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 Sargan test statistic, having a numerator that is the objective function minimized by the JIVE2 estimator of Angrist, Imbens, and Krueger (1999). Correct asymptotic critical values are derived for this test 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 asymptotics is based on the heteroskedasticity robust many instrument asymptotics of Chao et. al. (2010).