{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "## **3. Growing Along and Converging to the Balanced-Growth Equilibrium Path** \n", "\n", "### **3.1. The Balanced-Growth Equilibrium Path** \n", "\n", "#### **3.1.1. The Balanced-Growth Equilbrium Capital Intensity $\\kappa^*$** \n", "\n", "We define $\\kappa^*$ as that value of capital-intensity $\\kappa$ for which, at the current levels of the parameters $n, g, \\delta, s$, and $\\theta$:\n", "\n", ">(2.2.10) $\\frac{s}{\\kappa} - \\delta = n + g$\n", "\n", "is satisfied. That is true if and only if:\n", "\n", ">(3.1.1) $\\kappa^* = \\frac{s}{n+g+\\delta}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the capital-intensity $\\kappa = \\kappa^*$, then it is constant. The economy is then in balanced growth.\n", "\n", "From (2.1.2) we see that—as capital-intensity $\\kappa$ is then constant at the value $\\kappa^*$—the proportional growth rate $g_Y$ of total income and production in the economy $Y$ is then equal to n+g, the sum of the growth rate $n$ of the labor force. From (2.1.3) we see that—as capital-intensity $\\kappa$ is then constant at the value $\\kappa^*$—the proportional growth rate $g_y$ of output per worker is than equal to teh proportional growth rate $g$ of the efficiency of labor. From (2.1.1) we see that the proportional growth rate $g_K$ of the economy's total capital stock is then the same $n + g$ as the growth rate $g_Y$ of income and production $Y$.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **3.1.2. Calculating the Balanced-Growth Equilbrium Path** \n", "\n", "We can then—if we know the parameter values of the model, the initial values $L_0$ and $E_0$ of the labor force and labor efficiency at some time we index equal to 0, and that the economy is on its balanced-growth equilibrium path—calculate what all variables of interest in the economy will be at any time whatsoever:\n", "\n", "Total income and prdouction will be:\n", "\n", ">(3.1.2) $Y^*_t = \\left(\\kappa^* \\right)^\\theta E_t L_t $$\n", "= \\left(\\kappa^* \\right)^\\theta e^{gt}E_0 e^{nt}L_0$$\n", "= \\left(s/(n+g+\\delta) \\right)^\\theta e^{gt}E_0 e^{nt}L_0$\n", "\n", "Income and production per worker will be:\n", "\n", ">(3.1.3) $y^*_t = \\left(\\kappa^* \\right)^\\theta E_t $$\n", "= \\left(\\kappa^* \\right)^\\theta e^{gt}E_0$$\n", "= \\left(s/(n+g+\\delta) \\right)^\\theta e^{gt}E_0$\n", "\n", "The capital stock will be:\n", "\n", ">(3.1.4) $K^*_t = \\kappa^* Y^*_t$$\n", "= \\left(s/(n+g+\\delta) \\right)^{(1+\\theta)} e^{gt}E_0 e^{nt}L_0$\n", "\n", "The labor force will be:\n", "\n", ">(3.1.5) $L^*_t = e^{nt}L_0$\n", "\n", "And labor efficiency will be:\n", "\n", ">(3.1.6) $E^*_t = e^{gt}E_0$\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **3.2. Converging to the Balanced-Growth Equilibrium Path** \n", "\n", "#### **3.2.1. The Dynamics of Capital Intensity** \n", "\n", "But what if $\\kappa ≠ \\kappa^*$? What happens then? Since $s = \\kappa^*(n+g+\\delta)$, we can multiply (2.2.9) by $\\kappa$ and then rewrite it in terms of the equilibrium capital-intensity $\\kappa^*$ as:\n", "\n", ">(3.2.1) $\\frac{d\\kappa}{dt} = s/(1+\\theta) - (n+g+\\delta)\\kappa/(1+\\theta)$\n", "\n", ">(3.2.2) $\\frac{d\\kappa}{dt} = (n+g+\\delta)\\kappa^*/(1+\\theta) - (n+g+\\delta)\\kappa/(1+\\theta)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">(3.2.3) $\\frac{d\\kappa}{dt} = - \\frac{n+g+\\delta}{1+\\theta} (\\kappa-\\kappa^*)$\n", "\n", "This is of the form of the very first differential equations one encounters in