.ipynb_checkpoints/xinyue_linear_regression-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"880000\"> DeLong's Macroeconomics </font>\n",
    "\n",
    "Last edited: 2019-10-20\n",
    "\n",
    "# <font color=\"880000\"> Python and Economics 2: Linear Regression in Python </font>\n",
    "\n",
    "A large portion of this lecture is taken from QuantEcon <https://quantecon.org>. You can read the more detailed contents of the lecture here: <https://python.quantecon.org/ols.html>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    " \n",
    "- [Overview](#Overview)  \n",
    "- [Simple Linear Regression](#Simple-Linear-Regression)  \n",
    "- [Extending the Linear Regression Model](#Extending-the-Linear-Regression-Model)  \n",
    "- [Endogeneity](#Endogeneity)   \n",
    "- [Exercises](#Exercises)  \n",
    "- [Solutions](#Solutions)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "Linear regression is a standard tool for analyzing the relationship between two or more variables.\n",
    "In this lecture, we’ll use the Python package `statsmodels` to estimate, interpret, and visualize linear regression models.\n",
    "Along the way, we’ll discuss a variety of topics, including\n",
    "- simple and multivariate linear regression  \n",
    "- visualization  \n",
    "- endogeneity and omitted variable bias  \n",
    "- two-stage least squares  \n",
    "\n",
    "As an example, we will replicate results from Acemoglu, Johnson and Robinson’s seminal paper [[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001).\n",
    "You can download a copy [here](https://economics.mit.edu/files/4123).  \n",
    "In the paper, the authors emphasize the importance of institutions in economic development. The main contribution is the use of settler mortality rates as a source of *exogenous* variation in institutional differences.\n",
    "\n",
    "Let’s start with some imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.iolib.summary2 import summary_col\n",
    "from linearmodels.iv import IV2SLS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to what’s in Anaconda, this lecture will need the following libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: linearmodels in /srv/app/venv/lib/python3.6/site-packages\n",
      "Requirement already satisfied: pandas>=0.20 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: statsmodels>=0.8 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: numpy>=1.13 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: cached-property>=1.5.1 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: mypy-extensions>=0.4 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: patsy in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: scipy>=0.18 in /srv/app/venv/lib/python3.6/site-packages (from linearmodels)\n",
      "Requirement already satisfied: pytz>=2011k in /srv/app/venv/lib/python3.6/site-packages (from pandas>=0.20->linearmodels)\n",
      "Requirement already satisfied: python-dateutil>=2.5.0 in /srv/app/venv/lib/python3.6/site-packages (from pandas>=0.20->linearmodels)\n",
      "Requirement already satisfied: six in /srv/app/venv/lib/python3.6/site-packages (from patsy->linearmodels)\n"
     ]
    }
   ],
   "source": [
    "!pip install linearmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Linear Regression\n",
    "\n",
    "[[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) wish to determine whether or not differences in institutions can help to explain observed economic outcomes.\n",
    "How do we measure *institutional differences* and *economic outcomes*?\n",
    "\n",
    "In this paper,\n",
    "- economic outcomes are proxied by log GDP per capita in 1995, adjusted for exchange rates.  \n",
    "- institutional differences are proxied by an index of protection against expropriation on average over 1985-95, constructed by the [Political Risk Services Group](https://www.prsgroup.com/).  \n",
    "\n",
    "These variables and other data used in the paper are available for download on Daron Acemoglu’s [webpage](https://economics.mit.edu/faculty/acemoglu/data/ajr2001).\n",
    "We will use pandas’ `.read_stata()` function to read in data contained in the `.dta` files to dataframes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hide-output": false
   },
   "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>shortnam</th>\n",
       "      <th>euro1900</th>\n",
       "      <th>excolony</th>\n",
       "      <th>avexpr</th>\n",
       "      <th>logpgp95</th>\n",
       "      <th>cons1</th>\n",
       "      <th>cons90</th>\n",
       "      <th>democ00a</th>\n",
       "      <th>cons00a</th>\n",
       "      <th>extmort4</th>\n",
       "      <th>logem4</th>\n",
       "      <th>loghjypl</th>\n",
       "      <th>baseco</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AFG</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>93.699997</td>\n",
       "      <td>4.540098</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AGO</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.363636</td>\n",
       "      <td>7.770645</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>280.000000</td>\n",
       "      <td>5.634789</td>\n",
       "      <td>-3.411248</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ARE</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>7.181818</td>\n",
       "      <td>9.804219</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ARG</td>\n",
       "      <td>60.000004</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.386364</td>\n",
       "      <td>9.133459</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>68.900002</td>\n",
       "      <td>4.232656</td>\n",
       "      <td>-0.872274</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ARM</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.682482</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  shortnam   euro1900  excolony    avexpr  logpgp95  cons1  cons90  democ00a  \\\n",
       "0      AFG   0.000000       1.0       NaN       NaN    1.0     2.0       1.0   \n",
       "1      AGO   8.000000       1.0  5.363636  7.770645    3.0     3.0       0.0   \n",
       "2      ARE   0.000000       1.0  7.181818  9.804219    NaN     NaN       NaN   \n",
