Goodness of Fit Tests for Moment Condition Models

Abstract

This paper proposes novel methods for the construction of tests for models specified by unconditional moment restrictions. It exploits the classical-like nature of generalized empirical likelihood (GEL) to define Pearson-type statistics for over-identifying moment conditions and parametric constraints based on constrasts of GEL implied probabilities which are natural by-products of GEL estimation. As is increasingly recognized, GEL can possess both theoretical and empirical advantages over the more standard generalized method of moments (GMM). Monte Carlo evidence comparing GMM, GEL and Pearsontype statistics for over-identifying moment conditions indicates that the size properties of a particular Pearson-type statistic is competitive in most and an improvement over other statistics in many circumstances.