mathematics: it is the exponential equation $dx/dt = k x$, with the constant $k$ here equal to $-(n+g+\\delta)/(1+\\theta)$. This equation has the solution, if the value of capital-intensity $\\kappa$ is known at some time $t=0$ to be $\\kappa_0$:\n", "\n", ">(3.2.4) $\\kappa = \\kappa^* + e^{-((n+g+\\delta)/(1+\\theta))t}(\\kappa_0 - \\kappa^*)$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(3.2.3) holds always, for that moment's values of $n, g, \\delta, \\theta$ , and $s$, whatever they may be. \n", "\n", "(3.2.4) holds only while $n, g, \\delta, \\theta$ , and $s$ are constant. If any of them change, you then have to recalibrate and recompute, with a new initial value of $\\kappa_0$, equal to its value when the model's parameters jumped, and a new and different value of $\\kappa^*$. \n", "\n", "If $n, g, \\delta, \\theta$, and $s$are constant or near-constant, then (3.2.4) is a very powerful tool: it tells us that the economy's capital-intensity $\\kappa$ follows over time a path of exponential convergence. It is, at time zero, equal to its initial condition $\\kappa_0$. It then converges towards its asymptote $\\kappa^*$, reducing the gap between its value and $\\kappa^*$ at any time t to a fraction $1/e$ of its previous value as of time $t + \\Delta_{1/e}t$, where this $1/e$ convergence time is:\n", "\n", ">(3.2.5) $\\Delta_{1/e}t = (n+g+\\delta)/(1+\\theta)$.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **3.2.2. Gaining Intuition About the Convergence of Capital-Intensity to $\\kappa^*$** \n", "\n", "Immediately below this paragraph are some Python code cells to help you gain some intuition with respect to the dynamics by which the capital-intensity $\\kappa$ of an economy following the Solow growth model converges to its balanced-growth equilibrium value $\\kappa^*$. Once again, play with the code cells—it is the only way to make the algebra real:\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# CODE CELL: CONVERGENCE OF 𝜅 TO 𝜅^*\n", "#\n", "# this code cell plots how the the economy's\n", "# capital-intensity 𝜅 converges to its steady-\n", "# state balanced-growth level 𝜅^* no matter what\n", "# the initial condition 𝜅_0.\n", "#\n", "# either accept the values given below in the block for \n", "# the parameters s, n, g, 𝛿, and θ, and the intitial\n", "# condition on capital-intensity 𝜅_0, plus the time T \n", "# you wish to calculate convergence for, or substitute \n", "# your own preferred values in the relevant code lines \n", "# in the block. then execute this code cell, and see\n", "# what results:\n", "\n", "# ----\n", "# BEGIN BLOCK\n", "\n", "T = 200\n", "\n", "𝜅_0 = 8\n", "s = 0.20\n", "n = 0.01\n", "g = 0.015\n", "𝛿 = 0.025\n", "θ = 1\n", "\n", "# END BLOCK\n", "# ----\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "𝜅_star = s/(n+g+𝛿)\n", "𝜅_max = 2*𝜅_star\n", "𝜅_min = 0.5\n", "\n", "𝜅_star_series = [𝜅_star]\n", "𝜅_series = [𝜅_0]\n", "\n", "for t in range(T):\n", " 𝜅_star_series = 𝜅_star_series + [𝜅_star]\n", " 𝜅_series = 𝜅_series + [𝜅_star + (𝜅_series[t-1] - 𝜅_star)*np.exp(-(n+g+𝛿)/(1+θ))]\n", "\n", "\n", "𝜅_convergence_df = pd.DataFrame()\n", "𝜅_convergence_df['steady_state_capital_intensity'] = 𝜅_star_series\n", "𝜅_convergence_df['capital_intensity'] = 𝜅_series\n", "\n", "ax = plt.gca()\n", "\n", "𝜅_convergence_df.capital_intensity.plot(ax=ax)\n", "𝜅_convergence_df.steady_state_capital_intensity.plot(ax=ax,\n", " title = 'Convergence of Capital-Intensity')\n", "\n", "ax.set_xlabel(\"Date\")\n", "ax.set_ylabel(\"Capital-Intensity\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# CODE CELL: DEFINITION OF CLASS 𝜅_convergence_graph\n", "#\n", "# this is a reference copy of the 𝜅_convergence_graph\n", "# Python class. it will be kept in the delong_classes\n", "# local file and accessed as:\n", "#\n", "# delong_classes.