Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects
Causal Question / Estimand
The dynamic (event-time) path of treatment effects — the cohort-average treatment effect on the treated at each relative period, CATT(,) (Causal-Estimand) — for an absorbing treatment adopted at staggered dates.
Identification Strategy
Shows that in a TWFE event-study regression with leads and lags, the coefficient on a given relative period is a contaminated linear combination of CATTs from other relative periods (weights that need not sum to one and can be negative). As a consequence, apparent pre-trends can arise purely from effect heterogeneity, not from a real violation of parallel trends. Proposes the interaction-weighted (IW) estimator: estimate cohort-by-relative-period effects via saturated interactions (using never-treated or last-treated cohorts as controls), then aggregate with sensible weights.
Key Assumptions
Parallel-Trends across cohorts, No-Anticipation (no effect in pre-periods), and a clean control group (never-treated or last-to-be-treated). SUTVA throughout. The IW estimator avoids the Negative-Weighting / contamination that afflicts TWFE leads and lags under Treatment-Effect-Heterogeneity.
Threats to Validity
If no never-treated group exists, the last-treated cohort must serve as control, with its own caveats. Genuine anticipation breaks the pre-period interpretation. The diagnosis warns against reading TWFE event-study pre-trend coefficients as clean specification tests.
Setting / Data
n/a — econometric methodology. Empirical application revisiting the effect of women’s political representation / an event-study application illustrating TWFE vs IW.
Key Claims
- TWFE event-study lead/lag coefficients are contaminated across periods under heterogeneous effects.
- Pre-trend tests from TWFE event studies can spuriously fail even when parallel trends holds.
- The interaction-weighted estimator delivers uncontaminated dynamic effect estimates.
Connections
- Companion diagnosis: GoodmanBacon2021-DiDVariationInTiming
- Robust-estimator family: CallawaySantAnna2021-DiDMultiplePeriods, DeChaisemartinDHaultfoeuille2020-IntertemporalTE, Wooldridge2021-TWFEMundlakDiD
- Connects to pre-testing critiques: RothPretrends2022-PretestWithCaution
- Robust imputation estimator that cites this contamination result: BorusyakEtAl2024-RevisitingEventStudyDesigns
- See also: DeChaisemartinDHaultfoeuille2023-TWFESurvey, Negative-Weighting, DiD
Citation
Sun, L., & Abraham, S. (2021). Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects. Journal of Econometrics, 225(2), 175–199. https://doi.org/10.1016/j.jeconom.2020.09.006