{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", "\n", "# *Numerical Methods for Economists: The Solow (1956) Model*\n", "\n", "Welcome to the first official *Numerical Methods for Economists* lab session! This focus of this lab session will be solving and simulating the Solow model of economic growth from Chapter 1 of Romer's *Advanced Macroeconomics*. Although Romer's treatment is excellent, I highly recommend reading [Solow's original journal article](http://www.csus.edu/indiv/o/onure/econ200A/Readings/Solow.pdf).\n", "\n", "Here is a quick summary of what we will cover today:\n", "\n", "* **Task 1:** Coding the Solow model in Python.\n", "* **Task 2:** Calibrating the model using data from the Penn World Tables.\n", "* **Task 3:** Graphical analysis of the Solow model using Matplotlib.\n", "* **Task 4:** Assessing the stability of the Solow model.\n", "* **Task 5:** Simulating the Solow model.\n", "* **Task 6:** Finite-difference methods for solving initial value problems.\n", "* **Task 7:** Piece-wise linear interpolation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 1: Coding the Solow model in Python \n", "\n", "In this task you will learn how to program a continuous time version of the Solow model in Python. Before we starting writing code, we should stop and think about the \"primitives\" (i.e., basic bulding blocks) of a Solow model. Writing code that uses the only the most basic bulding blocks will allows us to use the same code to solve and simulate as a general a model as possible.\n", "\n", "The classic Solow growth model is completely described by the equation of motion for capital (per person/effective person)\n", "\n", "\$$\n", " \\dot{k} = sf(k(t)) - (n + g + \\delta)k(t). \\tag{1.1}\n", "\$$\n", "\n", "Thus in order to construct the equation of motion for capital, we need only specify a functional form for $f$ and provide some values for the parameters $s,\\ n,\\ g,\\ \\delta,\\ \\alpha$. A common functional form for technology is the [constant elasticity of substitution (CES)](http://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) production function\n", "\n", "\$$\n", " Y(t) = \\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\tag{1.2}\n", "\$$\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", "\$$\n", " \\lim_{\\rho \\rightarrow 1} Y(t) = \\alpha K(t) + (1-\\alpha)A(t)L(t) \\tag{1.3}\n", "\$$\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", "\$$\n", " \\lim_{\\rho \\rightarrow -\\infty} Y(t) = \\min\\left\\{\\alpha K(t), (1-\\alpha) A(t)L(t)\\right\\} \\tag{1.4}\n", "\$$\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", "\$$\n", " \\lim_{\\rho \\rightarrow 0} Y(t) = K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\tag{1.5}\n", "\$$\n", "\n", "For the remainder of the lab we will work with the intensive form of the Cobb-Douglas prodution technology.\n", "\n", "\$$\n", " y(t) = \\frac{Y(t)}{A(t)L(t)} = f(k) = k(t)^{\\alpha} \\tag{1.6}\n", "\$$\n", "\n", "Now that we have chosen our functional form for production, we are ready to code the Solow model. We being with some standard import statements: \n", "\n", "* **[numpy](http://www.numpy.org/)**: The foundation upon which all scientific computing is Python is built.\n", "* **[pandas](http://pandas.pydata.org/)**: Kick-ass tool for data analysis in Python. Pandas combined with statsmodels can do most all of your econometrics. Pandas is quickly becoming a standard tool for analysis of financial data.\n", "* **[scipy](http://www.scipy.org/)**: SciPy is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. SciPy is built on top of NumPy.\n", "* **[matplotlib](http://matplotlib.org/)**: Primary graphics engine for Python.\n", "* **growth**: A Python module for solving and simulating continuous-time growth models." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import integrate, interpolate, 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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $f(k)$ and $f'(k)$ in Python:\n", "\n", "Once we have settled on the Cobb-Douglas functional form for production, we need to write [Python functions](http://www.greenteapress.com/thinkpython/html/thinkpython007.html) which encode the intensive form of the Cobb-Douglas production technology and the marginal product of capital. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def cobb_douglas_output(t, k, params):\n", " \"\"\"\n", " Cobb-Douglas 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", " \n", " # Cobb-Douglas production function\n", " y = k**alpha\n", " \n", " return y\n", "\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with Cobb-Douglas 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_k: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", "\n", " # marginal product of capital\n", " mpk = alpha * k**(alpha - 1)\n", "\n", " return mpk" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Quick note about docstrings and their importance:** Python documentation strings (or docstrings) provide a convenient way of associating documentation with Python modules, functions, classes, and methods. An object's docsting is defined by including a string constant as the first statement in the object's definition. Writing good docstrings for functions is an important part of of doing reproducible research. Never write a function without a docstring! " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# we can inspect a functions docstring using a question mark...\n", "cobb_douglas_output?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $\\dot{k}$ in Python:\n", "Next we need to write another Python function encoding the equation of motion for capital per effective person." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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", " # equation of motion for capital\n", " k_dot = s * cobb_douglas_output(t, k, params) - (n + g + delta) * k\n", " \n", " return k_dot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $\\frac{\\partial\\dot{k}}{\\partial k}$ in Python:\n", "The final piece of the Solow model is a Python function returning the value of the derivative of the equation of motion for capital (per worker/effective worker) with respect to $k$ (i.e., the [Jacobian](http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant) of the Solow model). " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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 person/effective person) 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", " k_dot = s * marginal_product_capital(t, k, params) - (n + g + delta)\n", " \n", " return k_dot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our model coded, we need to define some parameter values. Recall that the of exogenous parameters of the Solow Model with Cobb-Douglas production are...\n", "\n", "* $s$: savings rate \n", "* $n$: labor force growth rate\n", "* $g$: growth rate of technology \n", "* $\\alpha$: capital share of output \n", "* $\\delta$: rate of capital depreciation\n", "* $L(0)$: Initial value for labor supply.\n", "* $A(0)$: Initial level of technology.\n", " \n", "To store the values of the exogenous parameters of the Solow model we will create a [Python dictionary](http://www.greenteapress.com/thinkpython/html/thinkpython012.html). Where do we get these parameter values? Common method is to pull \"sensible\" values out of ones arse. A better method, which we will cover in the nest task, would be to calibrate the values of the parameters based on real world data. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# sensible parameter values for the Solow model\n", "solow_params = {'alpha':0.33, 'delta':0.04, 'n':0.01, 'g':0.02, 's':0.15, 'A0':1.0, 'L0':1.0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are ready to create an instance of the SolowModel Python class which will represent our Solow model!" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# inspect the SolowModel object...\n", "growth.SolowModel?