Small Sample Properties Of The Gmm And Gel Estimators

Asymptotic properties of generalized method of moments (GMM) and generalized empirical likelihood (GEL) are now proved in the econometric literature, but there is not enough literature on the small sample properties of GMM and GEL. Using Monte Carlo simulation with single linear structure model, this article presents compare studies on GMM and GEL. Although GMM and GEL asymptotically equivalent in large sample, the results show that the small sample behavior depends on the numbers of instruments, the endogenous strength of explanatory variables and the size of sample. It can be conclude that (1) if the sample size is large and the endogenous is strength, it is recommended to use the GMM estimator; (2) when the sample size is small or moderate and the endogenous is weak, it is recommended to use generalized empirical likelihood estimator.