_{t+1} &=& a_t (\\Rfree/\\PermGroFac_{t+1} )+ 1.\n", + "a_t &\\geq& \\underline{a}, \\\\\n", + "m_{t+1} &=& \\Rfree/\\PermGroFac_{t+1} a_t + 1.\n", "\\end{eqnarray*}" ] }, @@ -87,28 +99,32 @@ "source": [ "## Solution method for PerfForesightConsumerType\n", "\n", - "Because of the assumptions of CRRA utility, no risk other than mortality, and no artificial borrowing constraint, the problem has a closed form solution in which consumption is a linear function of resources, and the utility-inverse of the value function is also linear (that is, $u^{-1}(v)$ is linear in $m$). Details of the mathematical solution of this model can be found in the lecture notes [PerfForesightCRRA](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA). \n", + "Because of the assumptions of CRRA utility, no risk other than mortality, and no artificial borrowing constraint, the problem has a closed form solution. In fact, the consumption function is perfectly linear, and the value function composed with the inverse utility function is also linear. The mathematical solution of this model is described in detail in the lecture notes [PerfForesightCRRA](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA).\n", "\n", - "The one period problem for this model is solved by the function $\\texttt{solveConsPerfForesight}$, which creates an instance of the class $\\texttt{ConsPerfForesightSolver}$. To construct an instance of the class $\\texttt{PerfForesightConsumerType}$, several parameters must be passed to this constructor. " + "The one period problem for this model is solved by the function $\\texttt{solveConsPerfForesight}$, which creates an instance of the class $\\texttt{ConsPerfForesightSolver}$. To construct an instance of the class $\\texttt{PerfForesightConsumerType}$, several parameters must be passed to its constructor as shown in the table below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Example parameter values\n", + "## Example parameter values to construct an instance of PerfForesightConsumerType\n", "\n", "| Parameter | Description | Code | Example value | Time-varying? |\n", "| :---: | --- | --- | --- | --- |\n", "| $\\DiscFac$ |Intertemporal discount factor | $\\texttt{DiscFac}$ | $0.96$ | |\n", - "| $\\CRRA$|Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", + "| $\\CRRA $ |Coefficient of relative risk aversion | $\\texttt{CRRA}$ | $2.0$ | |\n", "| $\\Rfree$ | Risk free interest factor | $\\texttt{Rfree}$ | $1.03$ | |\n", "| $1 - \\DiePrb_{t+1}$ |Survival probability | $\\texttt{LivPrb}$ | $[0.98]$ | $\\surd$ |\n", "|$\\PermGroFac_{t+1}$|Permanent income growth factor|$\\texttt{PermGroFac}$| $[1.01]$ | $\\surd$ |\n", + "|$\\underline{a}$|Artificial borrowing constraint|$\\texttt{BoroCnstArt}$| $None$ | |\n", + "|$(none)$|Maximum number of gridpoints in consumption function |$\\texttt{aXtraCount}$| $200$ | |\n", "|$T$| Number of periods in this type's \"cycle\" |$\\texttt{T_cycle}$| $1$ | |\n", "|(none)| Number of times the \"cycle\" occurs |$\\texttt{cycles}$| $0$ | |\n", "\n", - "Note that the survival probability and income growth factor have time subscripts; likewise, the example values for these parameters are *lists* rather than simply single floats. This is because those parameters are in principle *time-varying*: their values can depend on which period of the problem the agent is in (for example, mortality probability depends on age). All time-varying parameters *must* be specified as lists, even when the model is being solved for an infinite horizon case where in practice the parameter takes the same value in every period.\n", + "Note that the survival probability and income growth factor have time subscripts; likewise, the example values for these parameters are *lists* rather than simply single floats. This is because those parameters are *time-varying*: their values can depend on which period of the problem the agent is in. All time-varying parameters *must* be specified as lists, even if the same value occurs in each period for this type.\n", + "\n", + "The artificial borrowing constraint can be any non-positive $\\texttt{float}$, or it can be $\\texttt{None}$ to indicate no artificial borrowing constraint. The maximum number of gridpoints in the consumption function is only relevant if the borrowing constraint is not $\\texttt{None}$; without an upper bound on the number of gridpoints, kinks in the consumption function will propagate indefinitely in an infinite horizon model if there is a borrowing constraint, eventually resulting in an overflow error. If there is no artificial borrowing constraint, then the number of gridpoints used to represent the consumption function is always exactly two.\n", "\n", "The last two parameters in the table specify the \"nature of time\" for this type: the number of (non-terminal) periods in this type's \"cycle\", and the number of times that the \"cycle\" occurs. *Every* subclass of $\\texttt{AgentType}$ uses these two code parameters to define the nature of time. Here, $\\texttt{T_cycle}$ has the value $1$, indicating that there is exactly one period in the cycle, while $\\texttt{cycles}$ is $0$, indicating that the cycle is repeated in *infinite* number of times-- it is an infinite horizon model, with the same \"kind\" of period repeated over and over.\n", "\n", @@ -123,23 +139,22 @@ "cell_type": "code", "execution_count": 2, "metadata": { - "code_folding": [ - 0 - ] + "code_folding": [] }, "outputs": [], "source": [ "PerfForesightDict = {\n", " # Parameters actually used in the solution method\n", - " \"CRRA\" : 2.0, # Coefficient of relative risk aversion\n", - " \"Rfree\" : 1.03, # Interest factor on assets\n", - " \"DiscFac\" : 0.96, # Default intertemporal discount factor\n", - " \"LivPrb\" : [0.98], # Survival probability\n", - " \"PermGroFac\" :[1.01], # Permanent income growth factor\n", - " \n", + " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n", + " \"Rfree\": 1.03, # Interest factor on assets\n", + " \"DiscFac\": 0.96, # Default intertemporal discount factor\n", + " \"LivPrb\": [0.98], # Survival probability\n", + " \"PermGroFac\": [1.01], # Permanent income growth factor\n", + " \"BoroCnstArt\": None, # Artificial borrowing constraint\n", + " \"aXtraCount\": 200, # Maximum number of gridpoints in consumption function\n", " # Parameters that characterize the nature of time\n", - " \"T_cycle\" : 1, # Number of periods in the cycle for this agent type\n", - " \"cycles\" : 0 # Number of times the cycle occurs (0 --> infinitely repeated)\n", + " \"T_cycle\": 1, # Number of periods in the cycle for this agent type\n", + " \"cycles\": 0, # Number of times the cycle occurs (0 --> infinitely repeated)\n", "}" ] }, @@ -147,7 +162,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Inspecting the solution\n", + "## Solving and examining the solution of the perfect foresight model\n", "\n", "With the dictionary we have just defined, we can create an instance of $\\texttt{PerfForesightConsumerType}$ by passing the dictionary to the class (as if the class were a function). This instance can then be solved by invoking its $\\texttt{solve}$ method." ] @@ -179,7 +194,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "[]\n" + "[]\n" ] } ], @@ -191,7 +206,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Each element of $\\texttt{solution}$ has a few attributes. To see all of them, we can use the $\\texttt{vars}$ built in function: the consumption functions are instantiated in the attribute $\\texttt{cFunc}$ of each element of $\\texttt{ConsumerType.solution}$. This method creates a (time varying) attribute $\\texttt{cFunc}$ that contains a list of consumption functions by age." + "Each element of $\\texttt{solution}$ has a few attributes. To see all of them, we can use the \\texttt{vars} built in function:\n", + "\n", + "the consumption functions reside in the attribute $\\texttt{cFunc}$ of each element of $\\texttt{ConsumerType.solution}$. This method creates a (time varying) attribute $\\texttt{cFunc}$ that contains a list of consumption functions." ] }, { @@ -203,7 +220,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "{'cFunc': , 'vFunc': , 'vPfunc': , 'vPPfunc': , 'mNrmMin': -50.49994992551661, 'hNrm': 50.49994992551661, 'MPCmin': 0.04428139169919579, 'MPCmax': 0.04428139169919579, 'mNrmSS': -50.49991081984768}\n" + "{'cFunc': , 'vFunc': , 'vPfunc': , 'vPPfunc': , 'mNrmMin': -50.49994992551661, 'hNrm': 50.49994992551661, 'MPCmin': 0.04428139169919579, 'MPCmax': 0.04428139169919579, 'mNrmSS': -50.49991081984768}\n" ] } ], @@ -215,7 +232,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The two most important attributes of a single period solution are the (normalized) consumption function $\\texttt{cFunc}$ and the (normalized) value function $\\texttt{vFunc}$; the marginal value function $\\texttt{vPfunc}$ is also constructed. Let's plot those functions near the lower bound of the permissible state space (the attribute $\\texttt{mNrmMin}$ tells us the lower bound of $m_t$ where the consumption function is defined)." + "The two most important attributes of a single period solution of this model are the (normalized) consumption function $\\texttt{cFunc}$ and the (normalized) value function $\\texttt{vFunc}$. Let's plot those functions near the lower bound of the permissible state space (the attribute $\\texttt{mNrmMin}$ tells us the lower bound of $m_t$ where the consumption function is defined)." ] }, { @@ -232,7 +249,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -244,9 +261,9 @@ } ], "source": [ - "print('Linear perfect foresight consumption function:')\n", + "print(\"Linear perfect foresight consumption function:\")\n", "mMin = PFexample.solution[0].mNrmMin\n", - "plotFuncs(PFexample.solution[0].cFunc,mMin,mMin+10.)" + "plotFuncs(PFexample.solution[0].cFunc, mMin, mMin + 10.0)" ] }, { @@ -263,7 +280,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -275,117 +292,82 @@ } ], "source": [ - "print('Perfect foresight value function:')\n", - "plotFuncs(PFexample.solution[0].vFunc,mMin+0.1,mMin+10.1)" + "print(\"Perfect foresight value function:\")\n", + "plotFuncs(PFexample.solution[0].vFunc, mMin + 0.1, mMin + 10.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Solution Method\n", - "\n", - "\n", - "### Recursive Formula for $\\kappa_{t}$\n", - "\n", - "The paper [BufferStockTheory](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/) has a few other results that are used in the solution code. One is [the recursive formula for the MPC](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/#MPCnvrs). Starting with the last period, in which $\\kappa_{T}=1$, the inverse MPC's (and therefore the MPC's themselves) can be constructed using the recursive formula:\n", - "\n", - "\\begin{align}\n", - "\\kappa_{t}^{-1} & = & 1 + \\kappa_{t+1}^{-1}(\\Rfree \\beta)^{1/\\rho}/G \n", - "\\end{align}\n", - "\n", - "### Consumption Function\n", - "\n", - "For the perfect foresight problem, there is a well-known [analytical solution]( http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/#cFuncAnalytical) for the consumption function: Calling $o_{t}$ 'overall wealth' (including market wealth plus human wealth $h_{t}$) and designating the marginal propensity to consume in period $t$ by $\\kappa_{t}$:\n", - "\n", - "\\begin{align}\n", - "\\mathrm{c}_{t} & = o_{t}\\kappa_{t}\n", - "\\end{align}\n", - "\n", - "and in our normalized model $o_{t} = m_{t}-1+h_{t}$ (the '-1' term subtracts off the normalized current income of 1 from market resources $m$ which were market wealth plus current income).\n", - "\n", - "### Value Function\n", - "\n", - "A convenient feature of the perfect foresight problem is that the value function has a simple [analytical form](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/#vFuncAnalytical):\n", + "An element of $\\texttt{solution}$ also includes the (normalized) marginal value function $\\texttt{vPfunc}$, and the lower and upper bounds of the marginal propensity to consume (MPC) $\\texttt{MPCmin}$ and $\\texttt{MPCmax}$. Note that with a linear consumption function, the MPC is constant, so its lower and upper bound are identical.\n", "\n", - "\\begin{align}\n", - "\\mathrm{v}_{t} & = \\mathrm{u}(\\mathrm{c}_{t}(m))\\kappa_{t}^{-1}\\\\\n", - " &= \\mathrm{u}(o_{t} \\kappa_{t}) \\kappa_{t}^{-1} \\\\ \n", - " &= \\mathrm{u}(o_{t})\\kappa_{t}^{1-\\rho} \\kappa_{t}^{-1} \\\\\n", - " &= \\mathrm{u}(o_{t})\\kappa_{t}^{-\\rho}\n", - "\\end{align}\n", + "### Liquidity constrained perfect foresight example\n", "\n", - "This means that the utility-inverse of the value function, ${\\scriptsize \\Lambda} \\equiv \\mathrm{u}^{-1}(\\mathrm{v})$, is linear:\n", - "\n", - "\\begin{align}\n", - "\\scriptsize \\Lambda_{t} & = o_{t} \\kappa_{t}^{-\\rho/(1-\\rho)}\n", - "\\end{align}\n", - "\n", - "When uncertainty or liquidity constraints are added to the problem, the ${\\scriptsize \\Lambda}$ function is no longer linear. But even in these cases, the utility-inverse of the value function is much better behaved (e.g., closer to linear; bounded over any feasible finite range of $m$) than the uninverted function (which, for example, approaches $-\\infty$ as $m$ approaches its lower bound).