𝜅_convergence_graph\n", "#\n", "# use this class to plot how the the economy's\n", "# capital-intensity 𝜅 converges to its steady-\n", "# state balanced-growth level 𝜅^* no matter what\n", "# the initial condition 𝜅_0:\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "class 𝜅_convergence_graph:\n", "\n", " def __init__(self, 𝜅_0 = 3,\n", " s = 0.20,\n", " n = 0.01,\n", " g = 0.015,\n", " 𝛿 = 0.025,\n", " θ = 1,\n", " T = 200):\n", " self.𝜅_0, self.s, self.n, self.g, self.𝛿, self.θ, self.T = 𝜅_0, s, n, g, 𝛿, θ, T \n", "\n", " def draw(self):\n", " \"Draw the convergence graph\"\n", " 𝜅_0, s, n, g, 𝛿, θ, T = self.𝜅_0, self.s, self.n, self.g, self.𝛿, self.θ, self.T\n", " 𝜅_star = s/(n+g+𝛿)\n", " 𝜅_max = 2*𝜅_star\n", " 𝜅_min = 0.5\n", "\n", " 𝜅_star_series = [𝜅_star]\n", " 𝜅_series = [𝜅_0]\n", "\n", " for t in range(T):\n", " 𝜅_star_series = 𝜅_star_series + [𝜅_star]\n", " 𝜅_series = 𝜅_series + [𝜅_star + (𝜅_series[t-1] - 𝜅_star)*np.exp(-(n+g+𝛿)/(1+θ))]\n", "\n", "\n", " 𝜅_convergence_df = pd.DataFrame()\n", " 𝜅_convergence_df['steady_state_capital_intensity'] = 𝜅_star_series\n", " 𝜅_convergence_df['capital_intensity'] = 𝜅_series\n", "\n", " ax = plt.gca()\n", " \n", " 𝜅_convergence_df.capital_intensity.plot(ax=ax)\n", " 𝜅_convergence_df.steady_state_capital_intensity.plot(ax=ax,\n", " title = 'Convergence of Capital-Intensity to Steady-State κ*')\n", " \n", " ax.set_xlabel(\"Date\")\n", " ax.set_ylabel(\"Capital-Intensity\")\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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rFEPEYLcgrpFSPieE+D7wPwdKKR8eaMb9YTQIRChvFL3BTzb+hIAMIBDcOvNW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\n4t9Yp/fiYmgnj4M+7p4vB4kgqQu1k1YSptGdatU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# CODE CELL: USING CLASS 𝜅_convergence_graph TO EXAMINE\n", "# THE CONVERGENCE OF A SOLOW GROWTH MODEL'S CAPITAL-\n", "# INTENSITY 𝜅 TO ITS BALANCED-GROWTH VALUE:\n", "#\n", "# 𝜅^* = s/(n+g+𝛿)\n", "#\n", "# either accept the values given below in the block for \n", "# the parameters s, n, g, 𝛿, and θ, and the intitial\n", "# capital-intensity conditions 𝜅_max and 𝜅_reduce, plus \n", "# the time T you wish to calculate convergence for, \n", "# or, alternatively, you can substitute your own preferred\n", "# values in the relevant code lines found inside of\n", "# the code block. then execute this code cell, and see\n", "# what results:\n", "\n", "# ----\n", "# BEGIN BLOCK\n", "\n", "𝜅_max = 10\n", "𝜅_reduce = 2\n", "s = 0.15\n", "n = 0.02\n", "g = 0.015\n", "𝛿 = 0.025\n", "θ = 2\n", "T = 200\n", " \n", "# END BLOCK\n", "# ----\n", "\n", "import delong_classes\n", "\n", "plt.cla()\n", "\n", "𝜅 = 𝜅_max\n", "for i in range(5):\n", " cg = delong_classes.