Tests for nonlinear restrictions under local misspecfication (with an application to the rational expectations hypothesis).

his paper develops 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 nuisance 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 hypothesis, are either correct or locally misspecied. We illustrate the proposed tests to evaluate the macro rational expectations hypothesis using U.S. data.