Ch10_IV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Instrumental Variables\n",
    "\n",
    "This notebook uses a function for 2SLS and illustrates it by redoing an example from Ch 10.3.3 in \"Principles of Econometrics\", 3rd edition (Hill, Griffiths and Lim)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions\n",
    "\n",
    "The key functions used for OLS and IV/2SLS are from the (local) `FinEcmt_OLS` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "MyModulePath = joinpath(pwd(),\"src\")\n",
    "!in(MyModulePath,LOAD_PATH) && push!(LOAD_PATH,MyModulePath);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "using FinEcmt_OLS, DelimitedFiles, LinearAlgebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading the Data\n",
    "\n",
    "The next cells replicates an old example from Hill et al (2008). See the lecture notes for more details.\n",
    "\n",
    "### A remark on the code\n",
    "The data set contains many different variables. To import them with their correct names, we create a named tuple of them by using the function `PutDataInNT()` from the `FinEcmt_OLS` module. (This is convenient, but not important for the focus of this notebook. An alternative is to use the `DataFrames.jl` package.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variables in X (use as, for instance, X.wage): \n",
      "(:taxableinc, :federaltax, :hsiblings, :hfathereduc, :hmothereduc, :siblings, :lfp, :hours, :kidsl6, :kids618, :age, :educ, :wage, :wage76, :hhours, :hage, :heduc, :hwage, :faminc, :mtr, :mothereduc, :fathereduc, :unemployment, :bigcity, :exper)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(x,header) = readdlm(\"Data/mrozEd.txt\",header=true)\n",
    "X          = PutDataInNT(x,header)                         #NamedTuple with X.wage, X.exper, etc\n",
    "\n",
    "c = ones(size(x,1))                                       #constant, used in the regressions\n",
    "\n",
    "println(\"The variables in X (use as, for instance, X.wage): \")\n",
    "printmat(keys(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS\n",
    "\n",
    "estimation of the log wage on education, experience and experience^2. Only data points where wage > 0 are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mOLS estimates:\u001b[22m\u001b[39m\n",
      "\n",
      "             coef       std\n",
      "c          -0.522     0.198\n",
      "educ        0.107     0.014\n",
      "exper       0.042     0.013\n",
      "exper^2    -0.001     0.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "vv     = X.wage .> 0     #find data points where X.wage > 0\n",
    "                         #OLS on wage>0\n",
    "(b_OLS,_,_,Covb,) = OlsGM(log.(X.wage[vv]),[c X.educ X.exper X.exper.^2][vv,:])\n",
    "Stdb_ols = sqrt.(diag(Covb))\n",
    "\n",
    "colNames = [\"coef\",\"std\"]\n",
    "rowNames = [\"c\",\"educ\",\"exper\",\"exper^2\"]\n",
    "printblue(\"OLS estimates:\\n\")\n",
    "printmat(b_OLS,Stdb_ols;colNames,rowNames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV (2SLS)\n",
    "\n",
    "using the function `TwoSLS()` function.\n",
    "\n",
    "In this application, the mother's education is used as an instrument for the person's education."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```\n",
       "TwoSLS(y,x,z,NWQ=false,m=0)\n",
       "```\n",
       "\n",
       "### Input\n",
       "\n",
       "  * `y::VecOrMat`:      Tx1 or T-vector of the dependent variable\n",
       "  * `x::VecOrMat`:      Txk matrix (or vector) of regressors\n",
       "  * `z::VecOrMat`:      TxL matrix (or vector) of instruments\n",
       "  * `NWQ:Bool`:         if true, then Newey-West's covariance matrix is used, otherwise Gauss-Markov\n",
       "  * `m::Int`:           scalar, bandwidth in Newey-West; 0 means White's method\n",
       "\n",
       "### Output\n",
       "\n",
       "  * `b::Vector`:             k-vector, regression coefficients\n",
       "  * `fnOutput::NamedTuple`:  with\n",
       "\n",
       "      * res                Tx1 or Txn matrix, residuals y - yhat\n",
       "      * yhat               Tx1 or Txn matrix, fitted values\n",
       "      * Covb               matrix, covariance matrix of vec(b) = [beq1;beq2;...]\n",
       "      * R2                 1xn, R2\n",
       "      * R2_stage1          k-vector, R2 of each x[:,i] in first stage regression on z\n",
       "      * δ_stage1           Lxk matrix, coeffs from 1st stage x = z'δ\n",
       "      * Stdδ_stage1        Lxk matrix, std of δ\n",
       "\n",
       "### Requires\n",
       "\n",
       "  * Statistics, LinearAlgebra\n",
       "  * CovNW\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@doc2 TwoSLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using CodeTracking\n",
    "#println(@code_string TwoSLS([1],[1],[1]))    #print the source code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mfirst-stage estimates: coeffs (each regression in its own column)\u001b[22m\u001b[39m\n",
      "                   c      educ     exper   exper^2\n",
      "c              1.000     9.775    -0.000     0.000\n",
      "exper          0.000     0.049     1.000    -0.000\n",
      "exper^2       -0.000    -0.001     0.000     1.000\n",
      "mothereduc     0.000     0.268    -0.000    -0.000\n",
      "\n",
      "\u001b[34m\u001b[1mfirst-stage estimates: std errors\u001b[22m\u001b[39m\n",
      "                   c      educ     exper   exper^2\n",
      "c              0.000     0.422     0.000     0.000\n",
      "exper          0.000     0.042     0.000     0.000\n",
      "exper^2        0.000     0.001     0.000     0.000\n",
      "mothereduc     0.000     0.031     0.000     0.000\n",
      "\n",
      "\u001b[34m\u001b[1mfirst-stage estimates: R²\u001b[22m\u001b[39m\n",
      "         c      educ     exper   exper^2\n",
      "       NaN     0.153     1.000     1.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(b_iv,fO2) = TwoSLS(log.(X.wage[vv]),[c X.educ X.exper X.exper.^2][vv,:],\n",
    "                      [c X.exper X.exper.^2 X.mothereduc][vv,:])\n",
    "\n",
    "zNames = [\"c\",\"exper\",\"exper^2\",\"mothereduc\"]\n",
    "\n",
    "printblue(\"first-stage estimates: coeffs (each regression in its own column)\")\n",
    "printmat(fO2.δ_stage1;colNames=rowNames,rowNames=zNames)\n",
    "\n",
    "printblue(\"first-stage estimates: std errors\")\n",
    "printmat(fO2.Stdδ_stage1;colNames=rowNames,rowNames=zNames)\n",
    "\n",
    "printblue(\"first-stage estimates: R²\")\n",
    "printmat(fO2.R2_stage1';colNames=rowNames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mIV estimates\u001b[22m\u001b[39m\n",
      "             coef       std\n",
      "c           0.198     0.471\n",
      "educ        0.049     0.037\n",
      "exper       0.045     0.014\n",
      "exper^2    -0.001     0.000\n",
      "\n",
      "\u001b[31m\u001b[1mThe results should be very close to Hill et al, 10.3.3,\u001b[22m\u001b[39m\n",
      "\u001b[31m\u001b[1mbut with small differences due to how df adjustments are made to variances\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "Stdb_iv = sqrt.(diag(fO2.Covb))\n",
    "printblue(\"IV estimates\")\n",
    "printmat(b_iv,Stdb_iv;colNames,rowNames)\n",
    "\n",
    "printred(\"The results should be very close to Hill et al, 10.3.3,\n",
    "but with small differences due to how df adjustments are made to variances\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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