General tests for nonlinear restrictions under local misspecification

Abstract

This paper proposes a GMM based test for non-linear hypothesis that is robust to locally misspecified possibly non-linear hypothesis. That is, the procedure is based on an initial consistent GMM estimator of the nuisance parameters under a given set of possibly nonlinear restrictions. The new test for one particular non-linear hypothesis is consistent and has correct asymptotic size independently of whether the other also non-linear hypothesis are either correct or locally misspecified. As an illustration we apply them to the study of the rational expectations (RE) and neutrality (NE) hypotheses. Contrary to previous findings, our alternative robust LM-type test estimates the model under both RE and NE, and rejects the RE hypothesis.