ExampleCodeIV

Below you can find functions that, inter alia, deliver an IV estimate, perform a Hausmann test on endogeneity and a Sargan test on instrument validity. More details on how to use these functions is provided in [IV].

IVest.m

This is the function that delivers IV parameter estimates. It will work for exactly and over-identified cases.

function [biv,bse,r2] = IVest(y,x,z);
% This function performs an IV estimation
% input:    y, vector with dependent variable
%           x, matrix with explanatory variable (include vector of ones if
%           you want constant
%           z, matrix with instrumental variables (at least as many cols as x)
% output:   biv, estimated parameters using IV
%           bse, standard errors for biv
%           r2, Rsquared

[n,kx] = size(x);       % sample size - n, number of explan vars (incl constant) - kx   
[n,kz] = size(z);       % sample size - n, number of instrumental vars - kz
pz     = z*inv(z'*z)*z';    % Projection matrix
xpzxi  = inv(x'*pz*x);      % this is also (Xhat'Xhat)^(-1) 

biv    = xpzxi*x'*pz*y;     % IV estimate
res    = y - x*biv;         % IV residuals
ssq    = res'*res/(n-kx);   % Sample variance for IV residuals
s      = sqrt(ssq);         % Sample Standard deviation for IV res
bse    = ssq*xpzxi;         % Variance covariance matrix for IV estimates
bse    = sqrt(diag(bse));   % Extract diagonal and take square root -> standard errors for IV estimators
ym     = y - mean(y);
r2     = 1 - (res'*res)/(ym'*ym);
end

Hausmann endogeneity test

This function can be used to perform to test whether a set of explanatory variables is endogenous or not.

<source> function [teststat,pval] = hausmann_iv_exog_test(y,x1,x2,z); % This function performs a test on variable exogeneity % see Heji et al. p. 411 % input: y, vector with dependent variable % x1, matrix with explanatory variable (include vector of ones if % you want constant which are assumed to be exogenous % x2, matrix with explanatory variables that are to be tested on % exogeneity % z, matrix with instrumental variables (at least as many cols as x) % output: teststat, calculated test statistic % pval, p-value

x = [x1 x2]; xxi = inv(x'*x); b = xxi*x'*y; res = y - x*b;

zzi = inv(z'*z); gam = zzi*z'*x2;  % This works even if we have more than one element in x2

                   % we get as many columns of gam as we have elements in x2

vhat = x2 - z*gam; [b,bse,res,n,rss,r2] = OLSest(res,[x vhat],0); teststat = size(res,1)*r2; pval = 1 - chi2cdf(teststat,size(x2,2)); <\source>