Recent Developments in Empirical Likelihood and Related Methods

This article reviews a number of recent contributions to estimation and inference for models defined by moment condition restrictions. The particular emphasis is on the generalized empirical likelihood class of estimators as an alternative to the generalized method of moments. Estimation methods for parameters defined through moment restrictions and their properties are described with tests of overidentifying moment restrictions and parametric hypotheses. Computational issues are discussed together with some proposals for their amelioration. Higher-order and other properties are also addressed in some detail. Models specified by conditional moment restriction models are considered, and the adaptation of these methods to weakly dependent data is discussed.