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create an instance of the SolowModel class representing our model!\n", "solow = growth.SolowModel(output=cobb_douglas_output, \n", " mpk=marginal_product_capital,\n", " k_dot=equation_of_motion_capital, \n", " jacobian=solow_jacobian, \n", " params=solow_params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding the steady state value of $k$ in Python \n", "When analyzing growth models we are often care about the long-run steady state of the model. Because the Solow Model is so simple, we can write down an analytic expression for the steady state value of capital (per worker/effective worker) in terms of the structural parameters of the model. \n", "\n", "\$$\n", " k^* = \\left(\\frac{s}{n+g+\\delta}\\right)^{\\frac{1}{1-\\alpha}} \\tag{1.7}\n", "\$$\n", "\n", "We code this expression as a Python function as follows..." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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", " \n", " return (s / (n + g + delta))**(1 / (1 - alpha))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..and then we add this expression to our SolowModel instance by first creating a Python dictionary containing the steady state expression and adding it to the model. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create a dictionary of steady state expressions...\n", "solow_steady_state_funcs = {'k_star':analytic_k_star}" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# add the dictionary of functions to the model\n", "solow.steady_state.set_functions(func_dict=solow_steady_state_funcs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 2: Calibration:\n", "\n", "In this task we a simple strategy for calibrating a Solow model with Cobb-Douglas production using data from the [Penn World Tables (PWT)](http://www.rug.nl/research/ggdc/data/penn-world-table).\n", "\n", "### Capital depreciation rate, $\\delta$: \n", "The PWT provides estimated depreciation rates that vary across both time and countries. As an estimate for the rate of capital depreciation for country $i$ I use the time-average of $\\verb|delta_k|_{it}$ as provided by the PWT. \n", "\n", "### Capital's share of output/income, $\\alpha$: \n", "Capital's share for country $i$ in year $t$, $\\alpha_{it}$ is computed as $\\alpha_{it} = 1 - \\verb|labsh|_{it}$, where $\\verb|labsh|_{it}$ is the labor share of output/income for country $i$ in year $t$ provided by the PWT. I then use the time-average of $\\alpha_{it}$ as the estimate of capital's share for country $i$.\n", "\n", "### Savings rate, $s$: \n", "As a measure of the savings rate for country $i$, I take the simple time-average of the annual investment share of real GDP, $\\verb|i_sh|$, for country $i$ from the PWT.\n", "\n", "### Labor force growth rate, $n$:\n", "To obtain a measure of the labor force growth rate for country $i$, I regress the logarithm of total employed persons, $\\verb|emp|$, in country $i$ from the PWT on a constant and a linear time trend.\n", "\n", "$$\\ln\\ \\verb|emp|_i = \\beta_0 + \\beta_1 \\verb|t| + \\epsilon_i \\tag{2.1}$$\n", "\n", "The estimated coefficient $\\beta_1$ is then used as my estimate for the $n$. To estimate the initial number of employed persons, $L_0$, I use $e^{\\beta_0}$ as the estimate for $L_0$.\n", "\n", "### Growth rate of technology, $g$:\n", "To obtain a measure of the growth rate of technology for country $i$, I first adjust the total factor productivity measure reported by the PWT, $\\verb|rtfpna|$ (which excludes the human capital contribution to TFP), and then regress the logarithm of this adjusted measure of TFP, $\\verb|atfpna|$, for country $i$ on a constant and a linear time trend.\n", "\n", "$$\\ln\\ \\verb|atfpna|_i = \\beta_0 + \\beta_1 \\verb|t| + \\epsilon_i \\tag{2.2}$$\n", "\n", "The estimated coefficient $\\beta_1$ is then used as my estimate for the $g$. To estimate the initial level of technology, $A_0$, I use $e^{\\beta_0}$ as the estimate for $A_0$.\n", "\n", "All of this is being done \"behind the scenes\". All you need to in order to calibrate the model is pick an [ISO 3 country code](http://en.wikipedia.org/wiki/ISO_3166-1_alpha-3)! Now let's calibrate a Solow model for the UK." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'A0': 0.94757946906339341,\n", " 'L0': 22.66865316643656,\n", " 'alpha': 0.36286396,\n", " 'delta': 0.041320667,\n", " 'g': 0.018602292580074467,\n", " 'n': 0.0036491168322516018,\n", " 's': 0.18750289,\n", " 'sigma': 1.0}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calibrate the Solow model for GBR\n", "growth.calibrate_cobb_douglas(model=solow, iso3_code='GBR')\n", "\n", "# display the results\n", "solow.params" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k* = 5.46097822832\n" ] } ], "source": [ "# display k_star for our chosen parameter values\n", "print 'k* =', analytic_k_star(solow.params)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'k_star': 5.4609782283190977}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compare with our model's dictionary of steady state values \n", "solow.steady_state.values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Short digression about numerical precision:\n", "\n", "The equation of motion for capital (per person/effective person) should return zero when evaluated at the steady state, $k^*$. Let's check whether or not it does..." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "capital(k*) = 0.0\n" ] } ], "source": [ "# very close, but not exactly zero!\n", "print 'capital(k*) =', solow.k_dot(0, analytic_k_star(solow.params), solow.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To a human this is almost, but not \"exactly\", zero. But for most computers there is no difference between this number and *exactly* zero! Why? No computer has infinite precision. Eventually, at a small enough resolution, a computer can no longer tell the difference between two floating point numbers. My computer, which is a 32-bit machine, has the following machine-$\\epsilon$ (i.e., machine \"epsilon\")." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.2204460492503131e-16" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# this is your machine epsilon\n", "np.finfo('float').eps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " If you have a 64-bit computer, then your machine-$\\epsilon$ will be even smaller!. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1: \n", "\n", "#### Part a)\n", "Derive analytical expressions for the deterministic steady state values of output per effective worker, $y$, and consumption per effective worker, $c$, and then use your results to fill in the blanks in the code below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytic_y_star(params): \n", " \"\"\"The steady-state level of output per effective worker.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " y_star = # insert your code here!\n", " \n", " return y_star\n", "\n", "def analytic_c_star(params): \n", " \"\"\"The steady-state level of consumption per effective worker.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " c_star = # insert your code here!\n", " \n", " return c_star" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part b)\n", "Create a new dictionary called new_steady_state_funcs containing the expression for $k^*, y^*,$ and $c^*$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part c)\n", "Use the set_functions method of the SolowModel class's steady_state attribute to add the new dictionary of steady state functions to your model. Then use the set_values method of the steady_state attribute to re-compute the steady state values." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part d)\n", "Examine the resulting dictionary which should now contain three values (one for $k^*, y^*$ and $c^*$)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2:\n", "\n", "Try calibrating your model and computing the steady state values for at least 5 different countries. How different are the steady state values across countries? Are there any groups of countries that you think might have systematically lower/higher steady state values?