{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
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# Numerical Methods for Economists:

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## RBC/DSGE modelling using Dynare++

" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from scipy import linalg, interpolate, io" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Task 1: How well do you know your single period utility function? RBC edition!\n", "\n", "This task will help you build some intuition for the intra-period trade-off between consumption and leisure that is the economic mechanism which propogates total factor productivity shocks in all basic real business cycle (RBC) models. In this lab we will assume that the representative household has the following flow utility function: \n", "\n", "$$u\\bigg(C_t, L_t\\bigg) = \\left(\\frac{C_t^{1 - \\theta} - 1}{1 - \\theta}\\right) + b \\left(\\frac{(1 - L_t)^{1 - \\omega} - 1}{1 - \\omega}\\right)$$\n", "\n", "where $C_{t}$, $L_{t}$ is labor (note that labor endowment has been normalized to 1!). The parameter $0 < \\theta$ is the coefficient of relative risk avesion, $0 < \\omega$ is the inverse inter-temporal elasticity of substitution between current and future leisure, and $0 < b$ controls the importance of leisure in determining flow utility. Note that if $\\theta = \\omega = 1$, then \n", "\n", "$$u\\bigg(C_t, L_t\\bigg) = \\ln C_t + b \\ln (1 - L_t)$$\n", "\n", "and we recover the flow utility function assumed by Romer and used in your lecture notes. Code this utility function in the cell below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def u(C, L):\n", " \"\"\" \n", " In the standard RBC model utility in each period is a function of \n", " consumption, C, and leisure, 1 - L. Note that the representative\n", " household's labor endowment has been normalized to 1 for simplicity. \n", " \n", " Arguments:\n", " \n", " C: (array) Consumption\n", " L: (array) Labor supply\n", " \n", " Returns:\n", " \n", " utility: (array) Flow utility of the representative agent.\n", " \n", " \"\"\"\n", " if theta == 1.0:\n", " utility_consumption = # insert your code here!\n", " else:\n", " utility_consumption = # insert your code here!\n", " \n", " if omega == 1.0:\n", " utility_leisure = # insert your code here!\n", " else:\n", " utility_leisure = # insert your code here!\n", " \n", " # flow utility is weighted sum of utilities from consumption and leisure\n", " utility = utility_consumption + b * utility_leisure\n", " \n", " return utility" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# my solution\n", "def u(C, L):\n", " \"\"\" \n", " In the standard RBC model utility in each period is a function of \n", " consumption, C, and leisure, 1 - L. Note that the representative\n", " household's labor endowment has been normalized to 1 for simplicity. \n", " \n", " Arguments:\n", " \n", " C: (array) Consumption\n", " L: (array) Labor supply\n", " \n", " Returns:\n", " \n", " utility: (array) Flow utility of the representative agent.\n", " \n", " \"\"\"\n", " if theta == 1.0:\n", " utility_consumption = np.log(C)\n", " else:\n", " utility_consumption = (C**(1 - theta) - 1) / (1 - theta)\n", " \n", " if omega == 1.0:\n", " utility_leisure = np.log(1 - L)\n", " else:\n", " utility_leisure = ((1 - L)**(1 - omega) - 1) / (1 - omega)\n", " \n", " # flow utility is weighted sum of utilities from consumption and leisure\n", " utility = utility_consumption + b * utility_leisure\n", " \n", " return utility" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Choose some parameter values\n", "b, theta, omega = 2.0, 1.0, 1.0\n", "\n", "# Check that the utility function is working properly!\n", "u(np.exp(1), 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise:\n", "\n", "First, let's plot the utility surface using matplotlib 3D graphics functions for $b=2.5, \\theta=1.0, \\omega=1.0$. What to you notice about the shape of the utility surface? Rotate the plot by altering the azim argument of the fig.gca() function. What do you notice about the marginal utilities of consumption and leisure? Finally, change the parameters $b,\\theta,\\omega$. Try to anticipate how parameter changes will alter the utility surface. Do the actual changes confirm your expectations? Or not?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/mpl_toolkits/mplot3d/proj3d.py:161: RuntimeWarning: invalid value encountered in true_divide\n", " txs, tys, tzs = vecw[0]/w, vecw[1]/w, vecw[2]/w\n" ] }, { "data": { "image/png": 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qbzJBVgeUJ0Bm7lS1Qoo6QVSPSOlF0IJOXUydItCtCp7sRASZEkVTZNh8PZ74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\nrKx8rO+OiL3ZmiDX+fn5qKysx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a new Figure object \n", "fig = plt.figure(figsize=(8,6))\n", "\n", "# create a 3D Axes object\n", "ax = fig.gca(projection='3d', elev=30, azim=310)\n", "\n", "# create a grid of (x,y) values which we will pass to function\n", "consumption = np.linspace(0, 10, 200)\n", "labor = np.linspace(0, 1, 20)\n", "L, C = np.meshgrid(labor, consumption)\n", "\n", "# Choose parameter values\n", "b, theta, omega = 5.0, 1.0, 1.0\n", "\n", "# we will actually plot output\n", "utility = u(C, L)\n", "\n", "# note the use of the new plot command!\n", "utility_surface = ax.plot_surface(L, C, utility, rstride=1, cstride=1, cmap=mpl.cm.terrain, \n", " linewidth=0, vmin=-10, vmax=np.max(utility), \n", " antialiased=False)\n", "\n", "# axes, labels, title, colorbar etc.\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 10)\n", "ax.set_xlabel(r'Labor, $L_{t}$', fontsize=15, family='serif')\n", "ax.set_ylabel(r'Consumption, $C_{t}$', fontsize=15, family='serif')\n", "ax.set_title(r'$u(C,\\ L)$ for $b=%.2f, \\theta=%.2f, \\omega=%.2f$' %(b, theta, omega), \n", " fontsize=20, family='serif')\n", "fig.colorbar(utility_surface, shrink=0.75, aspect=10)\n", "\n", "# display the plot!\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we plot utility \"slices\" for various values of the parameters $b$, $\\theta$, and $\\omega$. The code below fixes either consumption or labor supply and then loops over a fixed set of parameter values plotting \"slices\" of the utility surface. Example...\n", "\n", " for b in [0.5, 1.0, 1.5, 2.0]:\n", " \n", " plot stuff!\n", " \n", "Try changing the set of parameter values over which the code is looping. Can you explain in words how changes to each of the parameters impact household preferences?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n" ] }, { "data": { "image/png": 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GAtSBA671qXt3GDiw8SUpqb1fRdOMMWEPWKpnRETOXq2tZyI2YBk30u0ZIM9a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\na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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fix l_bar and c_bar\n", "L_bar, C_bar = 0.33, 1\n", "\n", "# create a new figure object!\n", "fig, axes = plt.subplots(1, 2, sharey=True, figsize=(12,6))\n", "ax1, ax2 = axes\n", "\n", "for b in [0.5, 1.0, 1.5, 2.0]:\n", " \n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax1.plot(consumption, u(consumption, L_bar), label='b=%g' %b)\n", "\n", " # axes, labels, title. legend, etc\n", " ax1.set_xlabel('Consumption, $C_{t}$', family='serif')\n", " ax1.set_ylabel(r'$u(C_{t}, \\bar{L})$', rotation='horizontal')\n", " ax1.set_title('A slice through $u(C_{t}, L_{t})$ at $L_{t}=%.2f$' %L_bar,\n", " family='serif')\n", "\n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax2.plot(labor, u(C_bar, labor), label='b=%g' %b)\n", "\n", " # axes, labels, title. legend, etc\n", " ax2.set_xlabel('Labor, $L_{t}$', family='serif')\n", " ax2.set_title('A slice through $u(C_{t}, L_{t})$ at $C_{t}=%.2f$' %C_bar,\n", " family='serif')\n", " \n", "ax2.legend(loc=0, frameon=False, prop={'family':'serif'})\n", "\n", "# tighten things up and add a title\n", "plt.tight_layout()\n", "plt.suptitle('Utility slices for various $b$', y=1.05, fontsize=20, family='serif') \n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:21: RuntimeWarning: divide by zero encountered in power\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:21: RuntimeWarning: divide by zero encountered in reciprocal\n" ] }, { "data": { "image/png": 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//j4fy4zg0Z0UsERkzKqqOvEKlDdM1dV1hqiZM+Hss+GGG5zHkyfrfigRERmb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\nfayZsQXHrJ7GR951fLdL2qSxjiv1z2D96lcwdy5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CkiRJUmk9N4M1XmzTLkmSJKm0agOW\nM1iSJEmSSqs2YNmmXZIkSVJpVQcslwhKkiRJKqnagLUuk2ndLkKSJEnSlFJtwHIGS5IkSVJp1QYs\nm1xIkiRJKq3agDUABixJkiRJRVUbsNa5RFCSJElSYdUGLNu0S5IkSSqt6oDlDJYkSZKkkqoNWLZp\nlyRJklRatQHLGSxJkiRJpVUbsGzTLkmSJKm0agOWbdolSZIklVZtwLJNuyRJkqTSqg1YtmmXJEmS\nVFrVAcsZLEmSJEklVRuwbNMuSZIkqbRqA5YzWJIkSZJKqzZg2aZdkiRJUmnVBizbtEuSJEkqrd6A\n5RJBSZIkSYVVG7BcIihJkiSptGoDljNYkiRJkkqrNmDZpl2SJElSadUGrAGXCEqSJEkqrNqAtc4l\ngpIkSZIKqzZg2aZdkiRJUmn1BixnsCRJkiQVVm3Ask27JEmSpNKqDVjOYEmSJEkqrdqAZZt2SZIk\nSaVVG7Bs0y5JkiSptHoDFrhEUJIkSVJR1QYsm1xIkiRJKq3agGWTC0mSJEmlVRuwnMGSJEmSVFq1\nAcsZLEmSJEmlVRuwbNMuSZIkqbRqA5Zt2iVJkiSVVm/AwjbtkiRJksqqNmDZ5EKSJElSadUGLJtc\nSJIkSSqt2oDlDJYkSZKk0qoNWAN2EZQkSZJUWLUBa51LBCVJkiQVVm3Ask27JEmSpNLqDVjYpl2S\nJElSWdUGLJtcSJIkSSqt2oBlm3ZJkiRJpVUbsJzBkiRJklRatQHLNu2SJEmSSqs6YLlEUJIkSVJJ\n1QYslwhKkiRJKq3agGWbdkmSJEmlVRuwnMGSJEmSVFq1ActzsCRJkiSVVm3ASmAzA5YkSZKkgqoN\nWLZolyRJklRatQHL5YGSJEmSSqs2YNngQpIkSVJp1QYsZ7AkSZIklVZtwHIGS5IkSVJpPRewIuIz\nEXFzRFwXERdExHZt2z4UEb+IiBUR8apN7eezu+468cVWor+/v9slTDoes9HxeI2ex0yTnT/Do+Px\nGj2P2eh5zMrouYAF/AuwR2buDfwc+BBAROwOHA3sDiwFzoyIYet/89y5BUqtg79so+cxGx2P1+h5\nzDTZ+TM8Oh6v0fOYjZ7HrIyeC1iZeXlmrm/uXgXMa24fBnw7M9dm5u3ALcD+XShRkiRJkobUcwFr\nI28GLmlu7wisbNu2EtipeEWSJEmSNIzIzPJvGnE5MGeITR/OzIua53wE2Cczj2zunwH8R2b+fXP/\nb4BLMvOCIfZf/i8lSeq6zJyQDkeOK5I0NY1lXJk+EYWMJDMP3tT2iPhjYBnwe20P/wrYue3+vOax\nofZvC0FJ0rhxXJEkdarnlghGxFLg/cBhmflU26bvAK+PiBkRsQBYBPy4GzVKkiRJ0lC6MoM1gjOA\nGcDl0bqW1b9n5jsz86aIOAe4CVgHvDO7sb5RkiRJkobRlXOwJEmSJKlGPbdE8JmIiKXNRYh/EREf\n6HY9vS4ido6IKyLixoj4aUSc0O2aJoOImBYR10TERd2uZTKIiNkRcV5zAfGbImJxt2vqZc0F1W+M\niBsi4h8iYotu19RrIuJrEXFvRNzQ9tj2EXF5RPw8Iv4lImaPcd8jjiMR8VfN9usi4iVj/XvUYqRj\nFhFvbI7V9RHxo4jYqxt19opO/60SEftFxLqIOKJkfb2ow9/LJc3Y/NOI6C9cYk/p4Hdyh4i4LCKu\nbY7XH3ehzJ4x1JgyxHNG9blfTcCKiGnAF2hdhHh34I8i4je7W1XPWwv8aWbuASwG3uUx68h7aS1V\ndfq3M/+XVsfP3wT2Am7ucj09KyJ2Ad5Gq4PqnsA04PXdrKlHfZ3WZ327DwKXZ+ZuwA+a+6PSyTgS\nEcuA52fmIuB/AV8affn16HDsvQ14eWbuBXwC+OuyVfaOTv+t0jzvL4DLgCndYKXD38vZwBeB38/M\nFwF/WLzQHtHhz9i7gWsy88XAEuD0iOjF04ZKGWpM2WAsn/vVBCxaFx2+JTNvz8y1wNm0Lk6sYWTm\nPZl5bXP7cVr/8N2xu1X1toiYR6vD5d8wxQe9TkTEdsDvZubXADJzXWY+0uWyetmjtL742KoZ7LZi\nmG6pU1lm/hvw0EYPHwp8o7n9DeAPxrDrTsaRDe+TmVcBsyPieWN4r1qMeMwy89/bfu+votUFeKrq\n9N8q7wHOA1aVLK5HdXLM3gCcn5krATLz/sI19pJOjtfdwKzm9izggcxcV7DGnjLMmNJu1J/7NQWs\nnYA72+57IeJRaL45fwmtwU/D+zytLpfru13IJLEAWBURX4+I5RFxVkRs1e2ielVmPgicDtwB3AU8\nnJnf725Vk8bzMvPe5va9wFhCTyfjyFDPmcqBYbRj71uASya0ot424vGKiJ1o/YN48Fvyqb5aopOf\nsUXA9s1pD1dHxJuKVdd7OjleZwF7RMRdwHW0VuZoeKP+3K8pYE31D6Axi4htaH1T9t5mJktDiIjX\nAvdl5jU4e9Wp6cA+wJmZuQ/wBGNYujVVRMSuwPuAXWjNJm8TEW/salGTUNNhdixjQqev2fj3fyqP\nPx3/3SPiFcCbgal8jnQnx+svgQ82P8eB400nx2xzWmPNMuDVwMciYtGEVtW7OjleHwauzcwdgRcD\nX4yIbSe2rElvVJ/7NQWsjS9EvDOthKlNiIjNgfOBb2XmP3W7nh73MuDQiPgl8G3glRHxzS7X1OtW\nAisz8z+b++fRGgQ1tN8CrszMweUaF9D6udPI7o2IOQARMRe4bwz76GQc6fii91NER2Nv09jiLODQ\nzNzUUpzadXK89gXObsaaI4EzI+LQQvX1ok6O2Z3Av2Tm6sx8APhXYO9C9fWaTo7Xy4BzATLzVuCX\nwAuKVDc5jfpzv6aAdTWwKCJ2iYgZwNG0Lk6sYUREAF8FbsrMv+x2Pb0uMz+cmTtn5gJajQd+mJnH\ndruuXpaZ9wB3RsRuzUMHATd2saRetwJYHBFbNr+fB9FqqKKRfQc4rrl9HDCWL4w6GUe+AxwL0HTE\nfLhtaeJUNOIxi4j5tL4sOCYzb+lCjb1kxOOVmQszc0Ez1pwH/ElmTuV/z3Tye/nPwO9Eq8vvVsAB\nTN3Pzk6O1wpa4wvNuUQvoNWMRkMb9ed+NR1DMnNdRLwb+B6tzltfzUy7lW3abwPHANdHxDXNYx/K\nzMu6WNNkMpWXBY3Ge4C/bz7obwWO73I9PSszr2tmRa+mdZ7fcqZwx7XhRMS3gQOBHSLiTuAk4FTg\nnIh4C3A78LrR7ne4cSQi3t5s/0pmXhIRyyLiFlpLXqf0z3Mnx4zW/59nAV9qfW/A2szcv1s1d1OH\nx0ttOvy9XBERlwHX0/rsPCszp2TA6vBn7BTg6xFxHa3JlhObc4CnpCHGlJNpLTsd8+e+FxqWJEmS\npHFS0xJBSZIkSeoqA5YkSZIkjRMDliRJkiSNEwOWJEmSJI0TA5YkSZIkjRMDliRJkiSNEwOWJEmS\nJI2Tai40LKl3RMRc4J3AKuAR4FFgVmZ+o6uFSZKKioh3AJ8CPgack5n3d7kkacI5gyWNQkTMjYjT\nI+KjEfHnEXF+c8X0nhcR79vo/n9GREzA+ywEvgl8PjP/qglVBwErx/u9JEktEbFfRPRHxI8i4oAO\nnv/GiHiwQGlXA1dk5pmGK00VkZndrkGaFCJiC+DfgD/IzLuax54LnJeZL+9qcR2IiF9m5oICUjh+\n5gAABDlJREFU73Ml8LHM/EHbY28Fzs3MRyb6/SVpqoqIk4GtM/PEDp8/4eNCRLyrqem0iXwfqZe4\nRFDq3GuB2wfDFUBm3hcRhwNExEm0fqcCWJOZn4iI44FTgK8AvwEsBF6bmY9FxAuADwA3AC8BPgHs\nC3wpM58VEfs3r3tf87pTgNOBvYAdgK8DrwYWte3zWOCvaC3H2BZ4MXACsD8wuxl8VwBPNs87MDPv\nGG3twx2giHgZsG17uGqcnZmPd3ykJUlj9WsrEyJiG+Bs4F+BFwD/sNEXYG8DdgL2AU7IzNubxzc1\nLnwZ2BV4QWaONFu2H/C3z/yvJU0eLhGUOrcrcM/GD2bmAxHxamC/zDwpMz8GLI6IgzPz67QCzY8y\n83haYerg5qVLgTXAF4CTgMcy82zg4Wa/Pwaubd3csJ+fZOaxwNPANpn5VuCawX1m5jeBh4DzM/Mk\n4FvAaZl5DvBwZn48M/8xMy8CbgdijLUP56VA/xDHyHAlSd0xQGvJ9mnA+4FPb7T9B5nZRzNeAHQw\nLlzVjEV/0sH770trmSDNvsd9abrUawxYUudWAnOG2bYncFvb/VtpzTQN+nnz31W0ZpYAzgLuo7Xs\n8OPA2g5quLX578Nttx9q2ycAmXlb2/P3GGGfY6l9OAO0Zsc2iIiZEfHK5vb+I7xekjS+NgNeEREf\nBd4GPKd94zDjxV5sely4uXnt8k29cUTMap73eHN/BvBqxwLVzoAlde5CYLeI2HHwgYh4QUT8M3Ad\nrRmuQYtozT5trP2buwOAUzNzMXAv8Kbm8cciYjDIzN/oNUPd/h/fBkbEYC27ATc2tweabXtt9PSx\n1D6cS2l90xnNewXwOuCKZvuyDvYhSRqbjZcH7gm8FZibmZ8EPv8/XjD0eHEtnY0LI9mPttkr4Bjg\nKhwLVDnPwZI6lJmrI+I1wJ9FxKPADFozWu/IzLsjYnFEnEJrgLsyM38QEQfTOn/p+Ij4BvC7wB4R\ncTGwPfC5iLiN1jlVX2ze6gvAGRHxH8B64JiI2K7Zz3ERcRGtbxKPiYi72vZ5SWauavbxe81a+ZcA\ng10OL46IzwJExA+b/b09Mz88ytq/2yyLvB54fWbe1HaMfhYRXwROj4ibaM1mfSczMyKWNe+9nc0u\nJGl8RcS+tD6nN4+IjzQPLwD+E1gUEacBDwKzmnOHtwJmAUdGxGxgb5r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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fix l_bar and c_bar\n", "L_bar, C_bar = 0.33, 1\n", "\n", "# create a new figure object!\n", "fig, axes = plt.subplots(1, 2, sharey=True, figsize=(12,6))\n", "ax1, ax2 = axes\n", "\n", "for theta in [0.5, 1.0, 1.5, 2.0]:\n", " \n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax1.plot(consumption, u(consumption, L_bar), label=r'$\\theta=%g$' %theta)\n", "\n", " # axes, labels, title. legend, etc\n", " ax1.set_xlabel('Consumption, $C_{t}$', family='serif')\n", " ax1.set_ylabel(r'$u(C_{t}, \\bar{L})$', rotation='horizontal')\n", " ax1.set_title('A slice through $u(C_{t}, L_{t})$ at $L_{t}=%.2f$' %L_bar,\n", " family='serif')\n", "\n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax2.plot(labor, u(C_bar, labor), label=r'$\\theta=%g$' %theta)\n", "\n", " # axes, labels, title. legend, etc\n", " ax2.set_xlabel('Labor, $L_{t}$', family='serif')\n", " ax2.set_title('A slice through $u(C_{t}, L_{t})$ at $C_{t}=%.2f$' %C_bar,\n", " family='serif')\n", " \n", "ax2.legend(loc=0, frameon=False, prop={'family':'serif'})\n", "\n", "# tighten things up and add a title\n", "plt.tight_layout()\n", "plt.suptitle(r'Utility slices for various $\\theta$', y=1.05, fontsize=20, family='serif') \n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:21: RuntimeWarning: divide by zero encountered in reciprocal\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:26: RuntimeWarning: divide by zero encountered in power\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:26: RuntimeWarning: divide by zero encountered in reciprocal\n" ] }, { "data": { "image/png": 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RyocGKR8aoiQaoSQ6RHE0QjgWIxyLURRPEEokCSUcRSkIuwDFFqI0VEJ5uIyK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\nkkqpEcdhmWBJkiRJKqXuzs6GexeWCZYkSZKkUlrU0dFwU7W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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fix l_bar and c_bar\n", "L_bar, C_bar = 0.33, 1\n", "\n", "# create a new figure object!