{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# DCEGM Upper Envelope\n", "## [\"The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks\"](https://onlinelibrary.wiley.com/doi/abs/10.3982/QE643)\n", "\n", "

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\n", "\n", "[![badge](https://img.shields.io/badge/Launch%20using%20-Econ--ARK-blue)](https://econ-ark.org/materials/dcegm-upper-envelope#launch)\n", "\n", "\n", "\n", "This notebook provides a simple introduction to the \"DCEGM\" algorithm . DCEGM extends the EGM method proposed in to problems with both continuous (e.g. consumption) and discrete (e.g. retirement) decisions.\n", "\n", "The main challenge for the EGM algorithm in discrete-continuous problems is that the discrete decisions generate \"kinks\" in the value function, making it non-concave and rendering the first order condition used by EGM a necessary but not sufficient for optimality. In practice, this causes the EGM inversion step to produce (resource, consumption) points that are not optimal. DCEGM incorporates a method to filter the points produced by EGM so that only the truly optimal ones are used in producing an approximation to the solution.\n", "\n", "This filtering process consists mainly of computing \"upper-envelopes\" of the candidate points: lines that are made up only of the points with the higher values.\n", "\n", "This notebook presents HARK's tool for calculating upper-envelopes and then uses it to solve a simple three-period discrete-continuous problem using DCEGM." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Upper envelopes\n", "\n", "Start by importing the tools." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# imports\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\")\n", "from HARK.rewards import CRRAutility, CRRAutilityP, CRRAutilityP_inv\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# here for now, should be\n", "# from HARK import discontools or whatever name is chosen\n", "from HARK.interpolation import LinearInterp\n", "from HARK.dcegm import calc_nondecreasing_segments, upper_envelope" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Applying EGM to value functions with kinks, as the ones that result from discrete-continuous problems, will often result in grids for market resources that are not monotonic and candidate choices at those points that are sub-optimal.\n", "Consider the following example output." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Value')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m_egm = np.array([0.0, 0.04, 0.25, 0.15, 0.1, 0.3, 0.6, 0.5, 0.35, 0.6, 0.75, 0.85])\n", "c_egm = np.array([0.0, 0.03, 0.1, 0.07, 0.05, 0.36, 0.4, 0.6, 0.8, 0.9, 0.9, 0.9])\n", "vt_egm = np.array([0.0, 0.05, 0.1, 0.04, 0.02, 0.2, 0.7, 0.5, 0.2, 0.9, 1.0, 1.2])\n", "plt.plot(m_egm, vt_egm)\n", "plt.xlabel(\"Resources\")\n", "plt.ylabel(\"Value\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two main issues:\n", "- The line implied by the points \"goes backwards\" at some points. This is because the m-grid is not monotonic.\n", "- Some segments of the line are under other segments of the line. This means that we have sub-optimal points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A first step in filtering out sub-optimal points is to split the previous line in its non-decreasing segments. This is achieved by HARK's function `calc_segments`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute non-decreasing segments\n", "start, end = calc_nondecreasing_segments(m_egm, vt_egm)\n", "\n", "# Plot them, and store them as [m, v] pairs\n", "segments = []\n", "for j in range(len(start)):\n", " idx = range(start[j], end[j] + 1)\n", " plt.plot(m_egm[idx], vt_egm[idx])\n", " segments.append([m_egm[idx], vt_egm[idx]])\n", "\n", "plt.xlabel(\"resources\")\n", "plt.ylabel(\"transformed values\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to produce the upper-envelope of these segments: a line comprised of the points that are not under any other segment. This is done by HARK's `upper_envelope`function. We now apply it and plot the result" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The function defines the upper envelope over a new grid, which it\n", "# uses to interpolate each of the non-decreasing segments.