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 3: Graphical analysis of the Solow model using Matplotlib\n", "\n", "In this task you will learn how to recreate some of the basic diagrams used to analyze the Solow model using the Python library [Matplotlib](http://matplotlib.org/). We start by changing different parameters to see how each change impacts the long-run steady state of the model. We then focus on short-run dynamics by plotting impulse response functions for various parameter changes.\n", "\n", "### Long-run comparative statics" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# set up inline plotting!\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RQmDkyJFwcnLCjz/+qHeeqvu/ISEhWvcNd+/erTV+TEwMunbtqvWHhJubG+zs7DTOCkeP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\nCdys3TRB7WXnhWj3aHjZecHLzgvWJgNn87WlBcjL4we3Wt1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OnAh/f/9OP7O1tcWRI0fw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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a new figure\n", "fig = plt.figure(figsize=(8,6))\n", "\n", "# create a Solow Diagram in one line!\n", "solow.plot_solow_diagram(gridmax=15)\n", "\n", "# Save and display the figure\n", "plt.savefig('graphics/Classic-Solow-Diagram.png')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose that we want to change parameter values of the model in order to see how the Solow diagram changes. The code in the cell below analyzes a doubling of the savings rate." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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+HahcGWjbFvj9d+C99zhimhSR77suLS0Nbm5ucHFxQdu2bbFixYps2wQEBMDU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\nSDo54TVw4EDk5+fDxMQE0dHRWLJkCWJjYxvuyOdzd0dohcz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a new figure\n", "fig = plt.figure(figsize=(8,6))\n", "\n", "# plot comparative statics for the solow model using one line of code!\n", "solow.plot_solow_diagram(gridmax=50, param='s', shock=2.0, reset=True)\n", "\n", "# display the figure\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3:\n", "\n", "Describe how, if at all, each of the following developments affects the break-even and actual-investment lines in our basic diagram for the Solow model:\n", "\n", "#### Part a) \n", "The rate of depreciation, $\\delta$, falls by 10%." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YIOdu27e3dAupAfhPJRPRDDETEdXb8ePA8uVATAxw/Xpl73bNGvZumxj2fImI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\nA15eFn5RiKhJM2/4tmwpq1qoWVCpVTibdRaJWYk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MzAxOTk4AABMTE9jb2yM5OVnkqHQn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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR\n", "%run exercise_3a.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part b)\n", "The rate of technology growth, $g$, doubles." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hdoRUC/yqZCK6LmYioho7dgxYsgSIigJu3DC0bletYuvWzrDlS0SkFo0GWL9e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\n9x1cXFyad6Tm9pLl5cJzbyMjgZMnhdt6xo4V7sMViYTiqMb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR\n", "%run exercise_3b.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part c)\n", "Capital's share of income/output, $\\alpha$, increases by 50%. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VOV5YWBi6dOmC+Ph4Va6LiAiAnBt+5kygUSM5fezPPwPHjgE+PkzuZoBt8MWw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\nuZmxI0cY27SJsTlzGAsLY8zZmTGJhC/OzoyFh/NzmzYxlpnJ7xGbzMx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR\n", "%run exercise_3c.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Short-run comparative statics\n", "\n", "Suppose that we start the Solow economy in steady-state with current parameter values and then at $t=2000$ shock the economy by doubling the savings rate. How should we expect the time-paths of captial, output, and consumption per effective worker to respond? \n", "\n", "We can assess the short-run comparative statics of the Solow model by plotting [impulse response functions (IRFs)](http://en.wikipedia.org/wiki/Impulse_response). The plot_impulse_response method of the SolowModel class can be used to plot three different types of impulse response functions (i.e., efficiency_units, per_capita, or levels) following a multiplicative shock to any of the models exogenous parameters. The syntax for plotting the IRF for a doubling of the savings rate in efficiency units would be as follows... " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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oEHbt2oW+fftWxUeromHDhnj33Xfx7rvv4s6dOwgNDUXLMp7gEx0drVsPDw9H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\ncjgcMsawjAdV7tQpadkya939qVPWOvz33pN69WJpDgAAKF6lfIPuww8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calibrate for the ZWE\n", "growth.calibrate_cobb_douglas(model=solow, iso3_code='ZWE')\n", "\n", "# plot the impulse response function\n", "fig_kwargs = {'figsize':(12,8)}\n", "solow.plot_impulse_response(variables='all', # which variables to plot? 'all', 'k', 'y', 'c'?\n", " param='s', # parameter we wish to shock\n", " shock=1.5, # magnitude of the multiplicative shock\n", " T=100, # length of the IRF \n", " color='b', # color for the irfs \n", " year=1970, # year in which the shock hits\n", " kind='efficiency_units', # what type of IRFs to plot\n", " log=False, # logarithmic scale for y-axis?\n", " reset=True, # reset parameter values following shock?\n", " **fig_kwargs) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Increasing the savings rate will cause both capital and output per effective worker to increase montonically towards their new, higher long-run steady state values. In the short-run, consumption per effective worker must fall; however, the long-run impact on consumption per effective worker is ambiguous and depends on the position of the *ex ante* and *ex post* steady state levels of capital per effecetive worker relative to the \"Golden-rule\" level and the magnitude of the shock." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4:\n", "\n", "Plot impulse response functions for the following parameter changes in efficiency units, per capita units, and levels by changing the kind argument of the plot_impulse_response method to kind=='efficiency_units', kind=='per_capita', kind=='levels', respectively.\n", "\n", "#### Part a) \n", "A positive shock to capital's share, $\\alpha$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0saVrV3vzLMEeAADvx5j9Ajh06JDuvfdepaamKjg4WE8++aQaNmyoKVOmSJIe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\n+q5dbYmM5MZZAPBVhH2HEPYBFLcTJ6S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Wd2++288je7v4ru/Sq69aT7ZNTpYWLZISElw9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\nFizQf/zHf2jNmjUaMGCAJGsFn5ycnFqfQ9hvXd98I61fL61bZ91kGx1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR in efficiency units\n", "%run exercise_4a.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part b)\n", "A negative shock to the population growth rate, $n$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JsjIFQlQhIEBGSIgBjzzyIObNm611N4iIuiSGfg0x9BORo7FVV//77/lITv4N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR in per capita units\n", "%run exercise_4b.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part c)\n", "A negative shock to the growth rate of technology, $g$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nbCgiIjKFlf4Oxko/dUdKpRLnz59HSkoKoqOjERYWZtRm165dsLGxQXR0NAIC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\nx+rdu7ecTqe7PTMzUw899JAqKio0d+5c/eIXv/DhKAGg5Tt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR in per capita units\n", "%run exercise_4c.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part d)\n", "A positive shock to the capital depreciation rate, $\\delta$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Xz9hmw4YN+uyzzzRnzpw8C0lLS1O/fv20dOlSVa9ePR+7UjTGjx+vlStXqm7d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\nQMrJkb7+2lopyFkOHrTqAgKKE/+ICCk83Crt2lmlcWMP/wAAQJ1Hsu8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR in efficiency units\n", "%run exercise_4d.