GMM Based Tests for Locally Misspecified Models

This paper shows that the standard Newey-West GMM based test is sensitive to the presence of locally misspecified alternatives. In particular, such test is shown to have incorrect size when the null model is locally contaminated, making the test spuriously reject the null hypothesis even when it is correct. After obtaining the distribution of the Newey-West test statistic under the misspecified alternative, the paper derives a Bera-Yoon modified test based on a restricted GMM estimator, which has the correct size under local misspecification. The paper can be seen as extending the likelihood based results of Saikkonen (1989), Davidson and MacKinnon (1987) and Bera and Yoon (1993) to the GMM framework, which does not require full specification of the underlying probabilistic model.