Instrumental variable regression

clear
set seed 1
set obs 10000
eststo clear

// Simulate data for IV regression
matrix input c = ( 1, .5, 0, .5\ ///
                  .5,  1, 0,  0\ ///
                   0,  0, 1,  0\ ///
                  .5,  0, 0,  1)
corr2data x u e z, corr(c)

// Calculate y
generate y = 1 + 2*x + 2*u + 5*e

// Without omitted variable bias
eststo: regress y x u

// With omitted variable bias
eststo: regress y x

// Reduced form
eststo: regress y z
local rf = _b[z]

// First stage
eststo: regress x z
local fs = _b[z]
predict xhat
predict xres, resid

// Two-stage predictor substitution (2SPS)
eststo: regress y xhat

// Two-stage residual inclusion (2SRI)
eststo: regress y x xres

// Two-stage least square (2SLS)
eststo: ivregress 2sls y (x = z)

// IV estimate = reduced form/first stage
di `rf'/`fs'



// Table
esttab, b(2) se(2) mtitle("DGP" "Bias" "Reduced form" "1st stage" "2SPS" "2SRI" "2SLS") ///
        coeflabel(x "Predictor x" ///
                  z "Instrument z" ///
                  xres "1st stage residual" ///
                  _cons "Intercept") ///
        rename(xhat x) drop(u) ///
        stats(N, label(Observations) fmt(%9.0gc)) ///
        title(Different varieties of instrumental variable regression) ///
        varwidth(20)