Edgeworth expansions for GEL estimators

Finite sample approximations for the distribution functions of Generalized Empirical Likelihood (GEL) are derived using Edgeworth expansions. The analytical results obtained are shown to apply to most of the common extremum estimators used in applied work in an i.i.d. sampling context. The GEL estimators considered include the Continuous Updating, Empirical Likelihood and Exponential Tilting estimators. These estimators are popular alternatives to Generalized Method of Moment (GMM) estimators and their finite sample properties are examined. In a Monte Carlo Experiment, higher order analytical corrections provided by Edgeworth approximations work well in comparison to first order approximations and improve inferences in finite samples.