𝜅_convergence_graph(𝜅_0=𝜅, s = s, n = n,\n", " g = g, 𝛿 = 𝛿, θ = θ, T = T)\n", " cg.draw()\n", " 𝜅 = 𝜅-𝜅_reduce\n", "\n", "plt.ylim(0, 𝜅_max)\n", "plt.show()\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "#### **3.2.3. The Dynamics of the Other Variables in the Economy** \n", "\n", "Given:\n", "\n", ">(3.2.4) $\\kappa = \\kappa^* + e^{-((n+g+\\delta)/(1+\\theta))t}(\\kappa_0 - \\kappa^*)$\n", "\n", "knowledge of the initial values of capital-intensity, the labor force , and the efficiency-of-labor $\\kappa_0, L_0,$ and $E_0$; and knowledge of the parameters $s, n, g, \\delta$; and $\\theta$; we can then immediately calculate the values from time $t = 0$, until some parameter shifts, of all the other variables in the economy from ths equations:\n", "\n", ">(3.2.6) $Y_t = \\left(\\kappa_t \\right)^\\theta E_t L_t = \\left(\\kappa_t \\right)^\\theta e^{gt}E_0 e^{nt}L_0$\n", "\n", ">(3.2.7) $y_t = \\left(\\kappa_t \\right)^\\theta E_t = \\left(\\kappa_t \\right)^\\theta e^{gt}E_0$\n", "\n", ">(3.2.8) $K_t = \\kappa_t Y_t$\n", "\n", ">(3.2.9) $L_t = e^{nt}L_0$\n", "\n", ">(3.2.10) $E_t = e^{gt}E_0$\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **3.2.4. Gaining Intuition About Convergence and Shocks** \n", "\n", "Immediately below this paragraph are some Python code cells to help you gain some intuition with respect to the dynamics by which an economy following the Solow growth model converges to and then follows along its balanced-growth path. The first cell below contains a reference copy of the delong_classes.solow Python class. The second cell below plots a six-panel figure showing the behavior of variables of interest for T periods from an arbitrary starting point. This second cell graphs both a baseline scenario, and an alternative scenario showing what happened after a discontinuous jump in parameters, or what would have happened alternatively had parameters jumped. Once again, play with the code cells—it is the only way to make the algebra real:\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# DEFINING THE delong_classes.solow PYTHON CLASS\n", "# \n", "# # this is a reference copy of the 𝜅_convergence_graph\n", "# Python class. it will be kept in the delong_classes\n", "# local file and accessed as:\n", "#\n", "# delong_classes.solow\n", "#\n", "# use this class to model the dynamic behavior of\n", "# an economy well-described by the Solow growth model:\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "class solow:\n", " \n", " \"\"\" \n", " Implements the Solow growth model calculation of the \n", " capital-output ratio κ and other model variables\n", " using the update rule:\n", " \n", " κ_{t+1} = κ_t + ( 1 - α) ( s - (n+g+δ)κ_t )\n", " \n", " Built upon and modified from Stachurski-Sargeant \n", " class **Solow** \n", " \n", " \"\"\"\n", " \n", " def __init__(self, n=0.01, # population growth rate\n", " s=0.20, # savings rate\n", " δ=0.03, # depreciation rate\n", " α=1/3, # share of capital\n", " g=0.01, # productivity\n", " κ=0.2/(.01+.01+.03), # current capital-labor ratio\n", " E=1.0, # current efficiency of labor\n", " L=1.0): # current labor force \n", "\n", " self.n, self.s, self.δ, self.α, self.g = n, s, δ, α, g\n", " self.κ, self.E, self.L = κ, E, L\n", " self.Y = self.κ**(self.α/(1-self.α))*self.E*self.L\n", " self.K = self.κ * self.Y\n", " self.y = self.Y/self.L\n", " self.α1 = 1-((1-np.exp((self.α-1)*(self.n+self.g+self.δ)))/(self.n+self.g+self.δ))\n", " self.initdata = vars(self).copy()\n", " \n", " def calc_next_period_kappa(self):\n", " \"Calculate the next period capital-output ratio.\"\n", " # Unpack parameters (get rid of self to simplify notation)\n", " n, s, δ, α1, g, κ= self.n, self.s, self.δ, self.α1, self.g, self.κ\n", " # Apply the update rule\n", " return (κ + (1 - α1)*( s - (n+g+δ)*κ ))\n", "\n", " def calc_next_period_E(self):\n", " \"Calculate the next period efficiency of labor.\"\n", " # Unpack parameters (get rid of self to simplify notation)\n", " E, g = self.E, self.g\n", " # Apply the update rule\n", " return (E * np.exp(g))\n", "\n", " def calc_next_period_L(self):\n", " \"Calculate the next period labor force.