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Regression Discontinuity Design with Spillovers

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  • Eric Auerbach
  • Yong Cai
  • Ahnaf Rafi

Abstract

This paper studies regression discontinuity designs (RDD) when linear-in-means spillovers occur between units that are close in their running variable. We show that the RDD estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. RDD estimates direct treatment effect when radius is of larger order than the bandwidth and total treatment effect when radius is of smaller order than the bandwidth. When the two are of similar order, the RDD estimand need not have a causal interpretation. To recover direct and spillover effects in the intermediate regime, we propose to incorporate estimated spillover terms into local linear regression. Our estimator is consistent and asymptotically normal and we provide bias-aware confidence intervals for direct treatment effects and spillovers. In the setting of Gonzalez (2021), we detect endogenous spillovers in voter fraud during the 2009 Afghan Presidential election. We also clarify when the donut-hole design addresses spillovers in RDD.

Suggested Citation

  • Eric Auerbach & Yong Cai & Ahnaf Rafi, 2024. "Regression Discontinuity Design with Spillovers," Papers 2404.06471, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2404.06471
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    References listed on IDEAS

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    1. Sobel, Michael E., 2006. "What Do Randomized Studies of Housing Mobility Demonstrate?: Causal Inference in the Face of Interference," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1398-1407, December.
    2. Yuchen Hu & Shuangning Li & Stefan Wager, 2022. "Average direct and indirect causal effects under interference [Estimating average causal effects under general interference, with application to a social network experiment]," Biometrika, Biometrika Trust, vol. 109(4), pages 1165-1172.
    3. Hudgens, Michael G. & Halloran, M. Elizabeth, 2008. "Toward Causal Inference With Interference," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 832-842, June.
    4. Yuchen Hu & Shuangning Li & Stefan Wager, 2021. "Average Direct and Indirect Causal Effects under Interference," Papers 2104.03802, arXiv.org, revised Jan 2022.
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    Cited by:

    1. Kirill Borusyak & Matan Kolerman-Shemer, 2024. "Regression discontinuity aggregation, with an application to the union effects on inequality," Papers 2501.00428, arXiv.org.
    2. Nicolas Debarsy & Julie Le Gallo, 2024. "Identification of spatial spillovers: Do’s and don'ts," Working Papers hal-04549691, HAL.
    3. Bermúdez-Barrezueta, Natalia & Desiere, Sam & Tarullo, Giulia, 2025. "Hiring Subsidies and Temporary Work Agencies," IZA Discussion Papers 17616, Institute of Labor Economics (IZA).

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