A new class of tests for overidentifying restrictions in moment condition models

Abstract

In this study, we propose a new class of tests for overidentifying restrictions in moment condition models, extending Neyman’s (1959) test for parameter hypotheses in maximum likelihood to generalized empirical likelihood (GEL). These tests lack the complicated saddle point problem seen in GEL estimation; only a consistent estimator, where n is the sample size, is needed. In addition to discussing their first-order properties, we establish that under some regularity conditions, these tests share the same higher-order properties as GEL overidentifying tests, given proper consistent estimators. A Monte Carlo simulation study shows that the new class of tests of overidentifying restrictions has better finite sample performance than the two-step GMM overidentification test, and compares well to several potential alternatives in terms of overall performance.