{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Stachurski Sargent Optimal Savings\n", "\n", "This notebook replicates the code from the [Optimal Savings](http://lectures.quantecon.org/py/ifp.html) lecture, outlines a minor issue with the bounds of optimization, and suggests a minimal solution. \n", "\n", "The notebook progresses as follows:\n", "\n", "1. Replicate code and figure from the [Optimal Savings](http://lectures.quantecon.org/py/ifp.html) lecture\n", "2. Demonstrate a minor issue with code when b!=0\n", "3. A simple solution?\n", "\n", "# 1. Replicate code and figure from [Optimal Savings](http://lectures.quantecon.org/py/ifp.html)\n", "\n", "The following code is directly copy-pasted from the [Optimal Savings](http://lectures.quantecon.org/py/ifp.html) lecture:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "\"\"\"\n", "Filename: ifp.py\n", "\n", "Authors: Thomas Sargent, John Stachurski\n", "\n", "Tools for solving the standard optimal savings / income fluctuation\n", "problem for an infinitely lived consumer facing an exogenous income\n", "process that evolves according to a Markov chain.\n", "\n", "References\n", "----------\n", "\n", "http://quant-econ.net/py/ifp.html\n", "\n", "\"\"\"\n", "from textwrap import dedent\n", "import numpy as np\n", "from scipy.optimize import fminbound, brentq\n", "from scipy import interp\n", "\n", "\n", "class ConsumerProblem(object):\n", " \"\"\"\n", " A class for solving the income fluctuation problem. Iteration with\n", " either the Coleman or Bellman operators from appropriate initial\n", " conditions leads to convergence to the optimal consumption policy.\n", " The income process is a finite state Markov chain. Note that the\n", " Coleman operator is the preferred method, as it is almost always\n", " faster and more accurate. The Bellman operator is only provided for\n", " comparison.\n", "\n", " Parameters\n", " ----------\n", " r : scalar(float), optional(default=0.01)\n", " A strictly positive scalar giving the interest rate\n", " beta : scalar(float), optional(default=0.96)\n", " The discount factor, must satisfy (1 + r) * beta < 1\n", " Pi : array_like(float), optional(default=((0.60, 0.40),(0.05, 0.95))\n", " A 2D NumPy array giving the Markov matrix for {z_t}\n", " z_vals : array_like(float), optional(default=(0.5, 0.95))\n", " The state space of {z_t}\n", " b : scalar(float), optional(default=0)\n", " The borrowing constraint\n", " grid_max : scalar(float), optional(default=16)\n", " Max of the grid used to solve the problem\n", " grid_size : scalar(int), optional(default=50)\n", " Number of grid points to solve problem, a grid on [-b, grid_max]\n", " u : callable, optional(default=np.log)\n", " The utility function\n", " du : callable, optional(default=lambda x: 1/x)\n", " The derivative of u\n", "\n", " Attributes\n", " ----------\n", " r, beta, Pi, z_vals, b, u, du : see Parameters\n", " asset_grid : np.ndarray\n", " One dimensional grid for assets\n", "\n", " \"\"\"\n", "\n", " def __init__(self, r=0.01, beta=0.96, Pi=((0.6, 0.4), (0.05, 0.95)),\n", " z_vals=(0.5, 1.0), b=0, grid_max=16, grid_size=50,\n", " u=np.log, du=lambda x: 1/x):\n", " self.u, self.du = u, du\n", " self.r, self.R = r, 1 + r\n", " self.beta, self.b = beta, b\n", " self.Pi, self.z_vals = np.array(Pi), tuple(z_vals)\n", " self.asset_grid = np.linspace(-b, grid_max, grid_size)\n", "\n", " def __repr__(self):\n", " m = \"ConsumerProblem(r={r:g}, beta={be:g}, Pi='{n:g} by {n:g}', \"\n", " m += \"z_vals={z}, b={b:g}, grid_max={gm:g}, grid_size={gs:g}, \"\n", " m += \"u={u}, du={du})\"\n", " return m.format(r=self.r, be=self.beta, n=self.Pi.shape[0],\n", " z=self.z_vals, b=self.b,\n", " gm=self.asset_grid.max(), gs=self.asset_grid.size,\n", " u=self.u, du=self.du)\n", "\n", " def __str__(self):\n", " m = \"\"\"\n", " Consumer Problem (optimal savings):\n", " - r (interest rate) : {r:g}\n", " - beta (discount rate) : {be:g}\n", " - Pi (transition matrix) : {n} by {n}\n", " - z_vals (state space of shocks) : {z}\n", " - b (borrowing constraint) : {b:g}\n", " - grid_max (maximum of asset grid) : {gm:g}\n", " - grid_size (number of points in asset grid) : {gs:g}\n", " - u (utility function) : {u}\n", " - du (marginal utility function) : {du}\n", " \"\"\"\n", " return dedent(m.format(r=self.r, be=self.beta, n=self.Pi.shape[0],\n", " z=self.z_vals, b=self.b,\n", " gm=self.asset_grid.max(),\n", " gs=self.asset_grid.size, u=self.u,\n", " du=self.du))\n", "\n", " def bellman_operator(self, V, return_policy=False):\n", " \"\"\"\n", " The approximate Bellman operator, which computes and returns the\n", " updated value function TV (or the V-greedy policy c if\n", " return_policy is True).