Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator
通过蒙特卡洛模拟比较广义经验似然估计量与k类估计量在线性工具变量模型中的有限样本表现，发现GEL估计量存在类似LIML的“无矩”问题，且均方误差更大，因此不推荐使用。
Comprehensive Monte Carlo evidence is provided that compares the finite sample properties of generalized empirical likelihood (GEL) estimators to the ones of k-class estimators in the linear instrumental variables (IV) model. We focus on sample median, mean, mean squared error, and on the coverage probability and length of confidence intervals obtained from inverting a t-statistic based on the various estimators. The results indicate that in terms of the above criteria, all the GEL estimators and the limited information maximum likelihood (LIML) estimator behave very similarly. This suggests that GEL estimators might also share the “no-moment” problem of LIML. At sample sizes as in our Monte Carlo study, there is no systematic bias advantage of GEL estimators over k-class estimators. On the other hand, the standard deviation of GEL estimators is pronouncedly higher than for some of the k-class estimators. Therefore, if mean squared error is used as the underlying loss function, our study suggests the use of computationally simple estimators, such as two-stage least squares, in the linear IV model rather than GEL. Based on the properties of confidence intervals, we cannot recommend the use of GEL estimators either in the linear IV model.