CIRJE-F-200 "Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator"
Author Name Kunitomo, Naoto and Yukitoshi Matsushita
Date March 2003
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Remarks Revised in December 2003; revised as CIRJE-F-577 (2008), CIRJE-F-611 (2009).
Abstract

The distributions of the Maximum Empirical Likelihood (MEL) estimator and the Generalized Method of Moments (GMM) estimator for the coefficient of one endogenous variable in a linear structural equation are evaluated numerically. Tables and figures are given for enough values of the parameters to cover most of interest. Comparisons of the distributions of the MEL estimator and the GMM estimator with their asymptotic expansions are made. We find that the MEL estimator does not have any moments of positive integer orders and careful analyses are needed to use its bias and mean squared error because usually they do not exist.