\n", "\n", " Parameters\n", " ----------\n", " V : array_like(float)\n", " A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals)\n", " return_policy : bool, optional(default=False)\n", " Indicates whether to return the greed policy given V or the\n", " updated value function TV. Default is TV.\n", "\n", " Returns\n", " -------\n", " array_like(float)\n", " Returns either the greed policy given V or the updated value\n", " function TV.\n", "\n", " \"\"\"\n", " # === Simplify names, set up arrays === #\n", " R, Pi, beta, u, b = self.R, self.Pi, self.beta, self.u, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " new_V = np.empty(V.shape)\n", " new_c = np.empty(V.shape)\n", " z_idx = list(range(len(z_vals)))\n", "\n", " # === Linear interpolation of V along the asset grid === #\n", " vf = lambda a, i_z: interp(a, asset_grid, V[:, i_z])\n", "\n", " # === Solve r.h.s. of Bellman equation === #\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " def obj(c): # objective function to be *minimized*\n", " y = sum(vf(R * a + z - c, j) * Pi[i_z, j] for j in z_idx)\n", " return - u(c) - beta * y\n", " c_star = fminbound(obj, np.min(z_vals), R * a + z + b)\n", " new_c[i_a, i_z], new_V[i_a, i_z] = c_star, -obj(c_star)\n", "\n", " if return_policy:\n", " return new_c\n", " else:\n", " return new_V\n", "\n", " def coleman_operator(self, c):\n", " \"\"\"\n", " The approximate Coleman operator.\n", "\n", " Iteration with this operator corresponds to policy function\n", " iteration. Computes and returns the updated consumption policy\n", " c. The array c is replaced with a function cf that implements\n", " univariate linear interpolation over the asset grid for each\n", " possible value of z.\n", "\n", " Parameters\n", " ----------\n", " c : array_like(float)\n", " A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals)\n", "\n", " Returns\n", " -------\n", " array_like(float)\n", " The updated policy, where updating is by the Coleman\n", " operator. function TV.\n", "\n", " \"\"\"\n", " # === simplify names, set up arrays === #\n", " R, Pi, beta, du, b = self.R, self.Pi, self.beta, self.du, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " z_size = len(z_vals)\n", " gamma = R * beta\n", " vals = np.empty(z_size)\n", "\n", " # === linear interpolation to get consumption function === #\n", " def cf(a):\n", " \"\"\"\n", " The call cf(a) returns an array containing the values c(a,\n", " z) for each z in z_vals. For each such z, the value c(a, z)\n", " is constructed by univariate linear approximation over asset\n", " space, based on the values in the array c\n", " \"\"\"\n", " for i in range(z_size):\n", " vals[i] = interp(a, asset_grid, c[:, i])\n", " return vals\n", "\n", " # === solve for root to get Kc === #\n", " Kc = np.empty(c.shape)\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " def h(t):\n", " expectation = np.dot(du(cf(R * a + z - t)), Pi[i_z, :])\n", " return du(t) - max(gamma * expectation, du(R * a + z + b))\n", " Kc[i_a, i_z] = brentq(h, np.min(z_vals), R * a + z + b)\n", "\n", " return Kc\n", "\n", " def initialize(self):\n", " \"\"\"\n", " Creates a suitable initial conditions V and c for value function\n", " and policy function iteration respectively.