clear
set obs 1000
* Generate instrument
generate z = rnormal(0,1)

* Generate error
generate e = rnormal(0,1)

* Generate endogenous regressor
gen x=z+e

* Generate dependent variable
gen y=1+1*x+e

* Generare many invalid instruments
generate x1 = x+rnormal(0,1)
generate x2 = x+rnormal(0,1)
generate x3 = x+rnormal(0,1)
generate x4 = x+rnormal(0,1)
generate x5 = x+rnormal(0,1)

* Do GMM regression with good instrument (estimates should be close to 1)
ivregress gmm y (x = z)

* Do GMM regression with good and bad instruments
ivregress gmm y (x = z x1-x5)

* Test validity of instruments (should reject)
estat overid

* Do GMM regression with bad instruments only
ivregress gmm y (x = x1-x5)

* Test validity of instruments (should reject but generally doesn't!)
estat overid