python/Python for Economists.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Economists\n",
    "<center>\n",
    "**Randall Romero-Aguilar PhD**\n",
    "<br>    \n",
    "[rromero@secmca.org](mailto:rromero@secmca.org)\n",
    "</center>    \n",
    "\n",
    "<br>\n",
    "<br>\n",
    "<p style=\"font-size:12px\">This article originally appeared in Spanish as [SECMCA Regional Economic Notes No. 93](http://www.secmca.org/NOTAS_ECONOMICAS/articulo93NOV2017.pdf) in December 2017.  This Jupyter notebook is a slightly modified version of the original, and was prepared on July 28, 2018.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of programming languages has become increasingly necessary in many of the tasks that we economist do, either because the theoretic models we develop lack analytic solutions, or because the new econometric estimator we wish to use is not yet available in a program with a graphical user interface (GUI, where we could just click with a mouse), or just because it is not efficient to analyze huge datasets with spreadsheets.\n",
    "\n",
    "<br>\n",
    "Those who wish to exploit the advantages of programming to do these tasks must first decide which of many programming languages to learn. For instance, to a greater or lesser extend the languages R, Python, Julia, Fortran, Gauss, and MATLAB are all used by economists. MATLAB has been especially popular in this field, and there are many tools that have been developed to be run in this program, among them [DYNARE](http://www.dynare.org/) and [IRIS](https://github.com/IRIS-Solutions-Team/IRIS-Toolbox/wiki/IRIS-Macroeconomic-Modeling-Toolbox) (to solve and estimate DSGE models), [CompEcon](http://www4.ncsu.edu/~pfackler/compecon/toolbox.html) (for computational economics), and [Econometrics](http://www.spatial-econometrics.com/) (for spacial econometrics).\n",
    "\n",
    "<br>\n",
    "Despite the fact that Python is not yet as popular as [MATLAB](https://www.mathworks.com) among economists, its popularity has certainly skyrocketed in recent years. For example, the following books use Python to do typical economists tasks:\n",
    "\n",
    "* [QuantEcon](http://www.quantecon.org/) by Thomas Sargent and John Stachurski.\n",
    "* [Economic Dynamics: Theory and Computation](http://www.amazon.com/dp/0262012774/ref=rdr_ext_tmb), by Stachurski.\n",
    "* [Python for Econometrics](http://www.kevinsheppard.com/Python_for_Econometrics), by Kevin Sheppard.\n",
    "\n",
    "<br>\n",
    "Python is a versatile and easy-to-learn language ---in fact [it is used extensively](http://m.cacm.acm.org/blogs/blog-cacm/176450-python-is-now-the-most-popular-introductory-teaching-language-at-top-us-universities/fulltext) in America's best universities to teach introductory programming courses. Its syntax is very clear, which makes developing and maintaining code easy. Because it is one of the most popular languages among computer programmers, there are abundant resources to learn it (books, Internet pages). It is an excellent tool to perform scientific calculation tasks (thanks to packages such as [Numpy](http://www.numpy.org/) and [Scipy](https://scipy.org/)), data management ([Pandas](http://pandas.pydata.org/)), visualization ([Matplotlib](http://matplotlib.org/)) and econometric modeling ([Statsmodels](http://www.statsmodels.org)).\n",
    "\n",
    "<br>\n",
    "Another advantage of using Python is that, unlike proprietary programs, Python and many of these complementary packages are completely free. The best way to get Python is through [Anaconda](https://www.continuum.io/downloads), a free distribution that includes more than 300 very useful packages in science, mathematics, engineering, and data analysis. Besides Python, Anaconda includes tools such as IPython (to run Python interactively), [Jupyter](http://jupyter.org/) (an editor that allows combining text, code and results in a single file, excellent for documenting your work), Spyder (a GUI for code editing, similar to that of MATLAB) and Conda (allows to install and update packages).\n",
    "\n",
    "<br>\n",
    "If you want to start working with Python, you should consider two issues. First, there are currently two versions of Python that are not entirely compatible with each other, the 2 (whose last update is 2.7) and the 3 (currently updated to 3.6). Personally, I recommend working with version 3.6 because it has significant improvements over version 2.7, and most of the packages needed to work in typical economists tasks have already been ported to 3.6.\n",
    "\n",
    "<br>\n",
    "Second, although Spyder facilitates code editing, more advanced users may prefer [PyCharm](https://www.jetbrains.com/pycharm/download/), an excellent Python editor whose “Community” version can be used for free. This editor makes it much easier to edit programs, because of features such as *autocomplete* (especially useful when we have not yet memorized Python functions), *syntax highlighting* (shows keywords in different color, to make it easier to understand the code's logic), and *debugger* (to partially run a program when it is necessary to find a bug).\n",
    "\n",
    "\n",
    "<br>\n",
    "The purpose of this note is to illustrate some of the common tasks that economists can do using Python. First, we use numerical techniques to solve two Cournot competition models presented by Miranda and Fackler (2002) using the \"CompEcon-python\" package (<small>This package was developed by the author and is based precisely on the *CompEcon toolbox*  for MATLAB from Miranda and Fackler</small>), which is freely available at [Github](https://github.com/randall-romero/CompEcon-python) (<small>Readers interested in the topic of computational economics will find more of these examples in Romero-Aguilar (2016)</small>). Second, it illustrates how to automate the collection of Internet data and its presentation in tables and graphs. Third, some examples of econometric models estimated with Python are shown.\n",
    "\n",
    "<br>\n",