\n", - "\n", - "Our procedure will therefore generically be to construct the inverse value function, and to obtain the value function from it by uninverting. That is, we construct an interpolating approximation of $\\scriptsize \\Lambda_{t}$ and compute value on-the-fly from\n", - "\n", - "\\begin{align}\n", - "\\mathrm{v}_{t}(m) & = \\mathrm{u}({\\scriptsize \\Lambda_{t}}(m))\n", - "\\end{align}\n", - "\n", - "In this case, the interpolation is exact, not an approximation: We need only two points to construct a line, so we choose the minimum possible value of normalized market resources, $\\texttt{mNrmMin}$, where $o_{t}=0$ so that $c_{t}=0$, and that minimum plus 1, where the inverted value function will have the value $\\kappa_{t}^{-\\rho/(1-\\rho)}$. From these we construct $vFuncNvrs$ as a linear interpolating function (which automatically extrapolates to the whole number line).\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Checking Solution Conditions\n", - "\n", - "The code performs tests for whether the supplied parameter values meet various conditions that determine the properties of the solution. Some conditions (like the Finite Human Wealth Condition) are required for the model to have a sensible solution, and if these conditions are violated the code generates a warning message. Other conditions govern characteristics of the model like whether consumption is falling (whether the consumer is 'absolutely impatient'). All conditions can manually be performed using the syntax below. The function returns \"False\" if none of the key conditions has been violated." + "Without an artificial borrowing constraint, a perfect foresight consumer is free to borrow against the PDV of his entire future stream of labor income-- his \"human wealth\" $\\texttt{hNrm}$-- and he will consume a constant proportion of his total wealth (market resources plus human wealth). If we introduce an artificial borrowing constraint, both of these features vanish. In the cell below, we define a parameter dictionary that prevents the consumer from borrowing *at all*, create and solve a new instance of $\\texttt{PerfForesightConsumerType}$ with it, and then plot its consumption function." ] }, { "cell_type": "code", "execution_count": 8, - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\n", - "The value of the absolute impatience factor (AIF) for the supplied parameter values satisfies the Absolute Impatience Condition.\n", - " Because the AIF < 1, the absolute amount of consumption is expected to fall over time.\n", - "\n", - "\n", - "The value of the Growth Patience Factor for the supplied parameter values satisfies the Perfect Foresight Growth Impatience Condition.\n", - " Therefore, for a perfect foresight consumer, the ratio of individual wealth to permanent income will fall indefinitely.\n", - "\n", - "\n", - "The value of the Return Patience Factor for the supplied parameter values satisfies the Return Impatience Condition.\n", - "\n", - "The Finite Human wealth factor value for the supplied parameter values satisfies the Finite Human Wealth Condition.\n" + "Liquidity constrained perfect foresight consumption function:\n" ] + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "PFexample.checkConditions(verbose=True)" + "LiqConstrDict = copy(PerfForesightDict)\n", + "LiqConstrDict[\"BoroCnstArt\"] = 0.0 # Set the artificial borrowing constraint to zero\n", + "\n", + "LiqConstrExample = PerfForesightConsumerType(**LiqConstrDict)\n", + "LiqConstrExample.cycles = 0 # Make this type be infinite horizon\n", + "LiqConstrExample.solve()\n", + "\n", + "print(\"Liquidity constrained perfect foresight consumption function:\")\n", + "plotFuncs(LiqConstrExample.solution[0].cFunc, 0.0, 10.0)" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ - "An element of $\\texttt{solution}$ also includes the (normalized) marginal value function $\\texttt{vPfunc}$, and the lower and upper bounds of the marginal propensity to consume (MPC) $\\texttt{MPCmin}$ and $\\texttt{MPCmax}$. Note that with a linear consumption function, the MPC is constant, so its lower and upper bound are identical." + "At this time, the value function for a perfect foresight consumer with an artificial borrowing constraint is not computed nor included as part of its $\\texttt{solution}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Simulating the model\n", + "## Simulating the perfect foresight consumer model\n", "\n", "Suppose we wanted to simulate many consumers who share the parameter values that we passed to $\\texttt{PerfForesightConsumerType}$-- an *ex ante* homogeneous *type* of consumers. To do this, our instance would have to know *how many* agents there are of this type, as well as their initial levels of assets $a_t$ and permanent income $P_t$.\n", "\n", - "### Setting Parameters\n", + "### Setting simulation parameters\n", "\n", "Let's fill in this information by passing another dictionary to $\\texttt{PFexample}$ with simulation parameters. The table below lists the parameters that an instance of $\\texttt{PerfForesightConsumerType}$ needs in order to successfully simulate its model using the $\\texttt{simulate}$ method.\n", "\n", @@ -413,30 +395,34 @@ "cell_type": "code", "execution_count": 9, "metadata": { - "code_folding": [ - 0 - ] + "pycharm": { + "name": "#%%\n" + } }, "outputs": [], "source": [ - "# Create parameter values necessary for simulation\n", "SimulationParams = {\n", - " \"AgentCount\" : 10000, # Number of agents of this type\n", - " \"T_sim\" : 120, # Number of periods to simulate\n", - " \"aNrmInitMean\" : -6.0, # Mean of log initial assets\n", - " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets\n", - " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income\n", - " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income\n", - " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor\n", - " \"T_age\" : None, # Age after which simulated agents are automatically killed\n", + " \"AgentCount\": 10000, # Number of agents of this type\n", + " \"T_sim\": 120, # Number of periods to simulate\n", + " \"aNrmInitMean\": -6.0, # Mean of log initial assets\n", + " \"aNrmInitStd\": 1.0, # Standard deviation of log initial assets\n", + " \"pLvlInitMean\": 0.0, # Mean of log initial permanent income\n", + " \"pLvlInitStd\": 0.0, # Standard deviation of log initial permanent income\n", + " \"PermGroFacAgg\": 1.0, # Aggregate permanent income growth factor\n", + " \"T_age\": None, # Age after which simulated agents are automatically killed\n", "}\n", "\n", - "PFexample(**SimulationParams) # This implicitly uses the assignParameters method of AgentType" + "# This implicitly uses the assignParameters method of AgentType\n", + "PFexample(**SimulationParams)" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "To generate simulated data, we need to specify which variables we want to track the \"history\" of for this instance. To do so, we set the $\\texttt{track_vars}$ attribute of our $\\texttt{PerfForesightConsumerType}$ instance to be a list of strings with the simulation variables we want to track.