General specification testing with locally misspecified models

BERA, ANIL; MONTES ROJAS, GABRIEL VICTORIO; SOSA ESCUDERO, WALTER

ECONOMETRIC THEORY

Cambridge University Press

Año: 2010 vol. 26 p. 1838 - 1845

0266-4666

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 GMM based tests. We also extend the method proposed in Bera and Yoon (Econometric Theory 9, 1993) 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 the Bera-Yoon likelihood based results as well as its use in the GMM environment.