    "For each of the problems, I provide Python code to solve it, along with brief explanations of how this code works. However, this note is not intended to teach programming in Python because, as mentioned above, there are already many high quality teaching resources for this purpose, including the site of [Google developers](https://developers.google.com/edu/python/), the site [learnpython](https://www.learnpython.org/), and several online courses at [edx](https://www.edx.org/course?search_query=python). Likewise, in the first two examples, the numerical methods implemented in Python are presented concisely, but readers interested in this topic are advised to consult the textbooks of Miranda and Fackler (2002), Judd (1998), and Press (2007)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1: A 2-firms Cournot model\n",
    "\n",
    "<br>\n",
    "Assume the market is controlled by two firms that compete with each other. For this duopoly, the inverse of the demand function is given by\n",
    "\\begin{equation*}\n",
    "P(q) = q^{-\\alpha}\n",
    "\\end{equation*}\n",
    "and both firms face quadratic costs\n",
    "\\begin{align*}\n",
    "C_1 &= \\tfrac{1}{2}\\beta_1q_1^2 \\\\\n",
    "C_2 &= \\tfrac{1}{2}\\beta_2q_2^2 \n",
    "\\end{align*}\n",
    "\n",
    "Firms profits are\n",
    "\\begin{align*}\n",
    "\\pi_1\\left(q_1, q_2\\right) &=P\\left(q_1+q_2\\right)q_1 - C_1\\left(q_1\\right) \\\\\n",
    "\\pi_2\\left(q_1, q_2\\right) &=P\\left(q_1+q_2\\right)q_2 - C_2\\left(q_2\\right) \n",
    "\\end{align*}\n",
    "\n",
    "In a Cournot equilibrium, each firm maximizes its profits taking as given the other firm's output. Thus, it must follow that \n",
    "\\begin{align*}\n",
    "\\frac{\\partial \\pi_1\\left(q_1, q_2\\right)}{\\partial q_1} &= P\\left(q_1+q_2\\right) + P'\\left(q_1+q_2\\right)q_1 - C'_1\\left(q_1\\right) = 0\\\\\n",
    "\\frac{\\partial \\pi_2\\left(q_1, q_2\\right)}{\\partial q_2}  &= P\\left(q_1+q_2\\right) + P'\\left(q_1+q_2\\right)q_2 - C'_2\\left(q_2\\right) = 0\n",
    "\\end{align*}\n",
    "\n",
    "Therefore, equilibrium output levels for this market are given by the solution to this nonlinear equation system\n",
    "\\begin{equation} \\label{eq:fzero}\n",
    "f\\left(q_1, q_2\\right) = \\begin{bmatrix}\n",
    "\\left(q_1+q_2\\right)^{-\\alpha} - \\alpha q_1 \\left(q_1+q_2\\right)^{-\\alpha - 1} - \\beta_1q_1 \\\\\n",
    "\\left(q_1+q_2\\right)^{-\\alpha} - \\alpha q_2 \\left(q_1+q_2\\right)^{-\\alpha - 1} - \\beta_2q_2\\end{bmatrix} \n",
    "= \\begin{bmatrix}0 \\\\ 0\\end{bmatrix}\\tag{1}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton's method\n",
    "To find the root of the function defined in (1) we will use Newton's method. In general, this method is applied to the function $f: \\Re^n \\to \\Re^n$ to find some (<small>Notice that, depending on the function, there could be more than one solution, or no solution at all.</small>) value $x^*$ such that $f(x^*)=0$. To that end, we start with a value $x_0 \\in \\Re^n$ and make the recursion\n",
    "\\begin{equation}\\label{eq:newton}\n",
    "x_{i+1} = x_i - J^{-1}(x_i) f(x_i) \\tag{2}\n",
    "\\end{equation}\n",
    "where $J(x_i)$ corresponds to the Jacobian of $f$ evaluated at $x_0$. In theory, following this recursion $x_i$ converges to $x^*$ as long as the $f$ function is continuously differentiable and the initial value $x_0$ is “sufficiently close” to the $x^*$ root."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving the model with Python\n",
    "\n",
    "First, we begin a Python session and import `compecon`.  This package is available in pip, and can be installed by typing\n",
    "    \n",
    "    pip install compecon\n",
    "\n",
    "in a command window.    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from compecon import NLP, gridmake\n",
    "from compecon.demos import demo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To solve this model computationally, we need to assign values to the parameters, so we set $\\alpha=0.625$, $\\beta_1=0.6$ and $\\beta_2=0.8$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.625\n",
    "beta = np.array([0.6, 0.8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The unknowns in our problem are the firms' output levels, $q_1$ and $q_2$. We define the `market` function to tell us total output and resulting price, given the levels of $q_1$ y $q_2$. Notice that both quantities are passed to this function in the  `q` vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def market(q):\n",
    "    quantity = q.sum()\n",
    "    price = quantity ** (-alpha)\n",
    "    return price, quantity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we define the `cournot` function, returning a two-element tuple: the objective function and its Jacobian matrix, both evaluated in a pair of quantities contained by the `q` vector. To make the code easier, notice that the (1) function can be written more succinctly as\n",
    "\\begin{equation*} \n",
    "f\\left(q_1, q_2\\right) = \\begin{bmatrix}\n",
    "P + \\left(P' - c_1\\right)q_1 \\\\\n",
    "P + \\left(P' - c_2\\right)q_2\\end{bmatrix}\n",
    "= \\begin{bmatrix}0 \\\\ 0\\end{bmatrix}\n",
    "\\end{equation*}\n",
    "and its Jacobian matrix is\n",
    "\n",
    "\\begin{equation*} \n",
    "J\\left(q_1, q_2\\right) = \\begin{bmatrix}\n",
    "2P' + P''q_1 - c_1 & P' + P''q_1 \\\\\n",
    "P' - P''q_2 & 2P' + P''q_2 - c_2\\end{bmatrix}\n",
    "\\end{equation*}\n",
    "\n",
    "<br>\n",
    "If we define total output as $Q=q_1 + q_2$, notice also that \n",
    "\\begin{equation*}\n",
    "P' = -\\alpha\\frac{P}{Q} \\qquad\\text{y que} \\qquad P''=-(\\alpha+1)\\frac{P'}{Q}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cournot(q):\n",
    "    P, Q = market(q)\n",
    "    P1 = -alpha * P/Q\n",
    "    P2 = (-alpha - 1) * P1 / Q\n",
    "    fval = P + (P1 - beta) * q\n",
    "    fjac = np.diag(2*P1 + P2*q - beta) + np.fliplr(np.diag(P1 + P2*q))\n",
    "    return fval, fjac"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we compute the equilibrium using Newton's method (equation (2)) to find the root of the `cournot` function. We set $q_0 = \\begin{bmatrix}0.2 & 0.2\\end{bmatrix}'$ as our initial value and iterate until the norm of the change between two successive values of the recursion is less than $10^{-10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n",
      "Total production is 1.5284 and price is 0.7671\n"
     ]
    }
