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A Split-Treatment Design

Author

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  • Jean-Baptiste Bonnier

    (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France)

Abstract

I devise a difference-in-differences design that accounts for the possibility that some treatment effect is split in the reactions to two or more events. At the intersection of settings with a single treatment and with multiple treatments, regression-based methods for this split-treatment design can be subject both to negative weights and contamination bias. I propose a simple solution, a first-difference regression with sample constraints in the spirit of Dube et al.’s (2023) LP-DiD, that allows to identify and estimate sensible causal parameters of interest. This estimator is efficient under random walk errors and unrestricted heterogeneity across groups and events.

Suggested Citation

  • Jean-Baptiste Bonnier, 2024. "A Split-Treatment Design," Working Papers 2024-11, CRESE.
    • Handle: RePEc:crb:wpaper:2024-11
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    References listed on IDEAS

    as
    1. Jordà , Òscar & Dube, Arindrajit & Girardi, Daniele & Taylor, Alan, 2023. "A Local Projections Approach to Difference-in-Differences Event Studies," CEPR Discussion Papers 18141, C.E.P.R. Discussion Papers.
    2. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    3. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    4. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    5. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    6. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
    7. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    8. Paul Goldsmith-Pinkham & Peter Hull & Michal Koles'ar, 2021. "Contamination Bias in Linear Regressions," Papers 2106.05024, arXiv.org, revised Feb 2024.
    9. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    10. Asaf Bernstein & Eric Hughson & Marc Weidenmier, 2019. "Counterparty Risk and the Establishment of the New York Stock Exchange Clearinghouse," Journal of Political Economy, University of Chicago Press, vol. 127(2), pages 689-729.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Difference-in-differences; Heterogeneous treatment effects; Multiple treatments; Contamination bias.;
    All these keywords.

    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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