arXiv 16 Jun 2026 · Econometrics
arXiv:2606.17977 · PDF · DOI · OpenAlex · Extracted main text
In difference-in-differences designs, the parallel trends assumption requires that the outcome gap between treated and control units would have remained flat absent treatment. Pre-treatment event studies frequently reject this flat-gap requirement. Existing responses include parametric trend controls and bounds on the treatment effect under assumptions about the magnitude of the violation. This paper shows that point identification of cohort-specific and aggregate treatment effects in staggered designs remains achievable under strictly weaker assumptions. I replace the flat-gap requirement with a hierarchy of higher-order conditions, Parallel[p], embed this framework in the group-time average treatment effect structure of Callaway and Sant'Anna (2021), and prove an aggregation theorem for the case where different cohorts are identified under different feasible polynomial orders, a challenge unique to staggered designs that has not been previously addressed. A sequential order-selection procedure guides applied practice. Monte Carlo evidence confirms that post-selection bootstrap coverage remains near-nominal and that inference is robust to realistic serial correlation. Applied to Medicaid expansion data, the method yields point estimates resting on an assumption the pre-treatment data do not reject, in contrast to the flat-gap requirement which those same data decisively reject.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Callaway, Brantly and Sant’Anna, Pedro HC (2021) Difference-in-differences with multiple time periods | 0.971 | 12 | 7 | 92% |
| 2 | Rambachan, Ashesh and Roth, Jonathan (2023) A more credible approach to parallel trends | 0.971 | 12 | 7 | 92% |
| 3 | Egami, Naoki and Yamauchi, Soichiro (2023) Using multiple pretreatment periods to improve difference-in-differences and staggered adoption designs | 0.843 | 3 | 3 | 100% |
| 4 | Roth, Jonathan (2022) Pretest with caution: Event-study estimates after testing for parallel trends | 0.737 | 3 | 2 | 100% |
| 5 | Mora, Ricardo and Reggio, Iliana (2019) Alternative diff-in-diffs estimators with several pretreatment periods | 0.644 | 2 | 2 | 100% |
| 6 | Dobkin, Carlos and Finkelstein, Amy and Kluender, Raymond and Notowi… (2018) The economic consequences of hospital admissions | 0.511 | 2 | 2 | 50% |
| 7 | Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program | 0.405 | 1 | 1 | 100% |
| 8 | Angrist, Joshua D and Pischke, Jörn-Steffen (2009) Mostly harmless econometrics: An empiricist's companion | 0.405 | 1 | 1 | 100% |
| 9 | Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… (2021) Synthetic difference-in-differences | 0.405 | 1 | 1 | 100% |
| 10 | Athey, Susan and Imbens, Guido W (2006) Identification and inference in nonlinear difference-in-differences models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 24 scored citations.