\n", "fig, axes = plt.subplots(1, 2, sharey=True, figsize=(12,6))\n", "ax1, ax2 = axes\n", "\n", "for omega in [0.5, 1.0, 1.5, 2.0]:\n", " \n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax1.plot(consumption, u(consumption, L_bar), label=r'$\\omega=%g$' %omega)\n", "\n", " # axes, labels, title. legend, etc\n", " ax1.set_xlabel('Consumption, $C_{t}$', family='serif')\n", " ax1.set_ylabel(r'$u(C_{t}, \\bar{L})$', rotation='horizontal')\n", " ax1.set_title('A slice through $u(C_{t}, L_{t})$ at $L_{t}=%.2f$' %L_bar,\n", " family='serif')\n", "\n", " # first subplot will fix l at some constant l_bar and plot u(C, l_bar)\n", " ax2.plot(labor, u(C_bar, labor), label=r'$\\omega=%g$' %omega)\n", "\n", " # axes, labels, title. legend, etc\n", " ax2.set_xlabel('Labor, $L_{t}$', family='serif')\n", " ax2.set_title('A slice through $u(C_{t}, L_{t})$ at $C_{t}=%.2f$' %C_bar,\n", " family='serif')\n", " \n", "ax2.legend(loc=0, frameon=False, prop={'family':'serif'})\n", "\n", "# tighten things up and add a title\n", "plt.tight_layout()\n", "plt.suptitle(r'Utility slices for various $\\omega$', y=1.05, fontsize=20, family='serif') \n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Task 2: Trade-off between consumption and leisure\n", "\n", "In order to graphically analyze the trade-off between consumption and leisure in two dimensions we need to be able to plot the set of indifference curves implied by the household's utility function. The code in the cell below defines a creates a contour plot of the above 3D utility surface in two dimensions and then overlays a set of contour lines for various values of utility. These contour lines are indifference curves!" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors_original != str('face'):\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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eRYj2akENcXJ328xYUyItRQ5yEnWTp0p0IcnSDqOz05ZF7vMzcdlWH0rZkqPr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\niJpQDBGNhIl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111)\n", "\n", "# Force logarithmic preferences!\n", "b, theta, omega = 2.0, 1.0, 1.0\n", "\n", "# we will actually plot output\n", "utility = u(C, L)\n", "\n", "# create the contour plot\n", "im = ax.imshow(utility, interpolation='gaussian', origin='lower', cmap=mpl.cm.terrain, \n", " vmin=-10, vmax=np.max(utility), extent=(0, 1, 0, 10), aspect=0.10)\n", "\n", "# demarcate the contours...\n", "CS = ax.contour(L, C, utility, np.linspace(-8, np.max(utility), 10), colors=np.repeat('k', 10), \n", " linewidths=1, linestyles='solid')\n", "ax.clabel(CS, inline=1, fmt='%1.2f')\n", "\n", "# axes, labels, title, colorbar etc.\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 10)\n", "ax.set_xlabel(r'Labor, $L_{t}$', fontsize=15, family='serif')\n", "ax.set_ylabel(r'Consumption, $C_{t}$', fontsize=15, family='serif')\n", "ax.set_title(r'$u(C,\\ L)$ for $b=%.2f, \\theta=%.2f, \\omega=%.2f$' %(b, theta, omega), \n", " fontsize=20, family='serif')\n", "fig.colorbar(utility_surface, shrink=0.75, aspect=10)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Static model\n", "To see what the above preferences imply about the optimal choices of household labor supply and consumption, suppose the representative agent lives for only a single period and has no initial wealth (for simplicity also assume that the houshold has only one member). These assumptions imply that the houshold budget constraint is simply $C = WL$, where $W$ is the real wage. Furthermore, for simplicity, suppose that $\\theta=\\omega=1$. To find optimal consumption bundle, set up the Lagrangian: \n", "\n", "$$\\mathcal{L} \\equiv ln\\ C + b\\ ln(1 - L) + \\lambda(wL - C)\\tag{2.1}$$\n", "\n", "FOC and the budget constraint yield a system of 3 equation in 3 unknowns $C, l, \\lambda$:\n", "\n", "$$\\frac{1}{C} - \\lambda = 0$$\n", "\n", "$$-\\frac{b}{1 - L} + \\lambda W = 0$$\n", "\n", "$$C = WL$$\n", "\n", "One can reduce the above to a 2 equation system in 2 unkowns by eliminating $\\lambda$:\n", "\n", "$$bC + WL = w$$\n", "\n", "$$C - WL = 0$$\n", "\n", "Or, equivalently \n", "\n", "$$\\begin{vmatrix} b & \\ W \\\\ 1 & -W\\end{vmatrix} \\begin{vmatrix}C \\\\ L \\end{vmatrix} = \\begin{vmatrix} W \\\\ 0 \\end{vmatrix}$$\n", "\n", "Note that this is a linear system of equations (which makes our life much easier!). Solving the system (via your favorite method for solving linear systems of equations) yields expressions for optimal choices of $C$ and $l$ as functions of prices (and model parameters):\n", "\n", "$$C(W; b) = \\frac{1}{1 + b}w \\tag{2.2}$$\n", "\n", "$$L(W; b) = \\frac{1}{1 + b} \\tag{2.3}$$\n", "\n", "$$\\lambda(W; b) = \\frac{1 + b}{W} \\tag{2.4}$$\n", "\n", "Note that the household's labor supply choice is indepedent of the real wage, $W$. This independence of labor supply and the real wage is a direct consequence of logarithmic utility and the assumption that houshold has no initial wealth and thus the income and substitution effects of a price change exactly offset one another. Also, note that the household will choose to consum a fixed fraction of its lifetime net worth (which in the case is just the value of their labor endowment for a single period!). This 'consume a fixed fraction of start of period net worth' decision rule is a direct consequence of logarithmic preferences. The code in the cell below uses the linear equation solver from the SciPy linear algebra package to solve for the optimal consumption-labor bundle." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal choice of consumption: 2.85714285714\n", "Optimal choice of labor supply: 0.285714285714\n", "Utility associated with optimal bundle: 0.208641532946\n" ] } ], "source": [ "# specify some model parameters\n", "b, W = 2.5, 10\n", "\n", "# Define the coefficient matrix, A, and vector of dependent values, d, for our two equation system\n", "A = np.array([[b, W], \n", " [1, -W]]) \n", "d = np.array([[W], \n", " [0]])\n", "\n", "# Solve the system of equations and assign the optimal choices for consumption and labor\n", "C_star, L_star = linalg.solve(A, d)[0,0], linalg.solve(A, d)[1,0] \n", "u_star = u(C_star, L_star)\n", "\n", "print(\"Optimal choice of consumption: \", C_star)\n", "print(\"Optimal choice of labor supply: \", L_star)\n", "print(\"Utility associated with optimal bundle:\", u_star)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can show the tangency condition graphically by overlaying the budget constraint across the contour plot and then plotting the contour line/indifference curve for u_star. The indifference curve should be exactly tangent to the budget constraint at the optimal consumption-labor supply bundle." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors_original != str('face'):\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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Pj//bBVR3EXgXYdLN83H8z27GzP/5BLaOG4vOah90ogt9qS+6OrrR3dkP3X26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OB0IpoF8G/M/I0m5l6AzczHNSTf3EfW2Cjs9F0ENLSWBdCT0CaMTQNsHdzZId1B2cJ8Y0jqkbOR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,8))\n", "ax = fig.add_subplot(111)\n", "\n", "# we will actually plot output\n", "utility = u(C, L)\n", "\n", "# re-create the contour plot\n", "im = ax.imshow(utility, interpolation='gaussian', origin='lower', cmap=mpl.cm.terrain, \n", " vmin=-10, vmax=np.max(utility), extent=(0, 1, 0, 10), aspect=0.10)\n", "\n", "# plot the budget constraint\n", "labor_supply = np.linspace(0, 1, 100)\n", "ax.plot(labor_supply, W * labor_supply, 'r-', label='$C=WL$')\n", "\n", "# demarcate the indifference curve...\n", "CS = ax.contour(L, C, utility, np.array([u_star]), colors='k', linewidths=1, \n", " linestyles='solid')\n", "ax.clabel(CS, inline=1, fmt='%1.4f')\n", "\n", "# mark the optimal bundle\n", "ax.hlines(C_star, 0, L_star, linestyle='dashed')\n", "ax.vlines(L_star, 0, C_star, linestyle='dashed')\n", "\n", "# axes, labels, title, colorbar etc.\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 10)\n", "ax.set_xlabel(r'Labor, $L_{t}$', fontsize=15, family='serif')\n", "ax.set_ylabel(r'Consumption, $C_{t}$', fontsize=15, family='serif')\n", "ax.set_title(r'$u(C,\\ L)$ for $b=%.2f, \\theta=%.2f, \\omega=%.2f$' %(b, theta, omega), \n", " fontsize=20, family='serif')\n", "ax.legend(loc='best', frameon=False)\n", "fig.colorbar(utility_surface, shrink=0.75, aspect=10)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2-period model\n", "The fact that the level of wage does not effect labor supply in a static model does not mean that variations in the real wage do not impact household labor supply when the time horizon is more than one period. Suppose that the representative household lives for two periods and that there is no uncertainty about future prices. Because of logarithmic preferences, the household will again follow the decision rule 'consume a fraction fixed fraction of the PDV of lifetime net worth.' We can derive this decision rule formally as follows. First, note that the household budget constraint is \n", "\n", "$$C_{0} + \\frac{1}{1 + r_{1}}C_{1} = W_{0}L_{0} + \\frac{1}{1 + r_{1}}W_{1}L_{1} \\tag{2.5}$$ \n", "\n", "where $r_{1}$ is the real interest rate. The Lagrangian for the household's two period optimization problem is \n", "\n", "$$\\mathcal{L} \\equiv ln(C_{0}) + b\\ ln(1-L_{0}) + \\beta[ln(C_{1}) + b\\ ln(1-L_{1})] + \\lambda\\left[W_{0}L_{0} + \\frac{1}{1 + r_{1}}W_{1}L_{1} - C_{0} - \\frac{1}{1 + r_{1}}C_{1}\\right] \\tag{2.6}$$ \n", "\n", "The houshold now chooses sequences of consumption and labor (i.e., representative household chooses $C_{0}, C_{1}, L_{0}, L_{1}$). The FOC along with the budget constraint imply a system of 5 equations in the 5 unknowns $C_{0}, C_{1}, L_{0}, L_{1}, \\lambda$ as follows:\n", "\n", "$$\\frac{1}{C_{0}} - \\lambda = 0$$\n", "\n", "$$\\beta\\frac{1}{C_{1}} - \\lambda \\frac{1}{1+r_{1}}= 0$$\n", "\n", "$$-\\frac{b}{1 - L_{0}} + \\lambda W_{0} = 0$$\n", "\n", "$$-\\beta\\frac{b}{1 - L_{1}} + \\lambda \\frac{1}{1 + r_{1}}W_{1} = 0$$\n", "\n", "$$C_{0} + \\frac{1}{1 + r_{1}}C_{1} = W_{0}L_{0} + \\frac{1}{1 + r_{1}}W_{1}L_{1}$$\n", "\n", "This 5 equation system can be reduced (by eliminating the Lagrange multiplier $\\lambda$) to a linear system of 4 equations in 4 unknowns:\n", "\n", "$$\\begin{vmatrix} b & \\ 0 & \\ W_{0} & 0 \\\\\\ \\beta(1 + r_{1}) & -1 & 0 & 0 \\\\\\ 0 & \\ b & 0 & W_{1} \\\\\\ 1 & \\frac{1}{1 + r_{1}} & -W_{0} & -\\frac{1}{1+r_{1}}W_{1} \\end{vmatrix} \\begin{vmatrix}C_{0} \\\\\\ C_{1} \\\\\\ L_{0} \\\\\\ L_{1}\\end{vmatrix} = \\begin{vmatrix} W_{0} \\\\\\ 0 \\\\\\ W_{1} \\\\\\ 0\\end{vmatrix}$$\n", "\n", "The above system can be solved in closde form using some method like Cramer's rule/substitution etc to yield the following optimal sequences/policies for consumption and labor supply:\n", "\n", "$$C_{0} = \\frac{1}{(1 + b)(1 + \\beta)}\\left(W_{0} + \\frac{1}{1 + r_{1}}W_{1}\\right) \\tag{2.7}$$\n", "\n", "$$C_{1} = \\left(\\frac{1 + r_{1}}{1 + b}\\right)\\left(\\frac{\\beta}{1 + \\beta}\\right)\\left(W_{0} + \\frac{1}{1 + r_{1}}W_{1}\\right) \\tag{2.8}$$\n", "\n", "$$L_{0} = 1 - \\left(\\frac{b}{W_{0}}\\right)\\left(\\frac{1}{(1 + b)(1 + \\beta)}\\right)\\left(W_{0} + \\frac{1}{1 + r_{1}}W_{1}\\right) \\tag{2.9}$$\n", "\n", "$$L_{1} = 1 - \\left(\\frac{b\\beta(1+r_{1})}{W_{1}}\\right) \\left(\\frac{1}{(1 + b)(1 + \\beta)}\\right)\\left(W_{0} + \\frac{1}{1 + r_{1}}W_{1}\\right) \\tag{2.10}$$\n", "\n", "Several important points to note about the above optimal consumption and labor supply policies. Household's lifetime net worth \n", "\n", "$$W_{0} + \\frac{1}{1 + r_{1}}W_{1}$$\n", "\n", "is the present discounted value of its labor endowment. Household's lifetime net worth depends on the wages in BOTH periods and future interest rate. This hints at a more general result: if the household has an infinite time horizon, lifetime net worth depends on the entire future path of wages and interest rates! In each period, houshold's consume a fraction of their lifetime net worth. Although the fraction changes in this simple two period model, if the household has an infinite horizon, the fraction of lifetime net worth consumed each period will be fixed and equal to \n", "\n", "$$\\frac{1}{(1 + b)(1 + \\beta + \\beta^2 + \\dots)}=\\frac{1 - \\beta}{1 + b}$$\n", "\n", "From the policy function for $L_{0}$, one can show that in order for the labor supply in period $t=0$ to be non-negative (which it must!), the following inequality must hold: \n", "\n", "$$\\left(\\frac{1}{1 + r_{1}}\\right)\\left(\\frac{W_{1}}{W{0}}\\right) \\lt \\frac{(1 + b)(1 + \\beta)}{b} - 1$$\n", "\n", "From the policy function for $L_{1}$, in order for the labor supply in period $t=1$ to be non-negative (which it must!), the following inequality must hold: \n", "\n", "$$(1 + r_{1})\\left(\\frac{W_{0}}{W_{1}}\\right) \\lt \\left(\\frac{1 + b}{b}\\right)\\left(\\frac{1 + \\beta}{\\beta}\\right) - 1$$\n", "\n", "### Exercise\n", "\n", "The code in the cells below walks you through some exercises deisgned to build your intuition about the inter-period tradeoffs between consumption and labor supply. Please try the following:\n", "\n", "1. Execute the code in each of the remaining cells in the task and interpret the results.\n", "2. Return to the cell just below this one and change the value of $b$ (either higher or lower is fine). Given your new value of $b$ try and predict the direction of the changes to the elements of the optimal sequences of $C$ and $L$. Check that the plots confirm your intuition. Remember, that a change in $b$ is changing the weight that the household places on utility from leisure relative to utility from consumption.\n", "3. Return to the cell just below this one and reset $b=2.5$. Alter the prices (i.e., wages and the interest rate) so that the labor supply choice in period $t=0$ is close to zero and then regenerate and interpret the contour plots.\n", "4. Return to the cell just below this one and reset $b=2.5$. Alter the prices so that the labor supply choice in period $t=1$ is close to zero and then regenerate and interpret the contour plots. \n", "\n", "Follow along and be sure to ask questions if you get stuck!" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PDV of Household's net worth (i.e., labor endowment): 9.878048780487806\n" ] } ], "source": [ "# define parameter values\n", "b, beta, theta, omega = 2.5, 0.99, 1.0, 1.0\n", " \n", "# Specify some prices (i.e., wages and interest rates) all of which households take as given\n", "W0, W1, r1 = 5, 5, 0.025\n", "\n", "# Calculate the household's initial net worth (i.e., the PDV of his labor endowment) given these prices\n", "networth = W0 + (1 / (1 + r1)) * W1\n", "\n", "print(\"PDV of Household's net worth (i.e., labor endowment):\", networth)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# is the non-negativity constraint on l0 satisfied by your chosen prices?\n", "(1 / (1 + r1)) * (W1 / W0) < ((((1 + b) * (1 + beta)) / b) - 1)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# is the non-negativity constraint on l1 satisfied by your chosen prices?\n", "(1 + r1) * (W0 / W1) < (((1 + b) / b) * ((1 + beta) / beta) - 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the coefficient matrix, $A$, and vector of dependent values, $d$, for our four equation system (i.e, with two periods agent must choose $C_{0}$, $L_{0}$, $C_{1}$, and $L_{1}$)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal C sequence: (1.4182410309386655, 1.4391600861450107)\n", "Optimal l sequence: (0.2908794845306672, 0.28041995692749472)\n", "Flow of utility: (-0.50990707530324508, -0.45865910672420063)\n" ] } ], "source": [ "A = np.array([[b, 0, W0, 0], \n", " [beta * (1 + r1), -1, 0, 0], \n", " [0, b, 0, W1], \n", " [1, 1 / (1 + r1), -W0, -(1 / (1 + r1)) * W1]])\n", "\n", "d = np.array([[W0], \n", " [0], \n", " [W1], \n", " [0]])\n", "\n", "# Solve the system of equations and assign the optimal choices for consumption and labor\n", "C_star0 = linalg.solve(A, d)[0,0]\n", "C_star1 = linalg.solve(A, d)[1,0] \n", "L_star0 = linalg.solve(A, d)[2,0]\n", "L_star1 = linalg.solve(A, d)[3,0]\n", "u_star0 = u(C_star0, L_star0)\n", "u_star1 = u(C_star1, L_star1)\n", "\n", "print(\"Optimal C sequence:\", (C_star0, C_star1)) \n", "print(\"Optimal l sequence:\", (L_star0, L_star1)) \n", "print(\"Flow of utility: \", (u_star0, u_star1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that C_star0, as obtained above, equates to the optimal value of consumption in period t=0 derived analytically (use Python as a calculator to compute the analytic solution!). Then do the same for C_star1, L_star0, and L_star1." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal C, t=0: 1.4182410309386655\n", "Optimal C, t=1: 1.4391600861450107\n", "Optimal l, t=0: 0.29087948453066725\n", "Optimal l, t=1: 0.28041995692749466\n" ] } ], "source": [ "# my solution \n", "print(\"Optimal C, t=0:\", (1 / ((1 + b) * (1 + beta))) * (W0 + (1 / (1 + r1)) * W1))\n", "print(\"Optimal C, t=1:\", ((1 + r1) / (1 + b)) * (beta / (1 + beta)) * (W0 + (1 / (1 + r1)) * W1))\n", "print(\"Optimal l, t=0:\", 1 - (b / W0) * (1 /((1 + b) * (1 + beta))) * (W0 + (1 / (1 + r1)) * W1))\n", "print(\"Optimal l, t=1:\", 1 - ((b * beta * (1 + r1)) / W1) * (1 /((1 + b) * (1 + beta))) * (W0 + (1 / (1 + r1)) * W1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's add the budget constraint in period $t=0$ as well as the contour line/indifference curve which satisfies the necessary tangency condition to the contour plot." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors_original != str('face'):\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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/Otx5kXWpPUKyDN1Ca1m+9uX5MSRP/7lLSdROuEjHtMatOPCf1Aw7EFq/nKxJ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\nedwuDAHLNiQOAET0BgAvAHA7gEcbQU4FILn0BgCPKpPZZqezaByema8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V6L2TvMwgF77hEjt4exzBlgynZ7y/XyBtc7JJ8QqY66yBJPE824fz0WfekijP58GTa/9WQ88Is/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,8))\n", "ax = fig.add_subplot(111)\n", "\n", "# we will actually plot output\n", "utility = u(C, L)\n", "\n", "# re-create the contour plot\n", "im = ax.imshow(utility, interpolation='gaussian', origin='lower', cmap=mpl.cm.terrain, \n", " vmin=-10, vmax=np.max(utility), extent=(0, 1, 0, 10), aspect=0.10)\n", "\n", "# plot the budget constraint\n", "labor_supply = np.linspace(0, 1, 100)\n", "ax.plot(labor_supply, W0 * labor_supply + (1 / (1 + r1)) * (W1 * L_star1 - C_star1), \n", " color='r', label=r'$C_{0}=W_{0}L_{0} + \\frac{1}{1 + r_{1}}(W_{1}L_{1}^* - C_{1}^*)$')\n", "\n", "# demarcate the indifference curve...\n", "CS = ax.contour(L, C, utility, np.array([u_star0]), colors='k', linewidths=1, linestyles='solid')\n", "ax.clabel(CS, inline=1, fmt='%1.4f')\n", "\n", "# mark the optimal bundle\n", "ax.hlines(C_star0, 0, L_star0, linestyle='dashed')\n", "ax.vlines(L_star0, 0, C_star0, linestyle='dashed')\n", "\n", "# axes, labels, title, colorbar etc.\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 10)\n", "ax.set_ylabel(r'Consumption, $C_{t}$', family='serif', fontsize=15)\n", "ax.set_xlabel(r'Labor, $L_{t}$', family='serif', fontsize=15)\n", "ax.set_title(r'Optimal bundle in period t=0 for $b=%.2f, \\beta=%.2f$' %(b, beta), \n", " fontsize=15, family='serif')\n", "ax.legend(loc=4, frameon=False)\n", "fig.colorbar(utility_surface, shrink=0.75, aspect=10)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the budget constraint for period $t=1$ and the indifference curve that is tangent with the budget constraint at the optimal consumption-labor bundle." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:19: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:24: RuntimeWarning: divide by zero encountered in log\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors_original != str('face'):\n", "/Users/drpugh/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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0xgCeSURfBrAPwI8z89eGETjVhF34fefAgiD3PHeoNzpx3WBldtL3+DKyfala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UFqGKZP1GlgeAHQI34VoBK1YtxR9+7k4A6fmffu67+M+/f3s6X63Skd1pDaxYuwx/+z8ewXs/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\nRkmELRWH0Y1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,8))\n", "ax = fig.add_subplot(111)\n", "\n", "# we will actually plot output\n", "utility = u(C, L)\n", "\n", "# re-create the contour plot\n", "im = ax.imshow(utility, interpolation='gaussian', origin='lower', cmap=mpl.cm.terrain, \n", " vmin=-10, vmax=np.max(utility), extent=(0, 1, 0, 10), aspect=0.10)\n", "\n", "# plot the budget constraint\n", "labor_supply = np.linspace(0, 1, 100)\n", "ax.plot(labor_supply, W0 * labor_supply + (1 / (1 + r1)) * (W1 * L_star1 - C_star1), color='r', alpha=0.25)\n", "ax.plot(labor_supply, W1 * labor_supply + (1 + r1) * (W0 * L_star0 - C_star0), color='r',\n", " label=r'$C_{1} = W_{1}L_{1} + (1 + r_{1})(W_{0}L_{0}^* - C_{0}^*)$')\n", "\n", "# demarcate the indifference curve...\n", "CS_0 = ax.contour(L, C, utility, np.array([u_star0]), colors='k', linewidths=1, linestyles='solid', alpha=0.25)\n", "CS_1 = ax.contour(L, C, utility, np.array([u_star1]), colors='k', linewidths=1, linestyles='solid')\n", "ax.clabel(CS_1, inline=1, fmt='%1.4f')\n", "\n", "# mark the optimal bundle\n", "ax.hlines(C_star1, 0, L_star1, linestyle='dashed')\n", "ax.vlines(L_star1, 0, C_star1, linestyle='dashed')\n", "\n", "# axes, labels, title, colorbar etc.\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 10)\n", "ax.set_ylabel(r'Consumption, $C_{t}$', family='serif', fontsize=15)\n", "ax.set_xlabel(r'Labor, $L_{t}$', family='serif', fontsize=15)\n", "ax.set_title(r'Optimal bundle in period t=1 for $b=%.2f, \\beta=%.2f$' %(b, beta),\n", " family='serif', fontsize=15)\n", "ax.legend(loc=4, frameon=False)\n", "fig.colorbar(utility_surface, shrink=0.75, aspect=10)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Task 3: Solving a Real Business Cycle (RBC) Model using Dynare++\n", "\n", "The remainder of the lab focuses on solving and analyzing the RBC/DSGE models using perturbation methods implemented in [Dynare++](http://www.dynare.org/documentation-and-support/dynarepp). Perturbation methods are *local* approximation methods: our strategy will be to pick a point in the state space of the model around which to approximate the decision rules of the representative household. Our solution will only be valid/accurate within some small neighborhood of our chosen point. Perturbation methods are fundamentally different from, say, numerical dynamic programming methods which can be used to find *global* approximations to the decision rules of the representative household.\n", "\n", "Those interested in the mathematical machinery of perturbation methods should consult Chapters 13 and 14 of [*Numerical Methods for Economists*](http://www.amazon.co.uk/Numerical-Methods-Economics-Kenneth-Judd/dp/0262100711) and the papers included in the literature folder." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A basic RBC model\n", "\n", "### Firms\n", "\n", "Representative firm has a constant returns to scale (CRTS), constant elasticity of substitution (CES) production function.\n", "\n", "$$Y_t = F(Z_t, K_t, L_t) = e^{Z_t} \\Bigg[\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}\\Bigg]^{\\frac{\\sigma}{\\sigma-1}} \\tag{3.1}$$\n", "\n", "Total factor productivity shocks, $Z_t$, are assumed to follow a first-order autoregressive process:\n", "\n", "$$Z_t = \\rho_z Z_{t-1} + \\epsilon_{z,t} \\tag{3.2}$$ \n", "\n", "where the disturbance, $\\epsilon_z$, is assumed to be Gaussian with zero mean and standard deviation $\\sigma_z$: $\\epsilon_z \\sim N(0, \\sigma_z)$. All markets are competitive and therefore factors are paid their respective marginal products.\n", "\n", "\\begin{align}\n", "W_t =& \\frac{\\partial F}{\\partial L_t} = \\left(\\frac{(1 - \\alpha)L_t^{-\\frac{1}{\\sigma}}}{\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}}\\right) Y_t \\tag{3.3} \\\\\n", "r_t =& \\frac{\\partial F}{\\partial K_t} = \\left(\\frac{\\alpha K_t^{-\\frac{1}{\\sigma}}}{\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}}\\right) Y_t \\tag{3.4}\n", "\\end{align}\n", "\n", "Joint assumption of constant returns to scale and perfect competition implies that representative firm earns zero profits.\n", "\n", "$$Y_t = W_t L_t + r_tK_{t-1} \\tag{3.5}$$\n", "\n", "\n", "### Households\n", "\n", "#### Preferences\n", "The lifetime utility of the representative household is:\n", "\n", "$$U = E\\left\\{\\sum_{t=0}^{\\infty} \\beta^t u\\bigg(C_t, L_t\\bigg)\\right\\}$$\n", "\n", "where the flow utility function has the following form.\n", "\n", "$$u\\bigg(C_t, L_t\\bigg) = \\left(\\frac{C_t^{1 - \\theta} - 1}{1 - \\theta}\\right) + b \\left(\\frac{(1 - L_t)^{1 - \\omega} - 1}{1 - \\omega}\\right)$$\n", "\n", "The parameter $0 < \\theta$ is the coefficient of relative risk avesion, $0 < \\omega$ is the inverse inter-temporal elasticity of substitution between current and future leisure, and $0 < b$ controls the importance of leisure in determining flow utility. Note that if $\\theta = \\omega = 1$, then \n", "\n", "$$u\\bigg(C_t, L_t\\bigg) = \\ln C_t + b \\ln (1 - L_t)$$\n", "\n", "and we recover the flow utility function assumed by Romer and used in your lecture notes.\n", "\n", "The household has two sources of income: labor income, $W_tL_t$, and capital income, $r_t K_{t-1}$. The household must divide its total income between consumption and investment:\n", "\n", "$$C_t + I_t = W_tL_t + r_tK_{t-1}$$\n", "\n", "The household's initial stock of capital, $K_0$, is assumed given, and its capital holdings evolve as follows.\n", "\n", "$$K_t = (1 - \\delta)K_{t-1} + I_t$$\n", "\n", "The representative household's objective is to solve:\n", "\n", "$$\\max_{\\{C\\}_{t=0}^{\\infty}, \\{L\\}_{t=0}^{\\infty}} E\\left\\{\\sum_{t=0}^{\\infty} \\beta^t\\Bigg[\\left(\\frac{C_t^{1 - \\theta} - 1}{1 - \n", "\\theta}\\right) + b \\left(\\frac{(1 - L_t)^{1 - \\omega} - 1}{1 - \\omega}\\right)\\Bigg]\\right\\}$$\n", "\n", "subject to the flow budget constraint and the equation of motion for capital stock. \n", "\n", "\\begin{align}\n", "C_t + I_t =& W_tL_t + r_tK_{t-1} \\tag{3.6a}\\\\\n", "K_t =& (1 - \\delta)K_{t-1} + I_t \\tag{3.6b}\n", "\\end{align}\n", "\n", "#### Solution to household's problem\n", "\n", "To solve the household's problem, combine the two constraints as follows:\n", "\n", "$$K_t = W_tL_t + (1 + r_t - \\delta)K_{t-1} - C_t$$\n", "\n", "and then form the Lagrangian.\n", "\n", "$$\\mathcal{L} \\equiv E\\left\\{\\sum_{t=0}^{\\infty} \\beta^t\\Bigg[\\left(\\frac{C_t^{1 - \\theta} - 1}{1 - \n", "\\theta}\\right) + b \\left(\\frac{(1 - L_t)^{1 - \\omega} - 1}{1 - \\omega}\\right) + \\lambda_t\\bigg[W_tL_t + (1 + r_t - \\delta)K_{t-1} - C_t - K_t\\bigg]\\Bigg]\\right\\}$$\n", "\n", "First-order necessary conditions are\n", "\n", "\\begin{align}\n", "\\frac{\\partial \\mathcal{L}}{\\partial C_t} = 0 \\implies& C_t^{-\\theta} = \\lambda_t \\\\ \n", "\\frac{\\partial \\mathcal{L}}{\\partial L_t} = 0 \\implies& b(1 - L_t)^{-\\omega} = W_t\\lambda_t\\\\\n", "\\frac{\\partial \\mathcal{L}}{\\partial K_t} = 0 \\implies& \\lambda_t = \\beta E_t\\bigg\\{\\lambda_{t+1}(1 + r_{t+1} - \\delta)\\bigg\\} \n", "\\end{align}\n", "\n", "Combine the first two FOCs and we get the intra-temporal trade-off between consumption and labor. Optimal choice of $C_t$ and $L_t$ should equate the benefit from an extra unit of leisure, $b(1-L_t)^{-\\omega}$, with the benefit from consuming $W_t$ units of the consumption good, $W_tC_t^{-\\theta}$. \n", "\n", "$$b(1 - L_t)^{-\\omega} = W_tC_t^{-\\theta} \\tag{3.7}$$\n", "\n", "Combine the first and the third FOCs and we get the inter-temporal trade-off between consumption (i.e., the consumption Euler equation). As usual, the consumption Euler equation implies that the optimal allocation of $C$ across time equates the benefit from an additional unit of consumption today with the *expected* benefit from and consuming that additional unit tomorrow.\n", "\n", "$$C_t^{-\\theta} = \\beta E_t\\bigg\\{C_{t+1}^{-\\theta}(1 + r_{t+1} - \\delta)\\bigg\\} \\tag{3.8}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model summary\n", "\n", "#### Equations\n", "Collecting the numbered equations from above yields the following system of 9 non-linear equations (only one of which involves computing expectations) in the 8 unknowns $Y, Z, K, L, W, r, C, I$. \n", "\n", "\\begin{align}\n", "0 =& Y_t - e^{Z_t} \\Bigg[\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}\\Bigg]^{\\frac{\\sigma}{\\sigma-1}} \\tag{3.1} \\\\ \\\\\n", "0 =& Z_t - \\rho_z Z_{t-1} - \\epsilon_{z,t} \\tag{3.2} \\\\ \\\\\n", "0 =& W_t - \\left(\\frac{(1 - \\alpha)L_t^{-\\frac{1}{\\sigma}}}{\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}}\\right) Y_t \\tag{3.3} \\\\ \\\\\n", "0 =& r_t - \\left(\\frac{\\alpha K_t^{-\\frac{1}{\\sigma}}}{\\alpha K_{t-1}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) L_t^{\\frac{\\sigma - 1}{\\sigma}}}\\right) Y_t \\tag{3.4} \\\\ \\\\\n", "0 =& Y_t - W_t L_t - r_tK_{t-1} \\tag{3.5} \\\\ \\\\\n", "0 =& C_t + I_t - W_tL_t - r_tK_{t-1} \\tag{3.6a}\\\\ \\\\\n", "0 =& K_t - (1 - \\delta)K_{t-1} - I_t \\tag{3.6b} \\\\ \\\\\n", "0 =& b(1 - L_t)^{-\\omega} - W_tC_t^{-\\theta} \\tag{3.7} \\\\ \\\\\n", "0 =& C_t^{-\\theta} - \\beta E_t\\bigg\\{C_{t+1}^{-\\theta}(1 + r_{t+1} - \\delta)\\bigg\\} \\tag{3.8}\n", "\\end{align}\n", "\n", "Wait a minute! If we have 9 equations, but only 8 unknowns doesn't this mean we have an over-identified system? Yes! Equation 3.5, which defines the zero profit condition, is redundant. Why include a redundant equation? We will use equation 3.5 as a \"sanity check\" to confirm that we have coded the model into Dynare++ correctly: we know that profits of the representative firm must be zero in every period, thus define an extra variable called zero_profit and check whether zero_profit $\\equiv Y_t - W_t L_t - r_tK_{t-1} = 0$ holds for our solution.