{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", "\n", "# *Numerical Methods for Economists: Lab Assignment The Solow (1956) Model*\n", "\n", "In this lab assignment you will analyze a version of the Solow model with a [constant elasticity of substituion (CES)](http://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) production function and attempt to \"explain\" observed patterns in capital's share in the U.S. between 1950-2011.\n", "\n", "A CES production function looks as follows...\n", "\n", "\\begin{equation}\n", " Y(t) = \\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\tag{1.2}\n", "\\end{equation}\n", "\n", "where $0 < \\alpha < 1$ and $-\\infty < \\rho < 1$. The parameter $\\rho = \\frac{\\sigma - 1}{\\sigma}$ where $\\sigma$ is the elasticity of substitution between factors of production. The CES production technology is popular because it nests several interesing special cases. In particular, if factors of production are perfect substitutes (i.e., $\\sigma = +\\infty \\implies \\rho = 1$), then output is just a linear combination of the inputs.\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 1} Y(t) = \\alpha K(t) + (1-\\alpha)A(t)L(t) \\tag{1.3}\n", "\\end{equation}\n", " \n", "On the other hand, if factors of production are perfect complements (i.e., $\\sigma = 0 \\implies \\rho = -\\infty$), then we recover the [Leontief production function](http://en.wikipedia.org/wiki/Leontief_production_function).\n", " \n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow -\\infty} Y(t) = \\min\\left\\{\\alpha K(t), (1-\\alpha) A(t)L(t)\\right\\} \\tag{1.4}\n", "\\end{equation}\n", "\n", "Finally, if the elasticity of substitution is unitary (i.e., $\\sigma=1 \\implies \\rho=0$), then output is [Cobb-Douglas](http://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas_production_function).\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 0} Y(t) = K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\tag{1.5}\n", "\\end{equation}" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext autoreload" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "%autoreload 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import integrate, linalg, optimize\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "\n", "# for the first few labs we will be working with models of growth\n", "import growth\n", "import pwt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part a) \n", "\n", "Show that the CES production function as defined by equation 1.2 exhibits constant returns to scale." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "Constant returns to scale requires that multiplying both factors of production by some fixed constant $c > 0$, causes output to change by the same factor.\n", "\n", "\\begin{align}\n", " F(cK, cAL) =& \\bigg[\\alpha (cK(t))^{\\rho} + (1-\\alpha) (cA(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& \\bigg[\\alpha c^{\\rho}K(t)^{\\rho} + (1-\\alpha) c^{\\rho}(A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& \\bigg[c^{\\rho}\\bigg(\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg)\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& c\\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& cF(K, AL)\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (10 points) Part b)\n", "Derive the intensive forms for both the general CES production function as defined by equation 1.2 and for its Cobb-Douglas special case defined by equation 1.5. Show that both of these intensive production functions are concave." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "The intensive form of the general CES production function is...\n", "\n", "\\begin{align}\n", "y(t) = \\frac{Y(t)}{A(t)L(t)} =& \\frac{1}{A(t)L(t)}\\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\frac{\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}}{(A(t)L(t))^{\\rho}}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha \\frac{K(t)^{\\rho}}{(A(t)L(t))^{\\rho}} + (1-\\alpha) \\frac{(A(t)L(t))^{\\rho}}{(A(t)L(t))^{\\rho}}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha \\bigg(\\frac{K(t)}{A(t)L(t)}\\bigg)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}}\n", "\\end{align}\n", "\n", "The intensive form of the Codd-Douglas special case is...\n", "\n", "\\begin{align}\n", "y(t) = \\frac{Y(t)}{A(t)L(t)} =& \\frac{1}{A(t)L(t)}K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\\\\n", "=& K(t)^{\\alpha}(A(t)L(t))^{-\\alpha} \\\\\n", "=& \\bigg(\\frac{K(t)}{A(t)L(t)}\\bigg)^{\\alpha} \\\\\n", "= & k(t)^{\\alpha}\n", "\\end{align}\n", "\n", "Concavity requires that $f'(k) > 0$ and $f''(k) < 0$. For the intensive form of the general CES production function these derivatives are messy!