Combining empirical likelihood and generalized method of moments estimators: Asymptotics and higher order bias

This paper proposes an estimator combining empirical likelihood (EL) and the generalized method of moments (GMM) by allowing the sample average moment vector to deviate from zero and the sample weights to deviate from n−1n−1. The new estimator may be adjusted through free parameter δ∈(0,1)δ∈(0,1) with GMM behavior attained as δ⟶0δ⟶0 and EL as δ⟶1δ⟶1. When the sample size is small and the number of moment conditions is large, the parameter space under which the EL estimator is defined may be restricted at or near the population parameter value. The support of the parameter space for the new estimator may be adjusted through δδ. The new estimator performs well in Monte Carlo simulations.