\n", "\n", @@ -453,21 +439,24 @@ "cell_type": "code", "execution_count": 10, "metadata": { - "code_folding": [ - 0 - ] + "pycharm": { + "name": "#%%\n" + } }, "outputs": [], "source": [ - "# Create PFexample object\n", - "PFexample.track_vars = ['mNrmNow']\n", + "PFexample.track_vars = [\"mNrmNow\"]\n", "PFexample.initializeSim()\n", "PFexample.simulate()" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "Each simulation variable $\\texttt{X}$ named in $\\texttt{track_vars}$ will have the *history* of that variable for each agent stored in the attribute $\\texttt{X_hist}$ as an array of shape $(\\texttt{T_sim},\\texttt{AgentCount})$. To see that the simulation worked as intended, we can plot the mean of $m_t$ in each simulated period:" ] @@ -476,14 +465,14 @@ "cell_type": "code", "execution_count": 11, "metadata": { - "code_folding": [ - 0 - ] + "pycharm": { + "name": "#%%\n" + } }, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -495,18 +484,21 @@ } ], "source": [ - "# Plot market resources over time\n", - "plt.plot(np.mean(PFexample.history['mNrmNow'],axis=1))\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Mean normalized market resources')\n", + "plt.plot(np.mean(PFexample.history[\"mNrmNow\"], axis=1))\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Mean normalized market resources\")\n", "plt.show()" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ - "A perfect foresight consumer can borrow against the PDV of his future income-- his human wealth-- and thus as time goes on, our simulated impatient agents approach the (very negative) steady state level of $m_t$ while being steadily replaced with consumers with roughly $m_t=1$.\n", + "A perfect foresight consumer can borrow against the PDV of his future income-- his human wealth-- and thus as time goes on, our simulated agents approach the (very negative) steady state level of $m_t$ while being steadily replaced with consumers with roughly $m_t=1$.\n", "\n", "The slight wiggles in the plotted curve are due to consumers randomly dying and being replaced; their replacement will have an initial state drawn from the distributions specified by the user. To see the current distribution of ages, we can look at the attribute $\\texttt{t_age}$." ] @@ -515,14 +507,14 @@ "cell_type": "code", "execution_count": 12, "metadata": { - "code_folding": [ - 0 - ] + "pycharm": { + "name": "#%%\n" + } }, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -534,18 +526,21 @@ } ], "source": [ - "# Plot the CDF\n", "N = PFexample.AgentCount\n", - "F = np.linspace(0.,1.,N)\n", - "plt.plot(np.sort(PFexample.t_age),F)\n", - "plt.xlabel('Current age of consumers')\n", - "plt.ylabel('Cumulative distribution')\n", + "F = np.linspace(0.0, 1.0, N)\n", + "plt.plot(np.sort(PFexample.t_age), F)\n", + "plt.xlabel(\"Current age of consumers\")\n", + "plt.ylabel(\"Cumulative distribution\")\n", "plt.show()" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "The distribution is (discretely) exponential, with a point mass at 120 with consumers who have survived since the beginning of the simulation.\n", "\n", @@ -560,14 +555,14 @@ "cell_type": "code", "execution_count": 13, "metadata": { - "code_folding": [ - 0 - ] + "pycharm": { + "name": "#%%\n" + } }, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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" ] @@ -579,33 +574,21 @@ } ], "source": [ - "# The final resulting distribution is reasonably coherent\n", "PFexample.initializeSim()\n", "PFexample.simulate(80)\n", - "PFexample.aNrmNow += -5. # Adjust all simulated consumers' assets downward by 5\n", + "PFexample.aNrmNow += -5.0 # Adjust all simulated consumers' assets downward by 5\n", "PFexample.simulate(40)\n", "\n", - "plt.plot(np.mean(PFexample.history['mNrmNow'],axis=1))\n", - "plt.xlabel('Time')\n", - "plt.ylabel('Mean normalized market resources')\n", + "plt.plot(np.mean(PFexample.history[\"mNrmNow\"], axis=1))\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Mean normalized market resources\")\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { - "@webio": { - "lastCommId": "779f6c5616b04b58baaaa0f6c348270c", - "lastKernelId": "a944b08f-0ae0-4c26-883f-9fab53a82ac3" - }, "jupytext": { - "cell_metadata_filter": "collapsed,code_folding", + "cell_metadata_filter": "collapsed,code_folding,pycharm", "formats": "ipynb,py:percent" }, "kernelspec": { @@ -623,51 +606,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.9" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": true - }, - "varInspector": { - "cols": { - "lenName": 16, - "lenType": 16, - "lenVar": 40 - }, - "kernels_config": { - "python": { - "delete_cmd_postfix": "", - "delete_cmd_prefix": "del ", - "library": "var_list.py", - "varRefreshCmd": "print(var_dic_list())" - }, - "r": { - "delete_cmd_postfix": ") ", - "delete_cmd_prefix": "rm(", - "library": "var_list.r", - "varRefreshCmd": "cat(var_dic_list()) " - } - }, - "types_to_exclude": [ - "module", - "function", - "builtin_function_or_method", - "instance", - "_Feature" - ], - "window_display": false + "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/examples/ConsIndShockModel/PerfForesightConsumerType.py b/examples/ConsIndShockModel/PerfForesightConsumerType.py index 9da14bc25..8925484ec 100644 --- a/examples/ConsIndShockModel/PerfForesightConsumerType.py +++ b/examples/ConsIndShockModel/PerfForesightConsumerType.py @@ -6,8 +6,8 @@ # text_representation: # extension: .py # format_name: percent -# format_version: '1.2' -# jupytext_version: 1.2.4 +# format_version: '1.3' +# jupytext_version: 1.5.2 # kernelspec: # display_name: Python 3 # language: python @@ -15,22 +15,27 @@ # --- # %% [markdown] -# # PerfForesightConsumerType +# # PerfForesightConsumerType: Perfect foresight consumption-saving -# %% {"code_folding": [0]} + +# %% code_folding=[0] # Initial imports and notebook setup, click arrow to show -from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType -from HARK.utilities import plotFuncs -from time import clock + +from copy import copy + import matplotlib.pyplot as plt import numpy as np -mystr = lambda number : "{:.4f}".format(number) + +from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType +from HARK.utilities import plotFuncs + +mystr = lambda number: "{:.4f}".format(number) # %% [markdown] -# The module $\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks that are either fully transitory or fully permanent. +# The module $\texttt{HARK.ConsumptionSaving.ConsIndShockModel}$ concerns consumption-saving models with idiosyncratic shocks to (non-capital) income. All of the models assume CRRA utility with geometric discounting, no bequest motive, and income shocks are fully transitory or fully permanent. # # $\texttt{ConsIndShockModel}$ currently includes three models: -# 1. A very basic "perfect foresight" model with no uncertainty (shocks are zero). +# 1. A very basic "perfect foresight" model with no uncertainty. # 2. A model with risk over transitory and permanent income shocks. # 3. The model described in (2), with an interest rate for debt that differs from the interest rate for savings. # @@ -42,58 +47,68 @@ # $\newcommand{\DiscFac}{\beta}$ # %% [markdown] -# ## Statement of the model +# ## Statement of perfect foresight consumption-saving model # -# The $\texttt{PerfForesightConsumerType}$ class solves the problem of a consumer with Constant Relative Risk Aversion utility +# The $\texttt{PerfForesightConsumerType}$ class the problem of a consumer with Constant Relative Risk Aversion utility # ${\CRRA}$ # \begin{equation} # U(C) = \frac{C^{1-\CRRA}}{1-\rho}, # \end{equation} -# who has perfect foresight about everything except whether he will die between the end of period $t$ and the beginning of period $t+1$. Permanent labor income $P_t$ grows from period $t$ to period $t+1$ by factor $\PermGroFac_{t+1}$. The consumer faces no artificial borrowing constraint: He is able to borrow against his entire future stream of income. +# has perfect foresight about everything except whether he will die between the end of period $t$ and the beginning of period $t+1$, which occurs with probability $\DiePrb_{t+1}$. Permanent labor income $P_t$ grows from period $t$ to period $t+1$ by factor $\PermGroFac_{t+1}$. # -# At the beginning of period $t$, the consumer has market resources $M_t$ (which includes both market wealth and currrent income) and must choose how much to consume $C_t$ and how much to retain in a riskless asset $A_t$, which will earn return factor $\Rfree$. The agent's flow of future utility $U(C_{t+n})$ from consumption is geometrically discounted by factor $\DiscFac$ per period. The consumer only experiences future value if he survives, which occurs with probability $1-\DiePrb_{t+1}$. +# At the beginning of period $t$, the consumer has an amount of market resources $M_t$ (which includes both market wealth and currrent income) and must choose how much of those resources to consume $C_t$ and how much to retain in a riskless asset $A_t$, which will earn return factor $\Rfree$. The consumer cannot necessarily borrow arbitarily; instead, he might be constrained to have a wealth-to-income ratio at least as great as some "artificial borrowing constraint" $\underline{a} \leq 0$. # -# For parallelism with the treatment of more complicated problems, we write the problem rather elaborately in Bellman form as: +# The agent's flow of future utility $U(C_{t+n})$ from consumption is geometrically discounted by factor $\DiscFac$ per period. If the consumer dies, he receives zero utility flow for the rest of time. +# +# The agent's problem can be written in Bellman form as: # # \begin{eqnarray*} # V_t(M_t,P_t) &=& \max_{C_t}~U(C_t) ~+ \DiscFac (1 - \DiePrb_{t+1}) V_{t+1}(M_{t+1},P_{t+1}), \\ # & s.t. & \\ # A_t &=& M_t - C_t, \\ +# A_t/P_t &\geq& \underline{a}, \\ # M_{t+1} &=& \Rfree A_t + Y_{t+1}, \\ -# Y_{t+1} &=& P_{t+1}, \\ +# Y_{t+1} &=& P_{t+1}, \\ # P_{t+1} &=& \PermGroFac_{t+1} P_t. # \end{eqnarray*} # -# The parameters of the consumer's problem are the coefficient of relative risk aversion $\CRRA$, the intertemporal discount factor $\DiscFac$, an interest factor $\Rfree$, and age-varying sequences of the permanent income growth factor $\PermGroFac_t$ and survival probability $(1 - \DiePrb_t)$. [These lecture notes](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA) show that under these assumptions the problem can be transformed into an equivalent problem stated in terms of *normalized* variables (represented in lower case); all real variables are divided by permanent income $P_t$ and value is divided by $P_t^{1-\CRRA}$. The Bellman form of the normalized model (see the lecture notes for details) is: +# The consumer's problem is characterized by a coefficient of relative risk aversion $\CRRA$, an intertemporal discount factor $\DiscFac$, an interest factor $\Rfree$, and age-varying sequences of the permanent income growth factor $\PermGroFac_t$ and survival probability $(1 - \DiePrb_t)$. +# +# While it does not reduce the computational complexity of the problem (as permanent income is deterministic, given its initial condition $P_0$), HARK represents this problem with *normalized* variables (represented in lower case), dividing all real variables by permanent income $P_t$ and utility levels by $P_t^{1-\CRRA}$. The Bellman form of the model thus reduces to: # # \begin{eqnarray*} # v_t(m_t) &=& \max_{c_t}~U(c_t) ~+ \DiscFac (1 - \DiePrb_{t+1}) \PermGroFac_{t+1}^{1-\CRRA} v_{t+1}(m_{t+1}), \\ # & s.t. & \\ # a_t &=& m_t - c_t, \\ -# m_{t+1} &=& a_t (\Rfree/\PermGroFac_{t+1} )+ 1. +# a_t &\geq& \underline{a}, \\ +# m_{t+1} &=& \Rfree/\PermGroFac_{t+1} a_t + 1. # \end{eqnarray*} # %% [markdown] # ## Solution method for PerfForesightConsumerType # -# Because of the assumptions of CRRA utility, no risk other than mortality, and no artificial borrowing constraint, the problem has a closed form solution in which consumption is a linear function of resources, and the utility-inverse of the value function is also linear (that is, $u^{-1}(v)$ is linear in $m$). Details of the mathematical solution of this model can be found in the lecture notes [PerfForesightCRRA](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA). +# Because of the assumptions of CRRA utility, no risk other than mortality, and no artificial borrowing constraint, the problem has a closed form solution. In fact, the consumption function is perfectly linear, and the value function composed with the inverse utility function is also linear. The mathematical solution of this model is described in detail in the lecture notes [PerfForesightCRRA](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA). # -# The one period problem for this model is solved by the function $\texttt{solveConsPerfForesight}$, which creates an instance of the class $\texttt{ConsPerfForesightSolver}$. To construct an instance of the class $\texttt{PerfForesightConsumerType}$, several parameters must be passed to this constructor. +# The one period problem for this model is solved by the function $\texttt{solveConsPerfForesight}$, which creates an instance of the