Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity∗

This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the overidentifying test statistic. Correct asymptotic critical values are derived for this statistic when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number instruments is fixed and there is homoskedasticity. This test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix. The distribution theory is based on the heteroskedasticity-robust, many-instrument asymptotics of Chao et al. (2010). In Monte Carlo experiments the rejection frequency of the test is found to be very insensitive to the number of instruments. This paper finds in Monte Carlo studies that the test is more accurate and less sensitive to the number of instruments than the Hausman-Sargan or GMM tests of overidentifying restrictions.