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part e)\n", "A negative shock to the savings rate, $s$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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H8jjm/OtKu4/w8HB169ZNBw4cKNAn3/364MGD5+2vX9J6FrV8+PDhuv766zVt2jQ999xz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\nprrMyTAeXLbNm6XRo2sW9CXJ45GmTJE++kj65BM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# my solution for GBR in efficiency units \n", "%run exercise_4e.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 4: Assessing the stability of the Solow Model \n", "\n", "So long as the initial levels of capital, labor, and technology are all strictly positive, the Solow model is globally stable: given any initial condition for capital per effective worker, $k$, the dynamics of the Solow model will push $k$ towards its long-run, steady state value, $k^*$. This information can be summarized graphically by a phase diagram. The SolowModel class has a method for plotting the phase diagram of the model..." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# calibrate the model to Germany\n", "growth.calibrate_cobb_douglas(model=solow, iso3_code='DEU')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compare to figure 1.3 from Chapter 1 of Romer's text!\n", "fig = plt.figure(figsize=(8,6))\n", "solow.plot_phase_diagram()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The phase diagram suggests another way to assess stability of the Solow model: the derivative of the equation of motion for capital per effective worker should be negative when evaluated at the steady state value, $k^*$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 5:\n", "Evaluate the Jacobian for the Solow model at the steady state value of capital per effective worker and confirm that the result is indeed negative." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can overlay a plot of the linearized equation of motion for capital (per person/effective person) for comparison purposes. For values of $k < k^*$, the linearized equation of motion will lead to an over-estimate of the true speeed of convergence; for value of $k > k^*$, the lineaized equation of motion will lead to an under estimate of the true speed of convergence. " ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ei7XH1jKvxTyK5ShmnxWLiEiKShdF/No1aNUKrl6FOXPMS8SckWGYJ8R9+y0s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\nCrUK1bI6qkg8Kd6d/umnn3LixAk+/fR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "solow.plot_phase_diagram(linearize=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the Germany, the speed of convergence computed using the linearized equation of motion over estimates the true speed of convergence implied by the model by roughly 1.1%." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "k_star = solow.steady_state.values['k_star']\n", "grid = np.linspace(0.5 * k_star, 1.5 * k_star, 1000)\n", "\n", "# percentage approximation error for speed of convergence...\n", "percentage_error = (solow.k_dot(0, grid, solow.params) - solow.linearized_k_dot(grid)) / solow.k_dot(0, grid, solow.params)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.010917816468389819" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# average error\n", "np.mean(percentage_error[np.isfinite(percentage_error)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 5: Simulating the Solow Model\n", "Before discussing these numerical methods we should stop and consider whether or not there are any special cases (i.e., combintions of parameters) for which the Solow model might have an analytic solution. Analytic results can be very useful in building intuition about the economic mechanisms at play in a model and they are invaluable for debugging code and assessing the accurayc of numerical methods.\n", "\n", "It just so happens that the Solow model with Cobb-Douglas production has a general analytic solution!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Analytic solution\n", "The Solow model with Cobb-Douglas production happens to have a completely general analytic solution (see handout for the mathematics if interested in how this result is derived).\n", "\n", "$$k(t) = \\left[\\left(\\frac{s}{n+g+\\delta}\\right)\\left(1 - e^{-(n + g + \\delta) (1-\\alpha) t}\\right) + k_0^{1-\\alpha}e^{-(n + g + \\delta) (1-\\alpha) t}\\right]^{\\frac{1}{1-\\alpha}}$$\n", "\n", "Here is a Python function encoding the analytic solution..." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def solow_analytic_solution(k0, t, params):\n", " \"\"\"\n", " Computes the analytic solution for the Solow model with Cobb-Douglas\n", " production technology.\n", " \n", " Arguments:\n", " \n", " k0: (float) Initial value for capital (per person/effective person) \n", " \n", " t: (array-like) (T,) array of points at which the solution is \n", " desired.\n", " \n", " params: (dict) Dictionary of model parameters.\n", " \n", " Returns:\n", " \n", " analytic_traj: (array-like) (T,2) array representing the analytic \n", " solution trajectory.\n", "\n", " \"\"\"\n", " # extract parameter values\n", " g = params['g']\n", " n = params['n']\n", " s = params['s']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " # lambda governs the speed of convergence\n", " lmbda = (n + g + delta) * (1 - alpha)\n", " \n", " # analytic solution for Solow model at time t\n", " k_t = (((s / (n + g + delta)) * (1 - np.exp(-lmbda * t)) + \n", " k0**(1 - alpha) * np.exp(-lmbda * t))**(1 / (1 - alpha)))\n", " \n", " # combine into a (T, 2) array\n", " analytic_traj = np.hstack((t[:,np.newaxis], k_t[:,np.newaxis]))\n", " \n", " return analytic_traj" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can generate an analytic trajectory for our Solow model like so..." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 5.34659456],\n", " [ 11.11111111, 7.05381168],\n", " [ 22.22222222, 8.25264562],\n", " [ 33.33333333, 9.07063436],\n", " [ 44.44444444, 9.62009231],\n", " [ 55.55555556, 9.98579925],\n", " [ 66.66666667, 10.22784247],\n", " [ 77.77777778, 10.38747556],\n", " [ 88.88888889, 10.49252128],\n", " [ 100. , 10.56154632]])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# specify some initial conditions\n", "k0 = 0.5 * solow.steady_state.values['k_star']\n", "\n", "# grid of t values for which we want to value of k(t)\n", "grid = np.linspace(0, 100, 10)\n", "\n", "# generate a trajectory!\n", "solow_analytic_solution(k0, grid, solow.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...and we can make a plot of this trajectory like so..." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TcHW1ysthqBMRkeN69Ai4dg24eBG4dOnJLfO/FQXw8QG8vHLuQVeoALi5qY+x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\n0KFDjdYLCwsz/H9ISAhC8jqt69mz6uV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# plot this trajectory\n", "analytic_trajectory = solow_analytic_solution(k0, grid, solow.params)\n", "plt.plot(grid, analytic_trajectory[:,1], 'r-')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15, family='serif')\n", "plt.title('Analytic trajectory for the Solow model', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...finally, let's plot trajectories for different initial conditions." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ipk2bhj179uDo0aOwsrLqkPn2qLHiLQIt4LbMDTfm3QCTd+nfI4QQQroxiUQC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\nAWl94EA+dkZEnRdb7OQ3Ll1y3i8/dAgYO1ZqmU+eLA2CIyI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# lower and upper bounds for initial conditions\n", "k_l = 0.5 * solow.steady_state.values['k_star']\n", "k_u = 2.0 * solow.steady_state.values['k_star']\n", "\n", "for k0 in np.linspace(k_l, k_u, 5):\n", " # plot this trajectory\n", " plt.plot(grid, solow_analytic_solution(k0, grid, solow.params)[:,1])\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15, family='serif')\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15, family='serif')\n", "plt.title('Analytic trajectories for the Solow model', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linearized solution:\n", "As discussed in your lectures, a commonly used approach to study the behavior of the Solow model is to linearize the equation of motion for capital (per person/effective person) around its long-run equilibrium value of $k^*$.