   ],
   "source": [
    "q = np.array([0.2, 0.2])\n",
    "\n",
    "for it in range(40):\n",
    "    f, J = cournot(q)\n",
    "    step = -np.linalg.solve(J, f)\n",
    "    q += step\n",
    "    if np.linalg.norm(step) < 1.e-10: break\n",
    "\n",
    "price, quantity = market(q)\n",
    "print(f'\\nCompany 1 produces {q[0]:.4f} units, while company 2 produces {q[1]:.4f} units.')\n",
    "print(f'Total production is {quantity:.4f} and price is {price:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After just five iterations, Newton's method converges to the solution, which Python prints to screen:\n",
    "```\n",
    "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n",
    "Total production is 1.5284 and price is 0.7671\n",
    "```\n",
    "\n",
    "<br>\n",
    "We see that the code has found the equilibrium to this market. \n",
    "\n",
    "<br>\n",
    "The `compecon` package provides the `NLP` (non-linear problem) class, useful to solve last problem without the need of coding Newton's algorithm. To use it, we create an instance of `NLP` from the `cournot` function, and simply call the `newton` method, using `q0` as initial value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n",
      "Total production is 1.5284 and price is 0.7671\n"
     ]
    }
   ],
   "source": [
    "q0 = np.array([0.2, 0.2])\n",
    "cournot_problem = NLP(cournot)\n",
    "q = cournot_problem.newton(q0)\n",
    "\n",
    "price, quantity = market(q)\n",
    "print(f'\\nCompany 1 produces {q[0]:.4f} units, while' +\n",
    " f' company 2 produces {q[1]:.4f} units.')\n",
    "print(f'Total production is {quantity:.4f} and price is {price:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After completing this code block, Python prints the following to screen:\n",
    "```\n",
    "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n",
    "Total production is 1.5284 and price is 0.7671\n",
    "```\n",
    "<br>\n",
    "As expected, we got the same result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 1 illustrates the problem we just solved, where the axes represent the output levels of each firm. The quasi-vertical white line represents the profit-maximizing output level for firm 1, taking the output of firm 2 as given. Similarly, the quasi-horizontal line represents the profit maximizing output level for firm 2, given firm 1 output. The solution to the problem corresponds to the intersection of these two lines. See also the path to convergence (blue line) from the initial $q_0 = \\begin{bmatrix}0.2 & 0.2\\end{bmatrix}'$ point to the solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 1 Convergence of Newton's method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d0d7b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "q1 = np.linspace(0.1, 1.5, n)\n",
    "q2 = np.linspace(0.1, 1.5, n)\n",
    "z = np.array([cournot(q)[0] for q in gridmake(q1, q2).T]).T\n",
    "\n",
    "steps_options = {'marker': 'o',\n",
    "                 'color': (0.2, 0.2, .81),\n",
    "                 'linewidth': 2.5,\n",
    "                 'markersize': 9,\n",
    "                 'markerfacecolor': 'white',\n",
    "                 'markeredgecolor': 'red'}\n",
    "\n",
    "contour_options = {'levels': [0.0],\n",
    "                   'colors': 'white',\n",
    "                   'linewidths': 2.0}\n",
    "\n",
    "\n",
    "Q1, Q2 = np.meshgrid(q1, q2)\n",
    "Z0 = np.reshape(z[0], (n,n), order='F')\n",
    "Z1 = np.reshape(z[1], (n,n), order='F')\n",
    "\n",
    "methods = ['newton', 'broyden']\n",
    "cournot_problem.opts['maxit', 'maxsteps', 'all_x'] = 10, 0, True\n",
    "\n",
    "qmin, qmax = 0.1, 1.3\n",
    "x = cournot_problem.zero(method='newton')\n",
    "demo.figure(\"Convergence of Newton's method\", '$q_1$', '$q_2$',\n",
    "            [qmin, qmax], [qmin, qmax])\n",
    "plt.contour(Q1, Q2, Z0, **contour_options)\n",
    "plt.contour(Q1, Q2, Z1, **contour_options)\n",
    "\n",
    "plt.plot(*cournot_problem.x_sequence, **steps_options)\n",
    "\n",
    "demo.text(0.85, qmax, '$\\pi_1 = 0$', 'left', 'top')\n",
    "demo.text(qmax, 0.55, '$\\pi_2 = 0$', 'right', 'center')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2: Solving an Cournot oligopoly model by collocation\n",
    "\n",
    "<br>\n",
    "To illustrate the implementation of the collocation method for implicit function problems, consider the case of a Cournot oligopoly. In the standard microeconomic model of the firm, the firm maximizes its profits by matching marginal revenue to marginal cost (MC). An oligopolistic firm, recognizing that its actions affect the price, knows that its marginal revenue is $p + q \\frac{dp}{dq}$, where $p$ is the price, $q$ the quantity produced, and $\\frac{dp}{dq}$ is the marginal impact of the product on the market price. Cournot's assumption is that the company acts as if none of its production changes would provoke a reaction from its competitors. This implies that:\n",
    "\\begin{equation}\n",
    "    \\frac{dp}{dq} = \\frac{1}{D'(p)} \\tag{3}\n",
    "\\end{equation}\n",
    "\n",
    "where $D(p)$ is the market demand curve.\n",
    "\n",
    "<br>\n",
    "Suppose we want to derive the firm's effective supply function, which specifies the amount $q = S(p)$ that it will supply at each price. The effective supply function of the firm is characterized by the functional equation\n",
    "\\begin{equation}\n",
    "    p + \\frac{S(p)}{D'(p)} - MC(S(p)) = 0 \\tag{4}\n",
    "\\end{equation}\n",
    "\n",
    "for every price $p>0$. In simple cases, this function can be found explicitly. However, in more complicated cases, there is no explicit solution. Suppose for example that demand and marginal cost are given by\n",
    "\\begin{equation*}\n",
    "D(p) = p^{-\\eta}  \\qquad\\qquad CM(q) = \\alpha\\sqrt{q} + q^2 \n",
    "\\end{equation*}\n",
    "\n",
    "so that the functional equation to be solved for $S(p)$ is\n",
    "\\begin{equation} \\label{eq:funcional}\n",
    "\\left[p - \\frac{S(p)p^{\\eta+1}}{\\eta}\\right] - \\left[\\alpha\\sqrt{S(p)} + S(p)^2\\right] = 0 \\tag{5}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The collocation method\n",