\n", "\n", " Returns\n", " -------\n", " V : array_like(float)\n", " Initial condition for value function iteration\n", " c : array_like(float)\n", " Initial condition for Coleman operator iteration\n", "\n", " \"\"\"\n", " # === Simplify names, set up arrays === #\n", " R, beta, u, b = self.R, self.beta, self.u, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " shape = len(asset_grid), len(z_vals)\n", " V, c = np.empty(shape), np.empty(shape)\n", "\n", " # === Populate V and c === #\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " c_max = R * a + z + b\n", " c[i_a, i_z] = c_max\n", " V[i_a, i_z] = u(c_max) / (1 - beta)\n", "\n", " return V, c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1 Exercise 1 Text\n", "\n", "The first exercise is to replicate the following figure, which compares PFI and VFI as solution methods\n", "\n", "![Exercise 1 Replication](./vfi_vs_pfi.png)\n", "\n", "The figure shows consumption policies computed by iteration of KK and TT respectively\n", "\n", "- In the case of iteration with TT, the final value function is used to compute the observed policy\n", "\n", "Consumption is shown as a function of assets with income zz held fixed at its smallest value\n", "\n", "The following details are needed to replicate the figure\n", "\n", "- (i) The parameters are the default parameters in the definition of consumerProblem\n", "- (ii) The initial conditions are the default ones from initialize()\n", "- (iii) Both operators are iterated 80 times\n", "\n", "## 1.2 Replicate Figure Using $b=0$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# import libraries: \n", "import sys\n", "import pylab as plt\n", "from scipy.interpolate import InterpolatedUnivariateSpline\n", "\n", "#-------------------------------------------------------------------------------\n", "# (i.a) Set up all default parameters, explicitly: \n", "#-------------------------------------------------------------------------------\n", "\n", "r = 0.01\n", "beta = 0.96\n", "b = 0.0\n", "\n", "grid_max = 16\n", "grid_size = 50\n", "\n", "u = np.log\n", "du = lambda x: 1/x\n", "\n", "Pi = ((0.6, 0.4), (0.05, 0.95))\n", "z_vals = (0.5, 1.0)\n", "\n", "TT = 80 \n", "\n", "# Create a grid for plotting that is much finer that the interpolation grid:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For convenience, define a function that runs the T-length iteration:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def run_iteration(T, cons_prob, c_tm1, v_tm1):\n", " new_c = np.repeat(np.nan, T) # Fill out an empty one...\n", " for t in range(T):\n", " if t%10 == 0:\n", " print(\"t=\",t)\n", "\n", " # Use try-except so can print both error messages \n", " #\n", " # First execute coleman operator inside its own try-except:\n", " try:\n", " Kc = cons_prob.coleman_operator(c=c_tm1)\n", " c_tm1 = Kc # ...yeah yeah not needed...\n", " except:\n", " if t < 5:\n", " print(\"NOTE: colman encountered this error:\\n\", sys.exc_info()[0])\n", "\n", " # Now execute bellman operator inside its own try-except;\n", " # this time also raise error encountered.\n", " try:\n", " new_V = cons_prob.bellman_operator(V=v_tm1, return_policy=False)\n", " new_c = cons_prob.bellman_operator(V=v_tm1, return_policy=True)\n", " v_tm1 = new_V\n", "\n", " except:\n", " if t < 5:\n", " print(\"NOTE: belman encountered this error:\\n\", sys.exc_info()[0])\n", " \n", " return c_tm1, new_c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now run the default consumer problem:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n" ] } ], "source": [ "#-------------------------------------------------------------------------------\n", "# (i.b) Create a consumer problem with default values: \n", "#-------------------------------------------------------------------------------\n", "consumer_prob = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "\n", "#-------------------------------------------------------------------------------\n", "# (ii) Init values from consumer_prob.initialize():\n", "#-------------------------------------------------------------------------------\n", "v_tm1, c_tm1 = consumer_prob.initialize()\n", "\n", "#-------------------------------------------------------------------------------\n", "# (iii) Iterate both operators 80 times:\n", "#-------------------------------------------------------------------------------\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob, c_tm1=c_tm1, v_tm1=v_tm1)\n", " \n", "# Define a function to create consumption functions:\n", "def create_linear_interp_functions(prob, fxn_points):\n", " '''\n", " Given the output of either bellman_operator or coleman_operator, \n", " return a tuple with a linear interpolation for each column. \n", " '''\n", " rxn_interp = []\n", " for i in