\n", "\n", "The code in the cell below computes analytic and linearized solution trajectories and then plots them for comparison." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XiYZL0h24PrkB58fX4fLoKlweXoGLYwKcXTQ4l7SDg1sxwNUVcHEx3FxdAWfn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\nLGxtbdG1a1esWLECXbt2zfIxs3qrtkSJElkug6V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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "\n", "# plot analytic and linearized trajectoryies\n", "k0 = 0.5 * solow.steady_state.values['k_star']\n", "grid = np.linspace(0, 100, 100)\n", "\n", "analytic_trajectory = solow_analytic_solution(k0, grid, solow.params)\n", "linearized_trajectory = solow.linearized_solution(k0, grid)\n", "\n", "plt.plot(grid, analytic_trajectory[:,1], 'r-', label='Analytic')\n", "plt.plot(grid, linearized_trajectory[:,1], 'b-', label='Linearized')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15, family='serif')\n", "plt.title('Analytic trajectory for the Solow model', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'})\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the approximation error of the linearized solution using the $L^2$ norm (i.e., euclidean distance).\n", "\n", "$$L^2 \\text{error} = \\left[\\sum_{i=0}^n(traj_{1,i} - traj_{2,i})^2\\right]^{\\frac{1}{2}}$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# inspect the source code for the get_L2_errors method\n", "solow.get_L2_errors??" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.86541144604327747" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the L2 errors\n", "solow.get_L2_errors(analytic_trajectory, linearized_trajectory)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternative way of computing the approximation error of the linearized solution using the $L^{\\infty}$ norm (i.e., maximal distance).\n", "\n", "$$L^{\\infty} \\text{error} = \\max_{i=1,\\dots,n} |traj_{1,i} - traj_{2,i}|$$" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.14817898066327295" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the maximal errors\n", "solow.get_maximal_errors(analytic_trajectory, linearized_trajectory)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the $L^2$ and $L^{\\infty}$ metrics are often used to measure approximation error, it is often not obvious how to interpret their magnitudes. Another measure, that is often more interpretable (if less formal), is to simply normalize the absolute differences between the two trajectories by the analytic solution and take the average." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0085749847823672325" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# absolute percentage errors \n", "np.mean(solow.compare_trajectories(analytic_trajectory, linearized_trajectory)[:,0] / analytic_trajectory[:,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, the absolute magnitude of the approximation error doesn't mean that much (obviously one would like it too be small!). What you should really care about is the size of these errors relative to other approximation methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 6: Finite-difference methods for solving initial value problems\n", "We are finally ready to discuss numerical methods for solving IVPs in general and the Solow model in particular. In general, an initial value problem (IVP) has the form\n", "\n", "\$$\n", "\t\\textbf{y}'= \\textbf{f}(t ,\\textbf{y}),\\ t \\ge t_0,\\ \\textbf{y}(t_0) = \\textbf{y}_0 \\tag{6.1}\n", "\$$\n", "\n", "where $\\textbf{f}:[t_0,\\infty) \\times \\mathbb{R}^n\\rightarrow\\mathbb{R}^n$ and the initial condition $\\textbf{y}_0 \\in \\mathbb{R}^n$ is a given vector. Note that we could also specify an initial value problem by replacing the initial condition with a terminal condition of the form $\\textbf{y}(T) = \\textbf{y}_T$. The key point is that the solution $\\textbf{y}(t)$ is pinned down at one $t\\in[t_0, T]$. In the case where $n=1$, then equation 1.2 reduces to a single differential equation; when $n>1$, equation 1.2 defines a system of ordinary differential equations. Initial value problems are perhaps the most basic example of a functional equation. The unknown in this problem is the function $\\textbf{y}(t): [t_0,T] \\subset \\mathbb{R}\\rightarrow\\mathbb{R}^n$ that satisfies the initial condition $\\textbf{y}(t_0) = \\textbf{y}_0$. So long as the function $\\textbf{f}$ is reasonably well-behaved, the function $\\textbf{y}(t)$ exists and is unique.\n", "\n", "Out Solow model with Cobb-Douglas production can be formulated as an initial value problem (IVP) as follows.\n", "\n", "\$$\n", " \\dot{k} = sk(t)^{\\alpha} - (n+g+\\delta)k(t),\\ t\\ge t_0,\\ k(t_0) = k_0 \\tag{6.1}\n", "\$$\n", "\n", "The solution to this IVP is a function $k(t)$ describing the time-path of capital per effective worker. Our objective in this section will be to explore methods for approximating the function $k(t)$. The methods we will learn are completely general and can be used to solve any IVP. Those interested in learning more about these methods should start by reading Chapter 10 of [*Numerical Methods for Economists*](http://mitpress.mit.edu/books/numerical-methods-economics) by Ken Judd before proceeding to John Butcher's excellent book entitled [*Numerical Methods for solving Ordinary Differential Equations*](http://www.shivanian.com/teaching%20avtivities/Butcher.pdf).\n", "\n", "### Forward Euler method\n", "\n", "The simplest scheme for numerically approximating the solution to an IVP is known as the *forward Euler method*. The basic idea behind the forward Euler method is to estimate the exact solution $k(t)$ by making the approximation $f(t, k(t)) \\approx f(t_0, k(t_0))$ for $t \\in [t_0, t_0 + h]$ and some sufficiently small $h > 0$. \n", "\n", "Integrating the Solow model and applying the Euler approximation yields the following.\n", "\n", "$$k(t) = k(t_0) + \\int_{t_0}^{t} f(\\tau, k(\\tau))d\\tau \\approx k_0 + (t - t_0)f(t_0, k_0) \\tag{6.2}$$\n", "\n", "For some ordered grid of values for $t_0, t_1 = t_0 + h, t_2 = t_0 + 2h, \\dots$, let $k_n$ denote the numerical estimate of the extact solution $k(t_n)$. Applying our approximation scheme to the initial condition yields the Euler estimate for $k_1$.\n", "\n", "$$k_1 = k_0 + h f(t_0, k_0) \\tag{6.3}$$\n", "\n", "Repeated application of the above idea yields a recursive formulation of the forward Euler method \n", "\n", "$$k_{n+1} = k_n + h f(t_n, k_n),\\ n=0,1,\\dots \\tag{6.4}$$\n", "\n", "where $h >0$ denotes the size of the step. \n", "\n", "
\n", " \n", "
