parameter formatting

econ-ark · Nov 23, 2023 · 7c99c8a · 7c99c8a
1 parent fd57329
commit 7c99c8a
Showing 1 changed file with 37 additions and 37 deletions.
diff --git a/examples/ConsIndShockModel/KinkedRconsumerType.ipynb b/examples/ConsIndShockModel/KinkedRconsumerType.ipynb
@@ -97,37 +97,37 @@
    "source": [
     "## Example parameter values to construct an instance of KinkedRconsumerType\n",
     "\n",
-    "The parameters required to create an instance of `KinkedRconsumerType` are nearly identical to those for `IndShockConsumerType`.  The only difference is that the parameter `Rfree` is replaced with `Rboro` and `Rsave`.\n",
+    "The parameters required to create an instance of `KinkedRconsumerType` are nearly identical to those for `IndShockConsumerType`.  The only difference is that the parameter $\\verb|Rfree|$ is replaced with $\\verb|Rboro|$ and $\\verb|Rsave|$.\n",
     "\n",
-    "While the parameter `CubicBool` is required to create a valid `KinkedRconsumerType` instance, it must be set to `False`; cubic spline interpolation has not yet been implemented for this model.  In the future, this restriction will be lifted.\n",
+    "While the parameter $\\verb|CubicBool|$ is required to create a valid `KinkedRconsumerType` instance, it must be set to `False`; cubic spline interpolation has not yet been implemented for this model.  In the future, this restriction will be lifted.\n",
     "\n",
     "| Parameter | Description | Code | Example value | Time-varying? |\n",
     "| :---: | --- | --- | --- | --- |\n",
-    "| $\\DiscFac$ |Intertemporal discount factor  | `DiscFac` | $0.96$ |  |\n",
-    "| $\\CRRA$ |Coefficient of relative risk aversion | `CRRA` | $2.0$ | |\n",
-    "| $\\Rfree_{boro}$ | Risk free interest factor for borrowing | `Rboro` | $1.20$ | |\n",
-    "| $\\Rfree_{save}$ | Risk free interest factor for saving | `Rsave` | $1.01$ | |\n",
-    "| $1 - \\DiePrb_{t+1}$ |Survival probability | `LivPrb` | $[0.98]$ | $\\surd$ |\n",
-    "|$\\PermGroFac_{t+1}$|Permanent income growth factor|`PermGroFac`| $[1.01]$ | $\\surd$ |\n",
-    "| $\\sigma_\\psi$ | Standard deviation of log permanent income shocks | `PermShkStd` | $[0.1]$ |$\\surd$ |\n",
-    "| $N_\\psi$ | Number of discrete permanent income shocks | `PermShkCount` | $7$ | |\n",
-    "| $\\sigma_\\theta$ | Standard deviation of log transitory income shocks | `TranShkStd` | $[0.2]$ | $\\surd$ |\n",
-    "| $N_\\theta$ | Number of discrete transitory income shocks | `TranShkCount` | $7$ |  |\n",
-    "| $\\mho$ | Probability of being unemployed and getting $\\theta=\\underline{\\theta}$ | `UnempPrb` | $0.05$ |  |\n",
-    "| $\\underline{\\theta}$ | Transitory shock when unemployed | `IncUnemp` | $0.3$ |  |\n",
-    "| $\\mho^{Ret}$ | Probability of being \"unemployed\" when retired | `UnempPrbRet` | $0.0005$ |  |\n",
-    "| $\\underline{\\theta}^{Ret}$ | Transitory shock when \"unemployed\" and retired | `IncUnempRet` | $0.0$ |  |\n",
-    "| $(none)$ | Period of the lifecycle model when retirement begins | `T_retire` | $0$ | |\n",
-    "| $(none)$ | Minimum value in assets-above-minimum grid | `aXtraMin` | $0.001$ | |\n",
-    "| $(none)$ | Maximum value in assets-above-minimum grid | `aXtraMax` | $20.0$ | |\n",
-    "| $(none)$ | Number of points in base assets-above-minimum grid | `aXtraCount` | $48$ | |\n",
-    "| $(none)$ | Exponential nesting factor for base assets-above-minimum grid | `aXtraNestFac` | $3$ | |\n",