       "3      ARG  60.000004       1.0  6.386364  9.133459    1.0     6.0       3.0   \n",
       "4      ARM   0.000000       0.0       NaN  7.682482    NaN     NaN       NaN   \n",
       "\n",
       "   cons00a    extmort4    logem4  loghjypl  baseco  \n",
       "0      1.0   93.699997  4.540098       NaN     NaN  \n",
       "1      1.0  280.000000  5.634789 -3.411248     1.0  \n",
       "2      NaN         NaN       NaN       NaN     NaN  \n",
       "3      3.0   68.900002  4.232656 -0.872274     1.0  \n",
       "4      NaN         NaN       NaN       NaN     NaN  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/ols/maketable1.dta')\n",
    "df1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s use a scatterplot to see whether any obvious relationship exists\n",
    "between GDP per capita and the protection against\n",
    "expropriation index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe4AAAFYCAYAAACVhB8+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAgAElEQVR4nO3da3BV9b3/8c+GEAghGAKbpCAWwfJHsQSUVBgFK4zgKagB5FBtqVGRqUOJgtpK8dLBAjooQ8U5WHT+BdRiDYFESKdmRDlYQcHKoXgUo6COV8CYkJCE3FznQSaRQC4rO+u+3q9H7Nz2dyW6P/v3/V1WxDAMQwAAwBe6uF0AAAAwj+AGAMBHCG4AAHyE4AYAwEcIbgAAfITgBgDAR+LcLsCM48fL3S7BUn369FRJSaXbZTiO6w6fsF471x0+Vl97NJrU6ucYcbsgLq6r2yW4gusOn7BeO9cdPk5eO8ENAICPENwAAPgIwQ0AgI8Q3AAA+AjBDQCAjxDcAAD4CMENAICPENwAAPgIwQ0AgI8Q3AAA+IgvzioHAMCLTlbW6NnCIpVW1Cg5MV5zpgxTr4R4W5+T4AYAIEbPFhZp36FjzT52R+bFtj4nrXIAAGJ0vLSqzcd2ILgBAIhRNDmhzcd2oFUOAECM5kwZJknN5rjtxogbAIBYGc4/JSNuAABixOI0AAB8hMVpAAD4CIvTAACh13ioyfHSKkWTExw51CRWbixOI7gBAJ5y+rzxJ1+XS7J/3jhWvRLidUfmxYpGk3T8eLkjz0lwAwA8xY1541hx5CkAIPSiyQlNI+3Gx17lxqpyghsA4CmN88Snz3F7lRvdAYIbAOApjfPGfuBGd4DgBgCH+Gm1NMxhVTkABJifVkuHgRVvpAK1qnzx4sXauXOn+vbtq+3bt0uSSktLtXDhQn3xxRcaOHCgVq9erXPOOceuEgDAU/y0WjoMYn0j1VLgR22ttDnbTk6bMWOGnnnmmWYfW7duncaNG6fCwkKNGzdO69ats+vpAcBz3DhlC607+m1F88clFa18ZXONgf/J1+Xad+iYnn25yI7yWmVbcGdkZJw1mt6xY4cyMzMlSZmZmXrllVfsenoA8Jw5U4YpY3h/DU5LUsbw/p5eLR1UJytrtDbvXS1dv09fFVc2+1xZRa2pn+F258TROe7i4mL1799fkhSNRlVcXOzk0wOAq/y0WjqoWtp33aiq2lxwu73P3LXFaZFIRJFIxNTX9unTU3FxXW2uyFnRaJLbJbiC6w6fsF471+1NpRU1rX6uptYwVf9dN12qtbkHdPTbSqWm9NQdM9MlOXftjgZ33759dezYMfXv31/Hjh1TSkqKqe8rKals/4t8xMnVh17CdYdPWK+d6/au5MTWV40bkun6b/2P4U3/rq6slhLjLb32tt4EOHpbz4kTJyovL0+SlJeXp0mTJjn59ACAkDt9ncGZuphrArvOtuBetGiRfv7zn+vjjz/WhAkTlJOTo3nz5umNN97Q5MmTtXv3bs2bN8+upwcA4CyN6wwezMpQQnzzKdju8f6YkrWtVb5q1aoWP75hwwa7nhIAEABmDkax4vCU4ef10f6Pvmn2ONZauTsYACC0zByMYsUpdLdMHa64l4s6dTMTN+4O5ugcNwAA7TGzT/rMjx346ButzXtXJ6taXzV+psa2+aL/bFgVvupvBzr8M9zY001wAwA8xcwJc2d+rKbuu5hPMevMSWhunIZHqxwA4Clm7sfd+LEDH32jmrrvmj4ey4i3M6Nm7g4GAAg9MyfMNX7N2rx3m80xd2TE27iw7NgZZ4V05GcE6u5gAHCiouFcaLtXByO8zIzOW3PmwrKe3eM04vwUz58hT3ADsM1TuQccWR2M8OrM+e9ntsT790nwxX97BDcA2xz9tnkL0szqYO5R3Xl0Mcxx+2YhsWJVOQDbpKb0bPbYzOpgv7x4epnb94v2i8kZ56pb14ZzTrt1jWjyZee6XJE5jLgB2OaOmemqrq4ztTq4M4dgoDm6GOb8V97/qrbekCTV1hv6ry3/q8fnX+5yVe0juAHYpnei+dXBsI5fW8BOq6iqbfOxVxHcABAwdDHMSezRTTUnq79/nNDNxWrMI7gBIGDoYphz7y9GaeVf/0cVVbVKTOime28a5XZJphDcACBrVmK7cacoxC6tT6Iv5rTPRHADgKzZT+7GnaIQPmwHAwBZsxKb1dxwAsENALJmPzl70uEEWuUAIGtWYrtxpyh0TBBOlSO4AUDWrMR2405R6JggnI1PqxwAEBpBWIdAcAMAQiMI6xBolQMAQiMIp8oR3ACA0AjCqXK0ygEA8BGCGwAAHyG4AQDwEea4AQCOCsIhKG4iuAEAjgrCIShuolUOAHBUEA5BcRPBDQBwVBAOQXETrXIAnsHcp7288vsNwiEobiK4AXgGc5/28srvNwiHoLiJ4AbgGV6c+/TKKNUKXvz9ouOY4wbgGV6c+2wcpX7ydbn2HTqmZ18ucrukmHnx94uOY8QNwDO8OPcZpFGqF3+/6DiCG4BneHHuM5qc0DQf3PjYr7z4+0XH0SoHgDZMn3C++iR1V3xcF/VJ6q7pV57vdkkIOYIbANqwddfHKimvVk3ddyopr9bW//7Y7ZIQcgQ3ALQhSHPcCAbmuAEEitXbt4I0x41gILgBBIrVh4ywEhteQ3ADCBSrW9usxIbXENwAAqWl1naQTj8DCG4AgdJSa/vZl71xRjdgBYIbgOPsHAG31NpmZXjn0LHwFoIbgOOcvksVK8M7xyt3FUMDghuA45weAbMyvHPoWHgLwQ3AcU6PgFkZ3jl0LLyF4AbgOEbA/sLfy1sIbsCn/LxgiBGwv/D38haCG/ApFgwB4cRNRgCfYsEQEE4EN+BTZy4QYsEQEA60ygGf8vOCIT/PzwNuI7gBn/LzgiHm54HYEdwALNc4oi6tqFFyYvxZI2rm54HYuRLcGzZsUE5OjgzD0KxZs5SVleVGGQBscvqIutHpI2oO9ABi53hwFxUVKScnRzk5OerWrZvmzp2rq666Sj/84Q+dLgWATdobUft5fh5wm+PBffjwYY0cOVIJCQ3vsDMyMlRYWKjbb7/d6VIA2KS9EbWf5+cBtzke3MOGDdPq1atVUlKiHj16aNeuXbr44rb/B+7Tp6fi4ro6VKEzotEkt0twBdcdDnfddKnW5h7Q0W8rlZrSU3fMTFfvxHCtGg/b37xRWK9bcu7aI4ZhGI4802lycnK0adMmJSQk6IILLlB8fLyWLFnS6tcfP17e6uf8KBpNCtw1mcF1h09Yr53rDh+rr72tNwGuLE6bNWuWZs2aJUlatWqVUlNT3SgDQACxRxxB50pwFxcXq2/fvvryyy9VWFioF1980Y0yAAQQe8QRdK4E94IFC1RaWqq4uDg99NBD6t27txtlAAggq/eIM4KH17gS3H/961/deFoAIWD1HvH2RvAtBXu0U88ItI2T0wB0iNdHoFbvEW9vBN9SsD94+7hOPSfQFoIbQId4fQ7Z6j3i7Y3gOb4VTiO4AXRIUIOqtU5CeyN4jm+F0whuwAJebx9bKahB1Vonob0RPMe3wmkEN2ABr7ePrRTUoIq1k8DxrXAawQ1YIKjt45Y4HVROdTOC2klwQnu3cYW1CG7AArzot+xERY3W5r3bqdB1qpsR1E6CE9q7jSusRXADFuBFv2VP5R7odOia6WZ0ZFTe2tfS8o5dmDpOXkBwAxbgRb9lR7+tbPY4lhd0M92MjozKw7QewSl0nJxFcAOwTWpKT334WWnT41he0M10Mzoy4mN0aL3Gv8npc9ywD8ENwDZ3zExXdXVdp6YQzHQzOjLis2J0GKbtf2Y0/o3CfFtPJxHcAGzTO9GZKYSOrDGwYj0C7Xa4ieAG4HsdWWNgxXoE2u1wUxe3CwAAvzmzvc5iLDiJETcAdBDb/+AmghtAaMW6yIztf3ATwQ3A92INYBaZwY8IbgC+F2sAs8gMfkRwwzT2rsKrYg1gTvyCHxHcMI22Irwq1gBmkRn8iOCGabQV4VWxBjCLzOBHBDdMo60IryKAESYEN0yjrQgA7iO4YRqjGgBwX5tHnn744YdN/66trdWf/vQn3XzzzXrkkUdUVcX8JgAATmszuH/72982/XvNmjX64IMPlJWVpdLSUi1fvtz24gAAQHNttsoNw2j69+uvv67nnntOiYmJGj9+vDIzM20vDkDHsNceCL52g/vUqVMyDENdu3ZVYmJiwzfFxSkujulxwGta2ms/Z/IwwhwIkDbT94MPPtDo0aNlGIYikYiOHj2q1NRUVVdX67vvvnOqRgAmtbTXnoNzYCW6Ou5rM7gPHTrU4serq6u1dOlSWwoCELuW9tpzcA6sxBtB97W5OO10ZWVlqqiokCT17t1bo0aNsq0oALGZM2WYMob31+C0JGUM7685U4addVAOB+egM3gj6L42R9xlZWV6/PHHtW3btqbtX6mpqbrttts0Z84cRwoEYF5Le+05OCe43Ghbc4Ki+9oM7t/97ncaOXKknnvuOW3btk19+vTR2LFjtWbNGpWUlCg7O9upOgHX+HFOz481nykI12A3N9rWvBF0X5vB/fnnn2vt2rWSpIsuukizZ8/WvHnz9OSTT+q6664juBEKfpzT82PNZwrCNdjNjbY1Jyi6r83gjkQiKi0tVXJysr744oumleTdu3dnOxhCw6kXRytHmEGYhwzCNdiNtnU4tZm+N998s6677jpddNFFOnjwoJYsWSJJ+uabbzRgwABHCgTc5tSLo5UjzCC8oAfhGuxG2zqc2gzumTNnatSoUfrwww913333afDgwZKkfv366emnn3aiPsB1Tr04WjnCDMILehCuwW60rcOp3X730KFDNXToUNXW1qqoqEiSNGTIEFrlCA2nXhytHGEG4QU9CNcA2MFU+r799tu6++671aNHD0kNB7CsWrVKl1xyia3FIRxYPdyAESYAM0wF99KlS7Vy5Ur95Cc/kdQQ5H/4wx/00ksv2VocwoHVww0YYQIww/TJaY2hLUljxoyxpRiEE6uHAcA8U8F9+eWXNxtdb9u2TVdccYVtRSFcOJITAMwz1SrfunWr/vKXv+j++++XJNXU1Cg5OVlbtmxRJBLRnj17bC0SwcbcLgCYZyq4c3Nz7a4DIcbcLgCYZyq4Bw4caHcdAHyupd0BUbeLAgLIVHCPHTtWkUik2ceSkpI0atQo3XvvvYpG+d8TCLuWdgc8ePu4ps+z7Q+whqng/sUvfqGysjLNnDlTkpSXl6euXbsqISFBDzzwgJ566ilbiwTgvI4GbXu7A9j2B1jDVHDv2rVLOTk5TY/vu+8+zZw5U7m5uZo6daptxQFwT0eDtr2T39j2B1jDVHCXlZU13