Robust Inference for GMM with Possibly Nonsmooth Moments

Abstract: This paper develops an asymptotic distribution theory for the Generalized Method of Moments (GMM) estimator when the moment condition is nonsmooth and misspecified. Our results extend existing theories for nonsmooth GMM to allow moment misspecification. Under misspecification, the conventional GMM variance estimators are inconsistent, and we show how to consistently estimate the true asymptotic variance for valid inference. Our results also extend the existing theories for the misspecified-GMM setup which assume the moment functions to be twice continuously differentiable. Detailed analyses of quantile regression with endogeneity under the location-scale model are provided to illustrate the application of the general results in the paper. Simulation evidence shows that our methods provide robust inference under misspecification.

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