Doubly weighted M-estimation for nonrandom assignment and missing outcomes

TL;DR

This paper introduces a robust doubly weighted M-estimator for treatment effect estimation that handles nonrandom assignment and missing outcomes, maintaining consistency under model misspecification.

Contribution

It develops a new class of estimators with robustness properties for causal inference with missing data and nonrandom treatment assignment.

Findings

Estimator is doubly robust for ATE with missing outcomes

Demonstrated effectiveness on National Supported Work data

Resilient to parametric misspecification in models

Abstract

This paper proposes a new class of M-estimators that double weight for the twin problems of nonrandom treatment assignment and missing outcomes, both of which are common issues in the treatment effects literature. The proposed class is characterized by a `robustness' property, which makes it resilient to parametric misspecification in either a conditional model of interest (for example, mean or quantile function) or the two weighting functions. As leading applications, the paper discusses estimation of two specific causal parameters; average and quantile treatment effects (ATE, QTEs), which can be expressed as functions of the doubly weighted estimator, under misspecification of the framework's parametric components. With respect to the ATE, this paper shows that the proposed estimator is doubly robust even in the presence of missing outcomes. Finally, to demonstrate the estimator's viability in empirical settings, it is applied to Calonico and Smith (2017)'s reconstructed sample from the National Supported Work training program.