Identification of dynamic treatment effects when treatment histories are partially observed

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.