\n", "\n", "Note that the forward Euler method \"overshoots\" the solution, $k(t)$, when it is concave. The opposite would be true if the solution had been convex. From the graphic it should be clear that the size of the error will depend criticaly on the choice of the step size, $h$. The step size parameter, $h$, controls the \"fineness\" of the $t$ grid: a smaller step size requires a larger number of grid points to cover any arbitrary interval $[t_0, t_0 + t^*]$. Does the forward Euler method converge to the exact solution, $k(t)$ on the arbitrary interval $[t_0, t_0 + t^*]$ as the step size, $h \\rightarrow 0$, toward zero? Yes it does! How fast does the forward Euler method converge to the true solution? Not very! The approximation error of the forward Euler method is proportional to the step size, $h$, implying that reducing the step size by a factor of 10 only reduces the approximation error by a factor of 10." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# check out the docstring\n", "solow.integrate?" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# solve the model using the forward Euler method\n", "k0 = 0.5 * solow.steady_state.values['k_star']\n", "forward_euler_traj = solow.integrate(t0=0, y0=k0, h=2.0, T=100, integrator='forward_euler')" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 5.34659456],\n", " [ 2. , 5.70623278],\n", " [ 4. , 6.04588732],\n", " [ 6. , 6.36588205],\n", " [ 8. , 6.66672075],\n", " [ 10. , 6.94903571],\n", " [ 12. , 7.21354791],\n", " [ 14. , 7.46103621],\n", " [ 16. , 7.69231342],\n", " [ 18. , 7.90820789],\n", " [ 20. , 8.10954935],\n", " [ 22. , 8.29715814],\n", " [ 24. , 8.47183713],\n", " [ 26. , 8.63436581],\n", " [ 28. , 8.78549597],\n", " [ 30. , 8.92594882],\n", " [ 32. , 9.05641307],\n", " [ 34. , 9.17754395],\n", " [ 36. , 9.28996276],\n", " [ 38. , 9.394257 ],\n", " [ 40. , 9.49098087],\n", " [ 42. , 9.58065603],\n", " [ 44. , 9.66377263],\n", " [ 46. , 9.74079046],\n", " [ 48. , 9.81214017],\n", " [ 50. , 9.87822466],\n", " [ 52. , 9.93942037],\n", " [ 54. , 9.99607873],\n", " [ 56. , 10.04852745],\n", " [ 58. , 10.09707193],\n", " [ 60. , 10.14199653],\n", " [ 62. , 10.18356584],\n", " [ 64. , 10.22202594],\n", " [ 66. , 10.25760554],\n", " [ 68. , 10.2905171 ],\n", " [ 70. , 10.32095791],\n", " [ 72. , 10.34911109],\n", " [ 74. , 10.37514652],\n", " [ 76. , 10.39922181],\n", " [ 78. , 10.42148306],\n", " [ 80. , 10.44206571],\n", " [ 82. , 10.46109527],\n", " [ 84. , 10.47868804],\n", " [ 86. , 10.49495172],\n", " [ 88. , 10.50998606],\n", " [ 90. , 10.52388344],\n", " [ 92. , 10.53672935],\n", " [ 94. , 10.54860295],\n", " [ 96. , 10.55957748],\n", " [ 98. , 10.56972072],\n", " [ 100. , 10.57909539]])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# examine the trajectory\n", "forward_euler_traj" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 3: 47.9 ms per loop\n" ] } ], "source": [ "# how fast is the forward euler method\n", "%timeit -n 1 -r 3 solow.integrate(0, 10, 2.0, 1000, integrator='forward_euler')" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZFfD3Bzp35mNoRDqASZ2IpJ7dduwAli8H7twBPv8cuHKFjd6IdAyr34lKkRzV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\n/k72bWSxsLBA06ZN8ffff+O9994DAPz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the forward euler approximation and the analytic solution\n", "plt.figure(figsize=(8,6))\n", "\n", "grid = forward_euler_traj[:,0]\n", "analytic_trajectory = solow_analytic_solution(k0, grid, solow.params)\n", "\n", "plt.plot(grid, forward_euler_traj[:,1], 'o', markersize=3.0, label='forward Euler')\n", "plt.plot(grid, analytic_trajectory[:,1], 'r-', label='Analytic')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15)\n", "plt.title('Approximation of $k(t)$ using the forward Euler method', fontsize=15, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This simple method already twice as accurate as linearized solution!" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.067926915448746072" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the max approximation error \n", "solow.get_maximal_errors(forward_euler_traj, analytic_trajectory)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Theory tells us that the approximation error of the forward Euler method is proportional to the step size, $h$. Thus if we decrease the step size by a factor of 10, then the approximation error should also fall by a factor of 10. Let's confirm this result... " ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0066323853348002615" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# decrease the step size by a factor of 10\n", "forward_euler_traj_2 = solow.integrate(0, k0, h=0.2, T=100, integrator='forward_euler')\n", "\n", "# compute new analytic trajectory\n", "grid = forward_euler_traj_2[:,0]\n", "analytic_trajectory_2 = solow_analytic_solution(k0, grid, solow.params)\n", "\n", "# compute the max approximation error\n", "solow.get_maximal_errors(forward_euler_traj_2, analytic_trajectory_2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the approximation error..." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# check out the docstring\n", "solow.plot_approximation_error?" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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s9erV7O7du3qVSfW7z79WHQNDIpGwyMhI1qZNG9amTRs2cOBAJpFIlJZRHPtD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\nAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "\n", "# plot the approximation errors\n", "ax, traj_error = solow.plot_approximation_error(forward_euler_traj, analytic_trajectory, log=True)\n", "traj_error.set_label('h=2.0')\n", "traj_error.set_marker('o')\n", "traj_error.set_linestyle('none')\n", "\n", "ax, traj_2_error = solow.plot_approximation_error(forward_euler_traj_2, analytic_trajectory_2, log=True)\n", "traj_2_error.set_label('h=0.2')\n", "traj_2_error.set_marker('o')\n", "traj_2_error.set_linestyle('none')\n", "\n", "# Change the title and add a legend\n", "plt.title('Approximation error using the forward Euler method', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backward Euler's method\n", "The next approximation scheme we are going to look at is called the *backward Euler method*. Starting from the initial condition, $k_0$, the backward Euler method estimates $k(t_1)$ using the following formula.\n", "\n", "$$k_1 = k_0 + h f(t_1, k_1) \\tag{6.5}$$\n", "\n", "This formula is a non-linear equation in the unknown $k_1$ and defines $k_1$ only *implicitly* in terms of $t_0, t_1$, and $k_0$ (all of which are given). Repeated application of the above idea yields a recursive formulation of the backward Euler method \n", "\n", "$$k_{n+1} = k_n + h f(t_{n+1}, k_{n+1}),\\ n=0,1,\\dots \\tag{6.6}$$\n", "\n", "where $h >0$ denotes the size of the step. Note that this method requires solving the same number of non-linear equation as there are grid points $t_n,\\ n=0,1,\\dots$. Lots of different methods exist for solving non-linear equations (or systems of non-linear equations) and solving non-linear equations continues to be a major research topic in numerical analysis. We will touch on some of these methods (the ones that have proven to be of use in economics research) in more detail later in the course. For now, I just want you to remember that you are solving a system of non-linear equations whenever you use any \"implicit\" method for solving an IVP.\n", "\n", "
\n", " \n", "
\n", "\n", "Note that the backward Euler method \"undershoots\" the solution, $k(t)$, but not quite as badly compared with the forward Euler method. The opposite would be true if the solution had been convex. As was the case with the forward Euler method, the backward Euler method is convergent and the approximation error is proportional to the step size, $h$. In practice, implicit methods like the backward Euler method have proven to be more \"stable\" (i.e., implicit methods don't always accumulate approximation error as fast as explicit methods) than explicit methods like the forward Euler method and for this reason most \"industrial strength\" IVP solvers tend to be at least partially implicit. " ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# solve the model using the backward Euler method\n", "backward_euler_traj = solow.integrate(0, k0, h=2.0, T=100, integrator='backward_euler')" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 5.34659456],\n", " [ 2. , 5.68732199],\n", " [ 4. , 6.00945951],\n", " [ 6. , 6.3134753 ],\n", " [ 8. , 6.59994302],\n", " [ 10. , 6.86950953],\n", " [ 12. , 7.12286994],\n", " [ 14. , 7.36074818],\n", " [ 16. , 7.58388198],\n", " [ 18. , 7.79301129],\n", " [ 20. , 7.98886939],\n", " [ 22. , 8.1721761 ],\n", " [ 24. , 8.34363276],\n", " [ 26. , 8.50391853],\n", " [ 28. , 8.65368775],\n", " [ 30. , 8.79356821],\n", " [ 32. , 8.92416007],\n", " [ 34. , 9.04603529],\n", " [ 36. , 9.15973754],\n", " [ 38. , 9.26578244],\n", " [ 40. , 9.36465799],\n", " [ 42. , 9.45682526],\n", " [ 44. , 9.54271918],\n", " [ 46. , 9.6227495 ],\n", " [ 48. , 9.69730174],\n", " [ 50. , 9.76673822],\n", " [ 52. , 9.83139917],\n", " [ 54. , 9.89160373],\n", " [ 56. , 9.94765107],\n", " [ 58. , 9.99982143],\n", " [ 60. , 10.04837711],\n", " [ 62. , 10.09356352],\n", " [ 64. , 10.13561012],\n", " [ 66. , 10.17473137],\n", " [ 68. , 10.21112759],\n", " [ 70. , 10.24498583],\n", " [ 72. , 10.27648071],\n", " [ 74. , 10.30577516],\n", " [ 76. , 10.33302115],\n", " [ 78. , 10.35836041],\n", " [ 80. , 10.38192509],\n", " [ 82. , 10.40383833],\n", " [ 84. , 10.4242149 ],\n", " [ 86. , 10.44316173],\n", " [ 88. , 10.46077843],\n", " [ 90. , 10.47715775],\n", " [ 92. , 10.49238607],\n", " [ 94. , 10.50654381],\n", " [ 96. , 10.51970585],\n", " [ 98. , 10.53194186],\n", " [ 100. , 10.5433167 ]])" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "backward_euler_traj" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 3: 236 ms per loop\n" ] } ], "source": [ "# how fast is the backwards Euler method?