This paper develops generalized method of moments-based (GMM-based) Lagrange multiplier tests for nonlinear hypotheses that are robust to locally misspecified possibly nonlinear alternatives. The procedure is based on an initial consistent GMM estimator of the parameters under a given set of nonlinear restrictions. The new test for one particular set of nonlinear hypotheses is consistent and has correct asymptotic size independently of whether the other, also nonlinear hypotheses, are correct or locally misspecified. To illustrate the usefulness of our proposed tests we consider testing rational expectations hypotheses using U.S. data.
Bera, A., Montes-Rojas, G., Sosa-Escudero, W., & Alejo, J. (2021). Tests for nonlinear restrictions under misspecified alternatives with an application to testing rational expectation hypotheses. The Econometrics Journal, 24(1), 41–57. https://doi.org/10.1093/ectj/utaa010