{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%load_ext autoreload" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "autoreload 2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import seaborn as sn\n", "\n", "import pycollocation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example: Solow model with Cobb-Douglas production

\n", "\n", "The Solow model is a model of economic growth as a process of physical capital accumulation. By far the most common version of the Solow model assumes Cobb-Douglas functional form for intensive output:\n", "\n", "$$ f(k) = k^{\\alpha}. $$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def cobb_douglas_output(k, alpha, **params):\n", " return k**alpha" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After a bit of algebra, the Solow model with Cobb-Douglas production can be reduced down to a single non-linear ordinary differential equation (ODE) and an initial condition for capital (per unit effective labor supply)...\n", "\n", "$$ \\dot{k}(t) = s k(t)^{\\alpha} - (g + n + \\delta) k(t),\\ k(0) = k_0 $$\n", "\n", "...the above equation says that the rate of change of the stock of physical capital (per unit effective labor supply), $\\dot{k}(t)$, is the difference between the actual level of investment in physical capital, $sk(t)^{\\alpha}$, and the amount of investment required to maintain the current level of physical capital, $(g + n + \\delta) k(t)$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def standard_solow_model(t, k, alpha, delta, g, n, s, **params):\n", " return [s * cobb_douglas_output(k, alpha) - (g + n + delta) * k]\n", "\n", "def initial_condition(t, k, k0, **params):\n", " return [k - k0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To complete the model we need to define some parameter values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "params = {'g': 0.02, 's': 0.1, 'n': 0.02, 'alpha': 0.15, 'delta': 0.04, 'k0': 1.0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Solving the model with pyCollocation

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Defining a `pycollocation.IVP` instance

" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pycollocation.problems.IVP?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "standard_solow_ivp = pycollocation.problems.IVP(bcs_lower=initial_condition,\n", " number_bcs_lower=1,\n", " number_odes=1,\n", " params=params,\n", " rhs=standard_solow_model,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding a good initial guess for $k(t)$\n", "\n", "Theory tells us that, starting from some initial condition $k_0$, the solution to the Solow model converges monotonically toward its long run equilibrium value $k^*$. Our initial guess for the solution should preserve this property..." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def equilibrium_capital(alpha, delta, g, n, s, **params):\n", " \"\"\"Equilibrium value of capital (per unit effective labor supply).\"\"\"\n", " return (s / (g + n + delta))**(1 / (1 - alpha))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def initial_mesh(t, T, num, problem):\n", " ts = np.linspace(t, T, num=num)\n", " kstar = equilibrium_capital(**problem.params)\n", " ks = kstar - (kstar - params['k0']) * np.exp(-ts)\n", " return ts, ks\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving the model" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pycollocation.solvers.Solver?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Orthogonal polynomial basis functions

" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Choose your basis functions and create a solver\n", "polynomial_basis = pycollocation.basis_functions.PolynomialBasis()\n", "solver = pycollocation.solvers.Solver(polynomial_basis)\n", "\n", "# compute the initial mesh\n", "boundary_points = (0, 100)\n", "ts, ks = initial_mesh(*boundary_points, num=1000, problem=standard_solow_ivp)\n", "\n", "# compute the initial coefs guess\n", "basis_kwargs = {'kind': 'Chebyshev', 'domain': boundary_points, 'degree': 15}\n", "k_poly = polynomial_basis.fit(ts, ks, **basis_kwargs)\n", "initial_coefs = k_poly.coef\n", "\n", "# specify the collocation nodes\n", "nodes = polynomial_basis.roots(**basis_kwargs)\n", "\n", "# solve the model!\n", "solution = solver.solve(basis_kwargs, boundary_points, initial_coefs,\n", " nodes, standard_solow_ivp)\n" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HNIbGAQCJLa1D2zBNvX2gSVlup2aOH2R1OQAA9CmtQ7um/pzafEHdXOaVy8m0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\nQhsAgCRBaAMAkCT+P4JwmKca1TPPAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_soln, = solution.evaluate_solution(ts)\n", "plt.plot(ts, k_soln)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qRCZfann2GEvnYeA5OG37CxSUoB3HokhQVlt5TTAaeAwFXVjZSFdV/0eN8HYG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\nZCP2HqnH3G5CWVFU7KutR5bFiIqSgQJbSESUGYQtnY11opd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_resids, = solution.evaluate_residual(ts)\n", "plt.plot(ts, k_resids)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CBQT9HN5xy4qG36+7LYg3Xb8UM/Gs5eJCAPj57nMYn0njjdctrUtL8HtXLcKW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\noP/KriTVuh63ipuILXTTtSpHQSiwgclJdqP3QJrBqyUwDFN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79u1TLBZTZ2enuru71d7e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\nYQQ5AACG/T+Frl5nd18a6gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_normalized_resids, = solution.normalize_residuals(ts)\n", "plt.plot(ts, np.abs(k_normalized_resids))\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

