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

Abstract

This paper extends Kiefer, Vogelsang, and Bunzel - (2000, Econometrica) and Kiefer and Vogelsang - (2002b, Econometric Theory) to propose a class of over-identifying restrictions (OIR) tests that are robust to heteroskedasticity and serial correlations of unknown form. These OIR tests do not require consistent estimation of the asymptotic covariance matrix and hence avoid choosing the bandwidth in nonparametric kernel estimation. By employing a suitable normalizing matrix to eliminate the nuisance parameters in the limit, these tests remain asymptotically pivotal. As opposed of the conventional OIR test, the proposed tests require only a consistent, but not necessarily optimal, GMM estimator. It is also shown that the asymptotic local power of these tests is invariant with respect to the choice of the weighting matrix for preliminary GMM estimator. Our simulations demonstrate that the proposed tests are properly sized in most cases and may have power comparable with that of the conventional OIR test.