Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix

We extend the KVB approach of Kiefer, Vogelsang, and Bunzel (2000, Econometrica) and Kiefer and Vogelsang (2002b, Econometric Theory) to construct a class of robust tests for over-identifying restrictions in the context of GMM. The proposed test does not require consistent estimation of the asymptotic covariance matrix but relies on kernel-based normalizing matrices to eliminate the nuisance parameters in the limit. Moreover, the proposed test is valid for any consistent GMM estimator, in contrast with the conventional test that requires the optimal GMM estimator, and hence is easy to implement. Our simulations show that the proposed test is properly sized and may even be more powerful than the conventional test computed with an inappropriate user-chosen parameter.