\n", "\n", "#### Parameters\n", "In order to solve the model, we will need to specify values for the following 9 parameters:\n", "\n", "* $0 < \\beta < 1$: Representative household's discount factor;\n", "* $0 < \\theta <\\infty$: Representative household's coefficient of relative risk aversion;\n", "* $0 < \\omega < \\infty$: Representative household's inverse of the inter-temporal elasticity of substitution of leisure;\n", "* $0 < b < \\infty$: Controls the importance of utility from leisure for the representative household;\n", "* $0 < \\delta < 1$: Depreciation factor for physical capital;\n", "* $0 < \\alpha < 1$: Controls the relative importance of capital and labor in production process;\n", "* $0 < \\sigma < \\infty$: Elasticity of substitution between capital and labor in production process;\n", "* $-1 < \\rho_z < 1$: Correlation of productivity process;\n", "* $0 < \\sigma_z < \\infty$: Standard deviation of productivity shocks.\n", "\n", "Because I want to focus on the numerical techniques used to solve RBC/DSGE models, we will simple specify values for these parameters and not bother estimating them using data. However, you should be aware taht there is an enormous literature on Bayesian and Maximum Likelihood methods for estimating DSGE models. Those interested in learning how to estimate DSGE modles should start by reading the Dynare [user's guide](http://www.dynare.org/documentation-and-support/user-guide/Dynare-UserGuide-WebBeta.pdf), [reference manual](http://www.dynare.org/wp-repo/dynarewp001.pdf), and citations therein. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding the model file\n", "\n", "Both Dynare and Dynare++ require us to create a text file summarizing the model that we wish to solve. The Dynare++ model file generally involves three commands that tell the program what are the model's variables, which of them are endogenous (and which are exogenous) and what are the model parameters.\n", "\n", "The commands are:\n", "\n", "* var starts a comma separated list of endogenous variables.\n", "* varexo starts a comma separated list list of exogenous variables that will be shocked.\n", "* parameters starts a comma separated list of parameters.\n", "\n", "**Example syntax:**\n", "\n", " var Y, K, L, C, I, r, W, Z, zero_profit;\n", " varexo eps_z;\n", " parameters b, alpha, beta, delta, sigma, theta, omega, rho_z, sigma_z;\n", "\n", "#### Exercise:\n", "\n", "The code in the cells below uses the %%writefile IPython magic command to create a new text file in your working directory called rbc_benchmark.mod and add some lines of code delaring endogenous and exogenous variables. \n", "\n", "** N.B.: Each line of the model file must end with a semi-colon. The most common syntax error when writing model files is to forget to end the line with a semi-colon!**" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%%writefile?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile rbc_benchmark.mod\n", "////////// Declare variables //////////\n", "\n", "/* \n", "\n", "///// Endogenous variables /////\n", " \n", " K: capital\n", " C: consumption\n", " Z: productivity\n", " Y: output\n", " I: investment\n", " W: real wage\n", " r: net interest rate\n", " L: labor supply\n", " zero_profit: zero profit condition\n", "\n", "*/\n", "var Y, K, L, C, I, r, W, Z, zero_profit;\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we declare the model's exogenous variables. Note the use of the -a option which tells IPython that we wish to append the contents of the cell to the current file rbc_benchmark.mod." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "///// Exogenous variables /////\n", "\n", "// eps_z: productivity shock \n", "varexo eps_z;\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we declare the model parameters. Note the use of the -a option which tells IPython that we wish to append the contents of the cell to the current file rbc_benchmark.mod." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "////////// Declare parameters //////////\n", "parameters b, alpha, beta, delta, sigma, theta, omega, rho_z;\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will also need to specify values for our parameters. I prefer to specify the values of each parameter on a separate line. I always include a short comment describing each parameter.\n", "\n", "**Example syntax:**\n", "\n", " // discount factor\n", " beta = 0.9896;\n", "\n", "#### Exercise:\n", "\n", "Using the %%writefile IPython magic command. Add the code from the example above which specifies a value for the discount factor. Using the example syntax as a guide, add additional lines of code to the text file defining values for the remaining parameters of the model. \n", "\n", "* Discount factor, $\\beta = 0.9896$\n", "* Coefficient of relative risk aversion, $\\theta = 2.5$\n", "* Inverse elasticity of substitution for leisure, $\\omega = 1.5$\n", "* Weight for leisure in utility, $b = 2.0$\n", "* Elasticity of substitution between capital and labor, $\\sigma = 0.75$\n", "* Relative weight of capital in production, $\\alpha = 0.40$\n", "* Depreciation rate of capital, $\\delta = 0.025$\n", "* Persistence of productivity process, $\\rho_z = 0.95$\n", "\n", "** N.B.: Each line of the model file must end with a semi-colon. The most common syntax error when writing model files is to forget to end the line with a semi-colon!**" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "// discount factor\n", "# insert your code here!\n", "\n", "// coefficient of relative risk aversion\n", "theta = 2.5;\n", "\n", "// inverse elasticity of substitution for leisure\n", "# insert your code here!\n", "\n", "// weight for leisure in utility\n", "b = 2.0;\n", "\n", "// elasticity of substitution between capital and labor\n", "# insert your code here!\n", "\n", "// relative weight of capital in production\n", "alpha = 0.40;\n", "\n", "// depreciation rate of capital\n", "# insert your code here!\n", "\n", "// persistence of productivity process\n", "rho_z = 0.95;\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model's equations are formulated in the same way in both Dynare and Dynare++: we specifiy a \"model block\" by inserting the following lines into our model file... \n", "\n", " model;\n", " \n", " // INSERT YOUR MODEL'S EQUATIONS HERE !\n", " \n", " end;\n", " \n", "The keywords model; and end; are how the program is able to find and then parse our model equations. Model equations can be specified as mathematical expressions using the following functions and operators:\n", "\n", "* Binary operators: + - * / ^.\n", "* Unary plus and minus as in a = -3; and a = +3; respectively.\n", "* Unary mathematical functions: log exp sin cos tan sqrt, where the logarithm has a natural base\n", "\n", "The Dynare++ manual also lists a symbolic differentiation operator diff(expr,symbol), where expr is a mathematical expression and symbol is a unary symbol (i.e., a variable or a parameter); for example \n", "\n", " diff(A*K(-1)^alpha*L^(1-alpha),K(-1))\n", "\n", "is internally expanded as \n", "\n", " A*alpha*K(-1)^(alpha-1)*L^(1-alpha).\n", " \n", "However, I have not been able to get model files to compile when using the diff operator.\n", "\n", "**Example syntax:**\n", "\n", " // consumption Euler equation (i.e., equation 3.7)\n", " C^(-theta) = beta * C(+1)^(-theta) * (1 + r(+1) - delta);\n", "\n", "In Dynare and Dynare++, the timing of each variable reflects the period in which that variable is decided. For instance, capital stock is not decided today, but yesterday (recall that it is a function of yesterday's investment and capital stock); it is what we call in the jargon a \"predetermined variable.\" Thus, even though in Romer's textbook (and in your lecture notes and in many published papers!) the equation of motion for capital is written \n", "\n", "$$K_{t+1} = (1 - \\delta)K_t + I_t$$\n", "\n", "in order to use Dynare and Dynare++ we must re-write this equation as\n", "\n", "$$K_t = (1 - \\delta)K_{t-1} + I_t$$\n", "\n", "which we would code in our model file as\n", "\n", " // household evolution of capital (i.e., equation 3.6b)\n", " K = (1 - delta) * K(-1) + I;\n", "\n", "A slightly more roundabout way to explain the same thing is that for stock variables, we must use a \"stock at the end of the period\" convention. It is investment during period $t$ that sets stock at the end of period $t$. Again a lot of papers use the \"stock at the beginning of the period\" convention. There is nothing wrong with this! But if you want to use either Dynare or Dynare++ to solve such a model then you will need to re-write the model using \"stock at the end of the period\" convention.\n", "\n", "#### Exercise:\n", "\n", "The code in the cell below adds the model expressions for the consumption Euler equation and the equation of motion for capital stock from the example above using the %%writefile IPython magic command. Using the example syntax as a guide, add additional expressions for each of the model equations. When you are finished you should have 9 equations: one for each of our 9 declared variables! Save your changes to the file rbc_benchmark.mod\n", "\n", "** N.B.: Each line of the model file must end with a semi-colon. The most common syntax error when writing model files is to forget to end the line with a semi-colon!**" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "////////// Model equations //////////\n", "\n", "model;\n", "\n", "// production (i.e., equation 3.1)\n", "# insert your code here!\n", "\n", "// productivity process (i.e., equation 3.2)\n", "Z = rho_z * Z(-1) + eps_z;\n", "\n", "// real wage (i.e., equation 3.3)\n", "# insert your code here!\n", "\n", "// rental rate (i.e., equation 3.4)\n", "r = ((alpha *K(-1)^(-1 / sigma)) / (alpha * K(-1)^((sigma - 1) / sigma) + (1 - alpha) * L^((sigma - 1) / sigma))) * Y;\n", "\n", "// check that zero profit condition holds (i.e., equation 3.5)\n", "zero_profit = Y - W * L - r * K(-1);\n", "\n", "// household budget constraint (i.e., equation 3.6a)\n", "# insert your code here!\n", "\n", "// household evolution of capital (i.e., equation 3.6b)\n", "K = (1 - delta) * K(-1) + I;\n", "\n", "// consumption Euler equation (i.e., equation 3.7)\n", "# insert your code here!\n", "\n", "// intra-temporal consumption/labor trade-off (i.e., equation 3.8)\n", "b * (1 - L)^(-omega) = W * C^(-theta);\n", "\n", "end;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Deterministic steady state\n", "In order to solve our RBC model using perturbation methods, we need to specify a point in state space around which we will approximate the decision rules of the representative household. By convention, NOT necessity, most researchers choose to approximate the decision rules around the deterministic steady state of the model. By definition, the deterministic steady state of the model is the point in state space where the model would remain in the absence of shocks: \n", "\n", "$$\\epsilon_{z,t} = 0\\ \\forall\\ t\\ \\implies Z_t = 0\\ \\forall\\ t.$$\n", "\n", "To solve for the deterministic steady state of our RBC model we need to find values $\\overline{Y}, \\overline{K}, \\overline{L}, \\overline{W}, \\overline{r}, \\overline{C}, \\overline{I}$ that jointy solve the following system of non-linear equations.\n", "\n", "\\begin{align}\n", "0 =& \\overline{Y} - \\Bigg[\\alpha \\overline{K}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) \\overline{L}^{\\frac{\\sigma - 1}{\\sigma}}\\Bigg]^{\\frac{\\sigma}{\\sigma-1}} \\tag{3.9}\\\\ \\\\\n", "0 =& \\overline{W} - \\left(\\frac{(1 - \\alpha)\\overline{L}^{-\\frac{1}{\\sigma}}}{\\alpha \\overline{K}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) \\overline{L}^{\\frac{\\sigma - 1}{\\sigma}}}\\right) \\overline{Y} \\tag{3.10}\\\\ \\\\\n", "0 =& \\overline{r} - \\left(\\frac{\\alpha \\overline{K}^{-\\frac{1}{\\sigma}}}{\\alpha \\overline{K}^{\\frac{\\sigma - 1}{\\sigma}} + (1 - \\alpha) \\overline{L}^{\\frac{\\sigma - 1}{\\sigma}}}\\right) \\overline{Y} \\tag{3.11}\\\\ \\\\\n", "0 =& \\overline{Y} - \\overline{C} - \\overline{I} \\tag{3.12}\\\\ \\\\\n", "0 =& \\overline{K} - (1 - \\delta)\\overline{K} - \\overline{I} \\tag{3.13}\\\\ \\\\\n", "0 =& b(1 - \\overline{L})^{-\\omega} - \\overline{W}\\overline{C}^{-\\theta} \\tag{3.14}\\\\ \\\\\n", "0 =& 1 - \\beta (1 + \\overline{r} - \\delta) \\tag{3.15}\n", "\\end{align}\n", "\n", "Mathematically, solving for a deterministic steady state of an RBC/DSGE model is a [root-finding problem](http://en.wikipedia.org/wiki/Root-finding_algorithm). Standard algorithms exist for solving root-finding problems (many of which have been implemented in the [scipy.optimize](http://docs.scipy.org/doc/scipy/reference/optimize.html) module). Those interested in the details should start with Chapter 5 of *Numerical Methods for Economists*. In practice, solving for deterministic steady state of the model can be quite difficult (particularly with large models which may have hundreds of equations that need to be solved simultaneously!). \n", "\n", "All algorithms for solving root finding problems require an initial guess of the correct solution in order to proceed. Sometimes (often?) any guess is good enough. However, sometimes a \"good\" initial guess must be supplied in order for the algorithm to terminate successfully/efficiently. Where do \"good\" initial guesses come from? Typically from analytic solutions to some special case of the general model.\n", "\n", "Suppose that representative household has logarithmic preferences, $\\theta=\\omega=1.0$; there is full capital depreciation, $\\delta=1.0$; and production is Cobb-Douglas, $\\sigma = 1.0$. Under these simplifying assumptions, the equations 3.9-3.15 reduce to...\n", "\n", "\\begin{align}\n", "0 =& \\overline{Y} - \\overline{K}^{\\alpha}\\overline{L}^{1-\\alpha} \\tag{3.16}\\\\ \\\\\n", "0 =& \\overline{W} - (1 - \\alpha)\\frac{\\overline{Y}}{\\overline{L}} \\tag{3.17}\\\\ \\\\\n", "0 =& \\overline{r} - \\alpha\\frac{\\overline{Y}}{\\overline{K}} \\tag{3.18}\\\\ \\\\\n", "0 =& \\overline{Y} - \\overline{C} - \\overline{I} \\tag{3.19}\\\\ \\\\\n", "0 =& \\overline{K} - \\overline{I} \\tag{3.20}\\\\ \\\\\n", "0 =& \\frac{b}{1 - \\overline{L}} - \\frac{\\overline{W}}{\\overline{C}} \\tag{3.21}\\\\ \\\\\n", "0 =& 1 - \\beta \\overline{r} \\tag{3.22}\n", "\\end{align}\n", "\n", "Now we bust out the pen and paper! From equation 3.22 we learn that\n", "\n", "$$\\overline{r} =\\frac{1}{\\beta} = \\alpha \\frac{\\overline{Y}}{\\overline{K}} \\implies \\frac{\\overline{K}}{\\overline{Y}} = \\alpha\\beta.