In this paper, we consider estimation of average treatment effect on the treated (ATT), an interpretable and relevant causal estimand to policy makers when treatment assignment is endogenous. By considering shadow variables that are unrelated to the treatment assignment but related to interested outcomes, we establish identification of the ATT. Then we focus on efficient estimation of the ATT by characterizing the geometric structure of the likelihood, deriving the semiparametric efficiency bound for ATT estimation and proposing an estimator that can achieve this bound. We rigorously establish the theoretical results of the proposed estimator. The finite sample performance of the proposed estimator is studied through comprehensive simulation studies as well as an application to our motivating study.

翻译：本文考虑处理组平均处理效应（ATT）的估计问题，该指标对政策制定者而言具有可解释性和相关性，尤其当处理分配存在内生性时。通过引入与处理分配无关但与感兴趣结果相关的影子变量，我们建立了ATT的可识别性。随后，我们通过刻画似然函数的几何结构、推导ATT估计的半参数效率界，并提出能够达到该界的估计量，聚焦于ATT的高效估计。本文严格建立了所提估计量的理论结果。通过全面的模拟研究以及一项应用至本项动机研究案例分析，我们验证了所提估计量的有限样本性能。