\n", "m_upper, v_upper, inds_upper = upper_envelope(segments)\n", "\n", "for j in range(len(start)):\n", " idx = range(start[j], end[j] + 1)\n", " plt.plot(m_egm[idx], vt_egm[idx])\n", "plt.plot(m_upper, v_upper, \".k\")\n", "plt.xlabel(\"resources\")\n", "plt.ylabel(\"transformed values\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And there we have it! a monotonic value without the sub-optimal points or reverse jumps!\n", "\n", "Having introduced the main tools, we are now ready to apply DCEGM to a simple example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# An example: writing a will\n", "### Author: [Mateo Velásquez-Giraldo](https://mv77.github.io/)\n", "\n", "We now present a basic example to illustrate the use of the previous tools in solving dynamic optimization problems with discrete and continuous decisions.\n", "\n", "The model represents an agent that lives for three periods and decides how much of his resources to consume in each of them. On the second period, he must additionally decide whether to hire a lawyer to write a will. Having a will has the upside of allowing the agent to leave a bequest in his third and last period of life, which gives him utility, but has the downside that the lawyer will charge a fraction of his period 3 resources.\n", "\n", "On each period, the agent receives a deterministic amount of resources $w$. The problem, therefore, is fully deterministic.\n", "\n", "I now present the model formally, solving it backwards.\n", "\n", "But first, some setup and calibration:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Import tools for linear interpolation and finding optimal\n", "# discrete choices.\n", "\n", "# Import CRRA utility (and related) functions from HARK\n", "\n", "# Solution method parameters\n", "aGrid = np.linspace(0, 8, 400) # Savings grid for EGM.\n", "\n", "# Model parameters\n", "\n", "# Parameters that need to be fixed\n", "# Relative risk aversion. This is fixed at 2 in order to mantain\n", "# the analytical solution that we use, from Carroll (2000)\n", "CRRA = 2\n", "\n", "# Parameters that can be changed.\n", "w = 1 # Deterministic wage per period.\n", "# Fraction of resources charged by lawyer for writing a will.\n", "willCstFac = 0.35\n", "DiscFac = 0.98 # Time-discount factor.\n", "\n", "# Define utility (and related) functions\n", "\n", "\n", "def u(x):\n", " return CRRAutility(x, CRRA)\n", "\n", "\n", "def uP(x):\n", " return CRRAutilityP(x, CRRA)\n", "\n", "\n", "def uPinv(x):\n", " return CRRAutilityP_inv(x, CRRA)\n", "\n", "\n", "# Create a grid for market resources\n", "mGrid = (aGrid - aGrid[0]) * 1.5\n", "mGridPlots = np.linspace(w, 10 * w, 100)\n", "mGridPlotsC = np.insert(mGridPlots, 0, 0)\n", "\n", "# Transformations for value funtion interpolation\n", "\n", "\n", "def vTransf(x):\n", " return np.exp(x)\n", "\n", "\n", "def vUntransf(x):\n", " return np.log(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The third (last) period of life\n", "\n", "In the last period of life, the agent's problem is determined by his total amount of resources $m_3$ and a state variable $W$ that indicates whether he wrote a will ($W=1$) or not ($W=0$).