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

15 Pages Posted: 19 Jun 2014

See all articles by Roni Israelov

Roni Israelov

AQR Capital Management, LLC

Steven Lugauer

University of Kentucky - Department of Economics

Date Written: October 1, 2013

Abstract

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.

Keywords: Generalized Method of Moments, Empirical Likelihood

JEL Classification: C

Suggested Citation

Israelov, Roni and Lugauer, Steven, Combining Empirical Likelihood and Generalized Method of Moments Estimators: Asymptotics and Higher Order Bias (October 1, 2013). Available at SSRN: https://ssrn.com/abstract=2334341 or http://dx.doi.org/10.2139/ssrn.2334341

Roni Israelov

AQR Capital Management, LLC ( email )

Two Greenwich Plaza, 3rd Floor
Greenwich, CT 06830
United States

HOME PAGE: http://www.aqrcapital.com

Steven Lugauer (Contact Author)

University of Kentucky - Department of Economics ( email )

Lexington, KY 40506
United States

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