-    "| $(none)$ | Additional values to add to assets-above-minimum grid | `aXtraExtra` | $None$ | |\n",
-    "| $\\underline{a}$ | Artificial borrowing constraint (normalized) | `BoroCnstArt` | $None$ | |\n",
-    "| $(none)$ |Indicator for whether `vFunc` should be computed | `vFuncBool` | $True$ | |\n",
-    "| $(none)$ |Indicator for whether `cFunc` should use cubic splines | `CubicBool` | $False$ |  |\n",
-    "|$T$| Number of periods in this type's \"cycle\" |`T_cycle`| $1$ | |\n",
-    "|(none)| Number of times the \"cycle\" occurs |`cycles`| $0$ | |\n",
+    "| $\\DiscFac$ |Intertemporal discount factor  | $\\verb|DiscFac|$ | $0.96$ |  |\n",
+    "| $\\CRRA$ |Coefficient of relative risk aversion | $\\verb|CRRA|$ | $2.0$ | |\n",
+    "| $\\Rfree_{boro}$ | Risk free interest factor for borrowing | $\\verb|Rboro|$ | $1.20$ | |\n",
+    "| $\\Rfree_{save}$ | Risk free interest factor for saving | $\\verb|Rsave|$ | $1.01$ | |\n",
+    "| $1 - \\DiePrb_{t+1}$ |Survival probability | $\\verb|LivPrb|$ | $[0.98]$ | $\\surd$ |\n",
+    "|$\\PermGroFac_{t+1}$|Permanent income growth factor| $\\verb|PermGroFac|$ | $[1.01]$ | $\\surd$ |\n",
+    "| $\\sigma_\\psi$ | Standard deviation of log permanent income shocks | $\\verb|PermShkStd|$ | $[0.1]$ |$\\surd$ |\n",
+    "| $N_\\psi$ | Number of discrete permanent income shocks | $\\verb|PermShkCount|$ | $7$ | |\n",
+    "| $\\sigma_\\theta$ | Standard deviation of log transitory income shocks | $\\verb|TranShkStd|$ | $[0.2]$ | $\\surd$ |\n",
+    "| $N_\\theta$ | Number of discrete transitory income shocks | $\\verb|TranShkCount|$ | $7$ |  |\n",
+    "| $\\mho$ | Probability of being unemployed and getting $\\theta=\\underline{\\theta}$ | $\\verb|UnempPrb|$ | $0.05$ |  |\n",
+    "| $\\underline{\\theta}$ | Transitory shock when unemployed | $\\verb|IncUnemp|$ | $0.3$ |  |\n",
+    "| $\\mho^{Ret}$ | Probability of being \"unemployed\" when retired | $\\verb|UnempPrbRet|$ | $0.0005$ |  |\n",
+    "| $\\underline{\\theta}^{Ret}$ | Transitory shock when \"unemployed\" and retired | $\\verb|IncUnempRet|$ | $0.0$ |  |\n",
+    "| $(none)$ | Period of the lifecycle model when retirement begins | $\\verb|T_retire|$ | $0$ | |\n",
+    "| $(none)$ | Minimum value in assets-above-minimum grid | $\\verb|aXtraMin|$ | $0.001$ | |\n",
+    "| $(none)$ | Maximum value in assets-above-minimum grid | $\\verb|aXtraMax|$ | $20.0$ | |\n",
+    "| $(none)$ | Number of points in base assets-above-minimum grid | $\\verb|aXtraCount|$ | $48$ | |\n",
+    "| $(none)$ | Exponential nesting factor for base assets-above-minimum grid | $\\verb|aXtraNestFac|$ | $3$ | |\n",
+    "| $(none)$ | Additional values to add to assets-above-minimum grid | $\\verb|aXtraExtra|$ | $None$ | |\n",
+    "| $\\underline{a}$ | Artificial borrowing constraint (normalized) | $\\verb|BoroCnstArt|$ | $None$ | |\n",
+    "| $(none)$ |Indicator for whether $\\verb|vFunc|$ should be computed | $\\verb|vFuncBool|$ | $True$ | |\n",
+    "| $(none)$ |Indicator for whether $\\verb|cFunc|$ should use cubic splines | $\\verb|CubicBool|$ | $False$ |  |\n",
+    "|$T$| Number of periods in this type's \"cycle\" | $\\verb|T_cycle|$ | $1$ | |\n",
+    "|(none)| Number of times the \"cycle\" occurs | $\\verb|cycles|$ | $0$ | |\n",
     "\n",
     "These example parameters are almost identical to those used for `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 `None`.  The cell below defines a parameter dictionary with these example values."
