Estimation of average treatment effects for massively unbalanced binary outcomes

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.