Generalized empirical likelihood testing in semiparametric conditional moment restrictions models

Abstract

This paper shows how generalized empirical likelihood can be used to obtain specification tests in semiparametric conditional moment restrictions models. The resulting test statistics are similar in spirit to classical Kolmogorov–Smirnov and Cramer von Mises goodness‐of‐fit statistics and are based on an integrated version of the original moment restrictions. The results are applied to test the correct specification of an instrumental variable smooth varying coefficient model and of a censored non‐linear quantile regression model. Monte Carlo results suggest that the proposed tests have competitive finite sample properties.