Identification of dynamic treatment effects when treatment histories are partially observed

TL;DR

This paper introduces a robust difference-in-differences method for identifying path-dependent treatment effects with partially observed treatment histories, improving accuracy under missing data and model misspecification.

Contribution

It proposes a novel estimator that remains consistent if any two of outcome, propensity score, or missing data models are correctly specified, enhancing robustness.

Findings

The method outperforms conventional estimators in simulations with missing data.

It provides more accurate treatment effect estimates under model misspecification.

Applications show substantial differences from traditional approaches.

Abstract

This paper presents a general difference-in-differences framework for identifying path-dependent treatment effects when treatment histories are partially observed. We introduce a novel robust estimator that adjusts for missing histories using a combination of outcome, propensity score, and missing treatment models. We show that this approach identifies the target parameter as long as \textit{any two} of the three models are correctly specified. The method delivers improved robustness against competing alternatives under the same set of identifying assumptions. Theoretical results and numerical experiments demonstrate how the proposed method yields more accurate inference compared to conventional and doubly robust estimators, particularly under nontrivial missingness and misspecification scenarios. Two applications demonstrate that the robust method can produce substantively different estimates of path-dependent treatment effects relative to conventional approaches.