class $\texttt{ConsPerfForesightSolver}$. To construct an instance of the class $\texttt{PerfForesightConsumerType}$, several parameters must be passed to its constructor as shown in the table below. # %% [markdown] -# ## Example parameter values +# ## Example parameter values to construct an instance of PerfForesightConsumerType # # | Parameter | Description | Code | Example value | Time-varying? | # | :---: | --- | --- | --- | --- | # | $\DiscFac$ |Intertemporal discount factor | $\texttt{DiscFac}$ | $0.96$ | | -# | $\CRRA$|Coefficient of relative risk aversion | $\texttt{CRRA}$ | $2.0$ | | +# | $\CRRA $ |Coefficient of relative risk aversion | $\texttt{CRRA}$ | $2.0$ | | # | $\Rfree$ | Risk free interest factor | $\texttt{Rfree}$ | $1.03$ | | # | $1 - \DiePrb_{t+1}$ |Survival probability | $\texttt{LivPrb}$ | $[0.98]$ | $\surd$ | # |$\PermGroFac_{t+1}$|Permanent income growth factor|$\texttt{PermGroFac}$| $[1.01]$ | $\surd$ | +# |$\underline{a}$|Artificial borrowing constraint|$\texttt{BoroCnstArt}$| $None$ | | +# |$(none)$|Maximum number of gridpoints in consumption function |$\texttt{aXtraCount}$| $200$ | | # |$T$| Number of periods in this type's "cycle" |$\texttt{T_cycle}$| $1$ | | # |(none)| Number of times the "cycle" occurs |$\texttt{cycles}$| $0$ | | # -# Note that the survival probability and income growth factor have time subscripts; likewise, the example values for these parameters are *lists* rather than simply single floats. This is because those parameters are in principle *time-varying*: their values can depend on which period of the problem the agent is in (for example, mortality probability depends on age). All time-varying parameters *must* be specified as lists, even when the model is being solved for an infinite horizon case where in practice the parameter takes the same value in every period. +# Note that the survival probability and income growth factor have time subscripts; likewise, the example values for these parameters are *lists* rather than simply single floats. This is because those parameters are *time-varying*: their values can depend on which period of the problem the agent is in. All time-varying parameters *must* be specified as lists, even if the same value occurs in each period for this type. +# +# The artificial borrowing constraint can be any non-positive $\texttt{float}$, or it can be $\texttt{None}$ to indicate no artificial borrowing constraint. The maximum number of gridpoints in the consumption function is only relevant if the borrowing constraint is not $\texttt{None}$; without an upper bound on the number of gridpoints, kinks in the consumption function will propagate indefinitely in an infinite horizon model if there is a borrowing constraint, eventually resulting in an overflow error. If there is no artificial borrowing constraint, then the number of gridpoints used to represent the consumption function is always exactly two. # # The last two parameters in the table specify the "nature of time" for this type: the number of (non-terminal) periods in this type's "cycle", and the number of times that the "cycle" occurs. *Every* subclass of $\texttt{AgentType}$ uses these two code parameters to define the nature of time. Here, $\texttt{T_cycle}$ has the value $1$, indicating that there is exactly one period in the cycle, while $\texttt{cycles}$ is $0$, indicating that the cycle is repeated in *infinite* number of times-- it is an infinite horizon model, with the same "kind" of period repeated over and over. # @@ -103,22 +118,23 @@ # # The cell below defines a dictionary that can be passed to the constructor method for $\texttt{PerfForesightConsumerType}$, with the values from the table here. -# %% {"code_folding": [0]} +# %% code_folding=[] PerfForesightDict = { # Parameters actually used in the solution method - "CRRA" : 2.0, # Coefficient of relative risk aversion - "Rfree" : 1.03, # Interest factor on assets - "DiscFac" : 0.96, # Default intertemporal discount factor - "LivPrb" : [0.98], # Survival probability - "PermGroFac" :[1.01], # Permanent income growth factor - + "CRRA": 2.0, # Coefficient of relative risk aversion + "Rfree": 1.03, # Interest factor on assets + "DiscFac": 0.96, # Default intertemporal discount factor + "LivPrb": [0.98], # Survival probability + "PermGroFac": [1.01], # Permanent income growth factor + "BoroCnstArt": None, # Artificial borrowing constraint + "aXtraCount": 200, # Maximum number of gridpoints in consumption function # Parameters that characterize the nature of time - "T_cycle" : 1, # Number of periods in the cycle for this agent type - "cycles" : 0 # Number of times the cycle occurs (0 --> infinitely repeated) + "T_cycle": 1, # Number of periods in the cycle for this agent type + "cycles": 0, # Number of times the cycle occurs (0 --> infinitely repeated) } # %% [markdown] -# ## Inspecting the solution +# ## Solving and examining the solution of the perfect foresight model # # With the dictionary we have just defined, we can create an instance of $\texttt{PerfForesightConsumerType}$ by passing the dictionary to the class (as if the class were a function). This instance can then be solved by invoking its $\texttt{solve}$ method. @@ -134,91 +150,52 @@ print(PFexample.solution) # %% [markdown] -# Each element of $\texttt{solution}$ has a few attributes. To see all of them, we can use the $\texttt{vars}$ built in function: the consumption functions are instantiated in the attribute $\texttt{cFunc}$ of each element of $\texttt{ConsumerType.solution}$. This method creates a (time varying) attribute $\texttt{cFunc}$ that contains a list of consumption functions by age. +# Each element of $\texttt{solution}$ has a few attributes. To see all of them, we can use the \texttt{vars} built in function: +# +# the consumption functions reside in the attribute $\texttt{cFunc}$ of each element of $\texttt{ConsumerType.solution}$. This method creates a (time varying) attribute $\texttt{cFunc}$ that contains a list of consumption functions. # %% print(vars(PFexample.solution[0])) # %% [markdown] -# The two most important attributes of a single period solution are the (normalized) consumption function $\texttt{cFunc}$ and the (normalized) value function $\texttt{vFunc}$; the marginal value function $\texttt{vPfunc}$ is also constructed. Let's plot those functions near the lower bound of the permissible state space (the attribute $\texttt{mNrmMin}$ tells us the lower bound of $m_t$ where the consumption function is defined). +# The two most important attributes of a single period solution of this model are the (normalized) consumption function $\texttt{cFunc}$ and the (normalized) value function $\texttt{vFunc}$. Let's