range(fxn_points.shape[1]):\n", " rxn_interp.append(InterpolatedUnivariateSpline( prob.asset_grid, fxn_points[:, i], k=1))\n", " return rxn_interp\n", "\n", "# Create linear interpolations of each function:\n", "c_pi = create_linear_interp_functions(consumer_prob, c_tm1)\n", "c_vi = create_linear_interp_functions(consumer_prob, new_c)\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SEsr69evw8cmKtXXw8Qnh6afr0aFDTp57DgIC3K5UUltix0mINztaazvEMW01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\naaPOiCKS7oSHh1O5cmWAytb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atY5cvPgDEyeuolSpO9wuSURExFUKCR69e79HeHgIzz47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\nmZm15SLBzMzM2nKRYGZmZm25SDAzM7O2XCSYmZl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eDGfOQLNmMGzYbtaseZ9evcbz+++/U6NGDcLDw2ncuDG5c+cOdMiSAkoSREQk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\nbrrp/6hW7XWuvDIvVavCQw+hOzaKiEi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#-------------------------------------------------------------------------------\n", "# (iv) Plot results with new colors:\n", "#-------------------------------------------------------------------------------\n", "\n", "plt.plot(plotgrid, c_vi[0](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[0](plotgrid), label=\"PI\", color='black')\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_vi[1](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[1](plotgrid), label=\"PI\", color='black')\n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# 2. Demonstrate a minor issue with code when b!=0\n", "Now set b to a handful of values. We can try a few things to show the problem:\n", "\n", "- b = 0.1\n", "- b = 2.0\n", "- b = -5.0 # just to show that it isn't that incorrectly. \n", "\n", "## 2.1 Demo: $b=0.1$\n", "\n", "Now try $b=0.1$; this should result in an error. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n", "('NOTE: error:\\n', )\n", "('****NOTE: error:\\n', )\n" ] }, { "data": { "image/png": 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ptjnnwk/SI/FBfVIiIqVQQQ+BPBrvC+SXXOYzYJ2Z/Whmi83sogKuV4qJc66/c67AZ5IT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\ncjTwS9BF5CafF8OKJ0fjpdeYfy1yMBZ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lpSVhFHAe0CCfYhERkQLy1VdfMWjQICZPnswJJ5zA4MGD6dy5M0cddZTfoUkU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\nc87xOxwRESmGlCREoWnTppGUlERSUhK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b = 0.1\n", "consumer_prob_b01 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_b01.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_b01, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi_b01 = create_linear_interp_functions(consumer_prob_b01, c_tm1)\n", "try:\n", " c_vi_b01 = create_linear_interp_functions(consumer_prob_b01, new_c)\n", "except:\n", " #c_vi = [np.repeat(np.nan, len(c_pi[k])) for k in range(len(c_pi)) ]\n", " print(\"NOTE: error:\\n\", sys.exc_info()[0])\n", "\n", "# Plot:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_pi_b01[0](plotgrid), label=\"PI\", color='black')\n", "try:\n", " plt.plot(plotgrid, c_vi_b01[0](plotgrid), label=\"VI\", color='blue')\n", "except:\n", " print(\"****NOTE: error:\\n\", sys.exc_info()[0])\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_pi_b01[1](plotgrid), label=\"PI\", color='black')\n", " \n", "try:\n", " plt.plot(plotgrid, c_vi_b01[1](plotgrid), label=\"VI\", color='blue')\n", "except:\n", " print(\"****NOTE: error:\\n\", sys.exc_info()[0])\n", " \n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Demo: $b=2.0$\n", "\n", "Now try $b=2.0$; this should result in an error. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('NOTE: belman encountered this error:\\n', )\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n", "('NOTE: error:\\n', )\n", "('****NOTE: error:\\n', )\n" ] }, { "data": { "image/png": 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Ikfzwww/ccMMNjB49mubNm6u/gUgJopAgIoVmw4YNPP/88yQlJXHo0CG6dOnC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\nYXOAPxfDsgVYvHgxt912G92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ASgMLzSzLBjszOw+YAywBqgMjgFfM7OY8xCsikm/ffPMNd955J82bN+eaa65h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\nfqFHjx6MHz+e++67j6eeeop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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b = 2.0\n", "consumer_prob_b2 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_b2.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_b2, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi_b2 = create_linear_interp_functions(consumer_prob_b2, c_tm1)\n", "try:\n", " c_vi_b2 = create_linear_interp_functions(consumer_prob_b2, new_c)\n", "except:\n", " #c_vi = [np.repeat(np.nan, len(c_pi[k])) for k in range(len(c_pi)) ]\n", " print(\"NOTE: error:\\n\", sys.exc_info()[0])\n", "\n", "# Plot:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_pi_b2[0](plotgrid), label=\"PI\", color='black')\n", "try:\n", " plt.plot(plotgrid, c_vi_b2[0](plotgrid), label=\"VI\", color='blue')\n", "except:\n", " print(\"****NOTE: error:\\n\", sys.exc_info()[0])\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_pi_b2[1](plotgrid), label=\"PI\", color='black')\n", "\n", "try:\n", " plt.plot(plotgrid, c_vi_b2[1](plotgrid), label=\"VI\", color='blue')\n", "except:\n", " print(\"****NOTE: error:\\n\", sys.exc_info()[0])\n", " \n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Demo: $b=-5.0$\n", "\n", "Now try $b=-5.0$; this doesn't throw an error but gives results that don't appear correct." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n" ] } ], "source": [ "b = -5.0\n", "consumer_prob_bminus5 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_bminus5.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_bminus5, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi_bm5 = create_linear_interp_functions(consumer_prob, c_tm1)\n", "c_vi_bm5 = create_linear_interp_functions(consumer_prob, new_c)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TU4s0wTYzRo0aRcOGDSlZsiQ1a9bksssuK7L9h5KSA5EwtXcvjBzpSEhYyIED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\nb7toEWzcCHfeGYLAREQk4ig5iAJHjx7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N4uL8jlhimZIEEZE85hwsXgwjR8Lcubtw7jVKlx4LrOWkk2pw220D6d69O1Wq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\nlCRITPntN3jzTZgxA5Yvh6J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotgrid = np.linspace((b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_vi_bm5[0](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi_bm5[0](plotgrid), label=\"PI\", color='black')\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_vi_bm5[1](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi_bm5[1](plotgrid), label=\"PI\", color='black')\n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. A Simple Solution\n", "\n", "There is a very simple solution: for each of the optimization/root-finding lines, search from a minimum of \"machine zero\" to the appropriate upper bound. (One could simply also use 0 as the lower bound, but I have occasionally hit errors doing this. Some optimizers like to try the lowest bound first; 0 of course doesn't play nicely with functions like log.)\n", "\n", "Look for the comments \n", "\n", " ## **** New code **** \n", " \n", "on the new code lines... tacky but easy to spot.\n", "\n", "\n", "I also re-run the demos below to show better-looking solutions. \n", "\n", "## 3.1 Code Replicated with Simple Solution" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "\"\"\"\n", "Filename: ifp.py\n", "\n", "Authors: Thomas Sargent, John Stachurski\n", "\n", "Tools for solving the standard optimal savings / income fluctuation\n", "problem for an infinitely lived consumer facing an exogenous income\n", "process that evolves according to a Markov chain.\n", "\n", "References\n", "----------\n", "\n", "http://quant-econ.net/py/ifp.html\n", "\n", "\"\"\"\n", "\n", "class ConsumerProblem(object):\n", " \"\"\"\n", " A class for solving the income fluctuation problem. Iteration with\n", " either the Coleman or Bellman operators from appropriate initial\n", " conditions leads to convergence to the optimal consumption policy.\n", " The income process is a finite state Markov chain. Note that the\n", " Coleman operator is the preferred method, as it is almost always\n", " faster and more accurate. The Bellman operator is only provided for\n", " comparison.\n", "\n", " Parameters\n", " ----------\n", " r : scalar(float), optional(default=0.01)\n", " A strictly positive scalar giving the interest rate\n", " beta : scalar(float), optional(default=0.96)\n", " The discount factor, must satisfy (1 + r) * beta < 1\n", " Pi : array_like(float), optional(default=((0.60, 0.40),(0.05, 0.95))\n", " A 2D NumPy array giving the Markov matrix for {z_t}\n", " z_vals : array_like(float), optional(default=(0.5, 0.95))\n", " The state space of {z_t}\n", " b : scalar(float), optional(default=0)\n", " The borrowing constraint\n", " grid_max : scalar(float), optional(default=16)\n", " Max of the grid used to solve the problem\n", " grid_size : scalar(int), optional(default=50)\n", " Number of grid points to solve problem, a grid on [-b, grid_max]\n", " u : callable, optional(default=np.log)\n", " The utility function\n", " du : callable, optional(default=lambda x: 1/x)\n", " The derivative of u\n", " min_c : float ## **** New code **** \n", " The minimum consumption value for use in the ## **** New code ****\n", " minimization and root-finding operations. Used for ## **** New code ****\n", " numerical purposes. ## **** New code **** \n", "\n", "\n", " Attributes\n", " ----------\n", " r, beta, Pi, z_vals, b, u, du : see Parameters\n", " asset_grid : np.ndarray\n", " One dimensional grid for assets\n", "\n", " \"\"\"\n", "\n", " def __init__(self, r=0.01, beta=0.96, Pi=((0.6, 0.4), (0.05, 0.95)),\n", " z_vals=(0.5, 1.0), b=0, grid_max=16, grid_size=50,\n", " u=np.log, du=lambda x: 1/x, min_c=1e-8):\n", " self.u, self.du = u, du\n", " self.r, self.R = r, 1 + r\n", " self.beta, self.b = beta, b\n", " self.Pi, self.z_vals = np.array(Pi), tuple(z_vals)\n", " self.asset_grid = np.linspace(-b, grid_max, grid_size)\n", " self.min_c = min_c ## **** New code **** \n", "\n", " def __repr__(self):\n", " m = \"ConsumerProblem(r={r:g}, beta={be:g}, Pi='{n:g} by {n:g}', \"\n", " m += \"z_vals={z}, b={b:g}, grid_max={gm:g}, grid_size={gs:g}, \"\n", " m += \"u={u}, du={du})\"\n", " return m.format(r=self.r, be=self.beta, n=self.Pi.shape[0],\n", " z=self.z_vals, b=self.b,\n", " gm=self.asset_grid.max(), gs=self.asset_grid.size,\n", " u=self.u, du=self.du)\n", "\n", " def __str__(self):\n", " m = \"\"\"\n", " Consumer Problem (optimal savings):\n", " - r (interest rate) : {r:g}\n", " - beta (discount rate) : {be:g}\n", " - Pi (transition matrix) : {n} by {n}\n", " - z_vals (state space of shocks) : {z}\n", " - b (borrowing constraint) : {b:g}\n", " - grid_max (maximum of asset grid) : {gm:g}\n", " - grid_size (number of points in asset grid) : {gs:g}\n", " - u (utility function) : {u}\n", " - du (marginal utility function) : {du}\n", " \"\"\"\n", " return dedent(m.format(r=self.r, be=self.beta, n=self.Pi.shape[0],\n", " z=self.z_vals, b=self.b,\n", " gm=self.asset_grid.max(),\n", " gs=self.asset_grid.size, u=self.u,\n", " du=self.du))\n", "\n", " def bellman_operator(self, V, return_policy=False):\n", " \"\"\"\n", " The approximate Bellman operator, which computes and returns the\n", " updated value function TV (or the V-greedy policy c if\n", " return_policy is True).\n", "\n", " Parameters\n", " ----------\n", " V : array_like(float)\n", " A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals)\n", " return_policy : bool, optional(default=False)\n", " Indicates whether to return the greed policy given V or the\n", " updated value function TV. Default is TV.\n", "\n", " Returns\n", " -------\n", " array_like(float)\n", " Returns either the greed policy given V or the updated value\n", " function TV.\n", "\n", " \"\"\"\n", " # === Simplify names, set up arrays === #\n", " R, Pi, beta, u, b = self.R, self.Pi, self.beta, self.u, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " new_V = np.empty(V.shape)\n", " new_c = np.empty(V.shape)\n", " z_idx = list(range(len(z_vals)))\n", "\n", " # === Linear interpolation of V along the asset grid === #\n", " vf = lambda a, i_z: interp(a, asset_grid, V[:, i_z])\n", "\n", " # === Solve r.h.s. of Bellman equation === #\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " def obj(c): # objective function to be *minimized*\n", " y = sum(vf(R * a + z - c, j) * Pi[i_z, j] for j in z_idx)\n", " return - u(c) - beta * y\n", " #c_star = fminbound(obj, np.min(z_vals), R * a + z + b)\n", " c_star = fminbound(obj, self.min_c, R * a + z + b) ## **** New code ****\n", " new_c[i_a, i_z], new_V[i_a, i_z] = c_star, -obj(c_star)\n", "\n", " if return_policy:\n", " return new_c\n", " else:\n", " return new_V\n", "\n", " def coleman_operator(self, c):\n", " \"\"\"\n", " The approximate Coleman operator.