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.

IVest.m

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

<source> 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 <\source>