On the second-order properties of empirical likelihood with moment restrictions

This paper considers the second-order properties of empirical likelihood (EL) for a parameter defined by moment restrictions, which is the inferential framework of the generalized method of moments. It is shown that the EL defined for this general framework still admits the delicate second-order property of Bartlett correction. This represents a substantial extension of all the established cases of Bartlett correction for the EL. An empirical Bartlett correction is proposed, which is shown to work effectively in improving the coverage accuracy of confidence regions for the parameter.