Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric speciﬁcation testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the eﬀicacy of the method are presented.
Kitamura, Yuichi, "Empirical Likelihood Methods in Econometrics: Theory and Practice" (2006). Cowles Foundation Discussion Papers. 1860.