30.7 Multiple Periods and Variation in Treatment Timing

TWFE has been extended beyond the simple DiD setup to multiple periods and staggered adoption (where treatment occurs at different times for different units). Such designs are common in applied economics, public policy, and longitudinal research. However, standard TWFE regressions can be biased in these contexts when treatment effects are heterogeneous across groups or over time.

30.7.1 Staggered Difference-in-Differences

In staggered treatment adoption (also called event-study DiD or dynamic DiD):

  • Different units adopt the treatment at different time periods.
  • Standard TWFE often produces biased estimates because it “pools” all treated units (regardless of when they started treatment) together, implicitly comparing newly treated units to already treated ones.
  • Treatments that occurred earlier may contaminate the counterfactual for later adopters if the model does not properly handle dynamic or heterogeneous effects (Wing et al. 2024; Baker, Larcker, and Wang 2022).
  • For applied guidance, see (Wing et al. 2024) and recommendations in (Baker, Larcker, and Wang 2022).

Researchers should be aware that standard TWFE can mix treatment effects of early adopters (long-exposed) with later adopters (newly exposed), potentially assigning negative weights to particular group comparisons (Goodman-Bacon 2021).

When using staggered adoption, the following assumptions are critical:

  1. Rollout Exogeneity
    Treatment assignment and timing should be uncorrelated with potential outcomes.

    • Evidence: Regress adoption on pre-treatment variables. And if you find evidence of correlation, include linear trends interacted with pre-treatment variables (Hoynes and Schanzenbach 2009)
    • Evidence: (Deshpande and Li 2019, 223)
      • Treatment is random: Regress treatment status at the unit level to all pre-treatment observables. If you have some that are predictive of treatment status, you might have to argue why it’s not a worry. At best, you want this.
      • Treatment timing is random: Conditional on treatment, regress timing of the treatment on pre-treatment observables. At least, you want this.

  2. No Confounding Events
    Ensure no other policies or shocks coincide with the staggered treatment rollout.

  3. Exclusion Restrictions

    • No Anticipation: Treatment timing should not affect outcomes prior to treatment.
    • Invariance to History: Treatment duration shouldn’t matter; only the treated status matters (often violated).

  4. Standard DID Assumptions

    • Parallel Trends (Conditional or Unconditional)
    • Random Sampling
    • Overlap (Common Support)
    • Effect Additivity

References

Baker, Andrew C, David F Larcker, and Charles CY Wang. 2022. “How Much Should We Trust Staggered Difference-in-Differences Estimates?” Journal of Financial Economics 144 (2): 370–95.
Deshpande, Manasi, and Yue Li. 2019. “Who Is Screened Out? Application Costs and the Targeting of Disability Programs.” American Economic Journal: Economic Policy 11 (4): 213–48.
Goodman-Bacon, Andrew. 2021. “Difference-in-Differences with Variation in Treatment Timing.” Journal of Econometrics 225 (2): 254–77.
Hoynes, Hilary W, and Diane Whitmore Schanzenbach. 2009. “Consumption Responses to in-Kind Transfers: Evidence from the Introduction of the Food Stamp Program.” American Economic Journal: Applied Economics 1 (4): 109–39.
Wing, Coady, Madeline Yozwiak, Alex Hollingsworth, Seth Freedman, and Kosali Simon. 2024. “Designing Difference-in-Difference Studies with Staggered Treatment Adoption: Key Concepts and Practical Guidelines.” Annual Review of Public Health 45.