Finite Sample Properties of One-step, Two-step and Bootstrap Empirical Likelihood Approaches to Efficient GMM Estimation

This paper compares conventional GMM estimators to empirical likelihood based GMM estimators which employ a semiparametric efficient estimate of the unknown distribution function of the data. One-step, two-step and bootstrap empirical likelihood and conventional GMM estimators are considered which are efficient for a given set of moment conditions. The estimators are subject to a Monte Carlo investigation using a specification which exploits sequential conditional moment restrictions for binary panel data with multipli-cative latent effects. Among other findings the experiments show that the one-step and two-step estimators yield coverage rates of confidence intervals below their nominal coverage probabilities. The bootstrap methods improve upon this result.