plot those functions near the lower bound of the permissible state space (the attribute $\texttt{mNrmMin}$ tells us the lower bound of $m_t$ where the consumption function is defined). # %% -print('Linear perfect foresight consumption function:') +print("Linear perfect foresight consumption function:") mMin = PFexample.solution[0].mNrmMin -plotFuncs(PFexample.solution[0].cFunc,mMin,mMin+10.) +plotFuncs(PFexample.solution[0].cFunc, mMin, mMin + 10.0) # %% -print('Perfect foresight value function:') -plotFuncs(PFexample.solution[0].vFunc,mMin+0.1,mMin+10.1) +print("Perfect foresight value function:") +plotFuncs(PFexample.solution[0].vFunc, mMin + 0.1, mMin + 10.1) # %% [markdown] -# ## Solution Method -# -# -# ### Recursive Formula for $\kappa_{t}$ -# -# The paper [BufferStockTheory](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/) has a few other results that are used in the solution code. One is [the recursive formula for the MPC](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/#MPCnvrs). Starting with the last period, in which $\kappa_{T}=1$, the inverse MPC's (and therefore the MPC's themselves) can be constructed using the recursive formula: -# -# \begin{align} -# \kappa_{t}^{-1} & = & 1 + \kappa_{t+1}^{-1}(\Rfree \beta)^{1/\rho}/G -# \end{align} -# -# ### Consumption Function -# -# For the perfect foresight problem, there is a well-known [analytical solution]( http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/#cFuncAnalytical) for the consumption function: Calling $o_{t}$ 'overall wealth' (including market wealth plus human wealth $h_{t}$) and designating the marginal propensity to consume in period $t$ by $\kappa_{t}$: -# -# \begin{align} -# \mathrm{c}_{t} & = o_{t}\kappa_{t} -# \end{align} -# -# and in our normalized model $o_{t} = m_{t}-1+h_{t}$ (the '-1' term subtracts off the normalized current income of 1 from market resources $m$ which were market wealth plus current income). -# -# ### Value Function -# -# A convenient feature of the perfect foresight problem is that the value function has a simple [analytical form](http://econ.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/#vFuncAnalytical): -# -# \begin{align} -# \mathrm{v}_{t} & = \mathrm{u}(\mathrm{c}_{t}(m))\kappa_{t}^{-1}\\ -# &= \mathrm{u}(o_{t} \kappa_{t}) \kappa_{t}^{-1} \\ -# &= \mathrm{u}(o_{t})\kappa_{t}^{1-\rho} \kappa_{t}^{-1} \\ -# &= \mathrm{u}(o_{t})\kappa_{t}^{-\rho} -# \end{align} -# -# This means that the utility-inverse of the value function, ${\scriptsize \Lambda} \equiv \mathrm{u}^{-1}(\mathrm{v})$, is linear: -# -# \begin{align} -# \scriptsize \Lambda_{t} & = o_{t} \kappa_{t}^{-\rho/(1-\rho)} -# \end{align} -# -# When uncertainty or liquidity constraints are added to the problem, the ${\scriptsize \Lambda}$ function is no longer linear. But even in these cases, the utility-inverse of the value function is much better behaved (e.g., closer to linear; bounded over any feasible finite range of $m$) than the uninverted function (which, for example, approaches $-\infty$ as $m$ approaches its lower bound). -# -# Our procedure will therefore generically be to construct the inverse value function, and to obtain the value function from it by uninverting. That is, we construct an interpolating approximation of $\scriptsize \Lambda_{t}$ and compute value on-the-fly from -# -# \begin{align} -# \mathrm{v}_{t}(m) & = \mathrm{u}({\scriptsize \Lambda_{t}}(m)) -# \end{align} -# -# In this case, the interpolation is exact, not an approximation: We need only two points to construct a line, so we choose the minimum possible value of normalized market resources, $\texttt{mNrmMin}$, where $o_{t}=0$ so that $c_{t}=0$, and that minimum plus 1, where the inverted value function will have the value $\kappa_{t}^{-\rho/(1-\rho)}$. From these we construct $vFuncNvrs$ as a linear interpolating function (which automatically extrapolates to the whole number line). +# An element of $\texttt{solution}$ also includes the (normalized) marginal value function $\texttt{vPfunc}$, and the lower and upper bounds of the marginal propensity to consume (MPC) $\texttt{MPCmin}$ and $\texttt{MPCmax}$. Note that with a linear consumption function, the MPC is constant, so its lower and upper bound are identical. # +# ### Liquidity constrained perfect foresight example # +# Without an artificial borrowing constraint, a perfect foresight consumer is free to borrow against the PDV of his entire future stream of labor income-- his "human wealth" $\texttt{hNrm}$-- and he will consume a constant proportion of his total wealth (market resources plus human wealth). If we introduce an artificial borrowing constraint, both of these features vanish. In the cell below, we define a parameter dictionary that prevents the consumer from borrowing *at all*, create and solve a new instance of $\texttt{PerfForesightConsumerType}$ with it, and then plot its consumption function. -# %% [markdown] -# ## Checking Solution Conditions -# -# The code performs tests for whether the supplied parameter values meet various conditions that determine the properties of the solution. Some conditions (like the Finite Human Wealth Condition) are required for the model to have a sensible solution, and if these conditions are violated the code generates a warning message. Other conditions govern characteristics of the model like whether consumption is falling (whether the consumer is 'absolutely impatient'). All conditions can manually be performed using the syntax below. The function returns "False" if none of the key conditions has been violated. +# %% pycharm={"name": "#%%\n"} +LiqConstrDict = copy(PerfForesightDict) +LiqConstrDict["BoroCnstArt"] = 0.0 # Set the artificial borrowing constraint to zero -# %% -PFexample.checkConditions(verbose=True) +LiqConstrExample = PerfForesightConsumerType(**LiqConstrDict) +LiqConstrExample.cycles = 0 # Make this type be infinite horizon +LiqConstrExample.solve() -# %% [markdown] -# An element of $\texttt{solution}$ also includes the (normalized) marginal value function $\texttt{vPfunc}$, and the lower and upper bounds of the marginal propensity to consume (MPC) $\texttt{MPCmin}$ and $\texttt{MPCmax}$. Note that with a linear consumption function, the MPC is constant, so its lower and upper bound are identical. +print("Liquidity constrained perfect foresight consumption function:") +plotFuncs(LiqConstrExample.solution[0].cFunc, 0.0, 10.0) + +# %% [markdown] pycharm={"name": "#%% md\n"} +# At this time, the value function for a perfect foresight consumer with an artificial borrowing constraint is not computed nor included as part of its $\texttt{solution}$. # %% [markdown] -# ## Simulating the