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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. The authors 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. The second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies they find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide remarkable improvements for the size properties.
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