Wild bootstrap test of overidentification with many instruments and heteroskedasticity

This note studies the validity of bootstrapping the test of overidentifying restrictions under many/many weak instruments and heteroskedasticity. We propose a wild bootstrap procedure and establish this bootstrap consistently estimates the null limiting distributions of a jackknife overidentification test statistic under this asymptotic framework, no matter studentized or not. Monte Carlo simulations show that the wild bootstrap provides more reliable inference than asymptotic critical values. In particular, the studentized wild bootstrap test has the best finite sample performance in terms of both size and power.