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GMM ESTIMATION AND UNIFORM SUBVECTOR INFERENCE WITH POSSIBLE IDENTIFICATION FAILURE

Published online by Cambridge University Press:  29 November 2013

Donald W.K. Andrews  and
Xu Cheng
Donald W.K. Andrews
Affiliation:
Cowles Foundation for Research in Economics, Yale University
Xu Cheng*
Affiliation:
University of Pennsylvania
*
*Address correspondence to Xu Cheng, Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA, 19104. e-mail: xucheng@econ.upenn.edu.
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Abstract

This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) 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 CSs are established.

The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t, and quasi-likelihood ratio tests and CSs 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.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 2 , April 2014 , pp. 287 - 333
Copyright
Copyright © Cambridge University Press 2013 

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