Optimal Estimation of Average Treatment Effect on the Treated Under Endogeneous Treatment Assignment

• Activity Number: 235 - Recent Advancements in Nonparametric and Semiparametric Methodologies and Their Applications
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Trinetri Ghosh* and Menggang Yu and Jiwei Zhao
• Companies: University of Wisconsin-Madison and University of Wisconsin-Madison and University of Wisconsin-Madison
• Keywords: Average treatment effect on the treated; non-ignorable missing data; semiparametric efficiency

Abstract

When evaluating a complex intervention, instead of average treatment effect (ATE), researchers are more interested in the average treatment effect on the treated (ATT), which is the quantity most relevant to policy makers. In this paper, we consider the ATT estimation motivated by a case study, where the treatment assignment might depend on the potential untreated outcome and hence is endogeneous. We study the scenario that the ATT can be identified. We investigate the optimal estimation of ATT by characterizing the geometric structure of the model. We derive the semiparametric efficiency bound for ATT estimation and propose estimator that can achieve this bound. Consistency and asymptotic normality of the proposed estimator are established. The finite-sample performance of the proposed estimator is studied through comprehensive simulations and an application to our motivation study.