    "In equation (5), the unknown is the supply *function* $S(p)$, which makes (5) and infinite-dimension equation. Instead of solving the equation directly, we will approximate its solution using $n$ Chebyshev polynomials $\\phi_i(x)$, which are defined recursively for $x \\in [0,1]$ as:\n",
    "\\begin{align*}\n",
    "\\phi_0(x) & = 1 \\\\\n",
    "\\phi_1(x) & = x \\\\\n",
    "\\phi_{k + 1}(p_i) & = 2x \\phi_k(x) - \\phi_{k-1}(x), \\qquad \\text{for} k = 1,2, \\dots\n",
    "\\end{align*}\n",
    "\n",
    "<br>\n",
    "In addition, instead of requiring that both sides of the equation be exactly equal over the entire domain of $p \\in \\Re^+$, we will choose $n$ Chebyshev nodes $p_i$ in the interval $[a, b]$:\n",
    "\\begin{equation} \\label{eq:chebynodes}\n",
    "p_i = \\frac{a + b}{2} + \\frac{ba}{2}\\ cos\\left(\\frac{n-i + 0.5}{n}\\pi\\right), \\qquad\\text{for } i = 1,2, \\dots, n  \\tag{6}\n",
    "\\end{equation}\n",
    "\n",
    "<br>\n",
    "Thus, the supply is approximated by\n",
    "\\begin{equation*}\n",
    "S(p_i) = \\sum_{k = 0}^{n-1} c_{k}\\phi_k(p_i)\n",
    "\\end{equation*}\n",
    "\n",
    "Substituting this last expression in (5) for each of the placement nodes (Chebyshev in this case) results in a non-linear system of $ n $ equations (one for each node) in $ n $ unknowns $ c_k $ (one for each polynomial of Cheybshev), which in principle can be solved by Newton's method, as in the last example. Thus, in practice, the system to be solved is\n",
    "\n",
    "\\begin{equation} \\label{eq:collocation}\n",
    "\\left[p_i - \\frac{\\left(\\sum_{k=0}^{n-1}c_{k}\\phi_k(p_i)\\right)p_i^{\\eta+1}}{\\eta}\\right] - \\left[\\alpha\\sqrt{\\sum_{k=0}^{n-1}c_{k}\\phi_k(p_i)} + \\left(\\sum_{k=0}^{n-1}c_{k}\\phi_k(p_i)\\right)^2\\right] = 0  \\tag{7}\n",
    "\\end{equation}\n",
    "\n",
    "for $i=1,2,\\dots,n$ and for $k=1,2,\\dots,n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving the model withPython\n",
    "To solve this model we start a new Python session:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from compecon import BasisChebyshev, NLP, nodeunif\n",
    "from compecon.demos import demo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and set the $\\alpha$ and $\\eta$ parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha, eta = 1.0, 3.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, we define a `lambda` function to represent the demand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = lambda p: p**(-eta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will approximate the solution for prices in the $p\\in [\\frac{1}{2}, 2]$ interval, using 25 collocation nodes. The `compecon` library provides the `BasisChebyshev` class to make computations with Chebyshev bases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "n, a, b =  25, 0.5, 2.0\n",
    "S = BasisChebyshev(n, a, b, labels=['price'], l=['supply'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's assume that our first guess is $S(p)=1$. To that end, we set the value of `S` to one in each of the nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = S.nodes\n",
    "S.y = np.ones_like(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important to highlight that in this problem the unknowns are the $c_k$ coefficients from the Chebyshev basis; however, an object of  `BasisChebyshev` class automatically adjusts those coefficients so they are consistent with the values we set for the function at the nodes (here indicated by the `.y` property).\n",
    "\n",
    "<br>\n",
    "We are now ready to define the objective function, which we will call `resid`. This function takes as its argument a vector with the 25 Chebyshev basis coefficients and returns the left-hand side of the 25 equations defined by (7). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def resid(c):\n",
    "    S.c = c  # update interpolation coefficients\n",
    "    q = S(p) # compute quantity supplied at price nodes\n",
    "    return p - q * (p ** (eta+1) / eta) - alpha * np.sqrt(q) - q ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `resid` function takes a single argument (the coefficients for the Chebyshev basis). All other parameters (`Q, p, eta, alpha` must be declared in the main script, where Python will find their values.\n",
    "\n",
    "<br>\n",
    "To use Newton's method, it is necessary to compute the Jacobian matrix of the function whose roots we are looking for. In certain occasions, like in the problem we are dealing with, coding the computation of this Jacobian matrix correctly can be quite cumbersome. The `NLP` class provides, besides the Newton's method (which we used in the last example), the Broyden's method, whose main appeal is that it does not require the coding of the Jacobian matrix (the method itself will approximate it)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving nonlinear equations by Broyden's method\n",
      "it    bstep  change\n",
      "--------------------\n",
      "   0     0  4.08e-01\n",
      "   1     0  8.95e-02\n",
      "   2     0  1.37e-02\n",
      "   3     0  2.01e-03\n",
      "   4     0  3.36e-04\n",
      "   5     0  8.11e-05\n",
      "   6     0  1.28e-05\n",
      "   7     0  2.80e-06\n",
      "   8     0  4.88e-07\n",
      "   9     0  7.55e-08\n",
      "  10     0  1.84e-08\n",
      "  11     0  1.88e-09\n",
      "  12     0  4.63e-10\n",
      "  13     0  5.88e-11\n",
      "  14     0  1.17e-11\n",
      "  15     0  2.48e-12\n",
      "  16     0  2.91e-13\n"
     ]
    }
   ],
   "source": [
    "cournot = NLP(resid)\n",
    "S.c = cournot.broyden(S.c, tol=1e-12, print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After 17 iterations, Broyden's method converges to the desired solution. We can visualize this in Figure 3, which shows the value of the function on 501 different points within the approximation interval. Notice that the residual plot crosses the horizontal axis 25 times; this occurs precisely at the collocation nodes (represented by red dots). This figure also shows the precision of the approximation: outside nodes, the function is within $5\\times10^{-11}$ units from zero.\n",
    "\n",
    "<br>\n",