SVMkkpKSnTy5ElJUrdu3eyrDoBrOhq07e0O4KYhgDVMBfecOXN0/fXX68orr5TUMAKfO3euKioqOPYUCKiOBm17uwPY9gdYI2IYhmHmCw8dOqR9+/ZJkjIyMjR8+HBbCzvd8ePl7X+Rj0SjSYG7JjO4bn85WVWjZ1/u3GIyv157Z3Hd4WP1tUejSa1+zvQtvoYOHaouXRoOWhsyZEjnqwJswupla7C/HvAm7g6GwGH1MoAg4+5gCBxWL+NMdGEQJKZb5dwdDH7B6mVvcjM86cIgSEwFd+Pdwa677jpJ3B0M3mbn6mVGbrFzMzzpwiBIXLk72Pr165WTk6NIJKJhw4ZpxYoV6t69e8erB1pg56IqRm6xczM86cIgSBy/O9jRo0e1ceNG/f3vf1ePHj105513qqCgQDNmzLDsOdA5jCpbx8gtdm6GJ3vIESSu3B2svr5ep06dUlxcnE6dOqX+/ftb+vPROYwqW8fILXZuhidb2xAkpg5gsfruYBs2bNDq1avVvXt3XX755Xr88cfb/Pq6unrFxXXt0HMgdotW/7c+/Ky06fGPBiVr1V1XuliRd5RV1Ght7gEd/bZSqSk9dcfMdPVOpBsBwDmO3x3sxIkT2rFjh3bs2KGkpCTdeeedys/P1/XXX9/q95SUVJr++X7g9dOFks8IouTEeEvq9fp1m3Xrf3x/amB1ZbWOV1a3+fV+vW4rpkz8eu2dxXWHj+dOTrPy7mC7d+/Wueeeq5SUFEnS5MmTtX///jaDG86yuqXZGAClFTVKToxnztwnmDIBvMnxu4MNGDBABw4cUFVVlXr06KE9e/bo4ot5MfASq+cDTw+ARl4KABbjtYyFeIA3OX53sPT0dE2ZMkXTp09XXFycLrzwQs2ePbvjlcM3vB4AnRlZBjn0WYgHeJOp4P7lL3+pMWPGNN0d7Kabbmq6O9iDDz7Y4SfNzs5WdnZ2h78P/uT1AOjMG4sgt5PZQgV4k+kjTy+44AJ17dqwsvv888+3rSAET+ML/ulz3F7SmTcWXu8mdEaYt1AFuZMC/zMV3AcPHlR2drbi4+NlGIbq6uq0Zs0ajRgxwu76EACNAeDVFaedGVl6vZuA2AS5kwL/MxXcy5Yt0/LlyzVu3DhJ0p49e/Twww/rhRdesLU4wAmdGVnSTg6mIHdS4H+mgruqqqoptCVp3LhxeuSRR2wrCvCLMLeTg4xOCrzMVHAnJCTorbfe0mWXXSZJ2rt3rxIS+A8ZQDDRSYGXmQru3//+97rzzjsVH9+wOKO2tlZPPPGErYUBgFvopMDLTAX3yJEjVVhYqI8//lhSw6ryjh68AgAAOq/N4K6qar4gY9CgQZKkuro61dXV0S6H69i2AyBs2gzu0aNHKxKJqPEGYo13CDMMQ5FIRO+//779FQJtYNsOgLBpM7gPHTrkVB1ATNi2AyBsTJ+cBniRX7bt0NIHYBWCG77ml207tPQBWIXghu/4ZfR6+n3IvzjW/KhXWvoAYkVww3f8Mnpt6T7kjbza0gfgfQQ3fMcvC9LOrKtn9zj175Pg6ZY+AO8juOE7flmQdmadI85P8WRnAIC/ENzwHb8sSPP6fcgB+BPBDd/xyznSXr8POQB/6uJ2AQAAwDyCGwAAHyG4AQDwEYIbAAAfYXEaPMsvJ6QBgJMIbniWX05IAwAn0SqHZ/nlhDQAcBIjbniWX05I85KWphdkiCkHIEAIbniWX05I85KWphckMeUABAjBDc/yywlpXmJmeoEpB8DfCG4gQFqbXnB6yuH0e5E3ntNOex6wBsENBEhb0wtOTjm0dC9yuieANQhunIX90/7V2vSC06HJjgDAPgQ3zsL+aWuEuV3MjgDAPgQ3zsJoyRphbhdzL3LAPgQ3zsJoyRpWvAHy67QF9yIH7ENw4yzsn7bGmW+ATlTUaOn6fR0KYKYtAJyJ4MZZ2D9tjdPbxd+UVqmkvFol5dUdCmCmLQCcieAGbHJ6u3jByldVUl7d9DmzAcy0Rfj4dXoEziG4HRTmVcZhF2sAM20RPkyPoD0Et4PCvMo47GINYKYtmgvDaJTpEbSH4HYQ/0OGl50BHIYwaxSG0WifXt31ib7vzvRJ6u5iNfAigttBzFfCDmEIs0ZhePNryGj+2DBa+UqEFcHtIA6lgB3CEGaNwvDmt/RkTZuPAYLbQRxKATuEIcwahWGxXpj+nogNwQ34nJth5vT8ehgW64XhzQk6h+AGfM7NMAvT/LpTwvDmBJ3Txe0CAPhXmObXAa8guAHE7Mz5V+ZjAfvRKjcpTHtlAbOYjwWcR3CbxFwecDbmYwHn0So3ibk8AIAXENwmMZcHAPACWuUmMZcHAPACgtsk5vIAAF5AcAMOYFcCAKsQ3IAD2JUAwCqOB/eRI0e0cOHCpsefffaZsrOzlZWV5XQpgGPYlQDAKo4H95AhQ5Sfny9Jqq+v14QJE3T11Vc7XQbgKO74BMAqrrbK9+zZo0GDBmngwIFulgHYjl0JAKzianAXFBRo2rRpbpYAOIJdCQCsEjEMw3DjiWtqajR+/HgVFBSoX79+bX5tXV294uK6OlRZcJyoqNFTuQd09NtKpab01B0z09U7kZXMAOBnro24d+3apREjRrQb2pJUUlLpQEXOiUaTdPx4eftf2Elr895tWsn84Welqq6uc3XU59R1e01Yr1sK77Vz3eFj9bVHo0mtfs61I08LCgo0depUt54+FFjJDADB40pwV1ZWavfu3Zo8ebIbTx8anK8OAMHjSqu8Z8+eeuutt9x46lBhJTMABA8npwUYK5kBIHgIbriOc7wBwLxQBTcB4U2c4w0A5oUquMMWEH55o8LqdwAwL1TBHbaA+P9/f1//81GxpIY3KrV19cq+Id3lqs7GOd4AYF6ogjtsAVH0WWmbj73CqdXvfulAOIXfB+BPoQru8G2PirTz2BucWv0etqmS9vD7APwpVMEdtu1R/29QsvZ/9M33j89LdrEa94VtqqQ9/D4Af3LtyFPY75apw5UxvL8GpyUpY3h/3fKz4W6X5CpOkmuO3wfgT6EacYdN2DoM7QnfVEnb+H0A/kRww3aNi6BKK2qUnBjv2iIo3sg0x+8D8CeCG7Y7fRFUIwIDAGLDHDdsxyIoALAOwQ3bsQgKAKxDqxy2a1z0dPocNwAgNgQ3bNe4CCoaTdLx4+XtfwMAoFUEN+BDHFcKhBfBDfgQx5UC4cXiNMCHWKkPhBfBDfgQK/WB8KJVDvgQx5UC4UVwO8grR3/C/ziuFAgvgttBHP0JAOgs5rgdxIIiAEBnEdwOYkERAKCzaJU7iKM/AQCdRXA7iKM/AQCdRascAAAfYcQNBJDVZ5lzNjrgHQQ3EEBWn2XO2eiAd9AqBwLI6q2HbGUEvIPgBgLI6q2HbGUEvINWORBAVp9lztnogHcQ3EAAWX2WOWejA95BqxwAAB8huAEA8BGCGwAAHyG4AQDwEYIbAAAfIbgBAPARghsAAB9hHzfQAUG62UaQrgUIE4Ib6IAg3WwjSNcChAmtcqADgnSzjSBdCxAmBDfQAUG62UaQrgUIE1rlQAcE6WYbQboWIEwIbqADgnSzjSBdCxAmtMoBAPARghsAAB8huAEA8BGCGwAAH2FxGtACThUD4FUEN9ACThUD4FW0yoEWcKoYAK8iuIEWcKoYAK+iVQ60gFPFAHiVK8FdVlam+++/X0VFRYpEIlq+fLlGjx7tRilAizhVDIBXuRLcy5Yt0/jx4/XEE0+opqZGp06dcqMMAAB8x/E57vLycu3bt0833HCDJCk+Pl69e/d2ugwAAHzJ8eD+/PPPlZKSosWLFyszM1NLlixRZWWl02UAAOBLEcMwDCef8ODBg5o9e7Y2bdqk9PR0/fGPf1SvXr101113tfo9dXX1iovr6mCVAAB4k+Nz3GlpaUpLS1N6erok6ZprrtG6deva/J6SkmCNyKPRJB0/Xu52GY7jusMnrNfOdYeP1dcejSa1+jnHW+XRaFRpaWk6cuSIJGnPnj0aOnSo02UAAOBLrqwqf+CBB3TPPfeotrZWgwYN0ooVK9woAwAA33EluC+88EJt2bLFjacGAMDXOPIUAAAfIbgBAPARx7eDAQCA2DHiBgDARwhuAAB8hOAGAMBHCG4AAHyE4AYAwEcIbgAAfMSVk9PCrL6+XjNnzlRqaqr+/Oc/u12OYyZOnKjExER16dJFXbt2Dc3JeWVlZbr//vtVVFSkSCSi5cuXa/To0W6XZasjR45o4cKFTY8/++wzZWdnKysry72iHLJ+/Xrl5OQoEolo2LBhWrFihbp37+52WY7YsGGDcnJyZBiGZs2aFdi/9+LFi7Vz50717dtX27dvlySVlpZq4cKF+uKLLzRw4ECtXr1a55xzjm01MOJ22MaNG0N7U5UNGzYoPz8/NKEtScuWLdP48eP1j3/8Q/n5+aH42w8ZMkT5+flNf+uEhARdffXVbpdlu6NHj2rjxo3Kzc3V9u3bVV9fr4KCArfLckRRUZFycnKUk5Oj/Px87dy5U59++qnbZdlixowZeuaZZ5p9bN26dRo3bpwKCws1bty4du942VkEt4O+/vpr7dy5UzfccIPbpcAB5eXl2rdvX9PfOz4+Xr1793a5Kmft2bNHgwYN0sCBA90uxRH19fU6deqU6urqdOrUKfXv39/tkhxx+PBhjRw5UgkJCYqLi1NGRoYKCwvdLssWGRkZZ42md+zYoczMTElSZmamXnnlFVtrILgdtHz5ct17773q0iWcv/bbbrtNM2bM0N/+9je3S3HE559/rpSUFC1evFiZmZlasmSJKiuDdW/59hQUFGjatGlul+GI1NRU3Xrrrbrqqqt0xRVXqFevXrriiivcLssRw4YN07/+9S+VlJSoqqpKu3bt0tdff+12WY4pLi5uepMWjUZVXFxs6/OFM0Fc8NprryklJUUXX3yx26W4YtOmTdq6dauefvppPf/889q3b5/bJdmurq5O7733nm688Ubl5eUpISHB9haal9TU1OjVV1/VNddc43Ypjjhx4oR27NihHTt26PXXX1dVVZXy8/PdLssRQ4cO1dy5c3Xbbbdp7ty5Gj58eGgHKJFIRJFIxNbnCOdv1gXvvPOOXn31VU2cOFGLFi3Sm2++qXvuucftshyTmpoqSerbt6+uvvpq/fvf/3a5IvulpaUpLS1N6enpkqRrrrlG7733nstVOWfXrl0aMWKE+vXr53Ypjti9e7fOPfdcpaSkqFu3bpo8ebL279/vdlmOmTVrlrZs2aLnn39e55xzjgYPHux2SY7p27evjh07Jkk6duyYUlJSbH0+gtshd999t3bt2qVXX31Vq1at0tixY/XYY4+5XZYjKisrdfLkyaZ/v/HGG/rRj37kclX2i0ajSktL05EjRyQ1zPeGYXFao4KCAk2dOtXtMhwzYMAAHThwQFVVVTIMI3R/78b28JdffqnCwkJde+21LlfknIkTJyovL0+SlJeXp0mTJtn6fGwHg+2Ki4s1f/58SQ2Ld6ZNm6YJEya4XJUzHnjgAd1zzz2qra3VoEGDtGLFCrdLckRlZaV2796tpUuXul2KY9LT0zVlyhRNnz5dcXFxuvDCCzV79my3y3LMggULVFpaqri4OD300EOBXYi5aNEi7d27VyUlJZowYYIWLFigefPm6a677tLmzZs1YMAArV692tYauK0nAAA+QqscAAAfIbgBAPARghsAAB8huAEA8BGCGwAAHyG4AQDwEYIbgCPq6+vdLgEIBIIbCMjZWkMAAALhSURBVKi7775bM2bM0LXXXqv58+frxIkTysrKanbnotdee01z5syR1HBUY3Z2tm644QZde+21euqppyQ1HKAzceJEHTx4UJK0detW3Xjjjaqrq9OWLVt0yy236Ne//rV+9rOf6Ve/+pWOHj0qSdqyZYuysrI0f/58TZs2TUVFRQ7/BoCAMgAEUnFxcdO/V61aZaxcudLIy8sz5s+f3/Tx3/zmN8bWrVsNwzCMrKwsY+/evYZhGEZ1dbVx4403Gv/85z8NwzCMN99805g8ebKxf/9+46c//anx5ZdfGoZhGLm5ucaPf/xj4/Dhw4ZhGMaaNWuMBQsWNH1u1KhRxqeffmr/xQIhwpGnQEDl5+dr27Ztqq2tVWVlpQYPHqz58+drxYoVKikpkSTt3btXjz76qCorK7V37159++23Td9fUVGhw4cP6/LLL9dll12madOm6aabbtKTTz6pH/zgB01fd+mll2rIkCGSGm40cfoZ1ZdcconOO+88h64YCAeCGwigt99+W5s2bdILL7yglJQUbdu2TS+++KISEhI0adIkbd++XZI0adIk9ezZUydPnlQkEtHmzZvVrVu3Fn/me++9p5SUlA7dZzkxMdGS6wHwPea4gQAqKytTr169lJycrJqaGuXm5jZ9bvr06dq6dau2bt2qGTNmSJJ69eqlSy+9tNn9wr/66isdP35ckrR+/fqmOe1nnnlG77//ftPXvfPOO/rkk08kSbm5uRo7dqwDVwiEFyNuIIDGjx+vl156SVOmTFGfPn00ZsyYpsVlY8aMabrN6pgxY5q+57HHHtOKFSuaWt2JiYlatmyZvvrqK23cuFGbN29WSkqKHn74YS1cuFCbN2+W1NAOf/TRR/Xpp5+qX79+WrlypcNXC4QLdwcDELMtW7Zo586deuKJJ9wuBQgNWuUAAPgII24AAHyEETcAAD5CcAMA4CMENwAAPkJwAwDgIwQ3AAA+QnADAOAj/wdB9NuVLZdu3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('seaborn')\n",
