SECOND-ORDER BIAS REDUCTION FOR NONLINEAR PANEL DATA MODELS WITH FIXED EFFECTS BASED ON EXPECTED QUANTITIES
针对非线性面板固定效应模型的最大似然估计存在偏误问题，本文提出一种基于期望量的二阶偏误校正方法，相比一阶方法在小样本（尤其少于10期）下表现更优。
In many nonlinear panel data models with fixed effects maximum likelihood estimators suffer from the incidental parameters problem, which often entails that point estimates are markedly biased. While the recent literature has mostly generated methods that yield a first-order bias reduction relative to maximum likelihood, we derive a first- and second-order bias correction of the profile likelihood based on “expected quantities” which differs from the corresponding correction based on “sample averages” derived in Dhaene and Sun (2021, Journal of Econometrics 220, 227–252). While consistency and asymptotic normality of our estimator are derived in a setting where both the number of individuals and the number of time periods grow to infinity, we illustrate in a simulation study that our second-order bias reduction indeed yields an estimator with substantially improved small sample properties relative to its first-order unbiased counterpart, especially when less than 10 time periods are available.