\n", "\n", "### The agent without a will\n", "\n", "An agent who does not have a will simply consumes all of his available resources. Therefore, his value and consumption functions will be:\n", "\n", "\\begin{equation}\n", "V_3(m_3,W=0) = u(m_3)\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "c_3(m_3, W=0) = m_3\n", "\\end{equation}\n", "\n", "Where $u(\\cdot)$ gives the utility from consumption. We assume a CRRA specification $u(c) = \\frac{c^{1-\\rho}}{1-\\rho}$.\n", "\n", "### The agent with a will\n", "\n", "An agent who wrote a will decides how to allocate his available resources $m_3$ between his consumption and a bequest. We assume an additive specification for the utility of a given consumption-bequest combination that follows a particular case in [Carroll (2000)](http://www.econ2.jhu.edu/people/ccarroll/Why.pdf). The component of utility from leaving a bequest $x$ is assumed to be $\\ln (x+1)$. Therefore, the agent's value function is\n", "\n", "\\begin{equation}\n", "V_3(m_3, W=1) = \\max_{0\\leq c_3 \\leq m_3} u(c_3) + \\ln(m_3 - c_3 + 1)\n", "\\end{equation}\n", "\n", "For ease of exposition we consider the case $\\rho = 2$, where [Carroll (2000)](http://www.econ2.jhu.edu/people/ccarroll/Why.pdf) shows that the optimal consumption level is given by\n", "\n", "\\begin{equation}\n", "c_3(m_3, W=1) = \\min \\left[m_3, \\frac{-1 + \\sqrt{1 + 4(m_3+1)}}{2} \\right].\n", "\\end{equation}\n", "\n", "The consumption function shows that $m_3=1$ is the level of resources at which an important change of behavior occurs: agents leave bequests only for $m_3 > 1$. Since an important change of behavior happens at this point, we call it a 'kink-point' and add it to our grids." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Agent without a will\n", "mGrid3_no = mGrid\n", "cGrid3_no = mGrid\n", "vGrid3_no = u(cGrid3_no)\n", "\n", "# Create functions\n", "c3_no = LinearInterp(mGrid3_no, cGrid3_no) # (0,0) is already here.\n", "vT3_no = LinearInterp(mGrid3_no, vTransf(vGrid3_no), lower_extrap=True)\n", "\n", "\n", "def v3_no(x):\n", " return vUntransf(vT3_no(x))\n", "\n", "\n", "# Agent with a will\n", "\n", "# Define an auxiliary function with the analytical consumption expression\n", "\n", "\n", "def c3will(m):\n", " return np.minimum(m, -0.5 + 0.5 * np.sqrt(1 + 4 * (m + 1)))\n", "\n", "\n", "# Find the kink point\n", "mKink = 1.0\n", "indBelw = mGrid < mKink\n", "indAbve = mGrid > mKink\n", "\n", "mGrid3_wi = np.concatenate([mGrid[indBelw], np.array([mKink]), mGrid[indAbve]])\n", "\n", "cGrid3_wi = c3will(mGrid3_wi)\n", "\n", "cAbve = c3will(mGrid[indAbve])\n", "beqAbve = mGrid[indAbve] - c3will(mGrid[indAbve])\n", "vGrid3_wi = np.concatenate(\n", " [u(mGrid[indBelw]), u(np.array([mKink])), u(cAbve) + np.log(1 + beqAbve)]\n", ")\n", "\n", "# Create functions\n", "c3_wi = LinearInterp(mGrid3_wi, cGrid3_wi) # (0,0) is already here\n", "vT3_wi = LinearInterp(mGrid3_wi, vTransf(vGrid3_wi), lower_extrap=True)\n", "\n", "\n", "def v3_wi(x):\n", " return vUntransf(vT3_wi(x))\n", "\n", "\n", "plt.figure()\n", "\n", "plt.plot(mGridPlots, v3_wi(mGridPlots), label=\"Will\")\n", "plt.plot(mGridPlots, v3_no(mGridPlots), label=\"No Will\")\n", "plt.title(\"Period 3: Value functions\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.plot(mGridPlotsC, c3_wi(mGridPlotsC), label=\"Will\")\n", "plt.plot(mGridPlotsC, c3_no(mGridPlotsC), label=\"No Will\")\n", "plt.title(\"Period 3: Consumption Functions\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The second period\n", "\n", "On the second period, the agent takes his resources as given (the only state variable) and makes two decisions:\n", "- Whether to write a will or not.\n", "- What fraction of his resources to consume.\n", "\n", "These decisions can be seen as happening sequentially: the agent first decides whether to write a will or not, and then consumes optimally in accordance with his previous decision. Since we solve the model backwards in time, we first explore the consumption decision, conditional on the choice of writing a will or not.