Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity Using Regularized Jackknife IV

This paper proposes a new overidentifying restrictions test in a linear model when the number of instruments (possibly weak) may be smaller or larger than the sample size n or even infinite in a heteroskedastic framework. The proposed J test combines two techniques: the Jackknife method and the regularization technique which consists in stabilizing the projection matrix. We theoretically show that our new test achieves the asymptotically correct size in the presence of many instruments. The simulation results demonstrate that our modified J statistic test has better empirical properties in small samples than existing J tests. We also propose a regularized F-test to assess the strength of the instruments, which is robust to heteroskedasticity and many instruments