Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators
比较了广义矩方法（GMM）与广义经验似然（GEL）估计量的高阶渐近性质，发现GEL能消除因矩函数与雅可比相关导致的偏差，而经验似然（EL）能消除因估计最优权重矩阵导致的偏差，且偏差校正后的EL具有类似最大似然的高阶有效性。
In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We use this structure to compare their higher order asymptotic properties. We find that GEL has no asymptotic bias due to correlation of the moment functions with their Jacobian, eliminating an important source of bias for GMM in models with endogeneity. We also find that EL has no asymptotic bias from estimating the optimal weight matrix, eliminating a further important source of bias for GMM in panel data models. We give bias corrected GMM and GEL estimators. We also show that bias corrected EL inherits the higher order property of maximum likelihood, that it is higher order asymptotically efficient relative to the other bias corrected estimators. Copyright Econometric Society 2004.