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GMM Estimation and Uniform Subvector Inference with Possible Identi…cation Failure



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GMM ESTIMATION AND UNIFORM SUBVECTOR INFERENCE WITH POSSIBLE IDENTIFICATION FAILURE By Donald W K Andrews and Xu Cheng October 2011 COWLES FOUNDATION DISCUSSION PAPER NO 1828 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven Connecticut 06520 8281 http cowles econ yale edu GMM Estimation and Uniform Subvector Inference with Possible Identi cation Failure Donald W K Andrews Cowles Foundation Yale University Xu Cheng Department of Economics University of Pennsylvania First Draft August 2007 Revised October 24 2011 Andrews gratefully acknowledges the research support of the National Science Foundation via grant numbers SES 0751517 and SES 1058376 The authors thank Xiaohong Chen Sukjin Han Yuichi Kitamura Peter Phillips Eric Renault Frank Schorfheide and Ed Vytlacil for helpful comments Abstract This paper determines the properties of standard generalized method of moments GMM estimators tests and con dence sets CS s in moment condition models in which some parameters are unidenti ed or weakly identi ed 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 identi cation 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 Keywords Asymptotic size con dence set generalized method of moments GMM estimator identi cation nonlinear models test Wald test weak identi cation JEL Classi cation Numbers C12 C15 1 Introduction This paper gives a set of GMM regularity conditions that are akin to the classic conditions in Hansen 1982 and Pakes and Pollard



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