    "One of the advantages of working with the `BasisChebyshev` class is that, once the collocation coefficients have been found, we can evaluate the supply function by calling the `S` object as if it were a Python function. Thus, for example, to find out the quantity supplied by the firm when the price is 1.2, we simply evaluate `print(S(1.2))`, which returns `0.4650`. We use this feature next to compute the effective supply curve when there are 5 identical firms in the market; the result is shown in Figure 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 2 Supply and demand when there are 5 firms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d4d5ffad30>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5f6fcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pplot = nodeunif(501, a, b)\n",
    "demo.figure('Cournot Effective Firm Supply Function', \n",
    "            'Quantity', 'Price', [0, 4], [a, b])\n",
    "plt.plot(5 * S(pplot), pplot, D(pplot), pplot)\n",
    "plt.legend(('Supply','Demand'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 3: Approximation residuals for equation (5)\n",
    "\n",
    "This block generates Figure 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5ffdf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = pplot \n",
    "demo.figure('Residual Function for Cournot Problem',\n",
    "            'Quantity', 'Residual')\n",
    "plt.hlines(0, a, b, 'k', '--', lw=2)\n",
    "plt.plot(pplot, resid(S.c))\n",
    "plt.plot(S.nodes,np.zeros_like(S.nodes),'r*');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 4: Change in the effective supply as the number of firms increases\n",
    "We now plot the effective supply for a varying number of firms; the result is shown in Figure 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5ffdeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = np.array([1, 3, 5, 10, 15, 20])\n",
    "demo.figure('Supply and Demand Functions', 'Quantity', 'Price', [0, 13])\n",
    "plt.plot(np.outer(S(pplot), m), pplot)\n",
    "plt.plot(D(pplot), pplot, linewidth=4, color='black')\n",
    "plt.legend(['m=1', 'm=3', 'm=5', 'm=10', 'm=15', 'm=20', 'demand']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Figure 4 notice how the equilibrium price and quantity change as the number of firms increases. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 5: Equilibrium price as a function of the number of firms\n",
    "\n",
    "The last figure in this example (Figure 5), shows the equilibrium price as a function of the number of firms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5ec1630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp = (b + a) / 2\n",
    "dp = (b - a) / 2\n",
    "m  = np.arange(1, 26)\n",
    "for i in range(50):\n",
    "    dp /= 2\n",
    "    pp = pp - np.sign(S(pp) * m - D(pp)) * dp\n",
    "\n",
    "demo.figure('Cournot Equilibrium Price as Function of Industry Size', \n",
    "            'Number of Firms', 'Price')\n",
    "plt.bar(m, pp);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 3: Importing data from Internet\n",
    "\n",
    "<br>\n",
    "Oftentimes we need to keep track of some economic indicators. This work usually requires visiting the website of a data provider, looking for the required indicators, downloading the data (possibly in several different files), copying them to a common file, arranging them properly, and only after completing these cumbersome tasks, plotting them. If this work has to be done periodically then it is also necessary to thoroughly document each of these steps so we can replicate them exactly in the future. Needless to say, if it is necessary to do all these tasks with numerous indicators, the work ends up demanding a considerable amount of time and is prone to many errors.\n",
    "\n",
    "<br>\n",
    "To facilitate this work, we can use Python to download data available in Internet directly, thanks to packages such as [pandas-datareader](https://pandas-datareader.readthedocs.io/en/latest/index.html). This is easily done when data providers supply an API ---application program interface--- which specifies how a language like Python can find the desired data.\n",
    "\n",
    "<br>\n",
    "Let us illustrate this with an example. Suppose we want recent data on economic growth for the member countries of the CMCA. The World Bank provides the relevant data in its “World Database”, which we can read with the `wb` module from `pandas_datareader`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pandas_datareader import wb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able to download data from the World Bank, we first need to know the exact code of the indicator we want to read. The first time we do this task we will not know this code, but we can look for it in the World Bank website or more easily from Python itself. For example, to find data on real GDP per capita, we run the following using the `.search` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>646</th>\n",
       "      <td>6.0.GDPpc_constant</td>\n",
       "      <td>GDP per capita, PPP (constant 2011 internation...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7858</th>\n",
       "      <td>NY.GDP.PCAP.KD</td>\n",
       "      <td>GDP per capita (constant 2010 US$)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7860</th>\n",
       "      <td>NY.GDP.PCAP.KN</td>\n",
       "      <td>GDP per capita (constant LCU)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7862</th>\n",
       "      <td>NY.GDP.PCAP.PP.KD</td>\n",
       "      <td>GDP per capita, PPP (constant 2011 internation...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7863</th>\n",
       "      <td>NY.GDP.PCAP.PP.KD.87</td>\n",
       "      <td>GDP per capita, PPP (constant 1987 internation...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        id                                               name\n",
       "646     6.0.GDPpc_constant  GDP per capita, PPP (constant 2011 internation...\n",
       "7858        NY.GDP.PCAP.KD                 GDP per capita (constant 2010 US$)\n",
       "7860        NY.GDP.PCAP.KN                      GDP per capita (constant LCU)\n",
       "7862     NY.GDP.PCAP.PP.KD  GDP per capita, PPP (constant 2011 internation...\n",
       "7863  NY.GDP.PCAP.PP.KD.87  GDP per capita, PPP (constant 1987 internation..."