B-spline basis functions

" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [], "source": [ "bspline_basis = pycollocation.basis_functions.BSplineBasis()\n", "solver = pycollocation.solvers.Solver(bspline_basis)\n", "\n", "ts, ks = initial_mesh(*boundary_points, num=250, problem=standard_solow_ivp)\n", "\n", "tck, u = bspline_basis.fit([ks], u=ts, k=5, s=0)\n", "knots, coefs, k = tck\n", "initial_coefs = np.hstack(coefs)\n", "\n", "basis_kwargs = {'knots': knots, 'degree': k, 'ext': 2}\n", "nodes = np.linspace(*boundary_points, num=249) \n", "solution = solver.solve(basis_kwargs, boundary_points, initial_coefs,\n", " nodes, standard_solow_ivp)\n" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solution.result.success" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_soln, = solution.evaluate_solution(ts)\n", "plt.plot(ts, k_soln)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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25GwcNrcbC+Z0Y8GcLgz0lzCrt4C+7vxBlQnajoNaPThXqha6e4vYsXMUk9Wg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\ntN98rWbKulwHW9yqJUCJiIh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_resids, = solution.evaluate_residual(ts)\n", "plt.plot(ts, k_resids)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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N4MnnT6Kxyo5SuxHrlpbh5g01i+ZGkxCifZoM5MlFFMh1LAsdyyDJC5oK5ABw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\nIiqdx86ys/v7UWfk8t9iqjsdD7MxFcjt05wXMFs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_normalized_resids, = solution.normalize_residuals(ts)\n", "plt.plot(ts, np.abs(k_normalized_resids))\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example: Generic Solow model of economic growth

\n", "\n", "Can we refactor the code above so that it can be solve a Solow model for arbitrary intensive production $f$? Yes! " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pycollocation.tests import models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example usage..." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def ces_output(k, alpha, sigma, **params):\n", " rho = (sigma - 1) / sigma\n", " if rho == 0:\n", " y = cobb_douglas_output(k, alpha)\n", " else:\n", " y = (alpha * k**rho + (1 - alpha))**(1 / rho)\n", " return y\n", "\n", "\n", "def ces_equilibrium_capital(g, n, s, alpha, delta, sigma, **params):\n", " \"\"\"Steady state value for capital stock (per unit effective labor).\"\"\"\n", " rho = (sigma - 1) / sigma\n", " if rho == 0:\n", " kss = (s / (g + n + delta))**(1 / (1 - alpha))\n", " else:\n", " kss = ((1 - alpha) / (((g + n + delta) / s)**rho - alpha))**(1 / rho)\n", " return kss\n", "\n", "\n", "ces_params = {'g': 0.02, 's': 0.1, 'n': 0.02, 'alpha': 0.15, 'delta': 0.04,\n", " 'sigma': 0.05, 'k0': 1.0}" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "generic_solow_ivp = models.SolowModel(ces_output,\n", " ces_equilibrium_capital,\n", " ces_params)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "polynomial_basis = pycollocation.basis_functions.PolynomialBasis()\n", "solver = pycollocation.solvers.Solver(polynomial_basis)\n", "\n", "basis_kwargs = {'kind': 'Chebyshev', 'domain': [0, 100], 'degree': 15}\n", "\n", "ts, ks = initial_mesh(basis_kwargs['domain'], 1000, standard_solow_ivp)\n", "k_poly = polynomial_basis.fit(ts, ks, **basis_kwargs)\n", "initial_coefs = k_poly.coef\n", "\n", "solution = solver.solve(basis_kwargs, initial_coefs, standard_solow_ivp)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HNIbGAQCJLa1D2zBNvX2gSVlup2aOH2R1OQAA9CmtQ7um/pzafEHdXOaVy8m0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\nQhsAgCRBaAMAkCT+P4JwmKca1TPPAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_soln, = solution.evaluate_solution(ts)\n", "plt.plot(ts, k_soln)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CBQT9HN5xy4qG36+7LYg3Xb8UM/Gs5eJCAPj57nMYn0njjdctrUtL8HtXLcKW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\nYQQ5AACG/T+Frl5nd18a6gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_normalized_resids, = solution.normalize_residuals(ts)\n", "plt.plot(ts, np.abs(k_normalized_resids))\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }