{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# DiscreteDP Example: Discrete Optimal Growth Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Daisuke Oyama**\n", "\n", "*Faculty of Economics, University of Tokyo*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider a discretized version of the (deterministic) optimal growth model\n", "discussed in\n", "[http://quant-econ.net/py/dp_intro.html](http://quant-econ.net/py/dp_intro.html).\n", "We provide a class DiscreteGrowthModel\n", "that wraps the setup and solution procedures in\n", "the [solution notebook](http://nbviewer.ipython.org/github/QuantEcon/QuantEcon.py/blob/master/solutions/discrete_dp_solutions.ipynb)\n", "for the exercise in the lecture." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import division, print_function\n", "import numpy as np\n", "import scipy.sparse as sparse\n", "import matplotlib.pyplot as plt\n", "from quantecon import compute_fixed_point\n", "from quantecon.markov import DiscreteDP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the following problem:\n", "\n", "\\begin{aligned}\n", "&\\max_{\\{c_t\\}_{t=0}^{\\infty}} \\sum_{t=0}^{\\infty} \\beta^t u(c_t) \\\\\n", "&\\ \\text{ s.t. }\\ k_{t+1} = f(k_t) - c_t,\n", " \\quad \\text{k_0: given},\n", "\\end{aligned}\n", "\n", "where\n", "$k_t$ and $c_t$ are the capital stock and consumption at time $t$, respectively,\n", "$u$ is the utility function,\n", "$f$ is the production function, and\n", "$\\beta \\in (0, 1)$ is the discount factor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We restrict the utility function $u$ and the production function $f$\n", "to the following classes of functions:\n", "$$\n", "u(c) =\n", "\\begin{cases}\n", "\\frac{c^{1-\\rho} - 1}{1 - \\rho} & \\text{if \\rho \\neq 1} \\\\\n", "\\log c & \\text{if \\rho = 1},\n", "\\end{cases}\n", "$$\n", "and\n", "$$\n", "f(k) = k^{\\alpha}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class DiscreteGrowthModel(object):\n", " \"\"\"\n", " Class representing the discrete optimal growth model.\n", " \n", " Parameters\n", " ----------\n", " alpha : scalar(float), optional(default=0.65)\n", " The parameter in the production function.\n", " \n", " beta : scalar(float), optional(default=0.95)\n", " The discount factor.\n", " \n", " rho : scalar(float), optional(default=1)\n", " The parameter in the utility function.\n", " \n", " grid_max : scalar(int), optional(default=2)\n", " The maximum grid value\n", " \n", " grid_size : scalar(int), optional(default=1500)\n", " The size of grid to use.\n", " \n", " \"\"\"\n", " def __init__(self, alpha=0.65, beta=0.95, rho=1,\n", " grid_max=2, grid_size=1500):\n", " self.alpha, self.rho = alpha, rho\n", " self._beta = beta\n", " self.grid = np.linspace(1e-6, grid_max, grid_size)\n", " \n", " C = self.f(self.grid).reshape(grid_size, 1) - \\\n", " self.grid.reshape(1, grid_size)\n", " s_indices, a_indices = np.where(C > 0)\n", " R = self.u(C[s_indices, a_indices])\n", " \n", " L = len(s_indices)\n", " data = np.ones(L)\n", " indptr = np.arange(L+1)\n", " Q = sparse.csr_matrix((data, a_indices, indptr), shape=(L, grid_size))\n", " \n", " self.ddp = DiscreteDP(R, Q, beta, s_indices, a_indices)\n", " \n", " self._mc = None\n", " self.num_iter = None\n", " \n", " def f(self, k):\n", " return k**self.alpha\n", " \n", " def u(self, c):\n", " rho = self.rho\n", " if rho == 1:\n", " util = np.log(c)\n", " else:\n", " util = (c**(1 - rho) - 1)/(1 - rho)\n", " return util\n", " \n", " @property\n", " def beta(self):\n", " return self._beta\n", " \n", " @beta.setter\n", " def beta(self, value):\n", " self._beta = value\n", " self.ddp.beta = self._beta\n", " self._mc = None\n", " self.num_iter = None\n", " \n", " def solve(self, w=None, *args, **kwargs):\n", " \"\"\"\n", " Solve the discrete dynamic programming problem.\n", " \n", " \"\"\"\n", " res = self.ddp.solve(v_init=w, *args, **kwargs)\n", " v = res.v\n", " c = self.sigma_to_c(res.sigma)\n", " self._mc = res.mc\n", " self.num_iter = res.num_iter\n", " return v, c\n", " \n", " def sigma_to_c(self, sigma):\n", " return self.f(self.grid) - self.grid[sigma]\n", " \n", " @property\n", " def mc(self):\n", " if self._mc is None:\n", " self.solve()\n", " return self._mc\n", " \n", " def generate_k_path(self, ts_length, k_init=None):\n", " \"\"\"\n", " Generate a trajectory of the capital stock.