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.