\n", "\n", " Iteration with this operator corresponds to policy function\n", " iteration. Computes and returns the updated consumption policy\n", " c. The array c is replaced with a function cf that implements\n", " univariate linear interpolation over the asset grid for each\n", " possible value of z.\n", "\n", " Parameters\n", " ----------\n", " c : array_like(float)\n", " A NumPy array of dim len(cp.asset_grid) times len(cp.z_vals)\n", "\n", " Returns\n", " -------\n", " array_like(float)\n", " The updated policy, where updating is by the Coleman\n", " operator. function TV.\n", "\n", " \"\"\"\n", " # === simplify names, set up arrays === #\n", " R, Pi, beta, du, b = self.R, self.Pi, self.beta, self.du, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " z_size = len(z_vals)\n", " gamma = R * beta\n", " vals = np.empty(z_size)\n", "\n", " # === linear interpolation to get consumption function === #\n", " def cf(a):\n", " \"\"\"\n", " The call cf(a) returns an array containing the values c(a,\n", " z) for each z in z_vals. For each such z, the value c(a, z)\n", " is constructed by univariate linear approximation over asset\n", " space, based on the values in the array c\n", " \"\"\"\n", " for i in range(z_size):\n", " vals[i] = interp(a, asset_grid, c[:, i])\n", " return vals\n", "\n", " # === solve for root to get Kc === #\n", " Kc = np.empty(c.shape)\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " def h(t):\n", " expectation = np.dot(du(cf(R * a + z - t)), Pi[i_z, :])\n", " return du(t) - max(gamma * expectation, du(R * a + z + b))\n", " #Kc[i_a, i_z] = brentq(h, np.min(z_vals), R * a + z + b)\n", " Kc[i_a, i_z] = brentq(h, self.min_c, R * a + z + b) ## **** New code ****\n", "\n", " return Kc\n", "\n", " def initialize(self):\n", " \"\"\"\n", " Creates a suitable initial conditions V and c for value function\n", " and policy function iteration respectively.\n", "\n", " Returns\n", " -------\n", " V : array_like(float)\n", " Initial condition for value function iteration\n", " c : array_like(float)\n", " Initial condition for Coleman operator iteration\n", "\n", " \"\"\"\n", " # === Simplify names, set up arrays === #\n", " R, beta, u, b = self.R, self.beta, self.u, self.b\n", " asset_grid, z_vals = self.asset_grid, self.z_vals\n", " shape = len(asset_grid), len(z_vals)\n", " V, c = np.empty(shape), np.empty(shape)\n", "\n", " # === Populate V and c === #\n", " for i_a, a in enumerate(asset_grid):\n", " for i_z, z in enumerate(z_vals):\n", " c_max = R * a + z + b\n", " c[i_a, i_z] = c_max\n", " V[i_a, i_z] = u(c_max) / (1 - beta)\n", "\n", " return V, c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Re-Run Demos \n", "\n", "Now re-run the demos:\n", "\n", "- b = 0.1\n", "- b = 2.0\n", "- b = -5.0 # just to show that it isn't that incorrectly. \n", "\n", "Here are all, one after another, in the following code block:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n" ] }, { "data": { "image/png": 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z6quvMm/eT/zzT3vgN5555gaffbaVEycGcOKEM59/Ds89J9Mi52VyusEGKaX4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\nJKEPRMCDD8LYsbtvK0lStTIk9IHBg2Fq7l0pJEm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N7Xghhnrzsd7Pzp8bkVMrnW8J/vvpLfk3sf8xlAKiVjZsaYyJs0tfqfRCRJoDK4BnjDG7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\n3/3OEwkz647XVfqE31nKQALwO7xekbbAq8BLZvZbX1NF7jk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OR/KvkM6pMO8KhF+Zt8TybjObYmZXZbJNMzt3SeBk/8pxIiKSfbfhLZL1frgDkfwt1BM1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\ntRUJwMe1HXzvvfcSFxdXaVtaWhppaWnnGU74y83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XgvAaUCOuBMFlC1An2rKXXMtFRJIkLCyML7/8En9/fzZs2EDBggXx9fWlQ4cO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\nq+M/+OAD3n77bd57770gR9ZwTJkyhUcffZQ5c+Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b = 0.1\n", "consumer_prob_b01 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_b01.