\n", " \n", " \"\"\"\n", " if k_init is None:\n", " k_init_ind = 0\n", " else:\n", " k_init_ind = np.searchsorted(self.grid, k_init)\n", " k_path_ind = self.mc.simulate(ts_length, init=k_init_ind)\n", " k_path = self.grid[k_path_ind]\n", " return k_path\n", " \n", " def bellman_operator(self, w, compute_policy=False):\n", " if compute_policy:\n", " sigma = np.empty(self.ddp.num_states, dtype=int)\n", " Tw = self.ddp.bellman_operator(w, sigma=sigma)\n", " c = self.sigma_to_c(sigma)\n", " return Tw, c\n", " else:\n", " Tw = self.ddp.bellman_operator(w)\n", " return Tw\n", " \n", " def compute_greedy(self, w):\n", " _, c = self.bellman_operator(w, compute_policy=True)\n", " return c" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Exact solution of the continuous version\n", "alpha, beta = 0.65, 0.95\n", "ab = alpha * beta\n", "c1 = (np.log(1 - ab) + np.log(ab) * ab / (1 - ab)) / (1 - beta)\n", "c2 = alpha / (1 - ab)\n", "def v_star(k):\n", " return c1 + c2 * np.log(k)\n", "\n", "def c_star(k):\n", " return (1 - ab) * k**alpha" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convergence of value iteration:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6jFisvOtRoZDB7Tairs6Eujoz6upMqK01QadjSWHrhVyOL4qCaU1lXNxOIxLJ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\nAUOeCAVaaOKngKr1EWuUmZpoEKNEslYnVK5i58qQ8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dgm = DiscreteGrowthModel()\n", "\n", "w = 5 * np.log(dgm.grid) - 25 # Initial condition\n", "n = 35\n", "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.set_ylim(-40, -20)\n", "ax.set_xlim(np.min(dgm.grid), np.max(dgm.grid))\n", "lb = 'initial condition'\n", "ax.plot(dgm.grid, w, color=plt.cm.jet(0), lw=2, alpha=0.6, label=lb)\n", "for i in range(n):\n", " w = dgm.bellman_operator(w)\n", " ax.plot(dgm.grid, w, color=plt.cm.jet(i / n), lw=2, alpha=0.6)\n", "lb = 'true value function'\n", "ax.plot(dgm.grid, v_star(dgm.grid), 'k-', lw=2, alpha=0.8, label=lb)\n", "ax.legend(loc='upper left')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", "1 6.924e+00 1.283e-02 \n", "2 4.107e+00 2.540e-02 \n", "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", "1 6.924e+00 1.333e-02 \n", "2 4.107e+00 2.541e-02 \n", "3 3.866e+00 3.903e-02 \n", "4 3.673e+00 5.133e-02 \n", "Iteration Distance Elapsed (seconds)\n", "---------------------------------------------\n", "1 6.924e+00 1.392e-02 \n", "2 4.107e+00 2.608e-02 \n", "3 3.866e+00 3.819e-02 \n", "4 3.673e+00 5.178e-02 \n", "5 3.489e+00 6.524e-02 \n", "6 3.315e+00 7.749e-02 \n" ] }, { "data": { "image/png": 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yyy0ON7D29vZGaWkpevfu7TBvUVERhg0bpr3u3r07QkJCUFhYiJiYmEbbjo2N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etbCA0NxeLFi/HTn/5U7Xm8e/du7Nu3DxEREfjwww+xZs0aj8fx5nNYtWoV/ud//gcRERH44IMP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\n8DQaZUl1+nQZsLm5n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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dgm = DiscreteGrowthModel()\n", "\n", "fig, ax = plt.subplots(3, 1, figsize=(8, 10))\n", "\n", "for i, n in enumerate((2, 4, 6)):\n", " ax[i].set_ylim(0, 1)\n", " ax[i].set_xlim(0, 2)\n", " ax[i].set_yticks((0, 1))\n", " ax[i].set_xticks((0, 2))\n", "\n", " w = 5 * dgm.u(dgm.grid) - 25 # Initial condition\n", " compute_fixed_point(dgm.bellman_operator, w, max_iter=n, print_skip=1)\n", " c = dgm.compute_greedy(w)\n", "\n", " ax[i].plot(dgm.grid, c, 'b-', lw=2, alpha=0.8,\n", " label='approximate optimal consumption policy')\n", " ax[i].plot(dgm.grid, c_star(dgm.grid), 'k-', lw=2, alpha=0.8,\n", " label='true optimal consumption policy')\n", " ax[i].legend(loc='upper left')\n", " ax[i].set_title('{} value function iterations'.format(n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dynamics of capital stock:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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h+PCMFrPWT26ZN5/0Fsgu9FBYclNEehZ16fdgHo+HiQUFmNhY+PxzsBbTvz+Z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\nJysrC4B169bR1NTE8OHDyczM5N577+3253VXx8H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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dgm = DiscreteGrowthModel() \n", "discount_factors = (0.9, 0.94, 0.98)\n", "series_length = 25\n", "k_init = 0.1\n", "\n", "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.set_xlabel(\"time\")\n", "ax.set_ylabel(\"capital\")\n", "ax.set_ylim(0.10, 0.30)\n", "\n", "for beta in discount_factors:\n", " dgm.beta = beta\n", " k = dgm.generate_k_path(ts_length=series_length, k_init=k_init)\n", " ax.plot(k, 'o-', lw=2, alpha=0.75, label=r'$\\beta = {}$'.format(beta))\n", "\n", "ax.legend(loc='lower right')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "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": "3.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }