On Bootstrap Validity for the Test of Overidentifying Restrictions with Many Instruments and Heteroskedasticity

This note studies the asymptotic validity of bootstrapping the test of overidentifying restrictions under many/many weak instruments and heteroskedasticity. We show that the wild bootstrap consistently estimates the null limiting distributions of a jackknife overidentification statistic under this asymptotic framework. In particular, such bootstrap validity holds even when the bootstrap procedure fails to mimic well the distribution of the jackknife instrumental variable estimator, an important component of the statistic of interest. Monte Carlo simulations show that the wild bootstrap provides a more reliable method than that based on asymptotic critical values to approximate the null distributions of interest under many/many weak instruments and heteroskedasticity.