\n", "%timeit -n 1 -r 3 solow.integrate(0, 10, 2.0, 1000, integrator='backward_euler') " ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1BAbC+PFQunS6i1MHN8ktsqWmnpyIiAiqVasGQLVq1di2bZujQhGRnODgQfji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\nX79+GDZsmGvZ7zLdt28fIiIiEBkZCbPZ3Oz6vbb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the backwards Euler approximation and the analytic solution\n", "plt.figure(figsize=(8,6))\n", "\n", "grid = backward_euler_traj[:,0]\n", "\n", "plt.plot(grid, backward_euler_traj[:,1], 'go', markersize=3.0, label='backward Euler')\n", "plt.plot(grid, analytic_trajectory[:,1], 'r-', label='Analytic')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15)\n", "plt.title('Approximation of $k(t)$ using the backward Euler method', fontsize=15)\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.064456094680954479" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the max approximation error...slightly better than the forward Euler method\n", "solow.get_maximal_errors(backward_euler_traj, analytic_trajectory)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trapezoidal rule\n", "The Euler method approximates the derivative of the solution by a constant in the interval $[t_n, t_{n+1}]$. Specifically, Euler's method assumes that the slope of the solution in the interval is equal to its value at the left end point, $f(t_n, y_n)$. Intuitively one might guess that a better way to approximate the derivative of the solution by a constant in the interval would be to take a simple average of the slope of the solution at both end points. This simple intuition is formalized by the following approximation scheme\n", "\n", "\\begin{align}\n", "\ty(t) =& y(t_n) + \\int_{t_n}^{t} f(\\tau, y(\\tau))d\\tau \\notag \\\\\n", "\t\\approx& y(t_n) + \\frac{1}{2}(t - t_n)f(t_0, y(t_n)) + \\frac{1}{2}(t - t_n)f(t_{n+1}, y(t_{n+1})) \\tag{6.7}\n", "\\end{align} \n", "\n", "which leads to the *trapezoidal rule*.\n", "\n", "\$$\n", "\ty_{n+1} = y_n + \\frac{1}{2}hf(t_0, y_n) + \\frac{1}{2}hf(t_{n+1}, y_{n+1}) \\tag{6.8}\n", "\$$\n", "\n", "Do we know that the trapezoidal rule converges to the exact solution $y(t)$ on the arbitrary interval $[t_0, t_0 + t^*]$ as we shrink the step size $h$ toward zero?. Yes! How fast does the trapezoidal rule converge to the exact solution? The trapezoidal rule can be shown to converge quadratically to the exact solution. This means that unlike the forward and backward Euler methods, which were only linearly convergent, with the trapezoidal rule, shrinking the step size by a factor of 10 will reduce the approximation error by a factor of $10^2$ = 100!\n", "\n", "
\n", " \n", "
\n", "\n", "The higher order of convergence means that the trapezoidal rule can often make due with a larger step size than the Euler method while still maintaining the same level of approximation error. However, the improved convergence properties of the trapezoidal rule do not come free (remember that there is no such thing as a free lunch!). The trapezoidal method is an implicit method, and each step requires solving a non-linear equation in the unknown $k_{n+1}$ as well as extra evaluation of the function $f$. In practice, however, the more rapid convergence of the trapezoidal method and ability to use a larger step size often more than compensate for the additional computational burden. " ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# solve the model using the trapezoidal rule\n", "trapezoidal_rule_traj = solow.integrate(0, k0, h=2.0, T=100, integrator='trapezoidal_rule')" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 5.34659456],\n", " [ 2. , 5.69651671],\n", " [ 4. , 6.02716816],\n", " [ 6. , 6.33895315],\n", " [ 8. , 6.63241531],\n", " [ 10. , 6.90819667],\n", " [ 12. , 7.16700587],\n", " [ 14. , 7.40959359],\n", " [ 16. , 7.63673345],\n", " [ 18. , 7.84920733],\n", " [ 20. , 8.0477941 ],\n", " [ 22. , 8.23326101],\n", " [ 24. , 8.40635729],\n", " [ 26. , 8.56780944],\n", " [ 28. , 8.7183178 ],\n", " [ 30. , 8.85855433],\n", " [ 32. , 8.9891611 ],\n", " [ 34. , 9.11074957],\n", " [ 36. , 9.22390028],\n", " [ 38. , 9.3291631 ],\n", " [ 40. , 9.42705761],\n", " [ 42. , 9.51807388],\n", " [ 44. , 9.60267335],\n", " [ 46. , 9.68128984],\n", " [ 48. , 9.75433066],\n", " [ 50. , 9.82217778],\n", " [ 52. , 9.88518903],\n", " [ 54. , 9.94369932],\n", " [ 56. , 9.99802178],\n", " [ 58. , 10.04844905],\n", " [ 60. , 10.09525433],\n", " [ 62. , 10.13869257],\n", " [ 64. , 10.17900155],\n", " [ 66. , 10.21640289],\n", " [ 68. , 10.25110307],\n", " [ 70. , 10.28329441],\n", " [ 72. , 10.31315589],\n", " [ 74. , 10.34085412],\n", " [ 76. , 10.36654406],\n", " [ 78. , 10.39036982],\n", " [ 80. , 10.4124654 ],\n", " [ 82. , 10.43295534],\n", " [ 84. , 10.45195539],\n", " [ 86. , 10.46957306],\n", " [ 88. , 10.48590825],\n", " [ 90. , 10.50105373],\n", " [ 92. , 10.51509562],\n", " [ 94. , 10.52811392],\n", " [ 96. , 10.54018286],\n", " [ 98. , 10.55137136],\n", " [ 100. , 10.56174336]])" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trapezoidal_rule_traj" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 3: 304 ms per loop\n" ] } ], "source": [ "# how fast is the trapezoidal rule\n", "%timeit -n 1 -r 3 solow.integrate(0, 10, h=2.0, T=1000, integrator='trapezoidal_rule')" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9oW1bJXQRO6Fr6iLZ2fnzMHky/PADVKkC//kPd+vU4avxg2ADul4uYmfU/S6S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\n5NSqVQtXV1fL36lpqa9atYqDBw8ybtw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the trapezoidal rule approximation and the analytic solution\n", "plt.figure(figsize=(8,6))\n", "\n", "grid = trapezoidal_rule_traj[:,0]\n", "\n", "plt.plot(grid, trapezoidal_rule_traj[:,1], 'yo', markersize=3.0, label='trapezoidal rule')\n", "plt.plot(grid, solow_analytic_solution(k0, grid, solow.params)[:,1], 'r-', label='Analytic')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15)\n", "plt.title('Approximation of $k(t)$ using the trapezoidal rule', fontsize=15)\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.00056222209814471569" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the max approximation error for the trapezoidal rule\n", "solow.get_maximal_errors(trapezoidal_rule_traj, analytic_trajectory)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# decrease the step size by a factor of 10...