$$\n", "\n", "Combining equations 3.19 and 3.20 and then ividing through the result by $Y$ yields\n", "\n", "$$\\frac{\\overline{C}}{\\overline{Y}} = 1 - \\frac{\\overline{K}}{\\overline{Y}} = 1 - \\alpha\\beta \\implies \\frac{\\overline{I}}{\\overline{Y}} = \\alpha\\beta.$$\n", "\n", "This result tells us that, in steady state, the representative household consumes a fraction $1-\\alpha\\beta$ of its income. Using this result as well as equation 3.17 to substitute for $\\overline{C}$ and $\\overline{W}$, repsectively, in equation 3.21 yields (after a bit of algebra!) an expression for the steady state labor supply.\n", "\n", "$$\\overline{L} = \\frac{1 - \\alpha}{1 - \\alpha + b(1 - \\alpha\\beta)}$$\n", "\n", "Substituting our expression for $\\overline{L}$ into equation 3.16 and making use of previous results allows us to work out the expression for $\\overline{K}$.\n", "\n", "$$\\overline{K} = \\alpha\\beta \\overline{Y} = \\alpha\\beta \\overline{K}^{\\alpha}\\overline{L}^{1-\\alpha} = \\alpha\\beta \\overline{K}^{\\alpha}\\left(\\frac{1 - \\alpha}{1 - \\alpha + b(1 - \\alpha\\beta)}\\right)^{1-\\alpha} \\iff \\overline{K} = (\\alpha\\beta)^{\\frac{1}{1-\\alpha}}\\left(\\frac{1 - \\alpha}{1 - \\alpha + b(1 - \\alpha\\beta)}\\right)$$\n", "\n", "Finally, we can solve for the steady state value of output as follows.\n", "\n", "$$\\overline{Y} = \\overline{K}^{\\alpha}\\overline{L}^{1-\\alpha} = (\\alpha\\beta)^{\\frac{\\alpha}{1-\\alpha}}\\left(\\frac{1 - \\alpha}{1 - \\alpha + b(1 - \\alpha\\beta)}\\right)$$\n", "\n", "We actually don't need to bother deriving expressions for $\\overline{C}, \\overline{I}$, and $\\overline{W}$ in terms of the structural parameters of the model! In sum, we use the following initial conditions as our guess for the steady state values for the general model...\n", "\n", "\\begin{align}\n", "\\overline{L} =& \\frac{1 - \\alpha}{1 - \\alpha + b(1 - \\alpha\\beta)} \\tag{3.23}\\\\ \\\\\n", "\\overline{K} =& (\\alpha\\beta)^{\\frac{1}{1-\\alpha}}\\overline{L} \\tag{3.24}\\\\ \\\\\n", "\\overline{Y} =& (\\alpha\\beta)^{\\frac{\\alpha}{1-\\alpha}}\\overline{L} \\tag{3.25}\\\\ \\\\\n", "\\overline{I} =& \\overline{K} \\tag{3.26}\\\\ \\\\\n", "\\overline{C} =& \\overline{Y} - \\overline{K} \\tag{3.27} \\\\ \\\\\n", "\\overline{W} =& (1 - \\alpha)\\frac{\\overline{Y}}{\\overline{L}} \\tag{3.28} \\\\ \\\\\n", "\\overline{r} =& \\frac{1}{\\beta} \\tag{3.29}\\\\ \\\\\n", "\\overline{Z} =& 0 \\tag{3.30}\n", "\\end{align}\n", "\n", "In order to use the built-in Dynare++ root-finding algorithm to find the steady state of our model, we need to get the expression defining our initial guess into our model file. The first step is to define 3 additional parameters, KSS, LSS, and YSS, representing the steady state values of $K$, $L$, and $Y$ for the special case of our general model. Open the file rbc_benchmark.mod and edit the declaration of model parameters to include KSS, LSS, and YSS. This line should look as follows:\n", "\n", " parameters b, alpha, beta, delta, sigma, theta, omega, rho_z, KSS, LSS, YSS;\n", "\n", "Now we need to add additional lines of code to define the values of KSS, LSS, and YSS in terms of the structural parameters of the model. Add the following lines of code to the rbc_benchmark.mod file (in the section where the structural parameters of the model are given values...NOT at the end of the file!):\n", "\n", " // steady state labor supply (computed for theta=omega=delta=sigma=1)\n", " LSS = (1 - alpha) / (1 - alpha + b * (1 - alpha * beta));\n", "\n", " // steady state capital (computed for theta=omega=delta=sigma=1)\n", " KSS = (alpha * beta)^(1 / (1 - alpha)) * LSS;\n", "\n", " // steady state output (computed for theta=omega=delta=sigma=1)\n", " YSS = KSS^alpha * LSS^(1 - alpha);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now specify our initial guess for the deterministic steady state of our general model by adding an \"initial value block\" to the end of the file rbc_benchmark.mod (i.e., *after* the model block!)." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "////////// Initial values for computing steady state //////////\n", "\n", "initval;\n", "K = KSS;\n", "L = LSS;\n", "Y = YSS;\n", "C = (1 - alpha * beta) * YSS;\n", "Z = 0.0;\n", "I = alpha * beta * YSS;\n", "W = (1 - alpha) * (YSS / LSS);\n", "r = (1 / beta);\n", "zero_profit = 0.0;\n", "end;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Variance-covariance structure of the exogenous shocks\n", "\n", "To complete the specification of our model, we need to specify the variance-covariance structure or the shocks driving the economy. In more complicated models, this matrix might be very large. In our toy RBC model, this matrix is the scalar $\\sigma_z$. My parameterization sets $\\sigma_z^2=0.007$. Add the following code to the bottom of the rbc_benchmark.mod file." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to rbc_benchmark.mod\n" ] } ], "source": [ "%%writefile -a rbc_benchmark.mod\n", "\n", "////////// Variance covariance matrix //////////\n", "vcov = [0.007];" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introducing Dynare++\n", "Dynare++ is a standalone C++ version of [Dynare](http://www.dynare.org/) specialized in computing $k$-order [Taylor approximations](http://en.wikipedia.org/wiki/Taylor_series) of dynamic stochastic general equilibrium (DSGE) models (if you weren't already aware, RBC models are a special case of DSGE models). The current version of Dynare++ is capable of approximating the decision rules (i.e., policy functions) around either a deterministic or stochastic steady state, run simulations, generate IRFs, etc. It is also able to check approximation errors of the solution.\n", "\n", "The main features of Dynare++ are:\n", "\n", "* Completely standalone, no need to install MATLABÂ® or GNU Octave\n", "* Output readable in MATLABÂ® and GNU Octave (and Python!)\n", "* Contains a tensor library for evaluation of Faa Di Bruno formula\n", "* Highly parallelized\n", "* Takes advantage of kronecker product structure\n", "* Links with ATLAS and LAPACK (industry standard linear algebra libraries)\n", "* Includes numerical integration module\n", "* Includes parser and derivator doing all derivatives symbolically\n", "\n", "I am only going to demonstrate a small subset of the functionality of Dynare and Dynare++. However, I have included .pdf copies of the Dynare user guide and reference manual, as well as a Dynare++ tutorial. Those of you interested in pursuing RBC/DSGE modelling for your MSc disseration or future PhD research should read these documents at some point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What are Taylor approximations?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x):\n", " \"\"\"Example function for demonstrating Taylor approximations.\"\"\"\n", " return x**0.25\n", "\n", "f_1st_order = interpolate.approximate_taylor_polynomial(f, x=1, degree=1, scale=0.01)\n", "f_2nd_order = interpolate.approximate_taylor_polynomial(f, x=1, degree=2, scale=0.01)\n", "f_3rd_order = interpolate.approximate_taylor_polynomial(f, x=1, degree=3, scale=0.01)\n", "f_4th_order = interpolate.approximate_taylor_polynomial(f, x=1, degree=4, scale=0.01)\n", "f_5th_order = interpolate.approximate_taylor_polynomial(f, x=1, degree=5, scale=0.01)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/drpugh/anaconda/lib/python3.4/site-packages/ipykernel/__main__.py:3: RuntimeWarning: invalid value encountered in power\n", " app.launch_new_instance()\n" ] }, { "data": { "image/png": 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ekYqIG9RzUMX5fdxM+ZVfbl4uH677kN/M/A2pz6Qy8OUh/HfGGlZM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\nc/VMMnMymbl6Jh0adiCQGiDQNUCf1n0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "ax1 = fig.add_subplot(111)\n", "\n", "# grid of points to evaluate function and its approximations\n", "grid = np.linspace(-1, 3, 10000)\n", "\n", "# plots of the function and its approximations (need to translate Taylor polynomial!)\n", "ax1.plot(grid, f(grid), label='f(x)')\n", "ax1.plot(grid, f_1st_order(grid - 1), label='1st-order')\n", "#ax1.plot(grid, f_2nd_order(grid - 1), label='2nd-order')\n", "#ax1.plot(grid, f_3rd_order(grid - 1), label='3rd-order')\n", "#ax1.plot(grid, f_4th_order(grid - 1), label='4th-order')\n", "#ax1.plot(grid, f_5th_order(grid - 1), label='5th-order')\n", "\n", "# axes, labels, title, legend, etc...\n", "ax1.set_xlabel('$x$', fontsize=15)\n", "ax1.set_ylabel('$f(x)$', rotation='horizontal', fontsize=15)\n", "ax1.set_title(r'Taylor series approximation of $f(x) = x^{\\alpha}$ at $x=1$', fontsize=20, family='serif')\n", "ax1.set_ylim(-0.5, 2.0)\n", "ax1.grid()\n", "ax1.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Execute the following command in order to confirm that Dynare++ has been added to your path correctly, and that it is fully functional. **N.B.: The ! tells IPython to send to command to your OS shell.** " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dynare++ v. 4.4.3. Copyright (C) 2004-2011, Ondra Kamenik\r\n", "Dynare++ comes with ABSOLUTELY NO WARRANTY and is distributed under\r\n", "GPL: modules integ, tl, kord, sylv, src, extern and documentation\r\n", "LGPL: modules parser, utils\r\n", " for GPL see http://www.gnu.org/licenses/gpl.html\r\n", " for LGPL see http://www.gnu.org/licenses/lgpl.html\r\n" ] } ], "source": [ "# confirm the Dynare++ is installed correctly!\n", "!dynare++ --version" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dyld: lazy symbol binding failed: Symbol not found: _dgetrf_\r\n", " Referenced from: /Applications/Dynare/4.4.3/dynare++/dynare++\r\n", " Expected in: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib\r\n", "\r\n", "dyld: Symbol not found: _dgetrf_\r\n", " Referenced from: /Applications/Dynare/4.4.3/dynare++/dynare++\r\n", " Expected in: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib\r\n", "\r\n" ] } ], "source": [ "# solve the model via linearization around the deterministic steady state...\n", "!dynare++ --order 1 --no-centralize --seed 42 --check PE --per 500 --check-num 100 rbc_benchmark_answers.mod\n", "\n", "# convert the output into a Python dictionary\n", "rbc_order1 = io.loadmat('rbc_benchmark_answers.mat')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember that Python dictionaries store information in key-value pairs. Our Python dictionary rbc_order1 has the following keys...." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "['dyn_i_L',\n", " 'dyn_i_K',\n", " 'dyn_irfp_eps_z_mean',\n", " 'dyn_i_I',\n", " 'dyn_i_C',\n", " 'dyn_ss',\n", " 'dyn_simul_errors',\n", " 'dyn_i_Z',\n", " 'dyn_i_Y',\n", " 'dyn_i_W',\n", " 'dyn_ellipse_errors',\n", " 'dyn_vcov',\n", " 'dyn_nboth',\n", " 'dyn_nstat',\n", " 'dyn_vcov_exo',\n", " 'dyn_i_r',\n", " 'dyn_vars',\n", " 'dyn_steady_states',\n", " 'dyn_irfp_eps_z_var',\n", " 'dyn_i_zero_profit',\n", " 'dyn_state_vars',\n", " 'dyn_g_1',\n", " 'dyn_g_0',\n", " 'dyn_mean',\n", " 'dyn_simul_points',\n", " 'dyn_irfm_eps_z_var',\n", " 'dyn_irfm_eps_z_mean',\n", " 'dyn_i_eps_z',\n", " 'dyn_npred',\n", " 'dyn_nforw',\n", " 'dyn_ellipse_points',\n", " 'dyn_shocks']" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# returns a list of the dictionary keys...\n", "rbc_order1.keys()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can access the values of the rbc_order1 dictionary using these keys. For example, if we want to access an array of endogenous variable names sorted by the Dynare++ internal ordering then we type..." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rbc_order1['dyn_vars']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...since we will be needing the indicies for our variables frequently in the code below we will store them in a Python dictionary." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{u'C ': 7,\n", " u'I ': 1,\n", " u'K ': 5,\n", " u'L ': 3,\n", " u'W ': 2,\n", " u'Y ': 0,\n", " u'Z ': 6,\n", " u'r ': 8,\n", " u'zero_profit': 4}" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create a dictionary using a dict comprehension\n", "rbc_variable_indices = {rbc_order1['dyn_vars'][i]:i for i in range(rbc_order1['dyn_vars'].size)}\n", "\n", "# display the result\n", "rbc_variable_indices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to access the array which stores the steady state values of the endogenous variables in the model, then we type..." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rbc_order1['dyn_ss'] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A detailed description of each of the keys can be found in section 7.2 of the [Dynare++ tutorial](http://www.dynare.org/documentation-and-support/dynarepp/dynare-tutorial.pdf)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting impulse response functions\n", "\n", "By default, Dynare++ simulates impulse response functions (IRFs) for all endogenous variables of the model. We can access the simulated IRFS using the appropriate dictionary keys. \n", "\n", "* 'dyn_irfm_eps_z_mean' for negative shocks \n", "* 'dyn_irfp_eps_z_mean' for postive shocks.\n", "\n", "**Note the subtle difference in the IRF keys!**" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# variables are ordering according to rbc_order1['dyn_vars']\n", "Y_bar, I_bar, W_bar, L_bar, zero_profit_bar, K_bar, Z_bar, C_bar, r_bar = rbc_order1['dyn_ss'] " ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7/28npp+ajgtfXkAD7QZixyGEEKWmNJcIkg8YY1h2fhmmOkwVO4oohn82HF+1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\nbH4zPt37KTeybxg0FlPNsSkxvSKgAq8MeFpdu8K+ferlhBM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# absolute deviations of Y and K in response to positive productivity shock\n", "plt.plot(rbc_order1['dyn_irfp_eps_z_mean'][0,:100], label='$Y$')\n", "plt.plot(rbc_order1['dyn_irfp_eps_z_mean'][5,:100], label='$K$')\n", "\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('Absolute deviations', fontsize=15, family='serif')\n", "plt.title(\"Output and capital IRFs\", fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default Dynare++ computes IRFs representing absolute deviations from the deterministic steady state. If we want IRFs representing percentage deviations then we will need to code them ourselves..." ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jEEIIIUzL5ofTAZ48AVdXuHoVcuc2+e6FEEKINJPh9LdwdoZmzWDtWq0jEUII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\nXvd1lS551j+zeoqZ9ImL1szdHebOVdupU/D11/CnP0FODow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EECZKirgQRio/P5/IyEjs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\nERdCCCFMlBRxIYQQwkRJERdCCCFM1P8DPZLtGry1oPMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# percentage deviations of Y and K in response to positive productivity shock\n", "plt.plot(100 * rbc_order1['dyn_irfp_eps_z_mean'][0,:100] / Y_bar, label='$Y$')\n", "plt.plot(100 * rbc_order1['dyn_irfp_eps_z_mean'][5,:100] / K_bar, label='$K$')\n", "\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('% deviations', fontsize=15, family='serif')\n", "plt.title(\"Output and capital IRFs\", fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we plot the responses of consumption, output, and investment to a negative productivity shock." ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/E3DhwgVUrVoVbm5uxg6FEEJIBVDh+/y5uZxeYmCzS16NixcvRmJiIlavXq2X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\n0W1KDaP5m4UZnvnI2Hxk7BnkbG0+1fw58gcA4Mp8ZuZ/8eJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# irfs for output, investment, and consumption in response to negative productivity shock \n", "plt.plot(100 * rbc_order1['dyn_irfm_eps_z_mean'][0,:100] / Y_bar, label='$Y$')\n", "plt.plot(100 * rbc_order1['dyn_irfm_eps_z_mean'][1,:100] / I_bar, label='$I$')\n", "plt.plot(100 * rbc_order1['dyn_irfm_eps_z_mean'][7,:100] / C_bar, label='$C$')\n", "\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('% deviations', fontsize=15, family='serif')\n", "plt.title(\"Output, consumption, and investment IRFs\", fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise:\n", "\n", "Using the above code snippets as a guide, plot the IRFs for the real wage and the labor supply in response to positive and negative productivity shocks." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating simulated data from the model\n", "\n", "An array of simulated time series data from the model can be accessed using the 'dyn_simul_points' key. Rows correspond to endogenous variables, columns to periods. Appears only if --check P option was passed when the solution was computed. The following code will produce a time series plot for $Y$..." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kyUA4HLQ8TtHHZJWBI0f0eWiooPgRdlNEExlnQJGBSLhVxqS47NwZeayxORCK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\nO+/ElClTA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# simulated data \n", "plt.plot(rbc_order1['dyn_simul_points'][0,:])\n", "plt.axhline(Y_bar, ls='dashed', color='k', label=r'$\\overline{Y}$')\n", "\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('Output, $Y_t$', fontsize=15, family='serif')\n", "plt.title(\"Time path of output\", fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a time series plot for consumption, $C_t$..." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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z7J+Tk+l8+8JC6k8HqD89WNEqBljgZUhIcLdlk8Dr2EC4GOBwDMIkYgB1dZ77\ns8PCgNhYaiF49126LZgtA7W1NMeAWjFQWEhfS0uNLReHYzRW/YduLgY4qglqH6BJxICtqMhzywBA\n4wYAYcBLSPC+UGZFq2XgwgX6WlQU3G3ZJPA6NhBuGeBwDMIkYgD19d5FurNph7Gx9DWYo+aZGIiJ\nAcrL3R/Pln1lFgIOJ1DhYoDjT4LaB2gSMZARFeWdZYC5BZgZ0STfyxCYGGjRQt3aBL/8AnTpAly5\nEtxt2STwOjYQAxbl4mKAwwE0L3RjGN7EDABCwCB7Uq6r875MZoWJgeRkdU/72dnAwIE0yyOHE8gY\ncF9zMcBRTdD6AF99FVi/3t+lAADYSku9swwMGEBfS0roa3OwDMhNqZSjvBxISQGqqoK3LZsIXscG\nsGkTFQJcDHA4BmCmlL0NDd5ZBh54gCbWYWIgmC0DbDaBWstAfb22bIUcjtmYNQs4dIi2fZ3hYoCj\nmqD1AZrIbJwREuKdZSA8HBg6tHlZBrSIgfh4oKoqeNuyieB1bBBWKxUDSplIPT2trmfjcAIRtals\nfYG3swkAKiaag2VALAbUuAm4ZYATyLBEYkwMuFvdVCNcDHBUE7Q+QPG0NLnlgb3FYgFOnFB1qK2y\n0jvLACAVA83BMhAdTT+7G+RFloGgbcsmgtexzrB7uaGBinydc4hwMcDhiMWAUYOn2hXGvI0ZAKgY\nKC2luQaag2XAYlHnKuCWAU4gw9yZtbXcMsDxL0HrAywvB/bvpwsEGSUGVM4LziBEP8tAfHzzsAwA\n6lwFTAzwmAGfwOtYZ5gYqKmhYmDvXl1Pz8UAh1NRQZ+iQ0P1X8qYuR2Yv88desYMJCQEt2WAzSYA\n1FsGoqNpnZhkyWoORzVMDFRU0AyEOmcX5WKAo5qg9QGWlwtiQO8n6epq6asrCIGtvp5bBtQitgy0\nbKlODISFAVFRsH39tfHla+YEbX/hL5gY2LDB+z5CBi4GOJzycprf3ggxwPzTaqYvNjTQSGFvU402\nF8uAWAwkJbnPIsmsLpWV6mM4OByzwPqQbdvUPVxohIsBjmqC0gfY0EAHh9hYanrTUwxcuAA89RR9\nr0YM1NUhQw/Fz87RnMRAVJT7Oha5YDK+/dbgwnGCsr/wJwbnQ+FigNO8uXSJ+ptDQ/W3DPzrX8Dr\nr9P3am5kPVwEgHCO5uQmiIpy/7TExMC6dfR4DieQ4GKAYxYC3gdosQDffy/ddvYs0L49fa93ACEL\nbgNUWwa3lV4sAAAgAElEQVRsagMNXcEtA/IwMRAWBtupU8aXr5kT8P2F2RCL3QsXdD89FwOc5gGL\n6s/NlW4/exZITaXv9bYMiH3/aua26zGTAGg+lgHxbAKNYoDPJuAEHOI+pE0b3U/PxQBHNQHtA2RP\ngo6ph8+dk1oG9Bw8WRZAQH3MAMum5w1iMcAtAwIiMZCRnGx8+Zo5Ad1fmJFffjH09FwMcJoHeXn0\n9cwZ6Xaxm0DvAMLiYuE9jxnQH0cx8OuvdJsSYstAMIskTnDyww+Gnp6LAY5qAtYHWF4OLFhA3z/7\nLFBQIOwzMmaguBh48EHg0UfVxwzoMUgxMdC2LbVOBKNJfP164MMPpWJg1y7gz39W/h9xzEB+vm/K\n2YwJ2P7CrBw5Ykh+AQYXA5zg5+ef6VPjDTfQz+L56I5iQM8n6StXgEGDgE6d1M0LrqvTJ2aAnaNF\nC5qM5+xZ789pNthTEhN2bHaAq8RDbN0HHjPACTRKS4GyMqBVK8MuwcUARzUB6wNkfvjOnYH0dGnc\ngJEBhMXFNBlORIRr8zXj9GlkdO3q/XXbtaOv0dFA166qV0wMKOrrgf/7P2DKFPo5MpK+ukrYJI4Z\n0HmRF44zAdtfmJGcHKBbN2r92r/fkEtwMcAJfsRPgdHRghggBMjPFwZPIywDiYnqxcCePcC113p/\n3SFD6GtMDNChg3OcRDBQVweMG0fFFiBYBqwyXdqSJVQkMMsLjxngBBrHjgE9etC/3/3OkEtwMcBR\nTcD6AJmJvr6eDpBMDJSW0sEhNpZ+Dg3Vd5AoLtYmBnJyYPM2FTFAAyHLy6lVICIiOAc+8bRCQLAI\nyNXz88/TV3HMgDhuhGMIAdtfmJFjx4Du3Q29BBcDnODHUQyw+bpiqwBATc165vzW6iYoKtJvjfKY\nGPoarE/BdXXSYCoWoHnliuv/s1p5zAAn8MjNpW4CA+FigKOagPUBylkGCgvpYjVt2wrHxcbSJ2q9\nYG6C8HB1YqCwEBkjR+p3fYAOfME4vdBRDFx7LY0HcbdYEUBjBng6YsMJ2P7CjJSV0YyiBsLFACf4\nYWLg8cepGNizh0bZ5+dLxYDYhaDHNRsaqC87IoKatd1RVERnAOiJ3q4Ps1BXJ3UTJCYCr73mLObk\n0jsHa51wghfH9m4AXAxwVBOwPsDqauCuu4DevemAf+wY3X7+vNRNoKcYKCmhLgKLRb2boLAQtqNH\n9bk+I1jdBLW1znOuxS4g8XGOhIXBJs4OyTGEgO0vzIhce9cZv4uBrKws9OrVC926dcOrr77qtL+q\nqgozZ85E//79MWLECPznP//xQyk5AU1NjTD1LCZGWMtezjKgl5uAuQgAdWKgoYGaAlkwo17oPUPC\nLDi6CQDpTBGGXL0Hq+uEE7zItXed8bsYWLRoETZs2ICdO3fitddew+XLlyX7N23ahJiYGBw8eBDv\nvPMOHnnkERA9VnbjaCZgfYDV1YIYiI4WkvCcPSu1DMTG6mcZYDMJAPdigBA6syE2FhmjRulzfUaw\nWgbkOkcly0CLFsB11wnbwsKQoXfHunUrD0p0IGD7CzPiOHvGAPwqBkqaTHXDhw9HWloaxo0bh717\n90qOSUhIQFlZGerq6lBUVITo6GhY9Jh+xWk+iMVATAwdeAHg5EkgJUU4Tk83wZUrwhx4d2LAaqVL\nK+uxSJEjwfoULNc5yv1+bP0CccCgEQLptttopksOxwiC3TKwb98+9OzZ0/65d+/e2LNnj+SY6dOn\no6GhAS1btsSwYcOwefNmXxeT00TA+gAdxQCjoACIixM+6ykGtFgGALqQUlSU/nUcrMFySm6Cykpp\n0KCCGLDp9TsDwvXq6misSDCKLw8I2P7CjAS7ZUAN69atQ2hoKM6fP49du3Zh4sSJaGRr03M4aqiu\nFha0EYuBoiLp07ieMQNqxQBry2zmgd40JzdBWBi1soiDBlknum6dsHKl3tYS1mZKS+lv/re/6Xdu\nDgfwiWVAh1VRPGfQoEFYsmSJ/fORI0dwA1tMpomsrCzcc889iI6OxpAhQ9CuXTvk5ORILAqMWbNm\noVOnTgCAxMREpKen2/1WTKXyz959ZpilPKo+V1fDdvkyYLMho0kM2ACgvNw+39xmswF5ecjIyQEI\ngS0z07vr//QTUFmJDACIiICtvJxe3/H49HT6+eBBoK5O/+/fNPCZ6vfQ43N5ObB/PzKa7nf7/ibr\ngO2//6Wfm5I+2X77jX5OS7MnHbLJ/R6efC4poe1p61b6ezed21T1xfuLwP5cWgocOABcuACbzYY8\nJmz1hPiZ9PR0kpmZSU6ePEl69OhBCgoKJPtff/11cv/995OGhgZy4sQJctVVV8mexwRfRR/q6wmp\nrvZ3KYKLhQsJWbuWvv/mG0KoYZf+nT8vHFdaSkhCAiG5ud5fc8kSQv76V/q+vJyQqCj5406coOVY\nuJCQ66/3/rqOvPYaIfPm6X9ef5OcTMilS87b27Uj5MwZ4fPevYQMHCg9pqqKkPBw/cryyy/CbwgQ\n8uST+p2bo0xBASEVFf4uhW9ITSXk9GmnzXqOe353E7z88suYO3cuxowZgwULFqBly5bYsGEDNmzY\nAACYNm0aQkJCMHDgQMyfPx9r1671c4kNJDcXuO8+IDnZ3yWRxVHtBwwsJz3gHKQnNs3HxdGphmoS\nBLnizTeBNWuEaYLh4crnZBnzLl82JmagObkJACFugCHnaw0Lg83b31gMy1lw7hx95eseAPBBf9Gq\nFTBjhrHXMAvB7iYAgBEjRuCoQ6KVuXPn2t8nJCQEtwAQM38+sHOnv0sRfLB17AEhZiAxkfr1Hf30\neszLv+8++srOHRpKYwMaGugiQmLEYkAcz6AXzSnPAOAcBMoCCMWw30AsEr2BzU7hYsD3GGEuNyM8\ngLCZ4ThH2mQw/1XAIe702YDL0v46Dih6RN+zoEA2g0EuCyEhdF1yNnA1WQZ0r+OwMOC99+jSp8HC\nxo10YSK5ztHRMiAnBgAaK6ImK6QaxJaBkBAuBprwSX/RXHI7BPvUQo4DenVOHCn19cLTIBMDbHVA\nx5wVekaai60OjmJgxw5g0CBh3YSCAuNmEzQ0ADk5+p/bXyxcSF/lnurlLANyoiEyUr/7rbycistz\n52gSq+Jifc7LcU9zmVnG1yZoZphcDARszICcm0CchliMnmZ1V2Jg1y76ysSAUTEDepjBzYaSkANU\nWwZsgH7LVVdUAB060PcpKYKloJnjk/6iOYgBQprH2gQcEXp1ThwpcgGE4jTEYrwVA+KEN8xNADiL\nAfZbV1XR15oa4ywDwYY4UZQjjpaBnBygafqhhPBwetzhw96Xp7JSEANt2ggxBBzjaQ5igMUaWY0d\nrrkYMBMmtwwEdMwAcxNYrXTAVloq2NuYAXHSIleWASYGSktpVHTT8YbEDAQbSlYdwFkMfP89MGyY\n02EZSUnAyy8D11zjfXnEloE2beiCU3z9FN/0F81BDPjAKgBwMWAuuGXAGMRuAgbLDuiIt5YBsYnY\nlRhgFoHiYqB9e/reiCmlwegmiIsDvvhCfp+jm+DUKaBbN+fjIiKA//1Pn/KIxUBMDLUI6ZXJkuOa\n5iAGfBA8COgkBsRTA0+fPq3HKZsn4sHi1Cn/lUOBgI0ZkJtCNmMGsGyZ87HeBhCKxYArN4GcGEhJ\nMSbPAKOhAdizBwj0e7SiQnkapqNloLBQVmTZamuB48f1Kw9blKq4GEhI4HED8FF/EYyzCQiRBvz6\nIHgQ8FIMzJ8/H6+//jo+//xz+7aGhgZ89dVXXhesWSIeLK6+2n/lCDbEbgJG+/bAypXOx+phGWjd\nmr4XWwbCw+XdBFeuSMSA7rAgO7buwtChwL336n8dX+JKDIgtA42N0tUjxYSHAxcv6l+e/HwuBnxJ\nMFoG9u6VTgUOBDfBihUrkJiYiK1bt2LUqFG49dZbsWXLFuxikdIc9RAiHSzKyvxXFgUCNmZAzk2g\nhLcxAyUlwqDu6CYQZ71TsAzoXsfMXB0fL7xXcpEECmotAyUl9LNMR5rRpo0x5SkqonXNgwh901+c\nPAl8/LHx1/ElrK9i/ZCP3ARue8idO3fi2muvRSxLrSqiTZs2mDZtGlq0aIFx48ahpKQE+/btQ+fO\nnQ0pbFCjZ3pUjhQtmeb0sAykpFB/tBo3wddfA//v/9H3zKKgJ0xUxscL899bttT/Or6kvFydZaCo\nSDkOQ/zbeEtlJS3PgQPUKjB/PrcM+BKTJ2vTDOt/zp2jM2Hq681hGbhy5QpSUlIwaNAgLF68WHa1\npHHjxgGgqYPHjBmDrl276l7QoKe6Wt8OygACOmbA0U2ghB4xA0qWATkxANDfvboaaNFC/zq++WZg\n0yYa4MbuXaWZFIGCWsuAQrwA0LQKnN7l6d8f6NKFuwma8Fl/YcSUXH/CXIgsbkyvtNlucHuF7t27\nY/r06bjnnnvQpUsXJDaZGMvKyvD555/jjjvugNXg+Y/NgpoaGiVttQaf0vU3Wt0E3oqBVq2AF1+U\nXtOVGAgLk02MowsxMTRY8rvv6JMrEPjT3qqrlQcAsWWgrExIUOSInk9aFRXSBbC4GPANISHApEnB\ntxAXEwMspkXLw4wXuO0h169fj40bNzptj4uLw/Dhw/HSSy/hpptuQo9gyn3uD6qr6YAQHi50ZoTI\nZ1nzEwEbM+BrN0FCAvDww9LtrsSA6CnVsDru3FkQAybPZ+ESlo1NKbpabBmorHRepbKJDJaISI+n\nSkdLBRcDAAzuL+rraVuIigq+hbjEwcWAtocZL3D7SB/h4omlXbt2ePTRR/HVV1+hmOfj9g6WNvWm\nm2ju9dBQbiHQCy3KWo8AwoQE5+2uxEBhoefXU0vnzsK8+kAWAw0N1Hqm9HuKLQNVVcqDPRMTeqwU\n6SgGlAIIJ08WpsJt20aTHnE8g/WXwbhEN7s/mRjwkZvArRgoVeFbW7hwIdavX69LgZotLGbg9deB\nV1+lpmaTCayAjRnQoqzFMQPl5cDPP2u7lidiYPZs+1vD6rhzZyA3l74PZDHgbilXlZYBm54CTI1l\ngBDg3/8Wnvruu8/ZehRkGNpfsHYQTGKgoYG2D0fLgFnEQJs2bZCdne3ymJCQEJBA90P6G5ashJGY\naDoxELB46iZ4800aFKYFd2KgpoYGBlVXA+++Cxw6BKSmaruGJ3TuLMzJDuRMl+7EgNgyUFmpbBmY\nNAno2VPexLxjB7BunfoyqREDzCLAXi9cUH9+jjNsul0giIEDB9TljfnTn2h7lRMDPogZcCsGFixY\ngD/84Q+46CZBx5kzZ3QrVLOkuFiaHMWEYiCgYwa0uAnYAMHmomtJTqMkBljSoUcfpdOF6uqAu+5y\nyo1vWB23aiU8JZ8/D2zfLuyrrwfOnjXmunqjxTJQVaUcMzBtGs3GKJfBLjsb+OkndeWpq6NP/eKA\nxJYtgUuXnI9jr2waMUthHKQY2l+wrHyBIAY++AD45Rf3xxUV0dfqatr3mC1moGPHjli8eDFGjRqF\n3bt3yx5TUFCAhmBMC+lLrlyRJoNJTBQaA8c7tFoGxB03oC1tbUUFIJOTAxERVCi89hr9HBnp2+BQ\ni4WKkPh4+uR7ww3Cvu++A2bN8l1ZvEGrm8BVgGBIiLwYqKpS70phVgHxb9mlC02G41hugLbFHTvo\n+549pceUlvJkRWphWfkCQQwcO6buuC5d6GtFBV2My2xuAgCYPn065s+fj5tuugnDhg3Dq6++im++\n+QZHjhzB5s2bMXr0aEyZMsXosgY3jmlTk5JMZxkIyJiBPXs8cxNcuAAsWEC3nTun/nq1tfLTBCMi\ngG+/FT4rDFKG1nHnzvIJhyoqAieOQK2bYMQIuvaEUsyAzaYsBqqr1ScBk8t50KkTzekgTpUrFpgl\nJfTJz3EQGzlSn1UUTYKhbVnsJjD7bALmMpLJ0SOBWZc++YT2/+yeNIubgLFw4UIcPHgQLVq0wLJl\nyzB27FhcffXVWLZsGVavXo2xY8caWc7gx9FN0KIFcPmy/8oTLAwdShfm0Zp06PhxIX2vOzFQU0Of\nDF1Ne4uIEM5ntfonUYqSGKiuNn+HynAnBlja56ws+tlVPYeG6mcZEBMdTS17589Lyw3QQay8nCZD\nEgeRArSdmXCBMlPCxEBoKM0nUVDg7xIpw6xG7jLzsjaybx+1LrJ70ixuAjHdu3fHp59+isLCQhw+\nfBjnzp3DiRMncOONNxpVvuaDo2WgTRv9FlLRiYCNGQC0WwbEVhl3YoCtAlhS4loMFBXRJ7/GRsVB\nytA6XrBAfpGiYBIDjq4XpZiBjAzXlgFvxABARRfzAQOCFaC+nv5Py5bOgZyBnhnSAZ/FDDz7rDSV\nt81mLkuX2uD62lqhvcbGStuM2cSA/Z+sVvTp0wdt27bVuzzNj9deA+bMcY4ZSEkxnRgIOMQ3odaY\nAeavS011b6Fh5r9Ll5RXGIuIoPkEWFCiPywDvXoB/fo5b6+pCR4xAEitH67q2WqlbcRx5TstlgGl\n6YuOMT/sfHV1zUYMGIrYTeDIyJF0po5ZUDt7p66OZqEF6Cu7J83mJuAYxEsvAW+95ewmaNOGbjfR\n2vNOPsD6euCNN/xSFlWIfbJaZxMwy0Dr1u5XkHQUA0qWgaoq4QlGYR0Kw+MyWJ2I21owWQYA4JVX\nhPcKmQDt9SxnHdBiGVBKbOQY88MytDIxkJzsPEgopU4OUAzPM6AkBgBzJWxTW5baWiH4OFAsAxwd\nYQONo5uAPSWYeXnOEyeAuXPNu6a4uLPVmnSIPdUlJgoR3qWlNPJ+8mRg4kThf9g0sosXBfOlIyyo\nkD21GrUWgTuGDAF27pQOdsFmGWBm+9WrgenTXR8rJwa0WAaUFhhTmg3kSgyIj+G4RskywKyBZnIT\nOMaGKFFbK1gG/BAzYPwVOK5hQWWOboIBA5SXX/UTTj5A1pmdP++bxDlaEd+Eam+miAj6vdhTXXS0\nEJy0ejXwl784/w+rhwsXXFsGAEH5K/gRDY/LCAmhZtSqKmHti2CzDLA6vuEGxeWa7fWsZBlQO5tA\nSQyILQNsqiNA67m8HOjYUWg3VVXUusTaa1lZULgMDI8ZkBMDTLibKfha3A+5Wm9GLAYc3QTcMtAM\nYCYkRzdBVBSweLG5M5WpnTLjL8RPXmrdBMnJ1LfPnupiYgTrjXgAFw8AVVXUrfPLL/SacoMV28YG\nKn9aU6xW2omyp6dAEwPurCrMMqAQPChBbkaBFstATY2yZYCJAXGkuzhmgA0Sn30G9O4txAi5c0uZ\ngVtuAdas8d/1mQVOPEgePy5MzTRTvyl2E7hyGThaBsRuAh4z0EyIjXV2EwA0iNBEjdrJBxhIYkCt\nsm7Zkj5VsI5cLAbETyHiAaC6GkhPp+tKNDbKX4sNYGygUjAd+nQNeFaGYHUTuBADusUMuLIMMEEp\nJwZatKDfpbFR+D5Hj9LXQEg8tG0b8NhjLg/RtS3Pmwc8+aTwWS5m4G9/E2KsqqrofWwGYVVVJUwr\ndPXbOsYMmHlqoRKnTRTkFpCEh9NOxTFzncnEgIT9+4G//pW+P3RI/fQZXyIecK0qm3qrVrTzlrMM\niG9IRzEwcKDwWc4M6CgGtC6ApDdiMVBdLT/FzoxoEQNqViTUI2ZAzlKhZBmor6dPhzExgktK7JJQ\nE7BqFnw5I2bDBprWlyHnJmAuV4DWafv2wO23+66MchBCf+PcXOCqq1z/tnV18mIgkNwEnTp1Qpcu\nXbB582Y9Ttf8qKig5iHHQSQuTtrA/YzEB/jvfwP//S99v2YNsGiRX8rkErFlQG3qX0fLQHQ0/Q0I\nURYDVVV02t6ddyqflw0YiYnA+vXA44/LHuazXA7R0VIx0MwsA25jBvS0DIjv4bo64X8iIqRrFQD0\nAcDslgHWVsRz+2XQvS2Lk/bIiQFWj1YrfV9TQ4Oc/QlzG1qt9Dd31a6CwU1w6NAhLF++HKtWrcLH\nZo5+NxPFxdSsBQhrczsiXoHNbDAXAVuU58AB/5VFiaoquuqgmkVCGC1a0E68sJDmCr/5ZnozV1RI\nO21Hy0BkpPvMeADNOT5vnmBV8RfithVIboL//U+9GFCadiYmJMT5u1dVeR9AKLYMiAeAujrhfg8P\np9cRX6t9e/NbBhwXYfIVHTvS1+XL6SJfLOkQgw2egwcLljdfrv/hyO7dtN9gojQy0nXOgWAIILz6\n6qvRuXNn/PDDD7gmiHJrG8qHHwL33y98luvgTCYGJD5A5r6YMoX6Os2YDpSt/tWnj/r/CQ2l1oFz\n56jAGTaM5po/eVL6WzhaBiIjXQ8+TAykpLi8vM9iBmJjhSfWQLIM/OMf7hdViolxO2CpihlQ4/pS\nCiBMSqIpkffu1SYGWrc2v2WguJgOVm6mQOrWltnvwO6hzEz6KmcZWL8eeOYZIRW0P92Xo0bRRalY\nuZlbSIlAjBloaGjAmTNncPr0aZw+fRqnTp3C448/juTkZHTr1k3vMgYnjp1vAIgBCRcv0pty40ba\ngfnracEVSk9t7mDTJJlK79kT+PVX6RQx8TTQ6mrqP3UlBtjvyzIQ+pu4OOEJNFAsA5cv04C73//e\n/bGtWqk7p9JsAkLU1YkrywAAzJghFQP19a7FgHg9e7NSUkLrV631xFvE6zoAQqwCW5uAUVdHLW/s\nSbx/fyqs1K4aqBd79giiv6xMEAPeuAnMJgYOHTqEiRMnIjExEWlpaejUqRM6deqEzp07Y+/evUaV\nMTgJQDGQkZFB835bLFR5s4EtMZE+Zfqqc1CLUnY4d7BgQ/bavTuQk0N/i/vvp2pf/MTBBgRXYoAd\n72a6m89iBuLiqMABAscycOwYzeSng+nXbcxASIi6QdlVACFAzf5ylgHmVqqpkd43bKElM1NcrEoM\n6NaW2e/ArsfuobAwad2zGQZs2/TpwPjxdHD2Jd9+K0wTLS+XigG1boLYWNoumSg1W8zAmjVrkJCQ\ngBdeeAE7d+7Erl277H/cPaCRABQDAIR12gsKgK5d6XurlXYOZrMOXLyo/glRTHKyNIc/y0JYWUnd\nBtHR1Cry/PN0vxo3Qdeu1N9tFuLiaNDn2bOBIwYKC90GrWnGUQwQQgfo5GR1vnslywDr1Fu1cu8m\nqKsDHnyQWj6YQDAzvrYMOIoBJvDDw6Vin+UeYH1pZCS1FPh6Rpb4XqqsFMqjxU0QFSXEs5gxA+Ev\nv/yC/fv3I1SmYKtWrdKtUM0CNWKAmZUaG9VPjTMQm82GDBacNXiwtIEmJJgv8OncOfpkppX//Ef6\n9BkdTc/FgoGY0l+7liaGYm4Cd4FtV1/t9tI2m8031gH2/S5eFPzjJmlnijQ06PaEZK9nRzFQU0N/\nx/h478SA1Urb0caNzm4CZk0QuwkSEqgACQTLgEoxoFtbZgPoL7/Q+J/rrqOfw8Kkdc8sA+LBNyUF\nOHPG+zJoQRxLUVIiFSdyQq++nj5c7d8viIGICGGdFDO6CXr06IFLCk9/DYEyT9ksOIoBuadKi0U6\nH9wMsMaalibdHhlprhSgAH3q9UQMsI6awSw04vnhAH1SBdS5CcwGszi9/77Q2ZrdOmDEE5KjGGBW\nHnFMhSuUAggBYXphTQ2wdCmd864UQMjaWyBYBoqLqXAhxDf5KVj/d/gwkJ0tjRlwZxnwR64W1i8A\ntE905yZo0wa4/nr6ni1oFRIirJPiIzeBpjvrjjvuwMyZM5GRkYFBgwYhsukmIIRg1apVuPXWWw0p\nZFDCOl422Cs9VbKBSE0CFYPJyMigi9wAziusRUYCw4c7r7HgT86e1WfNBPYbMMsA+61YJ8UGEE+E\nhwM+ixlgYuD554XZFmYX9Dp2ipKYAbEIYlYetWKgtFT53hSLgdRU+sryCjiKAXY/RURIVzs0IyUl\n1JLByq8Ql6N7zACDWbWGDnVtGYiMpKLF12JA/MBcVOTeTVBURP9mz6Z9yPr1dDtbTr2+3if9vyYx\nMGXKFADAN99847TP4s/5nIEIMyWx5C9KnZzZ4gbYgOEYNMWeio8doyvjmQHH9R48RckywGADyJw5\nwE03eX89XyBuU2yWRCBYBvR+QnKcTcCCTtWKgZwcQGkGFVusiFkCwsJoXYeEUDeCnGUgENwEFRU0\ndiM8nPZjRmcidBxAa2uBe++lC1E5pnp2tAzExmrrP2tqaJD0+PGel1cs5goLpXkGXFl9WrSg7WLe\nPPqZWQbMOLVw8ODBOHnyJH777Tenv8GDBxtVxuCjooLOhQWEhqs0H9ZEYsBmswkDhqMlg5U/J8en\nZXKJp7MJHHG0DIjFAEs3GhlJb2Q3eQTc4bM8A489BqxYQeuHdV6BIAZ06hQV8wyw31JNzEB1NY0l\n6dJFfj9rN0wMpKTQtLSs/YjFABPTgeAmYPcVK78CurVlNruDUVtLY5YsFveWgbAwbeJq82YqMryh\ntFTody5edO0mEGendFyl1scxAyAa+PTTTxX37dq1S8up7GRmZpKePXuSq666irzyyitO+9esWUPS\n09NJeno66du3LwkJCSFXrlxxOg6A7N/y5ctlr7t8+XL/HZ+bSwgdRghJSyMEIMs7dpQ/vm1bQvbu\nNU/5p02j5X76aenxHToETv1rPf7bbwn5/e8JSUkhJD+fkMJCstyg9rZ7927/f1+zHv/mm4TMmqXv\n+du3J+T774UD9+8nZMAAsnzAAPfnz80lpHNn1+cPCSFk2jRCNm2i7ahLF0JatFA+/pZb7N/RdPXP\nuOsusvzWW90ez9qyruUBCJk+ndYnIYTU1tL+U+l+nD+fkN691Z+/Tx/av