\n", "\n", "\\begin{align}\n", " f'(k) = \\frac{\\partial y(t)}{\\partial k(t)} =& \\alpha k(t)^{\\rho-1}\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} > 0 \\\\\n", " f''(k) = \\frac{\\partial^2 y(t)}{\\partial k(t)^2} =& \\alpha k(t)^{\\rho-1} \\frac{\\partial}{\\partial k}\\bigg(\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1}\\bigg) + \\frac{\\partial}{\\partial k}\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1} \\frac{\\partial}{\\partial k}\\bigg(\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1}\\bigg(\\bigg(\\alpha \\rho k(t)^{\\rho-1}\\bigg)\\bigg(\\frac{1}{\\rho} - 1\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1}\\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)\\bigg(1 - \\rho\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)^2\\bigg(1 - \\rho\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) - \\bigg(\\alpha(1 -\\rho)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& (1 -\\rho)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)^2 - \\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]\\bigg) \\\\\n", " =& (1 -\\rho)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg(\\alpha^2 k(t)^{2\\rho-2} - \\alpha^2 k(t)^{2\\rho-2} - (1-\\alpha)\\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg) \\\\\n", " =& -(1 -\\rho)(1-\\alpha)\\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2} < 0\\\\\n", "\\end{align}\n", "\n", "For the Cobb-Douglas special case, the derivatives are much nicer.\n", "\n", "\\begin{align}\n", "f'(k) =& \\alpha k(t)^{\\alpha-1} > 0 \\\\\n", "f''(k) =& -\\alpha (1 - \\alpha) k(t)^{\\alpha-2} < 0 \\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part c)\n", "\n", "Using your results from part b, complete the Python function below which defines output (per person/effective person) in terms of capital (per person/effective person) and model parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# you were given the following incomplete code...\n", "def ces_output(t, k, params):\n", " \"\"\"\n", " Intensive form for a CES production \n", " function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y: (array-like) Output (per person/ effective person)\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " y = # INSERT CODE HERE!\n", " else:\n", " y = # INSERT CODE HERE!\n", " \n", " return y" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should be completed as follows...\n", "def ces_output(t, k, params):\n", " \"\"\"\n", " Intensive form for a CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y: (array-like) Output (per person/ effective person)\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " y = k**alpha\n", " else:\n", " y = (alpha * k**rho + (1-alpha))**(1 / rho)\n", " \n", " return y" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part d)\n", "\n", "Using your results from part b, complete the Python function below which defines the marginal product of capital (per person/effective person) in terms of capital (per person/effective person) and model parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# you were given the following incomplete code...\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " mpk: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " mpk = # INSERT CODE HERE!\n", " else:\n", " mpk = # INSERT CODE HERE!\n", " \n", " return mpk" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should be completed as follows...\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " mpk: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " mpk = alpha * k**(alpha - 1)\n", " else:\n", " mpk = alpha * k**(rho - 1) * (alpha * k**rho + (1 - alpha))**((1 / rho) - 1)\n", " \n", " return mpk" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part e)\n", "\n", "Derive the equation of motion for capital per effective worker when the general CES production function defined by equation 1.2 and for the Cobb-Douglas special case defined by equation 1.5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "The key equation of the Solow model is the equation of motion for capital per effective worker, $k(t)=\\frac{K(t)}{A(t)L(t)}$. Application of the chain rule to $k(t)$ yields\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& \\frac{\\dot{K}A(t)L(t) - K(t)\\left[A(t)\\dot{L}(t) + \\dot{A}(t)L(t)\\right]}{[A(t)L(t)]^2} \\notag \\\\\n", "\t =& \\frac{\\dot{K}}{A(t)L(t)} - \\frac{K(t)}{A(t)L(t)}\\left(\\frac{\\dot{L}(t)}{L(t)} + \\frac{\\dot{A}(t)}{A(t)}\\right).