COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1828R

GMM Estimation and Uniform Subvector Inference
with Possible Identification Failure

Donald W.K. Andrews and Xu Cheng

October 2011
Revised January 2013

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.

Keywords: Asymptotic size, Confidence set, Generalized method of moments, GMM estimator, Identification, Nonlinear models, Test, Wald test, Weak identification

JEL Classification: C12, C15