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Estimation and Inference for Synthetic Control Methods with Spillover Effects

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  • Jianfei Cao
  • Connor Dowd

Abstract

Estimation and inference procedures for synthetic control methods often do not allow for the existence of spillover effects, which are plausible in many applications. In this paper, we consider estimation and inference for synthetic control methods, allowing for spillover effects. We propose estimators for both direct treatment effects and spillover effects and show that they are asymptotically unbiased. In addition, we propose an inferential procedure and show that it is asymptotically unbiased. Our estimation and inference procedure applies to cases with multiple treated units and/or multiple post-treatment periods, and to ones where the underlying factor model is either stationary or cointegrated. We discuss the bias from misspecified spillover structures and propose a test for correct specification. We apply our method to a classic empirical example that investigates the effect of California's tobacco control program as in Abadie et al. (2010) and find evidence of spillovers. We contrast our method with the pure-donor approach through a sensitivity analysis.

Suggested Citation

  • Jianfei Cao & Connor Dowd, 2019. "Estimation and Inference for Synthetic Control Methods with Spillover Effects," Papers 1902.07343, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:1902.07343
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    References listed on IDEAS

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    1. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2021. "An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1849-1864, October.
    2. Ferman, Bruno & Pinto, Cristine Campos de Xavier, 2016. "Revisiting the synthetic control estimator," Textos para discussão 421, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
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    5. Jinyong Hahn & Ruoyao Shi, 2017. "Synthetic Control and Inference," Econometrics, MDPI, vol. 5(4), pages 1-12, November.
    6. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
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    Cited by:

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    3. Evans Korang Adjei & Rikard Eriksson & Johan Lundberg, 2023. "The effects of a large industrial investment on employment in a remote and sparsely populated area using a synthetic control approach," Regional Science Policy & Practice, Wiley Blackwell, vol. 15(7), pages 1553-1576, September.
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    7. Aleksandar Kešeljević & Rok Spruk, 2024. "Estimating the effects of Syrian civil war," Empirical Economics, Springer, vol. 66(2), pages 671-703, February.
    8. Rebucci, Alessandro & Elenev, Vadim & , & Simeonova, Emilia, 2021. "Direct and Spillover Effects from Staggered Adoption of Health Policies: Evidence from Covid-19 Stay-at-Home Orders," CEPR Discussion Papers 16649, C.E.P.R. Discussion Papers.
    9. Stefano, Roberta di & Mellace, Giovanni, 2020. "The inclusive synthetic control method," Discussion Papers on Economics 14/2020, University of Southern Denmark, Department of Economics.
    10. Lee Kennedy-Shaffer & Alan Hamilton Kennedy, 2025. "Spillovers and Effect Attenuation in Firearm Policy Research in the United States," Papers 2506.01695, arXiv.org.
    11. Andrii Melnychuk, 2024. "Synthetic Controls with spillover effects: A comparative study," Papers 2405.01645, arXiv.org.
    12. Jianfei Cao & Shirley Lu & Hang Wu, 2019. "Synthetic Control Inference for Staggered Adoption," Papers 1912.06320, arXiv.org, revised Nov 2025.
    13. Mario Tello-Pacheco, 2023. "Los “spillovers” del COVID-19 sobre el empleo y el ingreso en Perú," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia, vol. 42(75), pages 161-195.
    14. Giulio Grossi & Marco Mariani & Alessandra Mattei & Patrizia Lattarulo & Ozge Oner, 2020. "Direct and spillover effects of a new tramway line on the commercial vitality of peripheral streets. A synthetic-control approach," Papers 2004.05027, arXiv.org, revised Nov 2023.
    15. Alessandro Rebucci & Jonathan S. Hartley & Daniel Jiménez, 2022. "An Event Study of COVID-19 Central Bank Quantitative Easing in Advanced and Emerging Economies," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Prediction and Macro Modeling, volume 43, pages 291-322, Emerald Group Publishing Limited.

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