Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure

106 Pages Posted: 12 Oct 2012 Last revised: 5 Nov 2012

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Xu Cheng

University of Pennsylvania - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: October 11, 2012

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

JEL Classification: C12, C15

Suggested Citation

Andrews, Donald W. K. and Cheng, Xu, Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure (October 11, 2012). Cowles Foundation Discussion Paper No. 1824R, Available at SSRN: https://ssrn.com/abstract=2160335 or http://dx.doi.org/10.2139/ssrn.2160335

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 )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.sas.upenn.edu/~xucheng/