Estimation of average treatment effects for massively unbalanced binary outcomes
针对二元结果中事件概率低导致的对数模型平均处理效应估计存在二阶偏误的问题，推导了偏误公式并提出了修正估计量，同时给出避免数值不稳定的计算技巧。
.The MLE of the ATE in the logit model for binary outcomes may have a significant second-order bias if the event has a low probability, which is the case we focus on in this article. We derive the second-order bias of the logit ATE estimator, and we propose a bias-corrected estimator of the ATE. We also propose a variation on the logit model with parameters that are elasticities. Finally, we propose a computational trick that avoids numerical instability in the case of estimation for rare events.