COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1724

Optimal Comparison of Misspecified Moment Restriction Models

Vadim Marmer and Taisuke Otsu

August 2009

 This paper considers optimal testing of model comparison hypotheses for misspecified unconditional moment restriction models. We adopt the generalized Neyman-Pearson optimality criterion, which focuses on the convergence rates of the type I and II error probabilities under fixed global alternatives, and derive an optimal but practically infeasible test. We then propose feasible approximation test statistics to the optimal one. For linear instrumental variable regression models, the conventional empirical likelihood ratio test statistic emerges. For general nonlinear moment restrictions, we propose a new test statistic based on an iterative algorithm. We derive asymptotic properties of these test statistics.

Keywords: Moment restriction, Model comparison, Misspecification, Generalized Neyman-Pearson optimality, Empirical likelihood, GMM

JEL Classification: C12, C14, C52