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_b01, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi = create_linear_interp_functions(consumer_prob, c_tm1)\n", "c_vi = create_linear_interp_functions(consumer_prob, new_c)\n", "\n", "# Plot:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_vi[0](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[0](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_pi_b01[0](plotgrid), label=\"PI, np.min(z_vals)\", color='black', linestyle='--')\n", "\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_vi[1](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[1](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_pi_b01[1](plotgrid), label=\"PI, np.min(z_vals)\", color='black', linestyle='--')\n", "\n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "\n", "# ==============================================================================\n", "\n", "\n", "b = 2.0\n", "consumer_prob_b2 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_b2.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_b2, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi = create_linear_interp_functions(consumer_prob, c_tm1)\n", "c_vi = create_linear_interp_functions(consumer_prob, new_c)\n", "\n", "# Plot:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_vi[0](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[0](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_pi_b2[0](plotgrid), label=\"PI, np.min(z_vals)\", color='black', linestyle='--')\n", "\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_vi[1](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[1](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_pi_b2[1](plotgrid), label=\"PI, np.min(z_vals)\", color='black', linestyle='--')\n", "\n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Finally Compare $b=5$ New to Previous $b=-5$\n", "\n", "Now try $b=5$ instead of $b=-5$, and compare results to *previous code* solution with $b=-5$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('t=', 0)\n", "('t=', 10)\n", "('t=', 20)\n", "('t=', 30)\n", "('t=', 40)\n", "('t=', 50)\n", "('t=', 60)\n", "('t=', 70)\n" ] }, { "data": { "image/png": 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SvlzDb4/j9B35zNvxSNbk0T4HxpiexrnC1inXbYUx5n5P7lNEJItrhjNZ0gRvByJZl6c7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\nzpyxvVfXrYKDBw8C0LFjx3rH3xQ0OVBKKdWkbrvtNgICAnj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Xrmy3Y6RqUqGUmgn4AT5AmFIqpgbijtb6oaXMf4EiWuuYuSi+AnoppcYDc4G6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\nCZCKCik25xyJiYnUrFmT/v37Bx1HREQCpscfUmzTpk1jzpw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ==============================================================================\n", "\n", "\n", "b = 5.0\n", "consumer_prob_b5 = ConsumerProblem(r=r, beta=beta, Pi=Pi, z_vals=z_vals, b=b, \n", " grid_max=grid_max, grid_size=grid_size, u=u, \n", " du=du)\n", "# Initialize\n", "v_tm1, c_tm1 = consumer_prob_b5.initialize()\n", "\n", "# Run iteration:\n", "c_tm1, new_c = run_iteration(T=TT, cons_prob=consumer_prob_b5, c_tm1=c_tm1, v_tm1=v_tm1)\n", "\n", "# Create linear interp:\n", "c_pi = create_linear_interp_functions(consumer_prob, c_tm1)\n", "c_vi = create_linear_interp_functions(consumer_prob, new_c)\n", "\n", "# Plot:\n", "plotgrid = np.linspace(-(b*1.01), grid_max, grid_size*3)\n", "\n", "plt.plot(plotgrid, c_vi[0](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[0](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_vi_bm5[0](plotgrid), label=\"VI, old b=-5\", color='blue', linestyle=\"--\")\n", "plt.plot(plotgrid, c_pi_bm5[0](plotgrid), label=\"PI, old b=-5\", color='black', linestyle=\"--\")\n", "\n", "plt.title(\"Replication with z at low value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()\n", "\n", "# For fun create this as well:\n", "plt.plot(plotgrid, c_vi[1](plotgrid), label=\"VI\", color='blue')\n", "plt.plot(plotgrid, c_pi[1](plotgrid), label=\"PI\", color='black')\n", "\n", "plt.plot(plotgrid, c_vi_bm5[1](plotgrid), label=\"VI, old b=-5\", color='blue', linestyle=\"--\")\n", "plt.plot(plotgrid, c_pi_bm5[1](plotgrid), label=\"PI, old b=-5\", color='black', linestyle=\"--\")\n", "\n", "plt.title(\"Replication with z at high value, b=\"+str(b))\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 1 }