Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure

Authors

Donald W.K. Andrews
Xu Cheng

Document Type

Discussion Paper

Publication Date

10-1-2011

CFDP Number

1824

CFDP Pages

71

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.

Comments

Supplement Materials, 34 pp

Recommended Citation

Andrews, Donald W.K. and Cheng, Xu, "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure" (2011). Cowles Foundation Discussion Papers. 2176.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2176