Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure

Donald Andrews () and Xu Cheng

No 1824R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS's) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS's. We provide methods of constructing QLR tests and CS's that are robust to the strength of identification. The results are applied to two examples: a nonlinear binary choice model and the smooth transition threshold autoregressive (STAR) model.

Keywords: Asymptotic size; Binary choice; Confidence set; Estimator; Identification; Likelihood; Nonlinear models; Test; Smooth transition threshold autoregression; Weak identification (search for similar items in EconPapers)
JEL-codes: C12 C15 (search for similar items in EconPapers)
Pages: 107 pages
Date: 2011-10, Revised 2012-10
Note: Includes Supplement
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Journal of Econometrics(March 2013), 173(1): 36-56

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Related works:
Journal Article: Maximum likelihood estimation and uniform inference with sporadic identification failure (2013)
Working Paper: Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure (2011)
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