arXiv 1 Mar 2026 · Econometrics
arXiv:2603.00868 · PDF · DOI · OpenAlex · Extracted main text
Two key identifying assumptions used to justify difference-in-differences are parallel trends and no anticipation, yet both may fail in practice. I propose a class of assumptions on anticipation and derive closed-form, sharp bounds on the average treatment effect on the treated while simultaneously relaxing parallel trends. Deviations from both assumptions are jointly disciplined using observed pre-trends. When some anticipation is imposed, the identified set under joint deviations can be shorter than under parallel trends violations alone. These bounds inform a sensitivity analysis assessing the robustness of qualitative conclusions to anticipation and parallel trends violations. I illustrate with an empirical application.
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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 | Dinerstein, M. and T. D. Smith (2021) Quantifying the Supply Response of Private Schools to Public Policies | 1.000 | 16 | 3 | 100% |
| 2 | Manski, C. F. and J. V. Pepper (2018) How do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity using Bounded-Variation Assumptions | 1.000 | 8 | 3 | 100% |
| 3 | Rambachan, A. and J. Roth (2023) A More Credible Approach to Parallel Trends | 1.000 | 8 | 3 | 100% |
| 4 | Masten, M. A. and A. Poirier (2020) Inference on Breakdown Frontiers | 1.000 | 7 | 3 | 100% |
| 5 | Malani, A. and J. Reif (2015) Interpreting Pre-Trends as Anticipation: Impact on Estimated Treatment Effects from Tort Reform | 0.874 | 6 | 2 | 100% |
| 6 | Callaway, B. and P. H. Sant’Anna (2021) Difference-in-Differences with Multiple Time Periods | 0.874 | 5 | 2 | 100% |
| 7 | Roth, J., P. H. Sant’Anna, A. Bilinski, and J. Poe (2023) What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature | 0.811 | 4 | 2 | 100% |
| 8 | Gong, A (2022) Bounds for Treatment Effects in the Presence of Anticipatory Behavior | 0.737 | 3 | 2 | 100% |
| 9 | Dinerstein, M. and T. D. Smith (2021) Data and Code for: Quantifying the Supply Response of Private Schools to Public Policies, Inter-University Consortium for Politi… | 0.693 | 5 | 1 | 100% |
| 10 | Baker, A., B. Callaway, S. Cunningham, A. Goodman-Bacon, and P. H. S… (2025) Difference-in-Differences Designs: A Practitioner's Guide | 0.585 | 3 | 1 | 100% |
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