    "\n",
    "df1.plot(x='avexpr', y='logpgp95', kind='scatter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows a fairly strong positive relationship between\n",
    "protection against expropriation and log GDP per capita.\n",
    "Specifically, if higher protection against expropriation is a measure of\n",
    "institutional quality, then better institutions appear to be positively\n",
    "correlated with better economic outcomes (higher GDP per capita).\n",
    "\n",
    "Given the plot, choosing a linear model to describe this relationship\n",
    "seems like a reasonable assumption.\n",
    "We can write our model as\n",
    "$$\n",
    "{logpgp95}_i = \\beta_0 + \\beta_1 {avexpr}_i + u_i\n",
    "$$\n",
    "where:\n",
    "- $ \\beta_0 $ is the intercept of the linear trend line on the\n",
    "  y-axis  \n",
    "- $ \\beta_1 $ is the slope of the linear trend line, representing\n",
    "  the *marginal effect* of protection against risk on log GDP per\n",
    "  capita  \n",
    "- $ u_i $ is a random error term (deviations of observations from\n",
    "  the linear trend due to factors not included in the model)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dropping NA's is required to use numpy's polyfit\n",
    "df1_subset = df1.dropna(subset=['logpgp95', 'avexpr'])\n",
    "\n",
    "# Use only 'base sample' for plotting purposes\n",
    "df1_subset = df1_subset[df1_subset['baseco'] == 1]\n",
    "\n",
    "X = df1_subset['avexpr']\n",
    "y = df1_subset['logpgp95']\n",
    "labels = df1_subset['shortnam']\n",
    "\n",
    "# Replace markers with country labels\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X, y, marker='')\n",
    "\n",
    "for i, label in enumerate(labels):\n",
    "    ax.annotate(label, (X.iloc[i], y.iloc[i]))\n",
    "\n",
    "# Fit a linear trend line\n",
    "ax.plot(np.unique(X),\n",
    "         np.poly1d(np.polyfit(X, y, 1))(np.unique(X)),\n",
    "         color='black')\n",
    "\n",
    "ax.set_xlim([3.3,10.5])\n",
    "ax.set_ylim([4,10.5])\n",
    "ax.set_xlabel('Average Expropriation Risk 1985-95')\n",
    "ax.set_ylabel('Log GDP per capita, PPP, 1995')\n",
    "ax.set_title('Figure 2: OLS relationship between expropriation \\\n",
    "    risk and income')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common technique to estimate the parameters ($ \\beta $’s)\n",
    "of the linear model is Ordinary Least Squares (OLS).\n",
    "As the name implies, an OLS model is solved by finding the parameters\n",
    "that minimize *the sum of squared residuals*, i.e.\n",
    "$$\n",
    "\\underset{\\hat{\\beta}}{\\min} \\sum^N_{i=1}{\\hat{u}^2_i}\n",
    "$$\n",
    "where $ \\hat{u}_i $ is the difference between the observation and\n",
    "the predicted value of the dependent variable.\n",
    "\n",
    "To estimate the constant term $ \\beta_0 $, we need to add a column\n",
    "of 1’s to our dataset (consider the equation if $ \\beta_0 $ was\n",
    "replaced with $ \\beta_0 x_i $ and $ x_i = 1 $)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "df1['const'] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can construct our model in `statsmodels` using the OLS function.\n",
    "We will use `pandas` dataframes with `statsmodels`, however standard arrays can also be used as arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "statsmodels.regression.linear_model.OLS"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg1 = sm.OLS(endog=df1['logpgp95'], exog=df1[['const', 'avexpr']], missing='drop')\n",
    "type(reg1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, we have simply constructed our model. We need to use `.fit()` to obtain parameter estimates\n",
    "$ \\hat{\\beta}_0 $ and $ \\hat{\\beta}_1 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "statsmodels.regression.linear_model.RegressionResultsWrapper"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = reg1.fit()\n",
    "type(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have the fitted regression model stored in `results`.\n",
    "To view the OLS regression results, we can call the `.summary()`\n",
    "method.\n",
    "\n",
    "Note that an observation was mistakenly dropped from the results in the\n",
    "original paper (see the note located in maketable2.do from Acemoglu’s webpage), and thus the\n",
    "coefficients differ slightly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               logpgp95   R-squared:                       0.611\n",
      "Model:                            OLS   Adj. R-squared:                  0.608\n",
      "Method:                 Least Squares   F-statistic:                     171.4\n",
      "Date:                Sun, 20 Oct 2019   Prob (F-statistic):           4.16e-24\n",
      "Time:                        22:13:25   Log-Likelihood:                -119.71\n",
      "No. Observations:                 111   AIC:                             243.4\n",
      "Df Residuals:                     109   BIC:                             248.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          4.6261      0.301     15.391      0.000       4.030       5.222\n",
      "avexpr         0.5319      0.041     13.093      0.000       0.451       0.612\n",
      "==============================================================================\n",
      "Omnibus:                        9.251   Durbin-Watson:                   1.689\n",
      "Prob(Omnibus):                  0.010   Jarque-Bera (JB):                9.170\n",
      "Skew:                          -0.680   Prob(JB):                       0.0102\n",