\n", "\\end{align}\n", "\n", "From here I need only substitute the equation of motion for capital and the expressions for the exogenous growth rates of labor and technology to obtain a first-order non-linear differential equation describing the evolution of capital per effective worker, $k(t)$.\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& \\frac{sY(t) - \\delta K(t)}{A(t)L(t)} - \\frac{K(t)}{A(t)L(t)}\\left(\\frac{\\dot{L}(t)}{L(t)} + \\frac{\\dot{A}(t)}{A(t)}\\right) \\notag \\\\\n", "\t=& s\\frac{Y(t)}{A(t)L(t)} - (n + g + \\delta)\\frac{K(t)}{A(t)L(t)} \\notag \\\\\n", " =& sy(t) - (n + g + \\delta)k(t) \\notag \\\\\n", "\\end{align} \n", "\n", "When the production function is CES, the equation becomes\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& s\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} - (n + g + \\delta)k(t).\n", "\\end{align} \n", "\n", "When the production function is Cobb-Douglas, the equation becomes\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& sk(t)^{\\alpha} - (n + g + \\delta)k(t).\n", "\\end{align} " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part f)\n", "\n", "Using your results from parts d) and e) and the Python function defining the equation of motion for capital (per person/effective person) complete the Python function which defines the Jacobian for the Solow model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def equation_of_motion_capital(t, k, params):\n", " \"\"\"\n", " Equation of motion for capital (per person/effective person).\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " k_dot: (array-like) Time-derivative of capital (per person/effective \n", " person).\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", " \n", " y = ces_output(t, k, params)\n", " \n", " k_dot = s * y - (n + g + delta) * k\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# you where given the following incomplete code...\n", "def solow_jacobian(t, k, params):\n", " \"\"\"\n", " The Jacobian of the Solow model.\n", " \n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " jac: (array-like) Value of the derivative of the equation of \n", " motion for capital (per worker/effective worker) with \n", " respect to k.\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " mpk = #INSERT YOUR CODE HERE\n", " \n", " k_dot = s * mpk - (n + g + delta)\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should have been completed as follows...\n", "def solow_jacobian(t, k, params):\n", " \"\"\"\n", " The Jacobian of the Solow model.\n", " \n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " jac: (array-like) Value of the derivative of the equation of \n", " motion for capital (per worker/effective worker) with \n", " respect to k.\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " mpk = marginal_product_capital(t, k, params) \n", " \n", " k_dot = s * mpk - (n + g + delta)\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part g)\n", "\n", "In the cell below, create a Python dictionary called `default_params` using the following values: $\\alpha$ = 0.33, $\\delta$ = 0.04, $\\sigma$ = 1.0, $g$ = 0.02, $n$ = 0.01, $s$ = 0.15, $L(0)$=1.0, $A(0)$=1.0." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT CODE HERE!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# my solution...\n", "default_params = {'alpha':0.5, 'delta':0.04, 'sigma':1.05, 'g':0.02, \n", " 'n':0.01, 's':0.15, 'A0':1.0, 'L0':1.0} " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part h)\n", "In the cell below, create instance of the `SolowModel` class called `model` using the results from parts c), d), f) and g)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT CODE HERE!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# my solution...\n", "model = growth.SolowModel(output=ces_output, \n", " mpk=marginal_product_capital,\n", " k_dot=equation_of_motion_capital, \n", " jacobian=solow_jacobian,\n", " params=default_params)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 61 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (10 points) Part i)\n", "\n", "Derive an analytic expression for the steady state value of capital (per person/effective person) using your result from part e) and use your result to complete the Python function in the cell below defining the analytic steady state value for $k$ as a function of model parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "When the production function is CES, the steady state value for capital (per person/effective person) is\n", "\n", "\\begin{align}\n", "0 =& s\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} - (n + g + \\delta)k^* \\\\\n", "s\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} =& (n + g + \\delta)k^* \\\\\n", "s^{\\rho}\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg] =& (n + g + \\delta)^{\\rho}k^{*\\rho} \\\\\n", "\\alpha s^{\\rho} k^{*\\rho} + (1-\\alpha)s^{\\rho} =& (n + g + \\delta)^{\\rho}k^{*\\rho} \\\\\n", "(1-\\alpha)s^{\\rho} =& (n + g + \\delta)^{\\rho}k^{*\\rho} - \\alpha s^{\\rho} k^{*\\rho} \\\\\n", "(1-\\alpha)s^{\\rho} =& \\bigg((n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}\\bigg) k^{*\\rho} \\\\\n", "k^{*\\rho} =& \\frac{(1-\\alpha)s^{\\rho}}{(n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}} \\\\\n", "k^* =& \\left(\\frac{(1-\\alpha)s^{\\rho}}{(n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}}\\right)^{\\frac{1}{\\rho}} \\\\\n", "\\end{align}\n", "\n", "Note that in order for $k^* > 0$ we require that the parameter $\\alpha$ satisfies\n", "\n", "\\begin{align}\n", "\\alpha < \\bigg(\\frac{n+g+\\delta}{s}\\bigg)^{\\rho}.\n", "\\end{align}\n", "\n", "When the production function is Cobb-Douglas, the steady state value for capital (per person/effective person) is\n", "\n", "\\begin{align}\n", "0 =& sk^{*\\alpha} - (n + g + \\delta)k^* \\\\\n", "sk^{*\\alpha} =& (n + g + \\delta)k^* \\\\\n", "sk^{*\\alpha-1} =& (n + g + \\delta) \\\\\n", "k^{*\\alpha-1} =& \\frac{n + g + \\delta}{s} \\\\\n", "k^* =& \\left(\\frac{s}{n + g + \\delta}\\right)^{\\frac{1}{1-\\alpha}}\n", "\\end{align} " ] }, { "cell_type": "code", "collapsed": false, "input": [ "### you were given the following incomplete code...\n", "def analytic_k_star(params): \n", " \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " k_star = # INSERT CODE HERE!\n", " else:\n", " k_star = # INSERT CODE HERE!\n", " \n", " return k_star" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "### which should be completed as follows...\n", "def analytic_k_star(params): \n", " \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas as special case\n", " if rho == 0:\n", " k_star = (s / (n + g + delta))**(1 / (1 - alpha))\n", " else:\n", " k_star = (((1 - alpha) * s**rho) / ((n + g + delta)**rho - alpha * s**rho))**(1 / rho)\n", " \n", " return k_star" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "def isfinite_k_star(params):\n", " \"\"\"Returns true if parameters are consistent with a finite k*.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " return alpha < ((n + g + delta) / s)**rho" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "isfinite_k_star(default_params)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "True" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part j)\n", "\n", "Using the code from the lab session as a guide, create a Python dictionary called `solow_steady_state_funcs` containing your result from part i) and add it to the model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT YOUR CODE HERE!!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# create a dictionary of steady state expressions...\n", "solow_steady_state_funcs = {'k_star':analytic_k_star}\n", "\n", "# add the dictionary of functions to the model\n", "model.steady_state.set_functions(solow_steady_state_funcs)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 62 }, { "cell_type": "code", "collapsed": false, "input": [ "# compute the steady state values\n", "model.steady_state.set_values()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 63 }, { "cell_type": "code", "collapsed": false, "input": [ "# compare this result to the one you obtained from part i\n", "model.steady_state.values" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 64, "text": [ "{'k_star': 4.72555503663348}" ] } ], "prompt_number": 64 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Execute the code in the cell below to calibrate the model for the U.S. using data from the Penn World Tables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calibrate the model!\n", "growth.calibrate_ces(model, 'USA', x0=[0.75, 1.01], method='Nelder-Mead', bounds=None)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.624288\n", " Iterations: 62\n", " Function evaluations: 145\n" ] } ], "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, "input": [ "# display the parameters...\n", "model.params" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 85, "text": [ "{'A0': 121.54997789817465,\n", " 'L0': 61.971196530271804,\n", " 'alpha': 0.91456643533201798,\n", " 'delta': 0.03761163,\n", " 'g': 0.03629411526782518,\n", " 'n': 0.015525562239498985,\n", " 's': 0.20732178,\n", " 'sigma': 0.78943070081394473}" ] } ], "prompt_number": 85 }, { "cell_type": "code", "collapsed": false, "input": [ "# check that k_star is finite!