Combining Empirical Likelihood and Generalized Method of Moments Estimators : Asymptotics and Higher Order Bias

This paper proposes an estimator that generalizes Empirical Likelihood (EL) estimation and Generalized Method of Moments (GMM) by allowing the sample average moment vector to deviate from zero and the sample weights to deviate from 1/n. Through a free parameter, delta, the properties of the estimator may be adjusted, with GMM and EL behavior respectively attained as delta goes to zero and delta goes to 1. When the sample size is small, the number of moment conditions is large, the moment equations are unbounded, or the model is misspecified, the parameter space under which the EL estimator is defined may be restricted and undefined at or near the population parameter value. The support of the parameter space for the PMM estimator may be adjusted through delta. In simulations, when the sample size is small and the number of moments is large, PMM's estimates are less volatile and its hypothesis tests are less mis-sized than those of EL and GMM