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Estimation and Inference with Weak, Semi-Strong, and Strong Identification

Donald W. K. Andrews

Yale University - Cowles Foundation

Xu Cheng

University of Pennsylvania - Department of Economics

October 7, 2010

Cowles Foundation Discussion Paper No. 1773

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) in a class of models in which the parameters are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's, including maximum likelihood (ML), least squares (LS), quantile, generalized method of moments (GMM), generalized empirical likelihood (GEL), minimum distance (MD), and semi-parametric estimators. The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic size (in a uniform sense) of standard tests and CS's is established. The results are applied to the ML estimator of an ARMA(1, 1) model and to the LS estimator of a nonlinear regression model.

Number of Pages in PDF File: 174

Keywords: Asymptotic size, Confidence set, Estimator, Identification, Nonlinear models, Strong identification, Test, Weak identification

JEL Classification: C12, C15

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Date posted: October 9, 2010  

Suggested Citation

Andrews, Donald W. K. and Cheng, Xu, Estimation and Inference with Weak, Semi-Strong, and Strong Identification (October 7, 2010). Cowles Foundation Discussion Paper No. 1773. Available at SSRN: http://ssrn.com/abstract=1688963 or http://dx.doi.org/10.2139/ssrn.1688963

Contact Information

Donald W. K. Andrews (Contact Author)
Yale University - Cowles Foundation ( email )
Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Xu Cheng
University of Pennsylvania - Department of Economics ( email )
160 McNeil Building
3718 Locust Walk
Philadelphia, PA 19104
United States
HOME PAGE: http://www.sas.upenn.edu/~xucheng/
Feedback to SSRN

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