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.

在许多具有固定效应的非线性面板数据模型中，最大似然估计量会遇到附带参数问题，这通常会导致点估计存在明显偏差。虽然最近的文献大多生成了相对于最大似然产生一阶偏差减少的方法，但我们基于“预期量”得出轮廓似然的一阶和二阶偏差校正，这与基于“样本平均值”源自 Dhaene 和 Sun（2021 年，计量经济学杂志220, 227–252）。虽然我们的估计器的一致性和渐近正态性是在个体数量和时间段数量都增长到无穷大的情况下得出的，但我们在模拟研究中说明，我们的二阶偏差减少确实产生了一个具有显着改进的估计器样本属性相对于其一阶无偏对应项，特别是当可用时间段少于 10 个时。