      "Kurtosis:                       3.362   Cond. No.                         33.2\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From our results, we see that\n",
    "\n",
    "- The intercept $ \\hat{\\beta}_0 = 4.63 $.  \n",
    "- The slope $ \\hat{\\beta}_1 = 0.53 $.  \n",
    "- The positive $ \\hat{\\beta}_1 $ parameter estimate implies that.\n",
    "  institutional quality has a positive effect on economic outcomes, as\n",
    "  we saw in the figure.  \n",
    "- The p-value of 0.000 for $ \\hat{\\beta}_1 $ implies that the\n",
    "  effect of institutions on GDP is statistically significant (using p <\n",
    "  0.05 as a rejection rule).  \n",
    "- The R-squared value of 0.611 indicates that around 61% of variation\n",
    "  in log GDP per capita is explained by protection against\n",
    "  expropriation.  \n",
    "\n",
    "\n",
    "Using our parameter estimates, we can now write our estimated\n",
    "relationship as\n",
    "\n",
    "$$\n",
    "\\widehat{logpgp95}_i = 4.63 + 0.53 \\ {avexpr}_i\n",
    "$$\n",
    "\n",
    "This equation describes the line that best fits our data, as shown in\n",
    "Figure 2.    \n",
    "We can use this equation to predict the level of log GDP per capita for\n",
    "a value of the index of expropriation protection.    \n",
    "For example, for a country with an index value of 7.07 (the average for\n",
    "the dataset), we find that their predicted level of log GDP per capita\n",
    "in 1995 is 8.38."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.515625"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_expr = np.mean(df1_subset['avexpr'])\n",
    "mean_expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.3771"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predicted_logpdp95 = 4.63 + 0.53 * 7.07\n",
    "predicted_logpdp95"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An easier (and more accurate) way to obtain this result is to use\n",
    "`.predict()` and set $ constant = 1 $ and\n",
    "$ {avexpr}_i = mean\\_expr $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.09156367])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.predict(exog=[1, mean_expr])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain an array of predicted $ {logpgp95}_i $ for every value\n",
    "of $ {avexpr}_i $ in our dataset by calling `.predict()` on our\n",
    "results.    \n",
    "Plotting the predicted values against $ {avexpr}_i $ shows that the\n",
    "predicted values lie along the linear line that we fitted above.\n",
    " The observed values of $ {logpgp95}_i $ are also plotted for\n",
    "comparison purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Drop missing observations from whole sample\n",
    "\n",
    "df1_plot = df1.dropna(subset=['logpgp95', 'avexpr'])\n",
    "\n",
    "# Plot predicted values\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "ax.scatter(df1_plot['avexpr'], results.predict(), alpha=0.5,\n",
    "        label='predicted')\n",
    "\n",
    "# Plot observed values\n",
    "\n",
    "ax.scatter(df1_plot['avexpr'], df1_plot['logpgp95'], alpha=0.5,\n",
    "        label='observed')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_title('OLS predicted values')\n",
    "ax.set_xlabel('avexpr')\n",
    "ax.set_ylabel('logpgp95')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extending the Linear Regression Model\n",
    "\n",
    "So far we have only accounted for institutions affecting economic\n",
    "performance - almost certainly there are numerous other factors\n",
    "affecting GDP that are not included in our model.     \n",
    "Leaving out variables that affect $ logpgp95_i $ will result in **omitted variable bias**, yielding biased and inconsistent parameter estimates.      \n",
    "We can extend our bivariate regression model to a **multivariate regression model** by adding in other factors that may affect $ logpgp95_i $.\n",
    "\n",
    "[[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) consider other factors such as:\n",
    "- the effect of climate on economic outcomes; latitude is used to proxy\n",
    "  this  \n",
    "- differences that affect both economic performance and institutions,\n",
    "  eg. cultural, historical, etc.; controlled for with the use of\n",
    "  continent dummies  \n",
    "\n",
    "Let’s estimate some of the extended models considered in the paper\n",
    "(Table 2) using data from `maketable2.dta`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "df2 = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/ols/maketable2.dta')\n",
    "\n",
    "# Add constant term to dataset\n",
    "df2['const'] = 1\n",
    "\n",
    "# Create lists of variables to be used in each regression\n",
    "X1 = ['const', 'avexpr']\n",
    "X2 = ['const', 'avexpr', 'lat_abst']\n",
    "X3 = ['const', 'avexpr', 'lat_abst', 'asia', 'africa', 'other']\n",
    "\n",
    "# Estimate an OLS regression for each set of variables\n",
    "reg1 = sm.OLS(df2['logpgp95'], df2[X1], missing='drop').fit()\n",
    "reg2 = sm.OLS(df2['logpgp95'], df2[X2], missing='drop').fit()\n",
    "reg3 = sm.OLS(df2['logpgp95'], df2[X3], missing='drop').fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have fitted our model, we will use `summary_col` to\n",
    "display the results in a single table (model numbers correspond to those\n",
    "in the paper)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Table 2 - OLS Regressions\n",
      "=========================================\n",
      "                 Model 1 Model 3 Model 4 \n",
      "-----------------------------------------\n",
      "const            4.63*** 4.87*** 5.85*** \n",
      "                 (0.30)  (0.33)  (0.34)  \n",
      "avexpr           0.53*** 0.46*** 0.39*** \n",
      "                 (0.04)  (0.06)  (0.05)  \n",
      "lat_abst                 0.87*   0.33    \n",
      "                         (0.49)  (0.45)  \n",
      "asia                             -0.15   \n",
      "                                 (0.15)  \n",
      "africa                           -0.92***\n",
      "                                 (0.17)  \n",
      "other                            0.30    \n",
      "                                 (0.37)  \n",
      "R-squared        0.61    0.62    0.72    \n",
      "No. observations 111     111     111     \n",
      "=========================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "info_dict={'R-squared' : lambda x: f\"{x.rsquared:.2f}\",\n",
    "           'No. observations' : lambda x: f\"{int(x.nobs):d}\"}\n",
    "\n",
    "results_table = summary_col(results=[reg1,reg2,reg3],\n",
    "                            float_format='%0.2f',\n",
    "                            stars = True,\n",
    "                            model_names=['Model 1',\n",
    "                                         'Model 3',\n",
    "                                         'Model 4'],\n",
    "                            info_dict=info_dict,\n",
    "                            regressor_order=['const',\n",
    "                                             'avexpr',\n",
    "                                             'lat_abst',\n",
    "                                             'asia',\n",
    "                                             'africa'])\n",
    "\n",
    "results_table.add_title('Table 2 - OLS Regressions')\n",
    "\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Endogeneity\n",
    "\n",
    "As [[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) discuss, the OLS models likely suffer from\n",
    "**endogeneity** issues, resulting in biased and inconsistent model\n",
    "estimates.    \n",
    "Namely, there is likely a two-way relationship between institutions and\n",
    "economic outcomes:\n",
    "- richer countries may be able to afford or prefer better institutions  \n",
    "- variables that affect income may also be correlated with\n",
    "  institutional differences  \n",
    "- the construction of the index may be biased; analysts may be biased\n",
    "  towards seeing countries with higher income having better\n",
    "  institutions  \n",
    "To deal with endogeneity, we can use **two-stage least squares (2SLS)\n",
    "regression**, which is an extension of OLS regression.\n",
    "\n",
    "This method requires replacing the endogenous variable\n",
    "$ {avexpr}_i $ with a variable that is:\n",
    "1. correlated with $ {avexpr}_i $  \n",
    "1. not correlated with the error term (ie. it should not directly affect\n",
    "  the dependent variable, otherwise it would be correlated with\n",
    "  $ u_i $ due to omitted variable bias)  \n",
    "The new set of regressors is called an **instrument**, which aims to\n",
    "remove endogeneity in our proxy of institutional differences.\n",
    "\n",
    "The main contribution of [[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) is the use of settler mortality rates to instrument for institutional differences. They hypothesize that higher mortality rates of colonizers led to the establishment of institutions that were more extractive in nature (less protection against expropriation), and these institutions still persist today.\n",
    "\n",
    "Using a scatterplot (Figure 3 in [[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001)), we can see protection against expropriation is negatively correlated with settler mortality rates, coinciding with the authors’ hypothesis and satisfying the first condition of a valid instrument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dropping NA's is required to use numpy's polyfit\n",
    "df1_subset2 = df1.dropna(subset=['logem4', 'avexpr'])\n",
    "\n",
    "X = df1_subset2['logem4']\n",
    "y = df1_subset2['avexpr']\n",
    "labels = df1_subset2['shortnam']\n",
    "\n",
    "# Replace markers with country labels\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X, y, marker='')\n",
    "\n",
    "for i, label in enumerate(labels):\n",
    "    ax.annotate(label, (X.iloc[i], y.iloc[i]))\n",
    "\n",
    "# Fit a linear trend line\n",
    "ax.plot(np.unique(X),\n",
    "         np.poly1d(np.polyfit(X, y, 1))(np.unique(X)),\n",
    "         color='black')\n",
    "\n",
    "ax.set_xlim([1.8,8.4])\n",
    "ax.set_ylim([3.3,10.4])\n",
    "ax.set_xlabel('Log of Settler Mortality')\n",
    "ax.set_ylabel('Average Expropriation Risk 1985-95')\n",
    "ax.set_title('Figure 3: First-stage relationship between settler mortality \\\n",
    "    and expropriation risk')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second condition may not be satisfied if settler mortality rates in the 17th to 19th centuries have a direct effect on current GDP (in addition to their indirect effect through institutions).     \n",
    "For example, settler mortality rates may be related to the current disease environment in a country, which could affect current economic performance.    \n",
    "[[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) argue this is unlikely because:\n",
    "- The majority of settler deaths were due to malaria and yellow fever\n",
    "  and had a limited effect on local people.  \n",
    "- The disease burden on local people in Africa or India, for example,\n",
    "  did not appear to be higher than average, supported by relatively\n",
    "  high population densities in these areas before colonization.  \n",
    "As we appear to have a valid instrument, we can use 2SLS regression to obtain consistent and unbiased parameter estimates. \n",
    "\n",
    "**First stage**\n",
    "\n",
    "The first stage involves regressing the endogenous variable\n",
    "($ {avexpr}_i $) on the instrument.     The instrument is the set of all exogenous variables in our model (and\n",
    "not just the variable we have replaced).  Using model 1 as an example, our instrument is simply a constant and\n",
    "settler mortality rates $ {logem4}_i $.\n",
    "Therefore, we will estimate the first-stage regression as\n",
    "$$\n",
    "{avexpr}_i = \\delta_0 + \\delta_1 {logem4}_i + v_i\n",
    "$$\n",
    "The data we need to estimate this equation is located in\n",
    "`maketable4.dta` (only complete data, indicated by `baseco = 1`, is\n",
    "used for estimation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 avexpr   R-squared:                       0.270\n",
      "Model:                            OLS   Adj. R-squared:                  0.258\n",