\"\n", " # Unpack parameters (get rid of self to simplify notation)\n", " n, L = self.n, self.L\n", " # Apply the update rule\n", " return (L*np.exp(n))\n", "\n", " def update(self):\n", " \"Update the current state.\"\n", " self.κ = self.calc_next_period_kappa()\n", " self.E = self.calc_next_period_E()\n", " self.L = self.calc_next_period_L()\n", " self.Y = self.κ**(self.α/(1-self.α))*self.E*self.L\n", " self.K = self.κ * self.Y\n", " self.y = self.Y/self.L\n", "\n", " def steady_state(self):\n", " \"Compute the steady state value of the capital-output ratio.\"\n", " # Unpack parameters (get rid of self to simplify notation)\n", " n, s, δ, g = self.n, self.s, self.δ, self.g\n", " # Compute and return steady state\n", " return (s /(n + g + δ))\n", "\n", " def generate_sequence(self, T, var = 'κ', init = True):\n", " \"Generate and return time series of selected variable. Variable is κ by default. Start from t=0 by default.\"\n", " path = []\n", " \n", " # initialize data \n", " if init == True:\n", " for para in self.initdata:\n", " setattr(self, para, self.initdata[para])\n", "\n", " for i in range(T):\n", " path.append(vars(self)[var])\n", " self.update()\n", " return path" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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goOiUU07pkLYppQ4/GjArpbqere/7eP66fjx20WCev64fW99POANee9i7d6/7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\nYKpSx3GE6YUW8rUGyvvuT0ovXB8K62HiQBIYi5uUYQQZ8LPWT9mckwXMx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wUurnRxLRMo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# CODE CELL: SIX-PANEL BASIC SOLOW GROWTH MODEL FIGURE\n", "#\n", "# use this code cell to create a six-panel time-series \n", "# figure of the most interesting economic variables in\n", "# the basic Solow growth model for T periods from an \n", "# arbitrary starting point. \n", "# \n", "# this cell graphs both a baseline scenario, and an \n", "# alternative scenario showing what happened after\n", "# a discontinuous jump in parameters, or what would \n", "# have happened alternatively had parameters jumped.\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import delong_classes\n", "\n", "T = 100\n", "\n", "s_base = delong_classes.solow(κ=4.0)\n", "s_base.scenario = \"base scenario\"\n", "s_alt = delong_classes.solow(κ=0.5)\n", "s_alt.scenario = \"alt scenario\"\n", "\n", "figcontents = {\n", " (0,0):('κ','Capital Output'),\n", " (0,1):('E','Efficiency of Labor'),\n", " (1,0):('L','Labor Force'),\n", " (1,1):('K','Capital Stock'),\n", " (2,0):('Y','Output'),\n", " (2,1):('y','Output-per-worker')\n", " }\n", "\n", "num_rows, num_cols = 3,2\n", "fig, axes = plt.subplots(num_rows, num_cols, figsize=(12, 12))\n", "for i in range(num_rows):\n", " for j in range(num_cols):\n", " for s in s_base, s_alt:\n", " lb = f'{s.scenario}: initial κ = {s.initdata[\"κ\"]}'\n", " axes[i,j].plot(s.generate_sequence(T, var = figcontents[i,j][0]),'o-', lw=2, alpha=0.5, label=lb)\n", " axes[i,j].set(title=figcontents[i,j][1])\n", "\n", "# global legend\n", "axes[(0,0)].legend(loc='upper center', bbox_to_anchor=(1.1,1.3))\n", "plt.suptitle('Solow Growth Model: Simulation Run', size = 20)\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "## **Lecture Notes: The Solow Growth Model** \n", "\n", "\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "* Further reading…\n", "\n", "
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