Second-order refinement of empirical likelihood ratio tests of nonlinear restrictions

Abstract

In this paper, we investigate the second-order properties of empirical likelihood ratio (ELR) tests of general nonlinear parametric restrictions for over-identified moment restriction models. We derive the stochastic expansion of the ELR statistic for this very large class of testing problems and its formal distributional expansion. We show that we can improve the size properties of the ELR tests via either Bartlett correction or pseudo observation adjustment. Monte Carlo experiments show that tests based on these modified ELR statistics exhibit good finite-sample properties. This article is protected by copyright. All rights reserved