model +# ## Simulating the perfect foresight consumer model # # Suppose we wanted to simulate many consumers who share the parameter values that we passed to $\texttt{PerfForesightConsumerType}$-- an *ex ante* homogeneous *type* of consumers. To do this, our instance would have to know *how many* agents there are of this type, as well as their initial levels of assets $a_t$ and permanent income $P_t$. # -# ### Setting Parameters +# ### Setting simulation parameters # # Let's fill in this information by passing another dictionary to $\texttt{PFexample}$ with simulation parameters. The table below lists the parameters that an instance of $\texttt{PerfForesightConsumerType}$ needs in order to successfully simulate its model using the $\texttt{simulate}$ method. # @@ -241,22 +218,22 @@ # # The cell below puts these parameters into a dictionary, then gives them to $\texttt{PFexample}$. Note that all of these parameters *could* have been passed as part of the original dictionary; we omitted them above for simplicity. -# %% {"code_folding": [0]} -# Create parameter values necessary for simulation +# %% pycharm={"name": "#%%\n"} SimulationParams = { - "AgentCount" : 10000, # Number of agents of this type - "T_sim" : 120, # Number of periods to simulate - "aNrmInitMean" : -6.0, # Mean of log initial assets - "aNrmInitStd" : 1.0, # Standard deviation of log initial assets - "pLvlInitMean" : 0.0, # Mean of log initial permanent income - "pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income - "PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor - "T_age" : None, # Age after which simulated agents are automatically killed + "AgentCount": 10000, # Number of agents of this type + "T_sim": 120, # Number of periods to simulate + "aNrmInitMean": -6.0, # Mean of log initial assets + "aNrmInitStd": 1.0, # Standard deviation of log initial assets + "pLvlInitMean": 0.0, # Mean of log initial permanent income + "pLvlInitStd": 0.0, # Standard deviation of log initial permanent income + "PermGroFacAgg": 1.0, # Aggregate permanent income growth factor + "T_age": None, # Age after which simulated agents are automatically killed } -PFexample(**SimulationParams) # This implicitly uses the assignParameters method of AgentType +# This implicitly uses the assignParameters method of AgentType +PFexample(**SimulationParams) -# %% [markdown] +# %% [markdown] pycharm={"name": "#%% md\n"} # To generate simulated data, we need to specify which variables we want to track the "history" of for this instance. To do so, we set the $\texttt{track_vars}$ attribute of our $\texttt{PerfForesightConsumerType}$ instance to be a list of strings with the simulation variables we want to track. # # In this model, valid elments of $\texttt{track_vars}$ include $\texttt{mNrmNow}$, $\texttt{cNrmNow}$, $\texttt{aNrmNow}$, and $\texttt{pLvlNow}$. Because this model has no idiosyncratic shocks, our simulated data will be quite boring. @@ -267,37 +244,34 @@ # # Finally, the $\texttt{simulate}$ method can be called. -# %% {"code_folding": [0]} -# Create PFexample object -PFexample.track_vars = ['mNrmNow'] +# %% pycharm={"name": "#%%\n"} +PFexample.track_vars = ["mNrmNow"] PFexample.initializeSim() PFexample.simulate() -# %% [markdown] +# %% [markdown] pycharm={"name": "#%% md\n"} # Each simulation variable $\texttt{X}$ named in $\texttt{track_vars}$ will have the *history* of that variable for each agent stored in the attribute $\texttt{X_hist}$ as an array of shape $(\texttt{T_sim},\texttt{AgentCount})$. To see that the simulation worked as intended, we can plot the mean of $m_t$ in each simulated period: -# %% {"code_folding": [0]} -# Plot market resources over time -plt.plot(np.mean(PFexample.history['mNrmNow'],axis=1)) -plt.xlabel('Time') -plt.ylabel('Mean normalized market resources') +# %% pycharm={"name": "#%%\n"} +plt.plot(np.mean(PFexample.history["mNrmNow"], axis=1)) +plt.xlabel("Time") +plt.ylabel("Mean normalized market resources") plt.show() -# %% [markdown] -# A perfect foresight consumer can borrow against the PDV of his future income-- his human wealth-- and thus as time goes on, our simulated impatient agents approach the (very negative) steady state level of $m_t$ while being steadily replaced with consumers with roughly $m_t=1$. +# %% [markdown] pycharm={"name": "#%% md\n"} +# A perfect foresight consumer can borrow against the PDV of his future income-- his human wealth-- and thus as time goes on, our simulated agents approach the (very negative) steady state level of $m_t$ while being steadily replaced with consumers with roughly $m_t=1$. # # The slight wiggles in the plotted curve are due to consumers randomly dying and being replaced; their replacement will have an initial state drawn from the distributions specified by the user. To see the current distribution of ages, we can look at the attribute $\texttt{t_age}$. -# %% {"code_folding": [0]} -# Plot the CDF +# %% pycharm={"name": "#%%\n"} N = PFexample.AgentCount -F = np.linspace(0.,1.,N) -plt.plot(np.sort(PFexample.t_age),F) -plt.xlabel('Current age of consumers') -plt.ylabel('Cumulative distribution') +F = np.linspace(0.0, 1.0, N) +plt.plot(np.sort(PFexample.t_age), F) +plt.xlabel("Current age of consumers") +plt.ylabel("Cumulative distribution") plt.show() -# %% [markdown] +# %% [markdown] pycharm={"name": "#%% md\n"} # The distribution is (discretely) exponential, with a point mass at 120 with consumers who have survived since the beginning of the simulation. # # One might wonder why HARK requires users to call $\texttt{initializeSim}$ before calling $\texttt{simulate}$: Why doesn't $\texttt{simulate}$ just call $\texttt{initializeSim}$ as its first step? We have broken up these two steps so that users can simulate some number of periods, change something in the environment, and then resume the simulation. @@ -306,16 +280,13 @@ # # In the cell below, we simulate our perfect foresight consumers for 80 periods, then seize a bunch of their assets (dragging their wealth even more negative), then simulate for the reamining 40 periods. -# %% {"code_folding": [0]} -# The final resulting distribution is reasonably coherent +# %% pycharm={"name": "#%%\n"} PFexample.initializeSim() PFexample.simulate(80) -PFexample.aNrmNow += -5. # Adjust all simulated consumers' assets downward by 5 +PFexample.aNrmNow += -5.0 # Adjust all simulated consumers' assets downward by 5 PFexample.simulate(40) -plt.plot(np.mean(PFexample.history['mNrmNow'],axis=1)) -plt.xlabel('Time') -plt.ylabel('Mean normalized market resources') +plt.plot(np.mean(PFexample.history["mNrmNow"], axis=1)) +plt.xlabel("Time") +plt.ylabel("Mean normalized market resources") plt.show() - -# %%