3lTP337kuUtW8ofP3y4\n9Njz512Xf9EiQhYuJGTtWsXy6IVHZ6qrqyPZ2dkkOzub1NXVeVWA9PR0kpmZSfLy8kiPHj1IQUGB\n4rHbtm0jo0ePlt2nZ6UYzrFjghjo1o2+Dh4sf+zo0YR8/bVvy+eKf/+blvfSJen2oUPp9ilTCPn4\nY0JGjfJP+cQkJhJSVOT9eX76iZD0dELi4wkpLiakvJx+1/btCfn1V0IiIry/hr9ITaXfJTqaCh0z\n85TOkwkAACAASURBVMYbhNxzj77nHD2akG3bhM/ffUeF36OPEvLcc67/98gRQnr1Ut7f2Cjc5++/\nT8jly/R9u3Z0/9SphGzZQsiMGYS8/Tbd9t57dLAzM7fdRshHHxHSsSMhJ0+q/79//IOQ48e1X2/r\nVkI6dRLqcsIEWm+ESOu4bVtCTp8mpL6efv7vf2lf262buuvk5wvn8oYOHWgZBw6k5xo/nm5/9llC\nHntMeuzJk8I1P/pIuq9LFyo477mHtn0Z9Bz3NM8jev7555GUlIQ+ffqgT58+aNGiBV544QWtpwEA\nlDTltx8+fDjS0tIwbtw4l8mL/vnPf2L69OkeXctUiM3+zDyoZMoS5zg3Aw0NwOTJzvP3Gxvpa04O\nNX0xU+eRIzQ4xh9UVurjJoiJoS4C5iaIiaGmwORkaib25eptesPKLk5/alaM8J1OmAB88onwmZnA\n1dx37hZNEsdRRUQIQWByboJAihmorBQCabWUdc4c4M9/1n69qippwHJxsVBf4jqurKT9KXMpMJeB\n2jLq5Z4pLaUpzJkLg51Xzk0gninmmJ2UuQkqKnwSQKhJDGzcuBGrV6/GjTfeiBdeeAEvvPACxo8f\nj2effRYbN27UfPF9+/ahZ8+e9s+9e/fGHoVsUZWVldi+fTsmT56s+TqmQ9wAWMNVaogJCcKiQH7G\nHjMgF8TFYgby84EffqCNvqIC6NuX+uF8TUMDDSiSyw6nleho4Phxek4m3uLiqBg4e9azlMcK+Cxm\ngCH2Z5pdDOg4m8BezwMGSONcmIBs3VrIIqcEC1hTQ329UNdM0JSUADNnAnl5UjEQaDEDW7cK978I\n2bbsyYyV6mqpGBDP3RdTUSHdLg7SVIMesVmE0FgTOTGQkCCsZMkQjwWOgahsNoF4sSMD0SSz161b\nhw8++ACjRo2yb3v44Yexa9cuPPTQQ7j33nt1LyBj27ZtGDZsGBJdTFubNWsWOnXqBABITExEenq6\nfXoLa5im+FxZCVtTmTOalK3tyhVAlKTDfnzTE4oZyv/zzz8jo1UrICTEeX+TYMm4+Wbgm29gq68H\nvvwSGQBQX+/78n79NRAWJtSvN+eLihJ+r6ZXm80G1NUh48IFIDJSt/IzfFZfTUmGbPX1wPffI6Np\nmVgztDenz7/+iowmMeDt+X5uWtUuo00b4OJFYX/TtDnbpUvAkSPS39vxfIcPI6Np8FG8Hvv/b78F\nWraknxsa6P7jx+nnPXtgO3qU3v/hdPDStf4Iga1pcR+P/v/pp2n/dMstQv919ChQU4OM2lrgtttg\ne/99oE0b5/7C8XxNYkDT9Ssraftk9XnlCr1+bKxwPADU1yOjSazbAOCnn5AxaZL6+jx2zPXvrebz\n735H+4vCQqC8nJ6vpobuLy5GRlMGV/vxrP0AwNGjyGgKQLbZbLR+m8SALTeXznJo2peXlwfd0eJT\n6NOnj0f7lCguLibp6en2zwsXLiSfffaZ7LG33nor2cL8RDJo/Cr+Zds2Qq6/nvqJ0tPpa2qq/LEr\nVxLypz/5tnyu2LSJkLvvdt7+u9/R77FgASFJSYR07Ur9gwAhf/6z78tZUEBIcrI+52psFL6fmJkz\nCVm82LXf2Oz060e/V48ehGRn+7s0rnn+eUIefljfcxYW0tgSxquvEnL//dTfPGiQ6//dtYuQkSNd\nH8P8wb/9Jnzu3p2+Z/FCAPWnE0LI7t2EjBjhyTdR5sYbCZk/3/P/B6R11LcvIYcO0Tin3bvp/h9+\nUHeeqVO1X3/lSkLuvVeI04mOptcVn5f9VVcL206epDE+cXHqrpOZSciwYYRYLDTuwBNOnqR9+a+/\nEvLWW7QcbGw8dcq5n9+5k/Yft9zifK5rr6X1OmSINMhVhJ7jniY3QUhICHbv3u20fffu3bBatacx\nTUhIAABkZWUhLy8PO3bswBCZOeolJSXIysrCpEmTNF/DlFRWCv4hVm9KpsHERNO4CQAo+23Fy4yy\nRCts/ro/MijqFS8AUL/kQw85b4+Lo/OcdXQT+BzW/uRW7zMbRuQZSEoSpv8B1B+dkKBuJU7xlEBX\njBwJNFlcAAj3D5sjn5wM3HknfR+u0Q+vhv/+V0hk4ynFxcCWLfQ9u7fCw4Vse6dOqTuPJ22MrYMy\nYACtR3G+f0BYBwIQfo+KCmqqDw93u9SyHXEeEU9dNT/9BKSn00yCbKltFieQmkrblPj3ra6m5fzP\nf5zPxZYZ91HSOU0j+Pz583HHHXdg2rRpeOWVV/DKK69g6tSpuOOOO7Bw4UKPCvDyyy9j7ty5GDNm\nDBYsWICWLVtiw4YN2LBhg/2YTz75BOPHj0dUIAdqiWEBOIDQGSt1APHxphEDNlcxAyyAkA2M1dX0\npgD8Iwb0yjHAmDbNbqazExdHb+5AjhlgAVjMP2lmdF6bAAD9/uJFtlh2vRYt3Ae+ugsgZDiWmQ1Y\nbK2KLl2ka97rHTPg7e/K+qisLPpaVUX7r6goIa7i9Gmnf5Nty56IgcuXgQ4d6EArzt3PKC2lyxWL\ny8r6Vy3iivXL7pIDuWL/fmDQIOk2dv2QENpnlJYK+1z1U0wM+CiAUFPMwLx583DlyhU888wz+PDD\nDwEAMTExWLZsGe677z6PCjBixAgcPXpUsm3u3LmSzzNnzsTMmTM9Or8pETeAkBC6spZSpjxvGqYR\nKHXIYssAIE2moVUMlJXR+vEmcjw3V9/I89BQYMQI6TZmGXBMzRxIsEEwLMz8YsCo5CssU2CHDvS1\nWzd1Uf1qxYCj1ZSJgV276HvxfiMsAxUV3tVbTAy9Jzt0oJ+ZZSAxkc6mAdQvUuZJkGpBgTB7ifWT\njvWuZKFhfZU7Idm6Nc38x5KKqVm+Wo4rV6QrngLS/js+noqBli3pZ5bKXI6YGPOKAQB44okn8Mgj\nj+D48eMAgG7duiFCj4jt5oTYMhARQaffKaVzNqJz8JCMjAxaVrmb6uWXgRMnBNOn+GbSIgYIoTfM\n3/4GzJ/veWF9kRaYiQEdl9VlAUk+o66Opo8OCTG/GNDRMiCpZ9ZBA8559wlRvjc9FQNsYGav4vPr\nvTAZE+nepOVm5Y+Pp78B678SEoC//IXukxk8Zduyp24CNni2aEFfmYWA4WrwZr+lK0thQQHwr3/R\nJcq9eQBjVhPGrl3SgdwxzTVLZS6Hjy0DHq1XGhERgb59+6Jv3752IeDJ1ELdOXzY3yVwz5UrwPbt\nQgOIiKA3qtIsCbNNNVKKGcjIAO65R34qn5bO7bff6Ku3Jn6r1fjpOAa4CXzO4cPAN99oT9vqD4zK\n0R4bSweB6mpq9k5MFNYPcPUkq3ZqoZKbgCEWA7Gx+i4Fzs6lppxKpKXROqmpofEHvXrRNt8U8wVA\nOhizfPpyeCIGysuFuADWT7ZtKz3G1bRAtW376FEhZsBTy4D4QQ+g8SLiVP1a3QRlZc7nNAi3YqCu\nrg6kSV1mZmYiKyvL6S8zMxPrvQ1Q0QMjplvozejRwI4dgq/N3UBiIjHgMmaAIScGtNxY7Df09in1\n+uuBzz7z7hzuiIvTPTbB5zEDrVrRDlBLoJW/MCLPACA8PW/YAJw8Cfz+9/SzO6ucWssAM68zHMVA\n9+7C+7g4qYvNW86eFZ7oPaWiAhgzhvZDP/xA+zBA2neJBf+wYcCtt8q35d27tYvOujrnOnPsN109\ncGhp297GDLgbuB3XvHDlJoiNpSsuRkT4ZG0Ct1fo168funfvjk8++QQjR45UPM4UqxaaPcAwN5f+\nuOfO0R/4zTcDSgwAcG+qlfs+WiwDLCrZ26dUtR21N7CnFccFRgKRQLEMGLGuO7u/1q4Fnn5a+F1Z\n3ICSiVbNbIKLF6UxJS++KA0wu3JF2m9FR1PxrNd3PXOGRuAz374nlJdT83xNDe2/2MJM4n5JLPj3\n7gWuuUb+XLW1NOPjHXeov744VkSpL2Qzl+TQ4mqNitLXMuCIo5vAVUKh2Fhg5UqgXTvPyqIRt2Lg\nueeeQ3JTZzd48GB88MEHdkuBGFOkCWYR7WblwAG6Brf4x3UXb2Gi9KQZGRnAnj2uVao3bgJCqKsB\n8P47a8kO5ylseqhjamYv8HnMACMQLAM6ugkk9cwGmJMnpb718HDXQlyN4HSMJ3n4YelnR/egxSKk\nv9YjMPX0aSoG1E79k6OiggreDz+k5vnhw+l2NmDedBN9/9lnwPLldFuvXsptWexeUEN9vSC6WOyA\nIw8+KDW/i3EnBsTjWXy88ZYBVs6hQ+mMFbaCrSMsW6Fj1kKDcHtn3SQKxPrTn/6EtLQ02eP++Mc/\n6lcqT/HHFDYtFBU5DxxqxICZLANa3ASDBgEPPADMmAGcP+/s53OEDUaTJ3v/nX1hGUhNpa86BhD6\njUCwDOjoJpAgbmvijtydEDeqjTFfsR5i4Nw56vP3NNU0CxhMSgJ+/ZX+sfUF2NP/3LnASy8Bd90l\nDHRKS7ID2ssitgw88gjtTxxZuVL5/9W4exjx8VTk//qrIHq04C6/idgywFLvX3ed/LFdu9JXH41r\nmgIIi2Tm3VZWVuK2225DCxbl6U8CQQw4RvW6EwPunk58iM1mc2++FH+fJ58E+vSh77dvd3+Bujp6\nI/XuHRhuAtbmdYz09XnMACNQLANGxAyI26z4twwLAw4dUj6JUW3M0ZTsDSUl9KneUzFw8SJ9GheL\nJJZD/9576aAfGUmj5sVP5mVlym1Z6xoAYjEQGgo0pexVjbtps45T/6ZNky5epQV3loGkJGn+igcf\nVHYDzJljfB8mQpMYePvtt522RUdH44EHHsCfPVmNSm8CQQw4iqZgjBkIC6N+xltuoQsVhYere8ph\ngUJMAB0+7PoJwxVqs8N5A4uTMbt7Sg2BYBkwajbBv/8tZIsTd+S//UbbsBJGWgb0CiKsqKCuCE8D\nCM+epQGQTDD98IOzqd4xJ0hoKBUzhAiDMLuP775bez/tbX4Jd5YBcXxAfDwVT54uWuRODKSkCMHj\nSUmCW0WJrVuBjz7yrCwa8WhqoSPdunVDsRmW2TW7GLhyRbtlwERiICMjw32HHBFBOzP2hBUeDkya\npO6pk3WuzDx7zTXAwYOeFdYXlgEA2LkTmDJFt9PxmAEX6OgmkNRzu3Y01wKgzcpjVFyKnpaBigrq\no/fUMnDuHNC+vdBP9e7tfIzjipfduwNlZci4dEmoH/bbxcR4ZxnwBHdiQNy/JiTQ7+PpWOJODLRp\nQ4MwAdczCRgTJgC33+5ZWTTiVgysXLkSVqsVVqsVmZmZ9vfiv44dO6I/SwfpT8wqBgihitrRMvDu\nu8CiRa7/10QBhADUxQw4JgRRm91ObBlgHYanna0vAggBOs0qkPMMMALFMmBEzAAgBLXJdeRK1imj\nrE8sgFAPysvp0y4hnlmwzp6lsTHsXpITS6z9swydvXoJ8+MBYPFiQZxHR2sTA8y6YLQYYP1yfDy1\ndBg1myAlhYoBQug1TJSwz20NT5o0yR40uHr1ajz++OOS2QQhISEYOHAgevXqZVwp1aLHetRGkJcH\n/L//R28SsWXg7rvd/6+JLAM2m40uQeqqQ46NdY6Q1ioGIiLolCjA8ycaX1kGdMZms/nHOhAIlgEd\n3QRO9czEgNxgp5Qlzqg2puc9X1FB78nQUHovaS0vy7DJhIRc/TMxwM7dpQvw7bewnT5Nl/B94QUa\nPxQWpl0MNDZSd5wHC+HZUeMmSE6mD2tsWqknYqC6mpbTlUBkYoAJSaPErQe4vbPS09OR3rTgTEVF\nhbnXCDCrZaC4mN7cnqw+ZSIxAMD901nv3sAXX0i3eWIZYFOhPP3uASoG/IbZLQMFBfQp1x+WgeJi\n34sBvX6L8nLa56gVA1OmAG+9JVj3CgvpQ4yr8rC6Yee+5hoauMj645tvFu7tqChtVg/xtEJPURNA\nyL5vbCw91hMxwALEXeXcadOGxgxUVprOoqhJbt1///1GlUMfzC4GPDELsYZsgiA1VTEDFgv1MYrh\nYkA1PGZAgdataaCfETEDgCAC5AYepXgoo9qYnjOIxJYBd0GElZU0P/+xY8K2y5fpU7MrMSC2DPz8\nM12OuaYGGatXU5FltUrdBK+/rt7ip8fiVGrcBJGRVPiwPAOejCVXrjgHiDsSGUnF2fnzpkuSp9n2\ncvHiRbzxxhuYMGECJk6ciI0bN+KSu3W/fYXZxYCagBFHLBZzddSeBHGpzQAmdhOwZZs96RSZn9Ho\n2QTBhNktAwyj0rK6ui99LQb0sgwsXkxnRIgtA67IyaGv4myFhYV09oCrhxFWd2FhdMU+sUmfPWmz\n+7Gigg6aapMgGSkG1qwB/vlP4SGNDeSRkd5ZBtyRkkK/fyBbBr7++mu0b98e999/P86fP49z585h\nwYIFaN++PXbs2GFUGdVjZjFACDXZedIATOIqUJVnQA4tloHwcGkH68n3Zh2IGVJka4TnGXCDEXkG\nAKBnTzpXXo5AtQy88AJ92o+NpfXmTgw0rUQrWeOlsJBaBmbOVK4fx5gBADh2DDaA+uBra+n3CQ8X\nBnYtSx4bJQYee4zWUU2N1GLraQChGssAQMVAXl5gi4GlS5di+fLlKCkpwcGDB/Hzzz+juLgYTz31\nFJYuXWpUGdVjZjEA0KQcnjSA+HjlDsnXGCkGWFCN+Mb05AkpQF0EfsVsloG6OmD/fvpePHAYFTNg\nsdAV5uRQ8nEbZX3SwzIgvt/i49VZBlg9M8sAITTYrVUr2m8p1Y/VSu83cV2wbKPMMsAyKj72GHDt\nter7M73EgFL/06uX4CZghIW5XnlRCbmp43K0aUNXfzSZ5VKTGKipqcHSpUsRLQqyiYmJwdKlS1Ht\n6VQMPTFSDJw963lkO2v4ngaNdOpkihUZM666ii6upPXm9CRmgFFTA2Rna7teAIsBHjPQxOefCwv6\nPP+8cN8YsTaBEn//O50zr5QAyMyWgYIC+gTa2EjrTo0YYH0460dPnKADvWMMkByRkdK6iIqiMwmY\nGCgtpWLAaqWDoVox4O20QkDeMsAG+sZG51gui8UzV4FcUjk5YmPptPIjR7Sd32A0iYGUlBTZ+ICC\nggJ07NjR/vkLx2hyX2GkGOjQga445gnihu+pGDh50rNr68lXX9FXrfXsydRCxvHjNKWxlgDKABYD\nfsPXloHjx+m6FUqwKV4FBVQIL1lCP/tyKtY99wBjx8qLgYIC6vc169TCixfpoMtcZWoCCKuraXwB\nGwR/+ok+xatxtzmKATaAMytHaakwYyMx0beWAbm2zeqXxXM5BnZ7IgbUWgZM2jdpEgMPPPAAZsyY\ngY0bN+Lo0aPIzs7GG2+8gfnz52PJkiU4ffo0Tp06hWeUVmEyGvEgtXOn/n72wkLP/k/c8D1pCCax\nDNg+/5y+YYFGatEqBsRJi5jpUsuqa75IRWwQzSZm4JNPgHXrlPezjjg7m5qqhw6ln8+e1eXyqutZ\nKTXwddfRshllGfBWmDExwFBrGUhMFOq+okIQZe5gachF2AAq3urqaEAwS0memKh+JT49phbK1Scb\nG65ccXYTAJ7FDai1DJgo0ZAYTZJr8uTJAIDdu3c77fvss8/s7y3+CtwSi4GxY4FNm+RXuPIUT59K\nxGLAk7pJSvJuPXK9YBH+WlfzkhMDeXnUDDl6tLCNiQGxv5F1GtnZdClWNfgq+2AwwZ6eGhqAb74B\nxo0z9nqusrQBwr1cWkrFQNu2wJdfCmmDfYWSGCgooK9GWQYuX/buHMXF0qdUNWKgpkYqBqqq1E9/\ni4qSrwsmBpibAPC9ZcCdGJCb8q3WMlBRIeSOUWsZYNfats39sT5EUy1fc801WLt2rSQDoRwPO67Z\n7StYB/LXv9JXT338SniaBcvb4L/oaFMER2aEhdEO+YYbtP2jnBiYOxf4+mtpqlcmBthCKGIxcP68\n+usFsJvA7zEDmZnA+PGeLxClFneDDGvvZWVUDKSkAE3Jz/RAdT3HxsoPzGyAMqtloLRU+lRfUQFk\nZdFZE0pUV1NTPhsoq6rcizaGjGUgA6BigLkJmBiIjVV/PxsVQMhmNxQWyrsJ1CRHYsmK2L2idjYB\nazNs9UeToKmW582bhxEs/7QL5s6d63GBvIKlufzjH+mr3ol6PLUMsCdqT9GawtMo1JrBHAkLA157\njf4ubLlOud+GDeJMdNXWCkJKi6AKYDHgN5hlwFfJreQGma+/pkF7H34oFQNseps/ULIMsAHKqNkE\n+/YBW7YA06d7dg4Wvc84e5YK8PvuU/4fRzeBFsuAY8wAw2oFcnOBjRuB+fPpNi1ix0jLQPv21OJa\nXOzsJoiLc79ypHhFRotFfZ4BJjxM5i7Q9Kg7b948xX03iJ4WXR1nKI5Pz2YRA3pYBkwgBmxnz3rW\nKbMOMytL2Cb32zhO1ercWbAMNBMx4PeYAaMtAgz2O4uf2HbuFJZrZfdyYaH7fO8e4HXMAOsLjLIM\n/PgjzeTnKeIncbXoLAZsgDCQnzolPAj4WgwoBRBGRdHA8Jwc54FZzTLSzPLM2rBWy4DJ+ihNtVxZ\nWYkvvvgCO3fuRE5ODgghsFgsIITg0KFDRpVRPY5iQC83ATuPpx0ly23uqak/KsoUYgBlZZ5ZBlij\nF3focpHNYjFQV0cTgmzYQD9rFQMBGkDoN3xtGWAdqLhNdehAX4uKhHvl4kX1pmojiImRT5BjpJtA\njyfGsjJ1UwLFMDdBbi79XFUluOzcIeMmACCIpuhoYOpU+l5LHgUjLQMRETQWJScHGDxYul/NMtKs\nDbM1H0pKhBkTrggGy8CaNWtw3333ITc3Fx07dkRaWpr9NcIMX8xxsHWn7NTCfEeeDOaNjbRRqY3K\nlcMMloHcXBozoKaxO8KCJsUxF+4sA6Gh9Ga5coX+v9roYyCgLQN+jxnwlWWACezSUmEba+OXLtF7\nLS7OMDGgup6V4nXMLgY8tQwkJOgWQJgBCDOD1q6VPhGrFQNG5RlgYqBdOzpt27HO4+KADz5wfT8w\nMcBexcGErjCpGNBUy1u2bEFOTg5ayqhFv8UJOCI2O6pNeekOJio8EQMsUtWb9RvMIAY+/RSYNs2z\nIEompsTfwZ1lAKA3VnExXU9di2WAzybQDrMM+EIMlJbSvPmANJ6G3a9lZfRea93a/5YBpahyo90E\n3uKNm0AcQKjFTeBoGTh4kD55b9wofRjSklRJr6mFcgGEERGCBUAugPCdd4C//U3ZOiIWA4TQ/k1N\nfbHf12RiQFPP3rt3b8QpPOE+8cQTuhTIKxxN8XqJAW8sA5WVtDMbOBBYudKz6/tLDBw7JkxprK6G\nzdNASHEnz1AjBlhn1rZts7EMmCZmwEhR8N13dJAHpBHbTHT7QAyormc237yhAXj6aWG72S0Dnlgj\nvYkZ6N8f6NpVsskmnt4ozh1ilgDCiAihj3EMIGT9ratETWIxUFtLy6mmrOwYoxbd8hBNYuChhx7C\nU089hf/+97+oc1Bac+bM0bVgHuE4aOolBtg5vRED+/YBy5Z5dn1/TS3s2ROYOJG+98Zcxzp5sdvG\n1WwCBuvMOnUSBg81BLAY8BvMMiD2gxqFuGMWt2tHMZCSAuTnm8MycOoUvX9Z8i8jZxNofaKXw9Fk\nrSY/g6MYUPukC9A1B8Q5QxisfsRiQEvMQE6O98mw2NLKYoErtgywMolRs2qqWAxUVKhvp8xtarKF\n1DSJgVatWmHbtm247rrrEBERAavVav/LzMw0qozqcRQDesUMsIbrjRjwBn+6CdjNUPf/2zvz8Ciq\nrP9/O/u+SBIWgSRA2JEE2ZQBEkQWMbKoqLyjIM47GQYeFhkdBN7hGUZRBhlQxtdBHPA3iy9uoygu\nDChtBASDmiCLDAhhkUXCkoUsZKnfHzc3Vd3ppaqrqquq+3yeJ0+nuqurb5+uuvdb55x7bj1yfZ0X\ne/fd7NGbGHD2DPALtUcPNjVKbnKbhRMIDc8Z4Oe6nqWJpR2ssxgICWHC78oVID2ddcpG5gxwMcDL\nge/ezR71DBMkJak/hvPc+S++8D4bSk3OgAtyc3PFAU96563EMzBnDqt9oYYBA5gYOHNGfE6uGPDU\nTqkYqK6Wly8A+C8vRyGKbvXmzJmDjh074uc//zluvvlmh9dWrlypacN8IiZG/BHdZQH7Au+8uNou\nK5N/kVhdDPAO5MYN35MgBw5ka4dfuCA+JydMwD+vQweWcX7+PMsf8AZ5BpTDPQO889OzNLEnz0D7\n9mw+PACsWcMejfYM1NQAJ06w7bNnWWfOc2f0WCtBCzFQW9t6JT6bzfNKi9wzUF7O9lMpBhyQDrZK\ncgZuvx1YsULdZ/fsyRac4n1oUxPLQZKKAecwwcKFTIRkZbkfvKVioLHR2PNUAxSJgQsXLqC4uBjh\nLk4mU6xaGBvL5iXHxgIffQQsWaLNcevqmOvu4EF2QlVW+lcMGDm1kHd29fWwnzrFMoR9ISqKTRV8\n5hl2EbrzDEgvSqkY6NwZOH1anhiwcAKh3W43xjvg7BkwSgx06CDmqaSns0etBiQJsu3MPQO8TYsW\nsfOXn196uHr18AwALPRTUsLEuSu4GOjTB9i0yXXNfgU42NhZDMj1DDQ2apNDIc0ne/ZZYOlS4Be/\nEEMyzp+Rn89yVn76SSwq5Iy0zkBDg+XFgKIwQZ8+fXDlyhWXr7Vr106TBqkiJoaJgehoefNE5XLj\nBlOWfJEUJQsgaSEGeDlff7qXeIEgqWdATcLLnXeyx3Pn2KOSMEH79ux/b+VBOeQZUI4/PQNSYSsV\nA+XljmKPJ5/5czVFZ7gYkF7HJSVscPjiC30+U4vBz5UYAMRloV1RW8v6zgkTWJhGq+vogw8cyyD7\nu84A4OhdPXZMbAfPZXBVppkLAHc3Yr6GCUyKIjEwdepUPPLII3j22Wexfft2FBYWorCwEJ9//jmW\nL1+uVxvlExMjuvDj4rQNE0g7KSW5CFqIgZAQdkH4c1U5XnZa4hnI7dPH9+P16MHuSPgCL0rCBO3b\nK3MtWlgMmCZnQM9zTXpdSsXAlStA797idnQ0kJoqr8SrQmTbOTKSDZLXr4tTzGpr/ed98rUPX1tN\n7wAAIABJREFUc7X4jpz3REWJMyhu3FAlTFpsfPfdjnfWSqcWahGKkXoGeB+TnCzelPDqiFL4a9Ja\nGJz77hNFhdIEQpOiSHJNnToVALB9+/ZWrxm2UqGUmBjm1omN1dYz4Kyye/eWf5euJCPXE1xN+3uQ\n46rcU6xRLqmpysQAd1G2bSu6FuvqWDzP0/K3p05ZNoHQMPzpGZBel9K7rqtXWVZ6Sgrw+OPsurlw\nwdiEq9BQZpvyctau06fZOeyvJNWEBDYoKe1f3bn4PYXZuBiIihKX9jV6IabGRm08A1IxwI+XlsY8\nljw51NVnA+x85SupcoqLxYWzGhqU3fTl5wPPP6+s/X5AkWdg8ODBOHnyJE6cONHqb7BzOUcjiIlh\nau3mm+UtNCEXPgg3Nckvz8nRwjMAKFPTapFOK5OECew//KDuuCkpLBv74kXXrjdnsWOzsYEgMlIU\nQ2fPskWP3FFRAfzpT5YVA4bXGfDHbALpdck7aN6hxsezThpgHXhIiC5JeorsHB3NvBb82v/0UxYq\n0FOYv/++WKbZl37MVZhgyxaWWe/pPVwMcM+Aiu/o1sb+rjMAOIoB/p3S0tj5lZHh+j2ePAPl5eLx\neJhAbj+flMRuaEyGIisvWbIE6Typx4kVajM+tSA2li3wccst7Iepq9PmZOIXls2mXKFr5RnQYllT\nuUhj85IwgepOOTWVJe98+SXrXAF2l5WaKn6Gu0Gcf39vFRD5hWt0xUarwT0DkqmkuiENDfD/r11j\n09pCQsROVYfEQZ/gd8qZmY7P6ykGsrLEmVFXr/pWQMhZDHi6oRAEcfDXKEzgFqU5A1qIQWnOAB/k\nvdVz8CQGKirE49XXi/kWFkaRZyA/P9/ta926dVPdGNXExLCqeZ06sUFbzspTcpCqbC4G5Lou+epY\nauEX0JUrbFaDnkhtVljIlpa9cQO5OTnqjtu2LXusqBAvNGkeghwxwO3ubrDiHajaZaMNwrCcgbAw\n5hbls4L0FAP8M2w2UQxcvSrmBvDrRcfOVZGdo6JcL9+tp/eJ/x6AKJzlwj17zjdBnm4oeEjAZhOn\nU6r0DLi1sdKcAa09A7x/8yZ0eB/lHG6uq2O2kYqBmhpVMy/MgA+F5l0zffp0rQ7lOzEx7K6Wr9YV\nHe1YaMJXpBcFP0E8lal09141REQA773HlhDu10/98Txx/bpjx/f3v2uTM8Ddcdevs+pygJhDAMgT\nA7wzczeVlat4i4oBw7DZmO25V8gfYiAiwtEzwMWAGT0DfMoywGK+gL6eAekAqFQMuMsX8HRHLq1L\nEBXFbqoqKwMzZ6CqCnjsMTFJ2tNnA609A3xbGiZwrutgQRSJgczMTHTp0gWZmZktf3z7yy+/1KuN\n8uF3nnwpVICFDNQuyyr1DPATRG65Vq3EQGSkON1Pb7ig+tnP2Hbz1Eb74cPqjisVA/y3iotjU7Qy\nM5WJAXfVILkIULKwkYkwLGcAYDb2pxiIjBR/R2nMVToo6YQiO99yCxMDvA/g7fSXGHBV5tcT7mYS\neLojlw5m0dEs3Mrf4yNubRwZyfpPOYJAS88Av5OvrATuvdd7+IGPG87eZVdiQMsCTQahSAwIgoDp\n06e3/E2dOhWdOnXCjRs38OSTT/rUgMLCQvTq1QtZWVlYt26dy32KioowaNAg9OrVy7N7jw823DPA\nB24li9y4Qho7M0oMREQ43g3rue789etskOZVJcPCtMmelooBnoyVkMDCEKWl2ogBfqF27qyurcFI\neLjY8flDDPA8Bf4cH4x4XogvK2TqAV+fw9ljoWZZcm+oGQDd1RjwdEfu7Bng6PEbhIYyW8bFAZ99\n5nlfLXMGeJ8hd0VH3sc69zXOeUkB4hlQdMZNnz4dy5Yta/X8vn378Prrr/vUgHnz5mH9+vVIT0/H\n2LFj8dBDDzkskSwIAmbOnIk1a9Zg9OjRKCsrc38wntzIPQM8vnzpEnOv+0pdnegi5CeINzFQWsqW\n7tRSDEhV/U8/ia52ramqYhcq71CaaxzkeipYIoe0NLbYy/LlzCU8dSq7k+cDkCdbyQ0TlJezpZZf\nfVVdWw3CsJwBgA1y3KOiZ7Iq/+1CQ8Vz2s+dqSI784I0kyczL8Fbb7FtPZeg5WJg0CDg66+Vvded\nGFASJtAAjzbmA+q77wJ5ee4Ts7UME5w6xQbwCxfk9Z28r3/nHeAvf2GLJknb7iwGtKgcaSCKZN/v\n3SzBO2TIEHyt9IQFUN7s0h0xYgTS09MxZswY7Nu3z2Gf/fv345ZbbsHo0aMBwEEotILfeSYmOj4v\njUv7gi9hgk8/ZfX4L13SLkwgFQNa1VBw5p57WG5CbKx4EYaEaCdq+OppycmsBv2NG+J30SpMwIsU\nEcq46SZx/Qh/ewak11hGhhhGMgM8OTohAbjrLv8U/+LX3oAByqcmuxNWrsIErjwz/nR3//nPnkWV\nlmGCV19lBZDOnWtdN8AVvK/fs0csMASIoUjnMIHFPQOqfUClpaXYuHEjInzofIuKitBTUgayd+/e\n2Lt3r8M+27Ztg81mw/Dhw5Gfn49t27a5P2B8vGMdaalnQA3SgVCuGNi6le2zZYt2ngFp7EqrGgrO\nfPAB8PrrTAxIE27q62EvKVF/fF7+MzlZnO4jdU27EwP8rsabGOAhDotiaM5AmzZMDISGup5OpRV8\nQOLhJ8BxMEpJcVzUSgcU2Zl7Fblr2R9TfPkAmJrq3gvmDrlhAr5Yz7VrjvbXaJaERxsXFQFvv83+\n9ySutAwTAGxgj4qSJ7BuvdX18+48AxbPGVAkuULcxI/i4+OxadMmTRrkTG1tLYqLi7Fjxw5UV1fj\nzjvvxMGDBxHtwvAzZsxARrN3ICkpCdn19WxhnUuXWk5M7rpStF1XB3tpKWC3I7dZDNi/+AJITXW9\n/+nTsL/3HjBtGnJffx2IiFD3+QDslZXA2bMtCwXZd+0CysvZ688/D3thIfD4474fn28DQGMj7OXl\nwKVLbLuiAvZr11B8/Lj4+b4ev9lrY798GTh0CLnNCz/ZAeDyZeQ2d0St3n/6NFBWhtxhw9j23r1A\nYSF7/+9/L+5fVwfExam3t0HbHEM+v7ERuZcuAVlZ7Hzq2FH98VNSgL592XZJCXLffpv93jNmAB06\nILc5ZmwvKQGuXFF/fsncLi4ulr+/zQb7zp1AURHbrq9n56vdrlv77Hv2sO02bdj1+NlnQEiIvPfX\n18NeW9u6fdeuIbdZDNjtdmDHDvH63rsXqK1l2zU17PsBqn6P4uJi969XVYmf5+l4zWEC1fZsXnUy\nt64O6NJF3vtXrEDuoUPA4487/t4VFWJ/BQBlZWx8aNdO9/OX/19aWgrNERTQo0cP4bXXXhM2bdok\nbNq0SXjttdeE3bt3C/X19UoO08K1a9eE7Ozslu05c+YIW7duddhn69atwm9+85uW7alTpwqffPJJ\nq2O5/CrJyYIACMIf/uBT+1r4