\n", "isfinite_k_star(model.params)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 86, "text": [ "True" ] } ], "prompt_number": 86 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part k)\n", "\n", "Using the code examples from the lab as a guide, generate a plot of the Solow diagram demonstrating how the output, actual investment, and breakeven investment curves shift as a result of a 50% *increase* in $\\sigma$ (i.e., the elasticity of substitution between capital and effective labor). Explain why, and in which direction, each curve shifts. Discuss the impact on the steady state levels of capital, output, and consumption per effective person." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# here is the code for generating the plot...\n", "plt.figure(figsize=(8,6))\n", "model.plot_solow_diagram(gridmax=300, N=1000, param='sigma', shock=1.05, reset=True) \n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAGYCAYAAABf16uoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBEEQUwySO0EQBEFMMUjuBEEQBDHF+H+hKnQtJrLSAgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 89 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "From your answer to part b) it can be shown that a positive shock to $\\sigma$ increases the marginal productivity of capital per effective worker. Following the positive shock to $\\sigma$ the current stock of capital per effective worker now has a higher marginal product and is therefore capable of producing more output per effective worker (i.e., $y$ jumps up!). Since a constant fraction of output is saved the positve shock to $\\sigma$ also leads to higher actual savings. Break even investment is unaffected by shocks to $\\sigma$. \n", "\n", "Following the positive shock to $\\sigma$ actual investment will exceed breakeven investment which causes capital per effective worker to rise towards its new, higher steady state value. Since steady state $k$ is higher following the shock, steady state $y$ must also be higher. Whether steady state consumption per effective worker is higher or lower depends on the old (i.e., pre-shock) and new (i.e., post-shock) steady state value of $k$ to its \"Golden-rule\" level. If the new steady state is closer (further away) to its \"Golden-rule\" level than the old steady state, then the new steady state $c$ will be higher (lower). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part l)\n", "\n", "Using code from the lab as a guide, generate impulse response functions (IRFs) in for the Solow model following a 50% *increase* in the elasticity of substitution between capital and effective labor, $\\sigma$. Discuss the resulting IRFs. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# here is the code snippet...\n", "fig_kwargs = {'figsize':(12,8)}\n", "model.plot_impulse_response(variables='all', param='sigma', shock=1.05, T=100, \n", " kind='efficiency_units', log=False, reset=True, **fig_kwargs)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAvsAAAIGCAYAAADKjUCJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer: \n", "The positive shock to $\\sigma$ increases the marginal capital, which raises output and actual investment. Break even investment is unaffected by an increase in $\\sigma$. Since, following the shock, actual investment exceeds break even investment $k$ begins to rise and continues to do so until it reaches its new, higher steady state level. \n", "\n", "Following the positive shock to $\\sigma$ the current stock of capital per effective worker now has a higher marginal product and is therefore capable of producing more output per effective worker. The shock to $\\sigma$ causes $y$ to jump up inititially and then, because $k$ continues to rise, $y$ also continues rising toward its new, higher steady state value. \n", "\n", "Following the positive shock to $\\sigma$ the current stock of capital per effective worker now has a higher marginal product and is therefore capable of producing more output per effective worker. The shock to $\\sigma$ causes $y$ to jump up inititially. Since consumption per effective worker is just a constant fraction of output per effective worker, the jump in $y$ causes $c$ to jump as well. The fact that $c$ transitions to a new, higher steady state level indicates that the economy has moved closer to its \"Golden-rule\" level." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part m:\n", "\n", "Using your results from part b), derive an expression for the elasticity of output per effective person with respect to capital per effective person, $\\alpha_k$, as a function of capital per effective person, $k$, and model parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\\begin{align}\n", " \\alpha_{k}(k) =& \\frac{k f'(k)}{f(k)} \\\\\n", " =&\\frac{k\\bigg[\\alpha k^{\\rho-1}\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^{\\frac{1}{\\rho}-1}\\bigg]}{\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^{\\frac{1}{\\rho}}}\\\\\n", " =&\\frac{\\alpha k^{\\rho}}{\\alpha k^{\\rho} + (1-\\alpha)}\\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part n)\n", "\n", "Differentiate your result from part m) with respect to capital per effective person, $k$, and discuss under what conditions the derivative will be positive, negative, or zero." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "\\begin{align}\n", " \\frac{\\partial \\alpha_{k}(k)}{\\partial k} =&\\frac{\\alpha \\rho k^{\\rho - 1}\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg) - \\alpha k^{\\rho}\\bigg(\\alpha\\rho k^{\\rho-1}\\bigg)}{\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^2}\\\\\n", " =&\\frac{\\alpha^2 \\rho k^{2\\rho - 1} + \\alpha(1-\\alpha)\\rho k^{\\rho-1} - \\alpha^2\\rho k^{2\\rho-1}}{\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^2}\\\\\n", " =&\\frac{\\alpha(1-\\alpha)\\rho k^{\\rho-1}}{\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^2}\\\\\n", "\\end{align}\n", "\n", "Result is more easily interpretable after subsituting $\\rho=\\frac{\\sigma-1}{\\sigma}$.\n", "\n", "\\begin{align}\n", " \\frac{\\partial \\alpha_{k}(k)}{\\partial k} =&\\frac{\\alpha(1-\\alpha)\\rho k^{\\rho-1}}{\\bigg(\\alpha k^{\\rho} + (1-\\alpha)\\bigg)^2}\\\\\n", " =&\\frac{\\alpha(1-\\alpha)\\bigg(\\frac{\\sigma-1}{\\sigma}\\bigg) k^{\\frac{1}{\\sigma}}}{\\bigg(\\alpha k^{\\frac{\\sigma-1}{\\sigma}} + (1-\\alpha)\\bigg)^2}\\\\\n", "\\end{align}\n", "\n", "Thus we find that $\\frac{\\partial \\alpha_{k}(k)}{\\partial k} > 0 \\iff \\sigma > 1$ which means that capital and effective labor are substitutes; $\\frac{\\partial \\alpha_{k}(k)}{\\partial k} < 0 \\iff \\sigma < 1$ which means that capital and effective labor are complements; and $\\frac{\\partial \\alpha_{k}(k)}{\\partial k} = 0 \\iff \\sigma = 1$ which means that production function is Cobb-Douglas. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part o)\n", "\n", "Use the fact that $\\frac{\\partial k}{\\partial s} > 0$ and the result from part n) to relate the sign of $\\frac{\\partial \\alpha_k(k)}{\\partial s}$ to the elasticity of substitution between capital and effective labor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "We find that $\\frac{\\partial \\alpha_k(k)}{\\partial s} = \\left(\\frac{\\partial k}{\\partial s}\\right)\\left(\\frac{\\partial \\alpha_{k}(k)}{\\partial k}\\right) > 0 \\iff \\sigma > 1$ which means that capital and effective labor are substitutes; similarly, $\\frac{\\partial \\alpha_k(k)}{\\partial s} < 0 \\iff \\sigma < 1$ which means that capital and effective labor are complements; and $\\frac{\\partial \\alpha_k(k)}{\\partial s} = 0 \\iff \\sigma = 1$ which means that production function is Cobb-Douglas. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (15 points) Part p)\n", "\n", "The code in the cell below regresses $\\alpha_k(k)$ on the investment's share of GDP for the U.S., $s$ during two different time periods: 1950-1970 and 1970-2011. Can you \"explain\" these pattern using your result from part o)?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(8,6))\n", "ax1 = fig.add_subplot(121)\n", "ax2 = fig.add_subplot(122)\n", "\n", "# capital's share for US (pre-1970)\n", "y = 1 - model.data.labsh.loc[:1970]\n", "\n", "# savings rate for US (pre-1970)\n", "x = model.data.csh_i.loc[:1970]\n", "\n", "# regress capital's share on savings rate \n", "res1 = pd.ols(y=y, x=x)\n", "\n", "ax1.scatter(x, y)\n", "ax1.set_xlabel('s', family='serif', fontsize=15)\n", "ax1.set_ylabel(r'$\\alpha_k(k)$', fontsize=15, family='serif', rotation='horizontal')\n", "ax1.set_title('U.S. pre-1970', family='serif', fontsize=15)\n", "\n", "# plot regression line pre-1970\n", "grid = np.linspace(0.15, 0.25, 100)\n", "ax1.plot(grid, res1.beta[1] + res1.beta[0] * grid, 'r')\n", "\n", "# capital's share for US (post-1970)\n", "y = 1 - model.data.labsh.loc[1970:]\n", "\n", "# savings rate for US (post-1970)\n", "x = model.data.csh_i.loc[1970:]\n", "\n", "# regress capital's share on savings rate post-1970\n", "res2 = pd.ols(y=y, x=x)\n", "\n", "ax2.scatter(x, y)\n", "ax2.set_xlabel('s', family='serif', fontsize=15)\n", "ax2.set_title('U.S. post-1970', family='serif', fontsize=15)\n", "\n", "# plot regression line post-1970\n", "grid = np.linspace(0.15, 0.25, 100)\n", "ax2.plot(grid, res2.beta[1] + res2.beta[0] * grid, 'r')\n", "\n", "fig.suptitle(\"Patterns in capital's share for the U.S?