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wb.search('gdp.*capita.*const').iloc[:,:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the dot followed by an asterisk (.\\*) indicates that any text in that position is a match. This function returns a data table with information about indicators that match the search criteria. In the preceding line, we use the code `.iloc[:,:2]` so that Python only prints the first two columns from that table.\n",
    "\n",
    "<br>\n",
    "After running that search, we choose the 'NY.GDP.PCAP.KD' indicator, whose description is “GDP per capita (constant 2010 US\\$)”. We define a variable with a list of country codes of the CMCA countries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "paises = ['CR', 'DO', 'GT', 'HN', 'NI', 'SV']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we proceed to reed data from 1991:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "datos = wb.download(indicator='NY.GDP.PCAP.KD',\n",
    "                    country=paises,start=1991, end=2016)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to read data for more than one indicator in a single call to the `wb.download` function, writing their codes in a list (just like we did to read data on all six countries at once). In any case, we get a data table in panel format, where each columns corresponds to one of the indicators. For our example in particular, where we only read one indicator, it would be useful if the table was arranged so that each row correspond to a year and each column to a country. We can achieve it with this instruction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "GDP = datos.reset_index().pivot('year','country')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once data is arrange this way, it is very easy to compute growth for all countries in a single step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "GROWTH = 100 * GDP.pct_change()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or to generate a formatted data table to be included in a \\LaTeX document"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\begin{tabular}{lrrrrrr}\n",
      "\\toprule\n",
      "{} & \\multicolumn{6}{l}{NY.GDP.PCAP.KD} \\\\\n",
      "country &     Costa Rica & Dominican Republic & El Salvador & Guatemala & Honduras & Nicaragua \\\\\n",
      "year &                &                    &             &           &          &           \\\\\n",
      "\\midrule\n",
      "2011 &           3.06 &               1.81 &        3.34 &      1.94 &     1.89 &      5.03 \\\\\n",
      "2012 &           3.59 &               1.42 &        2.34 &      0.80 &     2.24 &      5.24 \\\\\n",
      "2013 &           1.13 &               3.59 &        1.89 &      1.54 &     0.99 &      3.72 \\\\\n",
      "2014 &           2.40 &               6.35 &        1.49 &      2.03 &     1.29 &      3.60 \\\\\n",
      "2015 &           2.55 &               5.79 &        1.87 &      2.03 &     2.08 &      3.60 \\\\\n",
      "2016 &           3.10 &               5.41 &        2.06 &      1.04 &     2.02 &      3.50 \\\\\n",
      "\\bottomrule\n",
      "\\end{tabular}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#GROWTH.tail(6).round(2).to_latex('micuadro.tex')\n",
    "print(GROWTH.tail(6).round(2).to_latex())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In last instruction, the `.tail(6)` part indicates that we only want the last six observations, while the `.to_latex('micuadro.tex')` part exports that table to a file named 'micuadro.tex', which can later te included in a document. The  result of this code will look similar to this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"6\" halign=\"left\">NY.GDP.PCAP.KD</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th>Costa Rica</th>\n",
       "      <th>Dominican Republic</th>\n",
       "      <th>El Salvador</th>\n",
       "      <th>Guatemala</th>\n",
       "      <th>Honduras</th>\n",
       "      <th>Nicaragua</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2011</th>\n",
       "      <td>3.06</td>\n",
       "      <td>1.81</td>\n",
       "      <td>3.34</td>\n",
       "      <td>1.94</td>\n",
       "      <td>1.89</td>\n",
       "      <td>5.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012</th>\n",
       "      <td>3.59</td>\n",
       "      <td>1.42</td>\n",
       "      <td>2.34</td>\n",
       "      <td>0.80</td>\n",
       "      <td>2.24</td>\n",
       "      <td>5.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>1.13</td>\n",
       "      <td>3.59</td>\n",
       "      <td>1.89</td>\n",
       "      <td>1.54</td>\n",
       "      <td>0.99</td>\n",
       "      <td>3.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>2.40</td>\n",
       "      <td>6.35</td>\n",
       "      <td>1.49</td>\n",
       "      <td>2.03</td>\n",
       "      <td>1.29</td>\n",
       "      <td>3.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>2.55</td>\n",
       "      <td>5.79</td>\n",
       "      <td>1.87</td>\n",
       "      <td>2.03</td>\n",
       "      <td>2.08</td>\n",
       "      <td>3.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>3.10</td>\n",
       "      <td>5.41</td>\n",
       "      <td>2.06</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.02</td>\n",
       "      <td>3.50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        NY.GDP.PCAP.KD                                                    \\\n",
       "country     Costa Rica Dominican Republic El Salvador Guatemala Honduras   \n",
       "year                                                                       \n",
       "2011              3.06               1.81        3.34      1.94     1.89   \n",
       "2012              3.59               1.42        2.34      0.80     2.24   \n",
       "2013              1.13               3.59        1.89      1.54     0.99   \n",
       "2014              2.40               6.35        1.49      2.03     1.29   \n",
       "2015              2.55               5.79        1.87      2.03     2.08   \n",
       "2016              3.10               5.41        2.06      1.04     2.02   \n",
       "\n",
       "                   \n",
       "country Nicaragua  \n",
       "year               \n",
       "2011         5.03  \n",
       "2012         5.24  \n",
       "2013         3.72  \n",
       "2014         3.60  \n",
       "2015         3.60  \n",
       "2016         3.50  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GROWTH.tail(6).round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 6: GDP per capita growth in CARD, 1992-2016\n",
    "Finally, we plot the results in Figure 6. It is possible to enhance the aesthetic aspect of this figure by, for example, changing the legend position. Such enhancements are not presented here for space considerations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5fba1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GROWTH.columns = paises\n",
