Difference-in-Differences with Multiple Time Periods
Causal Question / Estimand
Builds the staggered-DiD estimand from the ground up as group-time average treatment effects ATT(,) — the effect for the cohort first treated at time , evaluated at time (Causal-Estimand). These disaggregated building blocks are then aggregated into event-study, calendar-time, or overall summaries with transparent, non-negative weights.
Identification Strategy
Estimate each ATT(,) directly by comparing a treatment cohort to a clean control group — never-treated or not-yet-treated units — using a doubly robust estimator. Avoids the contaminating already-treated comparisons that make TWFE biased under heterogeneity. Aggregation schemes (by event time, cohort, calendar time) convert the ATT(,) matrix into interpretable parameters.
Key Assumptions
Parallel-Trends (unconditional or Conditional-Parallel-Trends given covariates), No-Anticipation, existence of a valid comparison group (never-treated or not-yet-treated), Overlap (for the propensity-score component), and SUTVA.
Threats to Validity
No clean control group (no never-treated and limited not-yet-treated units); anticipation effects; conditional-PT covariate misspecification. Uniform inference bands are provided via the multiplier bootstrap to avoid multiple-testing pitfalls in event studies.
Setting / Data
n/a — econometric methodology (R package did). Empirical application: effect of
minimum-wage increases on teen employment across US counties with staggered changes.
Key Claims
- Define and identify ATT(,) with clean controls, sidestepping Negative-Weighting.
- Aggregate building blocks into policy-relevant summaries with sensible weights.
- Provide simultaneous (uniform) confidence bands for event-study plots.
Connections
- Robust-estimator response to: GoodmanBacon2021-DiDVariationInTiming, SunAbraham2021-EventStudies
- Uses the DR machinery of: SantAnnaZhao2020-DoublyRobustDiD, Abadie2005-SemiparametricDiD
- Extended to dosage by: CallawayGoodmanBaconSantAnna-ContinuousTreatment
- See also: DeChaisemartinDHaultfoeuille2023-TWFESurvey, DiD
Citation
Callaway, B., & Sant’Anna, P. H. C. (2021). Difference-in-Differences with Multiple Time Periods. Journal of Econometrics, 225(2), 200–230. https://doi.org/10.1016/j.jeconom.2020.12.001