    ]
@@ -272,16 +272,16 @@
     "\n",
     "| Description | Code | Example value |\n",
     "| :---: | --- | --- |\n",
-    "| Number of consumers of this type | `AgentCount` | $10000$ |\n",
-    "| Number of periods to simulate | `T_sim` | $500$ |\n",
-    "| Mean of initial log (normalized) assets | `aNrmInitMean` | $-6.0$ |\n",
-    "| Stdev of initial log  (normalized) assets | `aNrmInitStd` | $1.0$ |\n",
-    "| Mean of initial log permanent income | `pLvlInitMean` | $0.0$ |\n",
-    "| Stdev of initial log permanent income | `pLvlInitStd` | $0.0$ |\n",
-    "| Aggregrate productivity growth factor | `PermGroFacAgg` | $1.0$ |\n",
-    "| Age after which consumers are automatically killed | `T_age` | $None$ |\n",
+    "| Number of consumers of this type | $\\verb|AgentCount|$ | $10000$ |\n",
+    "| Number of periods to simulate | $\\verb|T_sim|$ | $500$ |\n",
+    "| Mean of initial log (normalized) assets | $\\verb|aNrmInitMean|$ | $-6.0$ |\n",
+    "| Stdev of initial log  (normalized) assets | $\\verb|aNrmInitStd|$ | $1.0$ |\n",
+    "| Mean of initial log permanent income | $\\verb|pLvlInitMean|$ | $0.0$ |\n",
+    "| Stdev of initial log permanent income | $\\verb|pLvlInitStd|$ | $0.0$ |\n",
+    "| Aggregrate productivity growth factor | $\\verb|PermGroFacAgg|$ | $1.0$ |\n",
+    "| Age after which consumers are automatically killed | $\\verb|T_age|$ | $None$ |\n",
     "\n",
-    "Here, we will simulate 10,000 consumers for 500 periods.  All newly born agents will start with permanent income of exactly $P_t = 1.0 = \\exp($ `pLvlInitMean` $)$, as `pLvlInitStd` has been set to zero; they will have essentially zero assets at birth, as `aNrmInitMean` is $-6.0$; assets will be less than $1\\%$ of permanent income at birth.\n",
+    "Here, we will simulate 10,000 consumers for 500 periods.  All newly born agents will start with permanent income of exactly $P_t = 1.0 = \\exp(\\verb|pLvlInitMean|)$, as $\\verb|pLvlInitStd|$ has been set to zero; they will have essentially zero assets at birth, as $\\verb|aNrmInitMean|$ is $-6.0$; assets will be less than $1\\%$ of permanent income at birth.\n",
     "\n",
     "These example parameter values were already passed as part of the parameter dictionary that we used to create `KinkyExample`, so it is ready to simulate.  We need to set the `track_vars` attribute to indicate the variables for which we want to record a *history*."
    ]
@@ -416,7 +416,7 @@
    "source": [
     "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).\n",
     "\n",
-    "The smaller point masses in this distribution are due to `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 `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."
+    "The smaller point masses in this distribution are due to $\\verb|HARK|$ 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 $\\verb|TranShkCount|$ 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."
    ]
   }
  ],