\n", "\n", "## An agent who decides not to write a will\n", "\n", "After deciding not to write a will, an agent solves the optimization problem expressed in the following conditional value function\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "\\nu (m_2|w=0) &= \\max_{0\\leq c \\leq m_2} u(c) + \\beta V_3(m_3,W=0)\\\\\n", "s.t.&\\\\\n", "m_3 &= m_2 - c + w\n", "\\end{split}\n", "\\end{equation}\n", "\n", "We can approximate a solution to this problem through the method of endogenous gridpoints. This yields approximations to $\\nu(\\cdot|w=0)$ and $c_2(\\cdot|w=0)$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Second period, not writing a will\n", "\n", "# Compute market resources at 3 with and without a will\n", "mGrid3_cond_nowi = aGrid + w\n", "# Compute marginal value of assets in period 3 for each ammount of savings in 2\n", "vPGrid3_no = uP(c3_no(mGrid3_cond_nowi))\n", "# Get consumption through EGM inversion of the euler equation\n", "cGrid2_cond_no = uPinv(DiscFac * vPGrid3_no)\n", "\n", "# Get beginning-of-period market resources\n", "mGrid2_cond_no = aGrid + cGrid2_cond_no\n", "\n", "# Compute value function\n", "vGrid2_cond_no = u(cGrid2_cond_no) + DiscFac * v3_no(mGrid3_cond_nowi)\n", "\n", "# Create interpolating value and consumption functions\n", "vT2_cond_no = LinearInterp(mGrid2_cond_no, vTransf(vGrid2_cond_no), lower_extrap=True)\n", "\n", "\n", "def v2_cond_no(x):\n", " return vUntransf(vT2_cond_no(x))\n", "\n", "\n", "c2_cond_no = LinearInterp(\n", " np.insert(mGrid2_cond_no, 0, 0), np.insert(cGrid2_cond_no, 0, 0)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An agent who decides to write a will\n", "\n", "An agent who decides to write a will also solves for his consumption dinamically. We assume that the lawyer that helps the agent write his will takes some fraction $\\tau$ of his total resources in period 3. Therefore, the evolution of resources is given by $m_3 = (1-\\tau)(m_2 - c_2 + w)$. The conditional value function of the agent is therefore:\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "\\nu (m_2|w=1) &= \\max_{0\\leq c \\leq m_2} u(c) + \\beta V_3(m_3,W=1)\\\\\n", "s.t.&\\\\\n", "m_3 &= (1-\\tau)(m_2 - c + w)\n", "\\end{split}\n", "\\end{equation}\n", "\n", "We also approximate a solution to this problem using the EGM. This yields approximations to $\\nu(\\cdot|w=1)$ and $c_2(\\cdot|w=1)$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Second period, writing a will\n", "\n", "# Compute market resources at 3 with and without a will\n", "mGrid3_cond_will = (1 - willCstFac) * (aGrid + w)\n", "# Compute marginal value of assets in period 3 for each ammount of savings in 2\n", "vPGrid3_wi = uP(c3_wi(mGrid3_cond_will))\n", "# Get consumption through EGM inversion of the euler equation\n", "cGrid2_cond_wi = uPinv(DiscFac * (1 - willCstFac) * vPGrid3_wi)\n", "# Get beginning-of-period market resources\n", "mGrid2_cond_wi = aGrid + cGrid2_cond_wi\n", "\n", "# Compute value function\n", "vGrid2_cond_wi = u(cGrid2_cond_wi) + DiscFac * v3_wi(mGrid3_cond_will)\n", "\n", "# Create interpolating value and consumption functions\n", "vT2_cond_wi = LinearInterp(mGrid2_cond_wi, vTransf(vGrid2_cond_wi), lower_extrap=True)\n", "\n", "\n", "def v2_cond_wi(x):\n", " return vUntransf(vT2_cond_wi(x))\n", "\n", "\n", "c2_cond_wi = LinearInterp(\n", " np.insert(mGrid2_cond_wi, 0, 0), np.insert(cGrid2_cond_wi, 0, 0)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The decision whether to write a will or not\n", "\n", "With the conditional value functions at hand, we can now express and solve the decision of whether to write a will or not, and obtain the unconditional value and consumption functions.