+c8F4bXX2P9/+hM75smT7vc/fFgQevYUhPffZ/v+4x/qPl8QBGHy\nZEGIjGTHAwTh44/F17p0Yc9pASAIERGCsHAh2962TRBGjxaEbt0E4ehR9ccvLWWfsWGDIBw7Jghd\nuwpCbi57LjtbEL7+2vX71q0ThDlzBOGdd9i+H34oCPn5rb/3ggWC8Pzz6tsZjMycyew5dqwgzJ6t\nzTETEgTh0iX2/4sviufvqVOCsH+/IAwYIL42Z442n6k348drd725o76efcZf/yoIUVGCUF0t/727\ndwvC0KGtn792TRDi48Xt9evZZxw+zPqTsWPZ8zU1ghAWpv93PHdOPB/cERrKbKGWLVvEzxoxQv77\nNm5s3cZnn2XbaWmCMGYM638nT2Z9k59ROIR7RJFnoKCgQNN6AonNd4mFhYXo3Lkztm/f3ipBcejQ\nofj973+P6upq1NbW4ttvv8Ww5rtDr2gVJqisFPMQFixg5XBdubaampgbjrvctJyCFOEU75OGCbRy\nT3F7NTWJCZN8jQct6gwALMkzPZ0lefIwAU/U8ZYzwIt9ACxMwBcXkU5Lc+ciJbzDa0t06SKu0KmW\n69fZuRrhFOaKinI8p62Uje2P84u7xuPjxcWS5F7n7q6jCKcwAe/DqqtbJxAuWgQ8/bTv7ZeDNJzn\naplgQWBhWa0WKuIoSSaXvm/wYDblkocJrl0DcnLYc8GWMzBs2DAsX74cJ5pdLn/+85+RkZGB2bNn\n46effvKpAWvXrkVBQQFGjx6NX//610hJScH69euxfv16AECbNm3w6KOPYuDAgZg8eTKWL1+OOKUx\nYbVioKLCcRpRWJjrnIGlS8VSnnqIAYAl3d1zj2PJYK3EAI+BNTSIYiAhgX3/ujrY9+/X5nNKS4Gx\nY0UxwEWIt9kEH3wgDii1tWxGBeCYP2ClQcUFzuECv8LFQOfOom3V0NDAOvPqaiamV650HHCkg5Mv\nq+ypQJWdN2zQvwqozcYGwYSE1snD3vAkBurqgCeeEPcDWF/ifN1o0Gd5tbE0bu8qR6WxkSUva7EI\nnvSznCtJekLatxYVsceKCvHcbduW3SwFW52B5557DidOnEB8fDxOnTqFhQsX4s4778SVK1ewks9J\nV8jIkSNx5MgRHD9+HHPnzgXAPBAFBQUt+8yaNQuHDx/G559/jgcffFD+wbXyDDjPSw0Pdy0G+NQT\nPcQA7ygXLWJ1FFwlEMqtfeAOaaUzZ8+AVmssSOFigA8I1dXuPQNhYSyp7P/+j21fvw78+CP7/8YN\n4M03WadBngHf4b95crKj2PQVLtL4bJHycoB79aKiHKe6uauaZ0ZSUhzLaOtFWBi7/vjCQd4YNYot\n4e5ODPA7bJ7fJb3unMWAP34L6R2/q0qxWk0rBBz7LiViwFWiYUWF6F1ITGS2vnrVOuevGxRZ+tix\nYygpKUFISAgWLVqE7t27Y8OGDRAEoWXqn6nQSwy48wzwE04PMcBP4LS01msu8NoLdXXqLh7pAMC9\nL/Hx7Ptfv47csWN9P7YrwsNZiIAPFlVV7sXAuXPs8YsvxLby5+rrgQMH2P8W9wzwhCFD4OdrUpK2\nYoD/NgBw++2s0Ex4eOswgR/naRtqZ7lwMSDXM7BzJ3DkCOubPIX0+LRNZ8+AVET/+teeVziUgSIb\nHz0K9O3r+JxW0woB38WA1I68NkFFBTvG+fNMQCckME+ahfsdQKFnIC0tDSEhIRAEAW+99RZ+9atf\nAQBsNhuqzbhKHBcDJ0+qmypVWelaDDQ1OYoCfsLx+JGWYqBLF/YYE8NOQGlnzf9Xu8SxNJ4o9Qxw\n22m9MIvNxr4PrxBZXu7e+9C1K3vkHVhFBVsK+eabHe+EyDPgO/x8TU7WZtVHLgaaw4oA2LoaGzaw\n317qGfBzmMAShIWxficqSv613Vw63O0gOmSI2Jd48gzExiovg+wrISHAffe1XvxNq2mFgO9igF8H\nO3cCPXqw/8vLRc9ATAzrIy9dCq4wQadOnfDWW2/hj3/8I8rKylpc9hcuXECVXvPetWDQIN/q+s+Y\nwe663XkGFi1yLHDEO1M9PAO33y7+n5jI2vXee+LnxcQon4/sjCsxICk8pEs8OyaG1X2Xbrvi3ntF\nrwDABF5iIvNgSHMNrORudoGhOQNSMaClZ+DUKfG5pCS2SAxgaAKhoXaWy5QpzBPIEwg9wQdSLgbc\nCfenn3acHw+w31qH60a2jXlI2Pk7ahkmkPYrN98s/328qq00VCMNE3DPQGOjpfsdQKEYmDt3Llav\nXo0//OEPWLFiBdq0aYOtW7eie/fuGDdunF5tVE9SkvsiNZ74f/8P+PxzdqFIT6aQEFa84ptvHO+g\n+MlQXa29GOjXT7zgU1KYUp08mV3QdXVsYNTDM8CRu0qjUmJiHNd+8HRBcTddUhJzK958s9j5cRvT\nHabvOIsBuct0u4N3nqdPiwm4UlEtTSC0uIjThY0b2d2mnDABt3Vjo2cxkJjIwjSLFwPPPsuec+UZ\n8Cd33MHu1p0FqF5hglGj5L+vTx92HfBlnQFHMcA9A86fYUEUWXrAgAHYu3cvampqWor+5Obm4sCB\nA0hLS9OlgaqIjmYufncxfjlcucLuPqUZrXv2sD/nPAn+GTx+xAcoLbJhpaSkiK7XQ4fYxR8fr94z\nIJ0umZrq+FpTkz5xVj4A8Q4vxIM+5WLgppvY9x4+nCUVShdRsvigYoqcgdhY9jtIRZYvSD0DAwcy\nAdurl/h6RAT7DEFg+/pRxFkiZ4AjJ4FQutqkNzEAiEKAhxxra+Ut3qMAWTa+do197vz5rUNTeoQJ\nfvzRt0Hbk2eAiwEL9zuAj+WIpdX/4uLikJGR4dPaBLqzbx/L8Od3j75QWen+5HEeuPjJ8sEH7MTg\nIkDru+qUFPGO6rvvWKcaHa2tZ0BSJlpzMSNFifckLo7N6502jf0uffuSZ0BLpL9FTIz6UAEvHX72\nLDB+PBv0pQMOP6+2bxcXxyJaI8czwG1944bnBELnAT85mdneKM9AYiI7D5zzoABtPQNhYcybyGuT\nKIVPGQdaewa4TS3uGfBJDDQ2NuLMmTM4ffo0Tp8+jVOnTuG3v/2t1m1TT0YGkJWlzjNQWen+InEn\nBvbudXSxqp3y54x0sSZeXzwsDNi8Wd1xb9xgnXZ5uaMA4CWE9Yiz8oFbbnLiN98wjwDAQifOMdIf\nf7S0GDA0ls1DQxERrjtnJRw5AkgXNvM0U2DsWDYg6bkksBOWyBngyEkg/PnP2SP3DLgbRFNTHe2c\nksIGNx3EgCIbuzrftMwZAIDu3X1/L/cMcLHFbRgXx/632bRPsPYzisRASUkJJkyYgKSkJKSnpyMj\nIwMZGRnIzMxstdqgqVDiGaiuZneenMpK94OLc0y1tlacjsOnvX34IXORaolUDJSXsxP1u+9YURc1\n8Ni9892DnBW+fIW7AZWszMb3ve02Me7Mxcvly5Z31xmG1DMQG6tuRsE//uG47ZyD4vy5lZV+FQOW\nQk4CIefGDc9hgtBQtpoqJzW19UJFRuDKE6WlZ0AtXAzwmWW8JktaGtuOjtbXg+oHFFl61apVSExM\nxOrVq9GtWzeHhYsWLFigeeM0Q4ln4PJl4JNPxO2KCvcXiXNSYm0t8NRTwP33iwVx7rpLeXu9ERvL\nBEthoegZ0OJEdFcBsH174MgRfeKsvN1KxACfGtS1qyj0pL+vhT0DhsayuZszPFx9mIBXa+N4EgP9\n+7PcDz+KAUvlDCipQOgtZwBwFPspKazP278fGDNGXTudUGRjV+JTy5wBtfAEwvJyZr+TJ9nzNptY\nGMriKBIDBw8exP79+xHmQq0tX75cs0ZpjhLPQG2tY4zfU5iAd5a8rjZX1/fco703wJl//hN48kmm\nUKOixJCFqxrfcpEm4kn5y1/0K7/K261EDPTu3XoqlVQMKF3/nWBwMRASoj5MUFcHzJ0L/OtfLGfA\n3W/y9tvAc8+xzpU8A66RW4EQAB5+mE159iQGpLHt1FQ2RbmmRn3OkRr8ESZQA092vXiRCajly4GZ\nM9lr3DNgcRSFCXr06OF2DYJGvaaeaYESz0BtreO+nsIEfH489xBwMbBlC/A//+N7e+USFSV6BqTF\nW3zFnWcgKwuYPFmfOCufg+7rAM7DBPz8W73ar5XstMbwnAEe3lIbJrhxA3jwQWDNGvF4roiOZnel\ngF8TCC2VM6DEM3D9OpvKKTd+nZLC+q9OnZhHU0NU5wyYKUxgs7H+9tQpVsGxfXsWpgSC0zMwdepU\nTJ8+Hbm5uRg0aBCimg0gCAKWL1+OSZMm6dJI1Sj1DDiLAXc/9IUL7LGqSiz648+TIipKzBngg+H1\n676rVE8LBenF3/7GLqannvLt/c6eASXVxYjW8PwQtWECXgmSiwB3Yk/6fADcXemCN88A9wZOmgS8\n+y7zsngqrCO9xvn1Mny451CO3vB1SqRcu2auGSbR0WyRNV7OmcOrRFocRWLg/mbl+Omnn7Z6zWbm\n5Al3Cwu5gocJuBu6osL9nSa/QJ09A/4iOlr0DHDU3M15mVeuS5yVV1ZcswZ49FHl7+fuu4YGIDvb\nMfnTgpgmlq02TMCFJR9gPHkGOH7sQ0xjZzl48wzwGg38huDkSSAvz/3+48axnI5Bg8TBVoc6MYps\n7EoM/Oc/6mYAaE1CAnD8eGsxEB8fEEJWUZhg8ODBOHnyJE6cONHqb/DgwXq1UT1hYcpzBrh4cB5s\nASAzU/zfZjNODPAwgfQzfRUDjY3AvHn+9wxwsrJYyWGlhIeLYYKxY41rf6ChRc6AVAy48wwEQCeq\nO97EwPXrzM68jzt50nOYICREzGnivw/3chqFK+/t0aPiegBmICGBtclZDGRlAT/7mTFt0hBFYmDJ\nkiUOUwqlfytWrNCrjepR6hkAxIvP1dKUJ06I8bWUFHEANkoMREYCf/wje85XMSBjISdTxlmlYQKz\nxBdVYBobu7pTUwKfpurNM8BFwjff+P5ZPmAaO8vBW5jAWQw0NcnPGWhsBHbtAv7wB/XtdEKRjV2J\ngXPnWC6DWUhIYLYaMsTx+a5dxdwYC6Oo98zPzwcANDQ04NixYwCArKwshIWFIc+TW8polHoGALEj\nLC93Pchw91pqqrGegbIy4N//ZvUMtmzxvQOX1t22EjyBMEDEgGngnoHp05mrdskSZe/nYQJvs0W4\nZ0DjUrgBhVLPAKBMDAwbpq59WuBKDBhd+8AZHsbSe6aYQSiuQPj8888jOTkZffr0QZ8+fXDTTTdh\n9erVerRNO3zxDEhdQa5mUPBpUEZ6BnhH+s477FFN0pdU/LjBlHFW3ok0NppnTrIKTGNjLgb+9jfg\n1VeVv58nEPJByV34hosE6eqffsA0dpaDUs8AIF8Yd+umrm0eUGRjV2LAbMuRV1ayxwC96VD0rTZs\n2ICVK1di/PjxuK15WsWePXvw3HPPISEhAf/93/+tSyNV44tnQMr5862fi4tjHVxCgnGegaYm9nj3\n3exRjWtXhhgwJdIEQqovoB0xMWxONeB58Sh3cM9AYqJjWWJnyDPgHbmeAem1LycZU+2qlFpiBc8A\nFwMBiqKr/M9//jPeeOMNvPnmm1iwYAEWLFiAt956C2+88QbWrVunVxvVo3RqoTPuxEBsLOvMamrE\nldf8efJyjwXvrOPifD9huUfh2jW3u5gyzhoTA3z5ZcCECUxjY2kCoS8eF55AGBoK/O537veLjGSl\ni/2c+GkaO8tBaZggJcUUU2wV5ww4e2/N6hkIUBT1no2NjRjlYi3oUaNGoYnfpZoRpUWHpPzud64r\no3ExwO/GGxqYGvfngDRpkuOdfFKS73f2/K5ixgzVzfIrs2ax3ygzMyDCBKZBKga42HzmGWDBAu8e\nmKYmzyvnSbHZgP/6L3VtDXTkhAliYkQxcOmSf9qlJdx7u20bm24cH28+MdC9u6ULmnlDkWcgNDQU\nO3fubPX8zp07HdYpMB1qPAO//z3wm9+03s/ZM2CES6tdO0C6WmRyssc7e49UVwMTJgC/+pXbXUwZ\nZ01JYcuJXrwYEJ4B09hYejfKr+2lS4Fvv/X+Xl6vwsS1R0xjZznI9Qzcfrup5uX7lDMwbhwrfw6w\n72ymMMG//y3v/LcoinrPWbNmYerUqbjjjjtwe3OxmN27d+Ozzz7DM888o0sDNUGNZ8AdZhADziQl\nieVklVJdbWwFMjW0bcu+dwCIAdMgHYBCQ5XFlz/6SCyPTahHbgLhSy+ZKw9ACdIbNn4d19aayzMQ\n4DlJim7nf/WrX+Hxxx/HBx98gPnz52P+/Pn46KOP8OSTT+KXv/ylXm1UjxLPgPNKhO6Ij2eCgIcJ\nzCIGrl717b3c1egB08ZZ27Zlq0QGQJjANDZ2FgP8/7o6dnckdUU3NbHKbJwpU/zXTh8xjZ3lINcz\nAJjKG6M4Z4Dvz8NLZgsTBDiKfftPPfUUrly5ggMHDuDAgQO4fPkynnjiCT3aph16eAZGjgRefFH0\nDPg7edAVSUnqwgRWVb5cDJBnQDsiI8VrITRUzEWpqGCr4kmX+d6yhVVhI/QhKsqzGLCyV48THs7q\n/gPidWy2MEGA41UMVFdXY8uWLXj//fdxrtkFHRkZib59+6Jv37748ssvdW+katTOJnBFdDRbhz08\nHDhwgJXNNPrEVSsGvHQopo2z9urFOo4A8AyYxsbSASgkRBQDlZXA9987Dk5Wm44KE9lZDlJh5gqp\nZ8BEKM4ZcP7fbGGCAMerGNi6dSsmT56MmTNntogBKZMmTcLSpUsDawljJUREiFP8jBYDN90kLqus\nFBlhAtPC64KTZ0A7nBMIeWXKCxfYErlqlsomlKEkTGBVpNcuhQkMwasY2LJlC6ZNm4bjx49joIsy\njN988w0KCwvxz3/+U5cGaoIengHpsc0ihNq1EwvFKEVGmMC0cVa+mEkAiAHT2Ng5Z4Df/e/fzx5d\nDU5lZeyxbVtgxAj926gC09hZDnITCE2G4pwBTlgYS4Tk61sQfsGrGPj222+xbNkyJLmZX5mZmYmN\nGzdix44dmjdOM/QWA7wYhdGegdRU5hnwRZxYOWeAL79qouQpy+PsGeBi4Kuv2KNUDPCk29RU9hgb\nC/z1r/5pZzAgZwljq6/+KBUDTU1MCISF+Vb9kvAJr5YOCwtDlpfkoG7duqGUJ3+Ykbg4oKpK3r6+\nhAl4R2l0QYqwMBYq4HdocrhyBfj4Y2vnDPCOxIKxa2dMY+PISDH/pKmJhQlCQ1mSV2io43XiXJmt\nqkpcyMukmMbOcvCWQGhSd7rPOQP19ab9ToGMVzHQ1nntZjeEmjl5KyFB/mp8vngG+LE7d1b2Xj1o\n107Z2uQvvADcdZe1cwY4vuZLEK2JjBTFVV0d+3/aNLb98MOOg5PztWVSt7Vl4QmE7moIBMLAKRUD\nDQ00k8AAvIqBuLg4HJfOIXbB8ePHEWfmO4GEBNaZDR/ufVU/X8RAbS0wYACwapXvbdSKxERld8h8\ngRgr5wxwzCxIZWIaG/PBJS6OuWwrKpjYbWpis2ikYkDqGWhqYm5rkwtL09hZDqGhzF222FkKAAAe\njElEQVTuLgnapGLA55yBhgaaSWAAXsXA/PnzMWnSJHz//fcuXz969CimTJmC37gq2WsWEhOZ63zX\nLu9FeXwJEwBAdrY57oaUzJwAFIkBU3PmDDB/vtGtCBx4R5yeLnoGEhNZXobzVDepGKipYa8HgDAz\nFZ6SCE0qBhQhTf6lMIEheE2/HjlyJCZOnIg+ffpgxIgRyMrKQmpqKi5duoRjx45h165dWLp0KUaO\nHOmP9vqG9KTytqCStNDK//yP92NzRWuWBB4lyZKAuAhTVZV1cwYAoGNHo1ugCaaxMe+cO3ZkdQXK\ny8W6984JbbW1wIoVwLp1zPNmZi9hM6axs1y4zV0tmmbSgdPnnAEKExiCrLlYzzzzDPLy8vC73/0O\nr7/+OqqrqxEXF4d+/frh3//+N/Ly8vRupzqkWebe7pq5GMjJAZYt835ss4kBpZ4Bzvnz1vYMENrC\nr5kuXYCSEhYm4F4k54S2ujo2k6CmhvIF9CLQPQOcSZMoTGAQsudtjB49Gnv27EFlZSUuXryI8vJy\n7N692/xCwBlv0+6kngE58DCBVcUA3/fsWevnDAQAprNxz54sZ4CHCYDWYYIbN9hMmupqWR4mM2A6\nO3tD6o0JDwdWrxZfq6sT+yETocjGvB/q1UsME5BnwK8ortJis9mQyucTWxGtxYDZPANKwwRS4UCe\nAcKZgQNZx1xRIbqoncME3H1dX8/2s0CYwHJIbd7QAHz9tfhaIHgGeL8cHi6GCaz+nSxG8FR0OHaM\nVarzJAYEwfpigHsGzp+XV4RHKhySkz3uark4qwUxlY2vXQMGDWIds7QOhbPLmleKi45miboW8AyY\nys5yiIpyXFFVWozHpJX6FNl4wAC29DXvv0gM+J3gEQPdunkvHcyrXgHyS9ty95xZOkB+MfH1Erwh\n9QyYRdAQ5iAxkZ1PjY3M/c89R648A5GRTDBMmkQeJj2Ij3csnCYV+oEwcIaEAOPHs/Otvt4cS8IH\nGYaLgcLCQvTq1QtZWVlYt25dq9ftdjsSExORk5ODnJwcPP30075/WGioZzEgPQHlDu7cM8DjqUaj\nJkzgBcvFWS2I6Wxss4lVNt2JgRs3HGPWFqgEaTo7eyMpCTh0CDhxgm1LPQMmFQM+2ZjCBIZh+Mou\n8+bNw/r165Geno6xY8fioYceQkpKisM+I0eOxPvvv6/+w+SKgV27gPbt5R2TiwGeaW00viYQtmmj\nT3sI6xMRwUIGXAy4ChNIxYC3Wh6EcpKSgNmzxfAl9wwE2oI+FCYwDEM9A+XNdxAjRoxAeno6xowZ\ng3379rXaT3BXhlMp3gZKLgZuuUVcdMUbvBM0i2eAf0duM2+2q68HFi6Utdqh5eKsFsSUNo6MZOcU\nDyO5CxPwc80CYsCUdvYEX/eE38zwein19WKFQpPhk40pTGAYhp5BRUVF6NmzZ8t27969sXfvXod9\nbDYb9uzZg+zsbDz++OP44YcffP9AT56BCxeADz9UfgKazTPAwwRc9HibPdHQwN5DFeMId/BznF8b\nznUGnD0D3kp+E8pxXgStqopV3SwpCaw7aAoTGIb55KQTAwYMwJkzZ1BUVITevXtj3rx5vh/Mkxh4\n5BHmhrO6GOCegRs32La3/AEuBmRguTirBTGljfldKL/7dK4zIO24v/sO2L3bv+3zAVPa2RPOYqCy\nEhgzBhg82LSDpk82pjCBYRiaMzBo0CA88cQTLduHDh3CuHHjHPaJl5TffOyxx7BkyRLU1dUh0sWJ\nMmPGDGRkZAAAkpKSkJ2d3eKqstvtQGUlcpvFAD9RW15vXqc9t1kMtHrd3XZ2Nts+cAD44Qfv++u9\n3exma/k+9fVAdLT7/RsagLAwWccvLi42/vsF+DbHLO3Jzc0FGhthZ0+y7chI2K9fF7dv3GDnW2Ki\nOdorY7u4uNhU7fG63bwSaW5ziMZ+6hRw9SpyAfZ7GN0+rfoL3n9t2QJkZLDvZ5LvY4Zt/n9paSm0\nxiZoFpD3jZycHLzwwgvo3Lkzxo0bh127djkkEF68eBFpaWmw2Wx4//33sW7dOmzfvr3VcWw2m/fc\ngjvuAJ56Chg9uvVrPCFn+HCgsFD+F6isZF6BxkZzxO2WLGGJXoMGAWPHsnnfnpIDn3qKTVtavNh/\nbSSsRXIySyDk11dNDXDTTezx5EmgXz9W18JV3XxCG376iZVHf+cdlrtRXs6KO/34I1sz4uhRo1uo\nDa+/DmzdCvzf/7Fpqu++a3SLTI2scU8mhs8mWLt2LQoKClBfX4+5c+ciJSUF69evBwAUFBTg7bff\nxssvv4ywsDDccsstWC0tw6kUT2ECm411dkrDBLGxwJ/+ZA4hAPgWJpBbU4EITpyvGZ5AKAhs7QL+\nHKEfaWnAAw8AGzYAQ4awmxBeS8QsIUotCAsT81EmTjS2LUGG4aPAyJEjceTIEYfnCgoKWv6fPXs2\nZs+erc2HeRIDoaGOGdNyCQkBFixQ3zat4BcTFwP80R0Kcwa424rQB1Pa2PmaCQlh14t06WKZ55BZ\nMKWdvREVxX6L6Giga1dg/372vEnFgE82jopiXqioKGDGDD2aRbjBcDHgVzyJAX5nb/XpLOHhLJub\nPAOEVlRXt34uKgq4fFncllP6mlAHv1FxrvAYSOGZlBTg3DlTLrwU6ATXKOCpzgCfWmd1McC/IxcB\n3sRAfb1sMWC5OykLYlobd+rkuB0Z6SgGLIZp7ewJ3jdFRzuGJU3qGfDJxqmpJAYMwiSBbj/hLUwA\nBIYYqK8nzwChLZmZjtsWFwOWhHsGoqMdV4Y0NgdcW1JT2cqXFgs7BQIkBjhcaVvd5caLdlCdAUti\nShuvWQOsWuX4nHOYwGKY0s7ekHoGpGLgzBlj2uMFn2zMK7kGksCxCMF1S+hJDPDwgdwyxGZFjmeg\nooJNTerUiTwDhHfmz2/9HHkG/A8XAzExLEcjNpblB3mrMmoleO5JRYWx7QhCgmsU8CQG+OCZnOy/\n9uiB89RCV7MJ/uu/2FxeQVAkBiwZZ7UYlrGxxT0DlrGzFB4miIhgYiwpCThyxLTTOlXZ2NssKEJz\nKEwAsHKr3DNgdTEgJ0xw6ZL4v4IEQoJogTwD/oeH806eZGGC5GTm3UtLM7ZdehBI3g6LQGIAcFxo\nJSfHv23SGl8SCClnwDRYxsY33ww0FwezIpaxsyvq6pgYcF6vwGT4bGNeAI7wK8ElBsLCXIsB6RKs\n3br5v11aorQCIV8ClSCU8OCDnpcDJ/Th4kXgtddEz0AgQp5KQwguq/Mqg844L8FqZeLiWHIgX0bW\nlRiQFog5fx5o107WoS0ZZ7UYlrHxffeZZz0OH7CMnZ3hIYE772w93dNk+Gxj7t0k/ErwiQFPnoFA\noH9/4Ntvgfbt2bani+qXvwSKi4GsLP+0jQgsuKik6oP+p21b9heIkKfSEKwp633FU85AoIiBDh3Y\n3drhw2wKEl/0QwrvvDdsYI98bq8XLB1ntQiWtLEFO29L2tli+GxjChMYQnBZ3ZNnIFDCBDYb0LEj\n8J//sMVM+Mpmrrj9dmDgQP+1jQhMLCgGCBND55MhkGcACCzPAMAW+6ioAHr1Yssrl5W53q+mBpg+\nXfZhLRtntRCWtLEF8wYsaWeLoSpngPA71ruK1RAMngFArKLYsydb9OOtt4Dt28XpOjxMcOVK4GYk\nE/7h1VeBv/7V6FYQgQSJAUMgMQCwJVpjY/3fHr1ISXF8bNsWGDOGrRMu5coV4KabZB+W4qz6Yzkb\nP/YY8NBDRrdCMZazswWhnAFrEVxiwF2dgevXW68RbmX43f4DD7CysTxvwHlmQXW19RdmIggisOjW\njVYtNIDgkmChoa6n2gWaZ+Duu9kgn5YGTJsG/Pgje76mBigqAvbsYdtJSYrivRRn1R+ysX8gO+uP\nzzZ+7z3Xs6AIXQkuzwAAPP106+cCzTNw663A44+z/2NiWN4AANTWAhs3ivspCBEQBEH4hbg4oE0b\no1sRdASXGNi1iz06q87q6sASA1JiYliVQYB5BqQVGBUmD1KcVX/Ixv6B7Kw/ZGNrEVxiYPFi9lhe\n7vj89euBFSaQEhMjhglqax3DJOQZIAiCIBBsYiA3lyWnOGfVB7pn4OxZ9r+zZ0Bm5UEOxVn1h2zs\nH8jO+kM2thbBJQYANgA6ewYCLYFQSnQ0m0IIMM9AZaX4WqAKIIIgCEIRJAaAwEsglMKn6Nx1F/MM\nSL97x46KDkUxQP0hG/sHsrP+kI2tRXBNLQSCzzNw4QJ7TExknoHqarZ95AjQo4dx7SIIgiBMQ3CK\nAeecgUD2DGRmsvLDUVHMM1BdDXz3HStVrBCKAeoP2dg/kJ31h2xsLYIvTJCQ4Bg3BwI7gfCRR4Cm\nJpY7wD0DgfpdCYIgCJ8IPjEQGclWKZQSyFMLOVLPgI9igGKA+kM29g9kZ/0hG1uL4BMD4eGtxUAw\n3C3HxjLREwzflSAIglBE8ImBiAjXC/YEumegXTuWTFhdzUIGPkAxQP0hG/sHsrP+kI2tRfCJAVee\ngUBOIOR06ACcOsUWJqIVwQiCIAgJwScGIiKYGBgzhmXVA8HhOm/fHjh+XNX3pBig/pCN/QPZWX/I\nxtYiOMVAfT2wfTuwdSt7LhgSCDt0AI4dC3zRQxAEQSgm+MSANExQUwMIQnB4BpKS2KOK70kxQP0h\nG/sHsrP+kI2tRfCJAWkCYU0NEwbBEEfnSYOBLnoIgiAIxQSnGKirY/9XVweHVwAAwpqLTaoQPRQD\n1B+ysX8gO+sP2dhaBJ8YCA8Hrl5l/58/HxzTCqXYbEa3gCAIgjAZwScGIiKAsjL2/+7dQFVVcHgG\nOCrEAMUA9Yds7B/IzvpDNrYWwSsGevRgXoLDh0kMEARBEEGN4WKgsLAQvXr1QlZWFtatW+d2v6Ki\nI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# simulated data \n", "plt.plot(rbc_order1['dyn_simul_points'][7,:], color='r')\n", "plt.axhline(C_bar, ls='dashed', color='k', label=r'$\\overline{C}$')\n", "\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('Consumption, $C_t$', fontsize=15, family='serif')\n", "plt.title(\"Time path of consumption\", fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise:\n", "\n", "Using the above code snippets as a guide, create time series plots of investment, the real wage and the rental rate of capital." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error analysis\n", "Passing the --check P command line option runs a random simulation and at each time point computes the model's residuals from following the approximately optimal policies for choosing consumption and labor supply. Ideally, these residuals would be zero for all $t$." ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6uyQCf6e4WBYG5eXeLUt9p6gIiI+n/0+f9m5ZjEZYErxDvRcJDz8MpKVRTEJg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\n2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# consumption euler residual across time\n", "euler_residuals_time = rbc_order1['dyn_simul_errors'][7,:]\n", "plt.plot(euler_residuals_time**2)\n", "\n", "plt.yscale('log')\n", "plt.xlabel('Periods', fontsize=15, family='serif')\n", "plt.ylabel('Squared residuals', fontsize=15, family='serif')\n", "plt.title('Euler residuals across time...', fontsize=20, family='serif')\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Passing the --check E command line option calculates the model residuals on an ellipse of the state variables. The method calculates the residuals at [low discrepancy sequence](http://en.wikipedia.org/wiki/Low-discrepancy_sequence) of points on the ellipse. The \"size\" of the ellipse is controled by the --check-scale float command line option. This sets the scaling factor for checking on ellipse to 0.5 * float. Default is value if 2.0. Both the residuals, 'dyn_ellipse_errors', and the points, 'dyn_ellipse_points', are reported." ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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16tQp32uDg4PljmfMmCEeh4aGiv//4YcfaNOmTeKxl5cXrVmzhoiITpw4QURE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\nvXpiWqtWrWjz5s1ERLRz507