Difference-in-Differences Estimators of Intertemporal Treatment Effects
Causal Question / Estimand
Dynamic treatment effects when the treatment may be non-binary, non-absorbing (can switch on and off), and outcomes respond to treatment lags. The target is the effect of having been exposed to a weakly higher treatment dose for periods — an event-study/intertemporal effect (Causal-Estimand).
Identification Strategy
Under a Parallel-Trends assumption, proposes event-study estimators for the effect of extra periods of (weakly higher) exposure, plus normalized estimators that recover a weighted average of the current treatment’s effect and its lags. Designed for general treatment paths where the cohort/absorbing-treatment estimators (Callaway–Sant’Anna, Sun–Abraham) do not directly apply.
Key Assumptions
Parallel-Trends (for the relevant exposure contrasts), No-Anticipation, a stable comparison group of units whose treatment does not change, and SUTVA.
Threats to Validity
The paper’s foil: standard TWFE regressions are biased under heterogeneous effects; worse, a local-projection version of those regressions is biased even with homogeneous effects. Requires “stayers” (units with unchanged treatment) to serve as controls; thin in some designs.
Setting / Data
n/a — econometric methodology (the did_multiplegt_dyn toolkit). Illustrated with
panel applications featuring switching treatments.
Key Claims
- Provides DiD estimators valid for non-binary, non-absorbing treatments with dynamic effects.
- TWFE and especially its local-projection variant are biased; the proposed event-study/normalized estimators are robust to Treatment-Effect-Heterogeneity.
- Distinguishes “exposure for periods” effects from contemporaneous effects.
Connections
- By the same authors: DeChaisemartinDHaultfoeuille2018-FuzzyDiD, surveyed in DeChaisemartinDHaultfoeuille2023-TWFESurvey
- Robust-estimator family alongside: CallawaySantAnna2021-DiDMultiplePeriods, SunAbraham2021-EventStudies, Wooldridge2021-TWFEMundlakDiD
- See also: CallawayGoodmanBaconSantAnna-ContinuousTreatment, DiD
Citation
de Chaisemartin, C., & D’Haultfœuille, X. (2024). Difference-in-Differences Estimators of Intertemporal Treatment Effects. The Review of Economics and Statistics (first version 2020). https://doi.org/10.1162/rest_a_01414