\n", "\n", "\\begin{equation}\n", "V_2(m_2) = \\max \\{ \\nu (m_2|w=0), \\nu (m_2|w=1) \\}\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "w^*(m_2) = \\arg \\max_{w \\in \\{0,1\\}} \\{ \\nu (m_2|w=w) \\}\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "c_2(m_2) = c_2(m_2|w=w^*(m_2))\n", "\\end{equation}\n", "\n", "We now construct these objects." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We can use the upper_envelope function to find which action\n", "# is optimal over the common grid of market resources, and\n", "# insert the exact point in which the two actions yield equal value\n", "# into the grid\n", "m2_env, vt2_env, inds2_env = upper_envelope(\n", " [[mGrid, vT2_cond_no(mGrid)], [mGrid, vT2_cond_wi(mGrid)]]\n", ")\n", "\n", "# Plot the optimal decision rule\n", "plt.plot(m2_env, inds2_env)\n", "plt.title(\"$w^*(m)$\")\n", "plt.ylabel(\"Write will (1) or not (0)\")\n", "plt.xlabel(\"Market resources: m\")\n", "plt.show()\n", "\n", "# With the decision rule, we can find unconditional consumption\n", "c2_env = np.zeros_like(m2_env) + np.nan\n", "c2_env[inds2_env == 0] = c2_cond_no(m2_env[inds2_env == 0])\n", "c2_env[inds2_env == 1] = c2_cond_wi(m2_env[inds2_env == 1])\n", "\n", "# And create the unconditional consumption and value functions\n", "vT2 = LinearInterp(m2_env, vt2_env, lower_extrap=True)\n", "\n", "\n", "def v2(x):\n", " return vUntransf(vT2(x))\n", "\n", "\n", "c2 = LinearInterp(m2_env, c2_env, lower_extrap=True)\n", "\n", "# The 'kink' is where the optimal action changes. Find its position to plot it\n", "kink_idx = np.where(np.diff(inds2_env) != 0.0)\n", "\n", "# Plot the conditional and unconditional value functions\n", "plt.plot(m2_env, v2_cond_wi(m2_env), label=\"Cond. Will\")\n", "plt.plot(m2_env, v2_cond_no(m2_env), label=\"Cond. No will\")\n", "plt.plot(m2_env, v2(m2_env), \"k--\", label=\"Uncond.\")\n", "plt.plot(m2_env[kink_idx], v2(m2_env[kink_idx]), \"rX\", label=\"Primary kink\")\n", "plt.title(\"Period 2: Value Functions\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()\n", "\n", "# Plot the conditional and unconditional consumption\n", "# functions\n", "plt.plot(m2_env, c2_cond_wi(m2_env), label=\"Cond. Will\")\n", "plt.plot(m2_env, c2_cond_no(m2_env), label=\"Cond. No will\")\n", "plt.plot(m2_env, c2(m2_env), \"k--\", label=\"Uncond.\")\n", "plt.plot(m2_env[kink_idx], c2(m2_env[kink_idx]), \"rX\", label=\"Primary kink\")\n", "plt.title(\"Period 2: Consumption Functions\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The first period\n", "\n", "In the first period, the agent simply observes his market resources and decides what fraction of them to consume. His problem is represented by the following value function\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "V (m_1) &= \\max_{0\\leq c \\leq m_1} u(c) + \\beta V_2(m_2)\\\\\n", "s.t.&\\\\\n", "m_2 &= m_1 - c + w.\n", "\\end{split}\n", "\\end{equation}\n", "\n", "Although this looks like a simple problem, there are complications introduced by the kink in $V_2(\\cdot)$, which is clearly visible in the plot from the previous block. Particularly, note that $V_2'(\\cdot)$ and $c_2(\\cdot)$ are not monotonic: there are now multiple points $m$ for which the slope of $V_2(m)$ is equal. Thus, the Euler equation becomes a necessary but not sufficient condition for optimality and the traditional EGM inversion step can generate non-monotonic endogenous $m$ gridpoints.\n", "\n", "We now illustrate this phenomenon." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# EGM step\n", "\n", "# Period 2 resources implied by the exogenous savings grid\n", "mGrid2 = aGrid + w\n", "# Envelope condition\n", "vPGrid2 = uP(c2(mGrid2))\n", "# Inversion of the euler equation\n", "cGrid1 = uPinv(DiscFac * vPGrid2)\n", "# Endogenous gridpoints\n", "mGrid1 = aGrid + cGrid1\n", "vGrid1 = u(cGrid1) + DiscFac * v2(mGrid2)\n", "\n", "plt.plot(mGrid1)\n", "plt.title(\"Endogenous gridpoints\")\n", "plt.xlabel(\"Position: i\")\n", "plt.ylabel(\"Endogenous grid point: $m_i$\")\n", "plt.show()\n", "\n", "\n", "plt.plot(mGrid1, vGrid1)\n", "plt.title(\"Value function at grid points\")\n", "plt.xlabel(\"Market resources: m\")\n", "plt.ylabel(\"Value function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous cell applies the endogenous gridpoints method to the first period problem. The plots illustrate that the sequence of resulting endogenous gridpoints $\\{m_i\\}_{i=1}^N$ is not monotonic. This results in intervals of market resources over which we have multiple candidate values for the value function. This is the point where we must apply the upper envelope function illustrated above.\n", "\n", "We finally use the resulting consumption and value grid points to create the first period value and consumption functions." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate envelope\n", "# The function operates with *transformed* value grids\n", "vTGrid1 = vTransf(vGrid1)\n", "\n", "# Form non-decreasing segments\n", "start, end = calc_nondecreasing_segments(mGrid1, vTGrid1)\n", "\n", "m_segments = []\n", "vT_segments = []\n", "c_segments = []\n", "for j in range(len(start)):\n", " idx = range(start[j], end[j] + 1)\n", " m_segments.append(mGrid1[idx])\n", " vT_segments.append(vTGrid1[idx])\n", " c_segments.append(cGrid1[idx])\n", "\n", "# Get the upper envelope using m and vT\n", "m1_env, vt1_env, idx_1 = upper_envelope(segments=list(zip(m_segments, vT_segments)))\n", "\n", "# Store the index at which the optimal segment changes\n", "sec_kink_idx = np.where(np.diff(idx_1) != 0.0)\n", "\n", "# Construct enveloped consumption\n", "c1_env = np.zeros_like(m1_env) + np.nan\n", "for k, c_segm in enumerate(c_segments):\n", " c1_env[idx_1 == k] = LinearInterp(m_segments[k], c_segm)(m1_env[idx_1 == k])\n", "\n", "# Create functions\n", "c1_up = LinearInterp(m1_env, c1_env)\n", "v1T_up = LinearInterp(m1_env, vt1_env)\n", "\n", "\n", "def v1_up(x):\n", " return vUntransf(v1T_up(x))\n", "\n", "\n", "# Show that there is a non-monothonicity and that the upper envelope fixes it\n", "plt.plot(mGrid1, vGrid1, label=\"EGM Points\")\n", "plt.plot(m1_env, v1_up(m1_env), \"k--\", label=\"Upper Envelope\")\n", "plt.plot(m1_env[sec_kink_idx], v1_up(m1_env[sec_kink_idx]), \"rX\", label=\"Crossings\")\n", "plt.plot()\n", "plt.title(\"Period 1: Value function\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()\n", "\n", "# Plot consumption\n", "plt.plot(mGrid1, cGrid1, label=\"EGM Points\")\n", "plt.plot(m1_env, c1_up(m1_env), \"k--\", label=\"Upper Envelope\")\n", "plt.plot(\n", " m1_env[sec_kink_idx], c1_up(m1_env[sec_kink_idx]), \"rX\", label=\"Secondary Kink\"\n", ")\n", "plt.title(\"Period 1: Consumption function\")\n", "plt.xlabel(\"Market resources\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# References\n", "[1] Iskhakov, F. , Jørgensen, T. H., Rust, J. and Schjerning, B. (2017), The endogenous grid method for discrete‐continuous dynamic choice models with (or without) taste shocks. Quantitative Economics, 8: 317-365. doi:10.3982/QE643\n", "\n", "[2] Carroll, C. D. (2006). The method of endogenous gridpoints for solving dynamic stochastic optimization problems. Economics letters, 91(3), 312-320.\n", "\n" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "collapsed,title", "encoding": "# -*- coding: utf-8 -*-", "formats": "ipynb,py:percent", "notebook_metadata_filter": "all", "rst2md": false }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.13" }, "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 } }, "nbformat": 4, "nbformat_minor": 4 }