    "GROWTH.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 7: GDP per capita growth in CARD, by country, 2011-2016\n",
    "\n",
    "It is also possible to plot each of the time series in a separate subplot, with the instruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d5ecc5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GROWTH.plot(subplots=True, layout=[2,3], sharey=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where we have specified that each time series should be plotted separately (`subplots=True`), be arranged in two rows and three columns (`layout=[2,3]`), and all subplots must have the same “y” axis (`sharey=True`, to facilitate country comparisons). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 4: Econometric estimations\n",
    "\n",
    "<br>\n",
    "The Python `statsmodels` package enable the estimation of many types of econometric models, although not as many as can be estimated using R. A simple illustration is the estimation of a Keynesian consumption function, \n",
    "\\begin{equation*}\n",
    "\\ln(c_t) = \\beta_0 + \\beta_1 \\ln(y_t) + \\epsilon_t\n",
    "\\end{equation*}\n",
    "\n",
    "where $c_t$ stands for consumption, $y_t$ income, $\\epsilon$ a stochastic shock. In this case $\\beta_1$ corresponds to the income elasticity of consumption.\n",
    "\n",
    "<br>\n",
    "Just like in the previous example, we will use `pandas-datareader` to import data from Internet. In this example we also import the `log` function from the `numpy` package to compute the logarithm of the data, as well as the `formula.api` module form `statsmodels` to estimate the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas_datareader.data as web\n",
    "from numpy import log\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once this is done, we are ready to import data. In this example, we use quarterly data on consumption and production in the United States, available in [FRED](https://fred.stlouisfed.org/), a database from the Federal Reserve Bank of Saint Louis. For “consumption” we use the “PCEC” (Personal Consumption Expenditures) series, and for “income” we use “GDP” (Gross Domestic Product)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "usdata = web.DataReader(['PCEC','GDP'],'fred', 1947, 2017)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After executing this instuction, the `usdata` variable points to a `pandas` data table, in which each column corresponds to a variable and each row to a quarter. We now estimate the model by ordinary least squares (`.ols`) and print a summary of the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   PCEC   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 6.154e+05\n",
      "Date:                Sat, 28 Jul 2018   Prob (F-statistic):               0.00\n",
      "Time:                        18:27:34   Log-Likelihood:                 584.98\n",
      "No. Observations:                 281   AIC:                            -1166.\n",
      "Df Residuals:                     279   BIC:                            -1159.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.6712      0.010    -64.053      0.000      -0.692      -0.651\n",
      "GDP            1.0268      0.001    784.505      0.000       1.024       1.029\n",
      "==============================================================================\n",
      "Omnibus:                       51.339   Durbin-Watson:                   0.075\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               85.582\n",
      "Skew:                           1.027   Prob(JB):                     2.61e-19\n",
      "Kurtosis:                       4.758   Cond. No.                         47.1\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "mod = smf.ols('PCEC ~ GDP', log(usdata)).fit()\n",
    "print(mod.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the `.ols` function takes two arguments, the formula specifying the model, and the name of the data table containing the variables. In this code block we specify the data as `log(usdata)`, which tells Python that we want the logarithm of the data, saving us the task of generating another data table with the transformed data beforehand (as would be necessary in, for example, Stata). \n",
    "\n",
    "<br>\n",
    "Alternatively, that line can also be written as\n",
    "```\n",
    "mod = smf.ols('log(PCEC) ~ log(GDP)', usdata).fit()\n",
    "```\n",
    "which is convenient in cases where not all variables must be transformed.\n",
    "\n",
    "<br>\n",
    "As it is expected in a regression of trending time series, the $R^2$ statistic is very close to one, and the Durbin-Watson statistic points to the high possibility of autocorrelation in the residuals. This document does not aim at being a guide of best practices in econometrics, but let us consider one last model in which consumption growth depends on income growth:\n",
    "\\begin{equation*}\n",
    "\\Delta\\ln(c_t) = \\beta_0 + \\beta_1 \\Delta\\ln(y_t) + \\epsilon_t\n",
    "\\end{equation*}\n",
    "\n",
    "with we estimate in Python with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>PCEC</td>       <th>  R-squared:         </th> <td>   0.490</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.488</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   267.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 28 Jul 2018</td> <th>  Prob (F-statistic):</th> <td>1.50e-42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:27:34</td>     <th>  Log-Likelihood:    </th> <td>  996.74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   280</td>      <th>  AIC:               </th> <td>  -1989.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   278</td>      <th>  BIC:               </th> <td>  -1982.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    0.0063</td> <td>    0.001</td> <td>    8.747</td> <td> 0.000</td> <td>    0.005</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GDP</th>       <td>    0.6130</td> <td>    0.038</td> <td>   16.346</td> <td> 0.000</td> <td>    0.539</td> <td>    0.687</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>102.218</td> <th>  Durbin-Watson:     </th> <td>   2.550</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1087.804</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.140</td>  <th>  Prob(JB):          </th> <td>6.11e-237</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>12.383</td>  <th>  Cond. No.          </th> <td>    90.9</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   PCEC   R-squared:                       0.490\n",
       "Model:                            OLS   Adj. R-squared:                  0.488\n",
       "Method:                 Least Squares   F-statistic:                     267.2\n",
