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GMM Estimation and Uniform Subvector Inference with Possible Identification Failure

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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d18a/d1828-ra.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1828.

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Length: 86 pages
Date of creation: Oct 2011
Date of revision: Jan 2013
Publication status: Published in Econometric Theory (April 2014), 20(2): 287-333
Handle: RePEc:cwl:cwldpp:1828r

Note: Contains supplement
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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Citations

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Cited by:
  1. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
  2. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
  3. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
  4. Jean-Marie Dufour & Joachim Wilde, 2013. "Weak Identification in Probit Models with Endogenous Covariates," Working Papers 95, Institute of Empirical Economic Research, revised 28 Feb 2013.

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