Simulation and theoretical studies have led to an increasing recognitionthat efficient generalized method of moments (GMM) estimators for modelsspecified through moment restrictions may be severely biased for the samplesizes typically encountered in applications. GMM bias is associated withparticular estimators for the Jacobian and efficient metric terms implicitin efficient GMM estimation. Inference procedures associated with efficientGMM may similarly be expected to deviate from the nominal normal or chisquare distributions provided by asymptotic theory. Recently a number ofother estimators which are asymptotically equivalent to GMM have beensuggested. Empirical likelihood, exponential tilting and continuous updatingestimators are particular examples.
This masterclass is concerned with a treatment of the class of generalizedempirical likelihood (GEL) methods for moment condition models. The GELclass of estimators includes empirical likelihood, exponential tilting andcontinuous updating as special cases as well as estimators based on theCressie-Read power divergence family of discrepancies. The GEL method offersattractive alternative one-step efficient estimators, not requiring explicitcalculation or estimation of the efficient metric as in GMM, that areasymptotically equivalent to those based on efficient two-step or iteratedGMM. GEL estimators are less prone to bias as factors that lead to bias inefficient GMM are either partially or completely absent. This particularproperty of GEL is especially attractive when the number of momentrestrictions is large.