I devise a difference-in-differences design that accounts for the possibility that some treatment effect is split in the reactions to two or more events. At the intersection of settings with a single treatment and with multiple treatments, regression-based methods for this split-treatment design can be subject both to negative weights and contamination bias. I propose a simple solution, a first-difference regression with sample constraints in the spirit of Dube et al.’s (2023) LP-DiD, that allows to identify and estimate sensible causal parameters of interest. This estimator is efficient under random walk errors and unrestricted heterogeneity across groups and events. In addition, this estimator has a larger appeal than this design as it more generally applies to settings with several nonlinearly-dependent treatments.
