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

Donald Andrews () and Xu Cheng

No 1773, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Asymptotic size; Confidence set; Estimator; Identification; Nonlinear models; Strong identification; Test; Weak identification (search for similar items in EconPapers)
JEL-codes: C12 C15 (search for similar items in EconPapers)
Pages: 173 pages
Date: 2010-10
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: Includes supplement.
References: Add references at CitEc
Citations: View citations in EconPapers (15)

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Related works:
Journal Article: Estimation and Inference With Weak, Semi‐Strong, and Strong Identification (2012)
Working Paper: Estimation and Inference with Weak, Semi-strong, and Strong Identification (2011)
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