General specification testing with locally misspecified models

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments-based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993, Econometric Theory 9, 649-658) for constructing RS tests that are robust to local misspecification to GMM-based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both likelihood and GMM-based results.