Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix

We propose new over-identifying restriction (OIR) tests that are robust to heteroskedasticity and serial correlations of unknown form. The proposed tests do not require consistent estimation of the asymptotic covariance matrix and hence avoid choosing the bandwidth in nonparametric kernel estimation. Instead, they rely on the normalizing matrices that can eliminate the nuisance parameters in the limit. Compared with the conventional OIR test, the proposed tests require only a consistent, but not necessarily optimal, GMM estimator. Our simulations demonstrate that these tests are properly sized and may have power comparable with that of the conventional OIR test.