\n", "trapezoidal_rule_traj_2 = solow.integrate(0, k0, h=0.2, T=100, integrator='trapezoidal_rule')" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5.6228340188368975e-06" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute the max approximation error for the trapezoidal rule\n", "solow.get_maximal_errors(trapezoidal_rule_traj_2, analytic_trajectory_2)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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S09P1Aoc+ffqgT58+Zrczfvx47bMYAPW45M4c056IiKimcunAQS6ff/452+qI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\nrAwZGRnM09+0remjKzd//vknNmzYgOzsbCiVysf65/JppS1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the approximation error\n", "fig = plt.figure(figsize=(8,6))\n", "\n", "# plot the approximation errors\n", "ax, traj_error = solow.plot_approximation_error(trapezoidal_rule_traj, analytic_trajectory, log=True)\n", "traj_error.set_label('h=2.0')\n", "traj_error.set_marker('o')\n", "traj_error.set_linestyle('none')\n", "\n", "ax, traj_2_error = solow.plot_approximation_error(trapezoidal_rule_traj_2, analytic_trajectory_2, log=True)\n", "traj_2_error.set_label('h=0.2')\n", "traj_2_error.set_marker('o')\n", "traj_2_error.set_linestyle('none')\n", "\n", "# Change the title and add a legend\n", "plt.title('Approximation error using the trapezoidal rule', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 7: Piece-wise Linear Interpolation\n", "\n", "The above approximation schemes all discretize the independent variable, $t$, and approximate the function $k(t)$ at only a finite number of grid points. What if we need to approximate the value of $k(t)$ in between grid points? Approximating the values of a function between grid points is called interpolation (interpolation happens to be a special case of another technique with which you are already very familiar...namely regression!).\n", "\n", "The specific interpolation routine that we will use is called [piece-wise linear interpolation](http://en.wikipedia.org/wiki/Linear_interpolation). Linear interpolation is the most basic a method of approximating the value of a function between two points. When you connect two dots with a straight line you are doing linear interpolation. Formally, linear interpolation approximates the function $k$ on the interval $t\\in[t_n, t_{n+1}]$ as \n", "\n", "$$k(t) \\approx k_n + \\frac{t - t_n}{t_{n+1} - t_n}(k_{n+1} - k_n). \\tag{7.1}$$\n", "\n", "Here is a nice graphic that gives the basic intuition linear interpolation...\n", "\n", "
\n", " \n", "
\n", "\n", "Linear interpolation is a simple, yet robust method, and it will usually be a good place to start when doing your own research projects." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# always check the docstring!\n", "solow.interpolate?" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create some grid of values for t\n", "grid = np.linspace(0, 100, 1000)\n", "\n", "# simulate a trajectory using linear interpolation to fill in the values between nodes\n", "interp_trapezoidal_rule_traj = solow.interpolate(traj=trapezoidal_rule_traj, ti=grid, k=1)\n", "\n", "# compute new analytic trajectory\n", "analytic_trajectory_3 = solow_analytic_solution(k0=k0, t=grid, params=solow.params)" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3hSI0HG7dXoJLg7a8FZbKzBHaPRYhRESlZNDkIDtmI7T7foUiOhbuJ25DKBXI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\nEisnJwejRo1CWlqa2R1hp0+fjszMTKSkpMDb2xu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the trapezoidal rule approximation and the analytic solution\n", "plt.figure(figsize=(8,6))\n", "\n", "plt.plot(grid, interp_trapezoidal_rule_traj[:,1], 'y', markersize=3.0, label='Trapezoidal rule (linear)')\n", "plt.plot(grid, analytic_trajectory_3[:,1], 'r-', label='Analytic')\n", "\n", "# demarcate k*\n", "plt.axhline(solow.steady_state.values['k_star'], linestyle='dashed', \n", " color='k', label='$k^*$')\n", "\n", "# axes, labels, title, etc\n", "plt.xlabel('Time, $t$', fontsize=15)\n", "plt.ylabel('$k(t)$', rotation='horizontal', fontsize=15)\n", "plt.title('Approximating $k(t)$ using the trapezoidal rule, redux', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MDAwMDBww5MDAwMDAwMDAgWpDDky1goGBgYGBQTCYagUDAwMDAwMDB6qNcmBg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the approximation error\n", "fig = plt.figure(figsize=(8,6))\n", "\n", "# plot the approximation errors\n", "ax, traj_error = solow.plot_approximation_error(interp_trapezoidal_rule_traj, analytic_trajectory_3, log=True)\n", "traj_error.set_label('h=2.0')\n", "\n", "# Change the title and add a legend\n", "plt.title('Trapezoidal rule with linear interpolation', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "None of the approximation schemes that we discussed today are robust enough to use in your own research. However all of the more sophisticated solvers are based on the same principles used in the approaches detailed above and in your notes. The point of this task was not to expose you to state of the art methods, but rather to give you some intuition as to how the more robust and sophisticated methods work. \n", "\n", "Four of the best, most widely used ODE integrators have been implemented in the scipy.integrate module (they are called dopri5, dop85, lsoda, and vode). Each of these integrators uses some type of adaptive step-size control: the integrator adaptively adjusts the step size $h$ in order to keep the approximation error below some user-specified threshold). The cells below contain code which compares the approximation error of the forward Euler with those of [lsoda](http://computation.llnl.gov/casc/nsde/pubs/u113855.pdf) and [vode](http://jeffreydk.site50.net/papers/BDFmethodpaper.pdf). Instead of simple linear interpolation (i.e., k=1), I set k=5 for 5th order [B-spline](http://en.wikipedia.org/wiki/B-spline) interpolation." ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# grid of interpolatiom points\n", "interp_grid = np.linspace(0, 200, 1000)\n", "\n", "# solve using the lsoda integrator\n", "kwargs={'with_jacobian':True, 'rtol':1e-9}\n", "lsoda_traj = solow.integrate(0, k0, 1.0, T=200, integrator='lsoda', **kwargs)\n", "lsoda_traj_interp = solow.interpolate(lsoda_traj, interp_grid, k=5)\n", " \n", "# solve using the vode integrator\n", "kwargs={'with_jacobian':True, 'method':'adams', 'rtol':1e-9}\n", "vode_traj = solow.integrate(0, k0, 1.0, T=200, integrator='vode', **kwargs)\n", "vode_traj_interp = solow.interpolate(vode_traj, interp_grid, k=5)\n", "\n", "# solve using the trapezoidal rule\n", "am1_traj = solow.integrate(0, k0, 1.0, T=200, integrator='backward_euler')\n", "am1_traj_interp = solow.interpolate(am1_traj, interp_grid, k=5)\n", "\n", "# compute the analytic trajectory\n", "grid = lsoda_traj[:,0]\n", "analytic_trajectory = solow_analytic_solution(k0, interp_grid, solow.params)\n", "\n", "# compute the linearized trajectory\n", "linearized_trajectory = solow.linearized_solution(k0, interp_grid)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/mfP44HXL4XAeJ/x2PIfzjPLXX39h8+bNOHv2LLKysmBoaIgOHTogIiICb7/9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\nG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "colors = mpl.cm.jet(np.linspace(0, 1, 4))\n", "\n", "# plot the approximation error for lsoda\n", "traj_error = solow.plot_approximation_error(lsoda_traj_interp, \n", " analytic_trajectory, \n", " log=True)[1]\n", "traj_error.set_label('lsoda')\n", "traj_error.set_color(colors[0])\n", "\n", "# plot the approximation error for vode\n", "traj_error_2 = solow.plot_approximation_error(vode_traj_interp, \n", " analytic_trajectory, \n", " log=True)[1]\n", "traj_error_2.set_label('vode')\n", "traj_error_2.set_color(colors[1])\n", "\n", "# plot the approximation error for trapezoidal rule\n", "traj_error_3 = solow.plot_approximation_error(am1_traj_interp, \n", " analytic_trajectory, \n", " log=True)[1]\n", "traj_error_3.set_label('Backward Euler')\n", "traj_error_3.set_color(colors[2])\n", "\n", "# plot the approximation error for linearized trajectory\n", "traj_error_4 = solow.plot_approximation_error(linearized_trajectory, \n", " analytic_trajectory, \n", " log=True)[1]\n", "traj_error_4.set_label('Linearization')\n", "traj_error_4.set_color(colors[3])\n", "\n", "# demarcate machine eps\n", "plt.axhline(np.finfo('float').eps, color='k', ls='--', \n", " label=r'Machine-$\\epsilon$')\n", "\n", "# change the title and add a legend\n", "plt.ylim(1e-18, 1e0)\n", "plt.title('The benefits of using adaptive step-size control\\n' + \n", " 'with linear multi-step methods', fontsize=20, family='serif')\n", "plt.legend(loc='best', frameon=False, prop={'family':'serif'}, bbox_to_anchor=(1.025, 1.0))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.4" } }, "nbformat": 4, "nbformat_minor": 0 }