Efficient Estimation of Average Treatment Effect on the Treated under Endogenous Treatment Assignment

TL;DR

This paper develops an efficient method for estimating the average treatment effect on the treated (ATT) in cases of endogenous treatment assignment, using shadow variables to achieve identification and optimal estimation.

Contribution

It introduces a novel estimator that attains the semiparametric efficiency bound for ATT using shadow variables, with rigorous theoretical validation.

Findings

The proposed estimator achieves the semiparametric efficiency bound.

Simulation studies demonstrate the estimator's superior finite sample performance.

Application to real data illustrates practical effectiveness.

Abstract

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 the outcomes of interest, 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.