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This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order reﬁnement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentiﬁed models. In simulation studies we ﬁnd that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.
Matsushita, Yukitoshi and Otsu, Taisuke, "Second-order Refinement of Empirical Likelihood for Testing Overidentifying Restrictions" (2011). Cowles Foundation Discussion Papers. 2134.