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Selection and Parallel Trends

Author

Listed:
  • Dalia Ghanem
  • Pedro H. C. Sant'Anna
  • Kaspar Wüthrich

Abstract

One of the perceived advantages of difference-in-differences (DiD) methods is that they do not explicitly restrict how units select into treatment. However, when justifying DiD, researchers often argue that the treatment is “quasi-randomly” assigned. We investigate what selection mechanisms are compatible with the parallel trends assumptions underlying DiD. We derive necessary and sufficient conditions for parallel trends that clarify whether and how selection can depend on time-invariant and time-varying unobservables. We also suggest a menu of interpretable primitive sufficient conditions for parallel trends, thereby providing the formal underpinnings for justifying DiD based on contextual information about selection into treatment. We provide results for both separable and nonseparable outcome models and show that this distinction has implications for the use of covariates in DiD analyses. Building on our analysis of nonseparable models, we connect DiD to the literature on nonparametric identification in panel models.

Suggested Citation

  • Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    • Handle: RePEc:ces:ceswps:_9910
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    Cited by:

    1. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Jan 2025.
    2. Gregory Faletto, 2023. "Fused Extended Two-Way Fixed Effects for Difference-in-Differences With Staggered Adoptions," Papers 2312.05985, arXiv.org, revised Apr 2025.
    3. Schubert, Torben & Darold, Denilton & Will, Markus, 2024. "Measuring the Causal Economic Effects of Scientific Research — Evidence from the Staggered Foundation of the SENAI Innovation Institutes in Brazil," Papers in Innovation Studies 2024/14, Lund University, CIRCLE - Centre for Innovation Research.
    4. Callaway, Brantly & Li, Tong, 2023. "Policy evaluation during a pandemic," Journal of Econometrics, Elsevier, vol. 236(1).
    5. Janys, Lena & Siflinger, Bettina, 2024. "Mental health and abortions among young women: time-varying unobserved heterogeneity, health behaviors, and risky decisions," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Yechan Park & Yuya Sasaki, 2024. "A Bracketing Relationship for Long-Term Policy Evaluation with Combined Experimental and Observational Data," Papers 2401.12050, arXiv.org.
    7. Torous William & Gunsilius Florian & Rigollet Philippe, 2024. "An optimal transport approach to estimating causal effects via nonlinear difference-in-differences," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-26.
    8. Han, Ning & Liu, Peixian & Zhong, Fanglei & Zhao, Dezhao, 2025. "Does public data access improve fiscal transparency? --On a quasi-natural experiment from government data platform access," Socio-Economic Planning Sciences, Elsevier, vol. 98(C).
    9. Cloud, Cannon & Heß, Simon & Kasinger, Johannes, 2023. "Shared e-scooter services and road safety: Evidence from six European countries," European Economic Review, Elsevier, vol. 160(C).
    10. Pedro Picchetti, 2023. "Identification in Endogenous Sequential Treatment Regimes," Papers 2311.18555, arXiv.org.
    11. Jonas M. Mikhaeil & Christopher Harshaw, 2025. "In Defense of the Pre-Test: Valid Inference when Testing Violations of Parallel Trends for Difference-in-Differences," Papers 2510.26470, arXiv.org, revised Jan 2026.
    12. Pi, Zhenyang & Wang, Ke, 2025. "Does lower electric vehicle production cost spur traditional automaker electrification? Spillovers of cost-reduction investments," Resource and Energy Economics, Elsevier, vol. 81(C).
    13. Sheelapriya, S. & Pirabu, J. Venkata & Karthikeyan, C. & Duraisamy, M. R., 2022. "Perception of Mango Growers towards Enhanced Freshness Formulation (EFF) Technology- A Study in Krishnagiri District of Tamil Nadu," Asian Journal of Agricultural Extension, Economics & Sociology, Asian Journal of Agricultural Extension, Economics & Sociology, vol. 40(10), pages 1-4.

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    Keywords

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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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