      "Method:                 Least Squares   F-statistic:                     22.95\n",
      "Date:                Sun, 20 Oct 2019   Prob (F-statistic):           1.08e-05\n",
      "Time:                        22:30:20   Log-Likelihood:                -104.83\n",
      "No. Observations:                  64   AIC:                             213.7\n",
      "Df Residuals:                      62   BIC:                             218.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          9.3414      0.611     15.296      0.000       8.121      10.562\n",
      "logem4        -0.6068      0.127     -4.790      0.000      -0.860      -0.354\n",
      "==============================================================================\n",
      "Omnibus:                        0.035   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.983   Jarque-Bera (JB):                0.172\n",
      "Skew:                           0.045   Prob(JB):                        0.918\n",
      "Kurtosis:                       2.763   Cond. No.                         19.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Import and select the data\n",
    "df4 = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/ols/maketable4.dta')\n",
    "df4 = df4[df4['baseco'] == 1]\n",
    "\n",
    "# Add a constant variable\n",
    "df4['const'] = 1\n",
    "\n",
    "# Fit the first stage regression and print summary\n",
    "results_fs = sm.OLS(df4['avexpr'],\n",
    "                    df4[['const', 'logem4']],\n",
    "                    missing='drop').fit()\n",
    "print(results_fs.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Second stage**\n",
    "\n",
    "We need to retrieve the predicted values of $ {avexpr}_i $ using\n",
    "`.predict()`.      \n",
    "We then replace the endogenous variable $ {avexpr}_i $ with the\n",
    "predicted values $ \\widehat{avexpr}_i $ in the original linear model.\n",
    "Our second stage regression is thus\n",
    "$$\n",
    "{logpgp95}_i = \\beta_0 + \\beta_1 \\widehat{avexpr}_i + u_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               logpgp95   R-squared:                       0.477\n",
      "Model:                            OLS   Adj. R-squared:                  0.469\n",
      "Method:                 Least Squares   F-statistic:                     56.60\n",
      "Date:                Sun, 20 Oct 2019   Prob (F-statistic):           2.66e-10\n",
      "Time:                        22:31:07   Log-Likelihood:                -72.268\n",
      "No. Observations:                  64   AIC:                             148.5\n",
      "Df Residuals:                      62   BIC:                             152.9\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "const                1.9097      0.823      2.320      0.024       0.264       3.555\n",
      "predicted_avexpr     0.9443      0.126      7.523      0.000       0.693       1.195\n",
      "==============================================================================\n",
      "Omnibus:                       10.547   Durbin-Watson:                   2.137\n",
      "Prob(Omnibus):                  0.005   Jarque-Bera (JB):               11.010\n",
      "Skew:                          -0.790   Prob(JB):                      0.00407\n",
      "Kurtosis:                       4.277   Cond. No.                         58.1\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "df4['predicted_avexpr'] = results_fs.predict()\n",
    "\n",
    "results_ss = sm.OLS(df4['logpgp95'],\n",
    "                    df4[['const', 'predicted_avexpr']]).fit()\n",
    "print(results_ss.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second-stage regression results give us an unbiased and consistent\n",
    "estimate of the effect of institutions on economic outcomes.\n",
    "The result suggests a stronger positive relationship than what the OLS\n",
    "results indicated.\n",
    "Note that while our parameter estimates are correct, our standard errors\n",
    "are not and for this reason, computing 2SLS ‘manually’ (in stages with\n",
    "OLS) is not recommended.\n",
    "\n",
    "We can correctly estimate a 2SLS regression in one step using the\n",
    "[linearmodels](https://github.com/bashtage/linearmodels) package, an extension of `statsmodels`.   \n",
    "Note that when using `IV2SLS`, the exogenous and instrument variables\n",
    "are split up in the function arguments (whereas before the instrument\n",
    "included exogenous variables)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                          IV-2SLS Estimation Summary                          \n",
      "==============================================================================\n",
      "Dep. Variable:               logpgp95   R-squared:                      0.1870\n",
      "Estimator:                    IV-2SLS   Adj. R-squared:                 0.1739\n",
      "No. Observations:                  64   F-statistic:                    37.568\n",
      "Date:                Sun, Oct 20 2019   P-value (F-stat)                0.0000\n",
      "Time:                        22:32:21   Distribution:                  chi2(1)\n",
      "Cov. Estimator:            unadjusted                                         \n",
      "                                                                              \n",
      "                             Parameter Estimates                              \n",
      "==============================================================================\n",
      "            Parameter  Std. Err.     T-stat    P-value    Lower CI    Upper CI\n",
      "------------------------------------------------------------------------------\n",
      "const          1.9097     1.0106     1.8897     0.0588     -0.0710      3.8903\n",
      "avexpr         0.9443     0.1541     6.1293     0.0000      0.6423      1.2462\n",
      "==============================================================================\n",
      "\n",
      "Endogenous: avexpr\n",
      "Instruments: logem4\n",
      "Unadjusted Covariance (Homoskedastic)\n",
      "Debiased: False\n"
     ]
    }
   ],
   "source": [
    "iv = IV2SLS(dependent=df4['logpgp95'],\n",