\", x=0.5, y=1.05, \n", " fontsize=20, family='serif')\n", "fig.tight_layout()\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAHICAYAAACszftMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "# summary of the regression results for 1950-1970\n", "print res1" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "-------------------------Summary of Regression Analysis-------------------------\n", "\n", "Formula: Y ~ + \n", "\n", "Number of Observations: 21\n", "Number of Degrees of Freedom: 2\n", "\n", "R-squared: 0.2033\n", "Adj R-squared: 0.1613\n", "\n", "Rmse: 0.0087\n", "\n", "F-stat (1, 19): 4.8476, p-value: 0.0402\n", "\n", "Degrees of Freedom: model 1, resid 19\n", "\n", "-----------------------Summary of Estimated Coefficients------------------------\n", " Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n", "--------------------------------------------------------------------------------\n", " x 0.3420 0.1553 2.20 0.0402 0.0375 0.6465\n", " intercept 0.2794 0.0307 9.12 0.0000 0.2193 0.3395\n", "---------------------------------End of Summary---------------------------------\n", "\n" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "# summary of the regression results for 1970-2011\n", "print res2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "-------------------------Summary of Regression Analysis-------------------------\n", "\n", "Formula: Y ~ + \n", "\n", "Number of Observations: 42\n", "Number of Degrees of Freedom: 2\n", "\n", "R-squared: 0.1669\n", "Adj R-squared: 0.1461\n", "\n", "Rmse: 0.0130\n", "\n", "F-stat (1, 40): 8.0161, p-value: 0.0072\n", "\n", "Degrees of Freedom: model 1, resid 40\n", "\n", "-----------------------Summary of Estimated Coefficients------------------------\n", " Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n", "--------------------------------------------------------------------------------\n", " x -0.2736 0.0966 -2.83 0.0072 -0.4630 -0.0842\n", " intercept 0.4104 0.0206 19.92 0.0000 0.3700 0.4508\n", "---------------------------------End of Summary---------------------------------\n", "\n" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "Consistency with the Solow model requires that...\n", "\n", "1. Capital and effective labor must have been \"substitutes\" $\\implies \\sigma > 1,\\ \\rho > 0$ for the U.S. between 1950-1970.\n", "2. Capital and effective labor must be \"complements\" $\\implies \\sigma < 1,\\ \\rho < 0$ for the U.S. between 1970-present.\n", "\n", "One possible story is that prior to 1970 advances in technology led to increased automation of production process (i.e., technology replaced people with machines!); after 1970, however, advances in technology were primarily driven by rise of computers which require skilled labor to operate efficiently (i.e., technology replaced a worker with a computer and a worker with skills to use it!).\n", "\n", "In case, you are wondering the values for $\\sigma$ calibrated to pre and post 1970's U.S. data are consistent with the above story. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calibrate the model for 1950-1970\n", "growth.calibrate_ces(model, 'USA', x0=[0.9, 1.05], method='Nelder-Mead', bounds=(1950, 1970))\n", "\n", "# display the parameters...\n", "model.params" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.069163\n", " Iterations: 60\n", " Function evaluations: 142\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 41, "text": [ "{'A0': 8.4013859704623151e-06,\n", " 'L0': 62.042847904603079,\n", " 'alpha': 0.92487514982243713,\n", " 'delta': 0.035311185,\n", " 'g': 0.24752114778989309,\n", " 'n': 0.013829716769131757,\n", " 's': 0.19696239,\n", " 'sigma': 1.0319048902747541}" ] } ], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "# calibrate the model for 1970-2011\n", "growth.calibrate_ces(model, 'USA', x0=[0.3, 0.35], method='Nelder-Mead', bounds=(1970, 2011))\n", "\n", "# display the parameters...\n", "model.params" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.177896\n", " Iterations: 68\n", " Function evaluations: 166\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 42, "text": [ "{'A0': 2144.4725557564207,\n", " 'L0': 66.08809869858429,\n", " 'alpha': 0.90974121093750004,\n", " 'delta': 0.038733795,\n", " 'g': 0.025180474313690131,\n", " 'n': 0.014127169172378055,\n", " 's': 0.21214846,\n", " 'sigma': 0.55418090820312549}" ] } ], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }