This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and conﬁdence sets (CS’s) in moment condition models in which some parameters are unidentiﬁed or weakly identiﬁed in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t , and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness to identiﬁcation problems. The results of the paper are applied to a nonlinear regression model with endogeneity and a probit model with endogeneity and possibly weak instrumental variables.
Andrews, Donald W.K. and Cheng, Xu, "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure" (2011). Cowles Foundation Discussion Papers. 2181.