    "            exog=df4['const'],\n",
    "            endog=df4['avexpr'],\n",
    "            instruments=df4['logem4']).fit(cov_type='unadjusted')\n",
    "\n",
    "print(iv.summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given that we now have consistent and unbiased estimates, we can infer\n",
    "from the model we have estimated that institutional differences\n",
    "(stemming from institutions set up during colonization) can help\n",
    "to explain differences in income levels across countries today.\n",
    "\n",
    "[[AJR01]](https://python.quantecon.org/zreferences.html#acemoglu2001) use a marginal effect of 0.94 to calculate that the difference in the index between Chile and Nigeria (ie. institutional\n",
    "quality) implies up to a 7-fold difference in income, emphasizing the\n",
    "significance of institutions in economic development."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "In the lecture, we think the original model suffers from endogeneity\n",
    "bias due to the likely effect income has on institutional development.\n",
    "\n",
    "Although endogeneity is often best identified by thinking about the data\n",
    "and model, we can formally test for endogeneity using the **Hausman\n",
    "test**.       \n",
    "We want to test for correlation between the endogenous variable,\n",
    "$ avexpr_i $, and the errors, $ u_i $\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    " H_0 : Cov(avexpr_i, u_i) = 0  \\quad (no\\ endogeneity) \\\\\n",
    " H_1 : Cov(avexpr_i, u_i) \\neq 0 \\quad (endogeneity)\n",
    " \\end{aligned}\n",
    "$$\n",
    "\n",
    "This test is running in two stages.    \n",
    "First, we regress $ avexpr_i $ on the instrument, $ logem4_i $\n",
    "\n",
    "$$\n",
    "avexpr_i = \\pi_0 + \\pi_1 logem4_i + \\upsilon_i\n",
    "$$\n",
    "\n",
    "Second, we retrieve the residuals $ \\hat{\\upsilon}_i $ and include\n",
    "them in the original equation\n",
    "\n",
    "$$\n",
    "logpgp95_i = \\beta_0 + \\beta_1 avexpr_i + \\alpha \\hat{\\upsilon}_i + u_i\n",
    "$$\n",
    "\n",
    "If $ \\alpha $ is statistically significant (with a p-value < 0.05),\n",
    "then we reject the null hypothesis and conclude that $ avexpr_i $ is\n",
    "endogenous.    \n",
    "Using the above information, estimate a Hausman test and interpret your\n",
    "results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "The OLS parameter $ \\beta $ can also be estimated using matrix\n",
    "algebra and `numpy`.  \n",
    "The linear equation we want to estimate is (written in matrix form)\n",
    "\n",
    "$$\n",
    "y = X\\beta + u\n",
    "$$\n",
    "\n",
    "To solve for the unknown parameter $ \\beta $, we want to minimize\n",
    "the sum of squared residuals\n",
    "\n",
    "$$\n",
    "\\underset{\\hat{\\beta}}{\\min} \\hat{u}'\\hat{u}\n",
    "$$\n",
    "\n",
    "Rearranging the first equation and substituting into the second\n",
    "equation, we can write\n",
    "\n",
    "$$\n",
    "\\underset{\\hat{\\beta}}{\\min} \\ (Y - X\\hat{\\beta})' (Y - X\\hat{\\beta})\n",
    "$$\n",
    "\n",
    "Solving this optimization problem gives the solution for the\n",
    "$ \\hat{\\beta} $ coefficients\n",
    "\n",
    "$$\n",
    "\\hat{\\beta} = (X'X)^{-1}X'y\n",
    "$$\n",
    "\n",
    "Using the above information, compute $ \\hat{\\beta} $ from model 1\n",
    "using `numpy` - your results should be the same as those in the\n",
    "`statsmodels` output from earlier in the lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "# Load in data\n",
    "df4 = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/ols/maketable4.dta')\n",
    "\n",
    "# Add a constant term\n",
    "df4['const'] = 1\n",
    "\n",
    "# Estimate the first stage regression\n",
    "reg1 = sm.OLS(endog=df4['avexpr'],\n",
    "              exog=df4[['const', 'logem4']],\n",
    "              missing='drop').fit()\n",
    "\n",
    "# Retrieve the residuals\n",
    "df4['resid'] = reg1.resid\n",
    "\n",
    "# Estimate the second stage residuals\n",
    "reg2 = sm.OLS(endog=df4['logpgp95'],\n",
    "              exog=df4[['const', 'avexpr', 'resid']],\n",
    "              missing='drop').fit()\n",
    "\n",
    "print(reg2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output shows that the coefficient on the residuals is statistically\n",
    "significant, indicating $ avexpr_i $ is endogenous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "β_0 = 4.6\n",
      "β_1 = 0.53\n"
     ]
    }
   ],
   "source": [
    "# Load in data\n",
    "df1 = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/ols/maketable1.dta')\n",
    "df1 = df1.dropna(subset=['logpgp95', 'avexpr'])\n",
    "\n",
    "# Add a constant term\n",
    "df1['const'] = 1\n",
    "\n",
    "# Define the X and y variables\n",
    "y = np.asarray(df1['logpgp95'])\n",
    "X = np.asarray(df1[['const', 'avexpr']])\n",
    "\n",
    "# Compute β_hat\n",
    "β_hat = np.linalg.solve(X.T @ X, X.T @ y)\n",
    "\n",
    "# Print out the results from the 2 x 1 vector β_hat\n",
    "print(f'β_0 = {β_hat[0]:.2}')\n",
    "print(f'β_1 = {β_hat[1]:.2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to use `np.linalg.inv(X.T @ X) @ X.T @ y` to solve\n",
    "for $ \\beta $, however `.solve()` is preferred as it involves fewer\n",
    "computations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"880000\"> \"Deep Roots\" Exercises </font>\n",
    "\n",
    "<img src=\"https://tinyurl.com/20190119a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "### <font color=\"000088\">Catch Our Breath—Further Notes:</font>\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "* weblog support <https://github.com/braddelong/LS2019/blob/master/xinyue_linear_regression.ipynb>\n",
    "* nbViewer <https://nbviewer.jupyter.org/github/braddelong/LS2019/blob/master/xinyue_linear_regression.ipynb>\n",
    "\n",
    "&nbsp;\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "date": 1571536807.3008244,
  "filename": "ols.rst",
  "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": "3.7.5"
  },
  "title": "Linear Regression in Python"
 },
 "nbformat": 4,
 "nbformat_minor": 4
}