Chapter23IVeconometrics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 23: An Econometric Perspective on the Instrumental Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seaborn          : 0.13.0\n",
      "scipy            : 1.11.1\n",
      "linearmodels     : 5.3\n",
      "matplotlib_inline: 0.1.6\n",
      "graphviz         : 0.20.1\n",
      "numpy            : 1.24.3\n",
      "matplotlib       : 3.7.2\n",
      "statsmodels      : 0.14.0\n",
      "pandas           : 2.0.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import linearmodels as lm\n",
    "\n",
    "# viz\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
    "plt.rc(\"font\", **font)\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
    "%matplotlib inline\n",
    "\n",
    "from utils import *\n",
    "\n",
    "np.random.seed(42)\n",
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark --iversions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "card_data = pd.read_csv(\"card1995.csv\")\n",
    "yn, dn, zn = [\"lwage\", \"educ\", \"nearc4\"]\n",
    "Y, D, Z = card_data[yn], card_data[dn], card_data[zn]\n",
    "xs = [\n",
    "    \"exper\",\n",
    "    \"expersq\",\n",
    "    \"black\",\n",
    "    \"south\",\n",
    "    \"smsa\",\n",
    "    \"reg661\",\n",
    "    \"reg662\",\n",
    "    \"reg663\",\n",
    "    \"reg664\",\n",
    "    \"reg665\",\n",
    "    \"reg666\",\n",
    "    \"reg667\",\n",
    "    \"reg668\",\n",
    "    \"smsa66\",\n",
    "]\n",
    "X = card_data[xs].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'tsls': 0.13150383624451933,\n",
       " 'lower CI': 0.02566476034018586,\n",
       " 'upper CI': 0.2373429121488528}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = f\"\"\"{yn} ~ 1 + {\" + \".join(xs)}\n",
    "            [{dn} ~ {zn}]\"\"\"\n",
    "mod = lm.iv.IV2SLS.from_formula(formula, data=card_data)\n",
    "iv_res2 = mod.fit(cov_type=\"robust\")\n",
    "\n",
    "iv_est, iv_se = iv_res2.params[-1], iv_res2.std_errors[-1]\n",
    "{\"tsls\": iv_est, \"lower CI\": iv_est - 1.96 * iv_se, \"upper CI\": iv_est + 1.96 * iv_se}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'tsls': 0.13150383624468942,\n",
       " 'lower CI': 0.025664760339922585,\n",
       " 'upper CI': 0.23734291214945624}"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# manual 2SLS\n",
    "Dhat = sm.OLS(D, np.c_[sm.add_constant(Z), X]).fit().predict()\n",
    "tslsreg = sm.OLS(Y, np.c_[sm.add_constant(Dhat), X]).fit()\n",
    "tslsest = tslsreg.params[1]\n",
    "# feature matrix\n",
    "XX = np.c_[sm.add_constant(Dhat), X]\n",
    "n, k = XX.shape\n",
    "corrxn = n / (n - k)  # for HC1\n",
    "# use correct residuals from 2nd stage\n",
    "epsi = Y - np.c_[sm.add_constant(D), X] @ tslsreg.params\n",
    "M = np.einsum(\"ij,i,ik->jk\", XX, epsi**2, XX)\n",
    "XtX = np.linalg.inv(XX.T @ XX)\n",
    "var_ehw = XtX @ M @ XtX\n",
    "iv_est2, iv_se2 = tslsest, np.sqrt(np.diag(var_ehw))[1]\n",
    "\n",
    "{\n",
    "    \"tsls\": iv_est2,\n",
    "    \"lower CI\": iv_est2 - 1.96 * iv_se2,\n",
    "    \"upper CI\": iv_est2 + 1.96 * iv_se2,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anderson Rubin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "  </g>\n",
       " </g>\n",
       " <defs>\n",
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       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from joblib import Parallel, delayed\n",
    "\n",
    "CIrange = np.arange(-0.1, 0.4, 0.001)\n",
    "\n",
    "\n",
    "def pvfun(t):\n",
    "    Y_t = Y - t * D\n",
    "    mod = sm.OLS(Y_t, np.c_[sm.add_constant(Z), X]).fit(cov_type=\"HC2\")\n",
    "    Tstat = mod.params[1] / mod.bse[1]\n",
    "    return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
    "\n",
    "\n",
    "Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
    "Pvalue = np.stack(Pvalue)\n",
    "lb, ub = CIrange[Pvalue >= 0.05].min(), CIrange[Pvalue >= 0.05].max()\n",
    "\n",
    "f, ax = plt.subplots(figsize=(6, 5))\n",
    "ax.plot(CIrange, Pvalue)\n",
    "ax.hlines(0.05, -0.1, 0.4, color=\"k\", linestyle=\"--\")\n",
    "ax.vlines([lb, iv_est2, ub], 0, 1, color=\"grey\", linestyle=\"--\")\n",
    "ax.set_title(\"Fieller-Anderson-Rubin Interval \\n Card's IV data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'tsls': 0.13150383624468942,\n",
       " 'lower CI': 0.02900000000000011,\n",
       " 'upper CI': 0.28100000000000036}"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{\n",
    "    \"tsls\": iv_est2,\n",
    "    \"lower CI\": lb,\n",
    "    \"upper CI\": ub,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### bonus: control function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.13150383624469544, 0.05159083734463283)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# one-shot estimate and SE\n",
    "Dhat = sm.OLS(D, np.c_[sm.add_constant(Z), X]).fit().predict()\n",
    "tslsreg = sm.OLS(Y, np.c_[sm.add_constant(D), D - Dhat, X]).fit(cov_type=\"HC1\")\n",
    "tslsreg.params[1], tslsreg.bse[1]"
   ]
  }
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