GMM Estimation and Uniform Subvector Inference with Possible Identification Failure

Authors

Donald W.K. Andrews
Xu Cheng

Document Type

Discussion Paper

Publication Date

10-1-2011

CFDP Number

1828R

CFDP Revision Date

2013-01-01

CFDP Pages

58

Abstract

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.

Comments

Supplement Materials, 30 pp

Recommended Citation

Andrews, Donald W.K. and Cheng, Xu, "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure" (2011). Cowles Foundation Discussion Papers. 2182.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2182