COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1791

Second-order Refinement of Empirical Likelihood
for Testing Overidentifying Restrictions

Yukitoshi Matsushita and Taisuke Otsu

April 2011

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

Keywords: Empirical likelihood; GMM; Overidentification test; Bartlett correction; Higher order analysis

JEL Classification: C12; C14