       "Date:                Sat, 28 Jul 2018   Prob (F-statistic):           1.50e-42\n",
       "Time:                        18:27:34   Log-Likelihood:                 996.74\n",
       "No. Observations:                 280   AIC:                            -1989.\n",
       "Df Residuals:                     278   BIC:                            -1982.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      0.0063      0.001      8.747      0.000       0.005       0.008\n",
       "GDP            0.6130      0.038     16.346      0.000       0.539       0.687\n",
       "==============================================================================\n",
       "Omnibus:                      102.218   Durbin-Watson:                   2.550\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1087.804\n",
       "Skew:                          -1.140   Prob(JB):                    6.11e-237\n",
       "Kurtosis:                      12.383   Cond. No.                         90.9\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smf.ols('PCEC ~ GDP', log(usdata).diff()).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that now the $R^2$ is no longer close to one, and that the Durbin-Watson statistic is closer to 2.0, indicating lack of autocorrelation. \n",
    "\n",
    "<br>\n",
    "This last line of code, where we estimate the model with first-differenced data, highlights one of the reasons why code written in Python is so concise: it is not always necessary to store intermediate results in variable, because we can simply chain sevearal operations. In the case at hand, we have specified a model (`.ols`), estimated it (`.fit`) and gotten a table summarizing the results (`.summary`). Similarly, we have computed the logarithm (`log`) of data in `usdata` table, and to its result we have computed its first-difference (`.diff`). To better appreciate how concise this code is, let us compare that line with the following block, which takes 8 lines of code to perform the same operations:\n",
    "\n",
    "```\n",
    "usdata['lPCEC'] = log(usdata['PCEC'])\n",
    "usdata['lGDP'] = log(usdata['GDP'])\n",
    "usdata['dlPCEC'] = usdata['lPCEC'].diff()\n",
    "usdata['dlGDP'] = usdata['lGDP'].diff()\n",
    "model = smf.ols('dlPCEC ~ dlGDP', usdata)\n",
    "results = model.fit()\n",
    "table = results.summary()\n",
    "print(table)\n",
    "```\n",
    "\n",
    "\n",
    "With results from last Table  at hand, we could predict that a one percentage point (p.p.) increase in GDP growth  would lead to a 0.618 p.p. increase in consumption growth. However, given that the data sample covers such a long period (nearly 70 years of quarterly observation), it is reasonable to wonder whether the parameters in this model are constant, given that several structural changes could have occurred along these years. One way to evaluate such posibility is to estimate the model with a rolling sample. In particular, we are going to estimate this model with 24 quarterly observations rolling window, changing the sample by one quarter in every step.\n",
    "\n",
    "In this case, since we are going to need growth data many times, it is more efficient to compute growth data only once and store it in a `growth` variable. With the `[1:]` code we are dropping the first observation, which we lose when we compute the first-order difference (`.diff`). Furthermore, we use the `.shape` property from the table to find out how many observations  `T` we have, and then we set the window range to `h=24` observations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "growth = (100*log(usdata).diff())[1:]\n",
    "T, nvar = growth.shape\n",
    "h = 24"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To faciliate next step, we define función `window_beta1`, which takes as its only argument the number of the last observation to be included in the estimation, and returns the value of the estimated GDP coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def window_beta1(k):\n",
    "    return smf.ols('PCEC~GDP',growth[k-h:k]).fit().params['GDP']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this, we are ready to estimate the model many times, adding the results to the `growth` table as the `beta1` “indicator”. Plotting the results we get Figure 8, where we clearly see that the effect of GDP growth on consumption growth is quite unstable, and thus the predictions made with the simple model could be very poor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Figure 8: Estimated effect of income over consumption, 24-observation rolling windows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d4d8cc2828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "growth.loc[h-1:,'beta1'] = [window_beta1(k) for k in range(h,T+1)]\n",
    "growth[['beta1']].plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejemplo 5: Documentos dinámicos\n",
    "\n",
    "<br>\n",
    "To conclude this note, I let the reader know that the original (PDF) version of this document is an example of what is known as a “dynamic document”, in the sense that it was generated by interweaving \\LaTeX code with Python code. The main benefit of this is that if in the future we need to update the previous examples (say to use updated data in the tables and graphs), it would suffice to rerun the code that generated that document (similarly to what we would do with this Jupyter notebook). It will not be necessary to use an Internet browser to get data, nor to copy-and-paste the graphs in the document.\n",
    "\n",
    "<br>\n",
    "Dynamic documents are extremely useful, because they enable significant time savings in the updating of periodic reports. Readers who are interested in learning how to create one of these documents will need to know \\LaTeX and to review the [pythontex](https://www.ctan.org/pkg/pythontex) documentation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "<br>\n",
    "Judd, Kenneth L. (1998). [Numerical Methods in Economics](https://mitpress.mit.edu/books/numerical-methods-economics). MIT Press. isbn: 978-0-262-\n",
    "10071-7.\n",
    "\n",
    "<br>\n",
    "Miranda, Mario J. and Paul L. Fackler (2002). [Applied Computational Economics and\n",
    "Finance](https://mitpress.mit.edu/books/applied-computational-economics-and-finance). MIT Press. isbn: 0-262-13420-9.\n",
    "\n",
    "<br>\n",
    "Press, William H., Saul A. Teukolsky, and William T. Vetterling and Brian P. Flannery\n",
    "(2007). [Numerical Recipes: The Art of Scientific Computing](http://www.numerical.recipes/). 3rd ed. Cambridge University Press. isbn: 978-0521880688.\n",
    "\n",
    "<br>\n",
    "Romero-Aguilar, Randall (2016). [CompEcon-Python](http://randall-romero.com/code/compecon/)\n",
    ". url: http://randall-romero.com/code/compecon/."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}