IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1912.06320.html

Synthetic Control Inference for Staggered Adoption

Author

Listed:
  • Jianfei Cao
  • Shirley Lu
  • Hang Wu

Abstract

We introduce a synthetic control methodology to study policies with staggered adoption. Many policies, such as the board gender diversity policies, are replicated by other policy setters at different time frames. Our method estimates the dynamic average treatment effects on the treated using variation introduced by the staggered adoption of policies. Our method gives asymptotically unbiased estimators of many interesting quantities and delivers asymptotically valid inference. By using the proposed method and national labor data in Europe, we find evidence that regulation on board gender diversity leads to an increase in full-time employment for female professionals.

Suggested Citation

  • Jianfei Cao & Shirley Lu & Hang Wu, 2019. "Synthetic Control Inference for Staggered Adoption," Papers 1912.06320, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:1912.06320
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1912.06320
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kenneth R. Ahern & Amy K. Dittmar, 2012. "The Changing of the Boards: The Impact on Firm Valuation of Mandated Female Board Representation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(1), pages 137-197.
    2. Jianfei Cao & Connor Dowd, 2019. "Estimation and Inference for Synthetic Control Methods with Spillover Effects," Papers 1902.07343, arXiv.org, revised Jan 2026.
    3. Seierstad, Cathrine & Opsahl, Tore, 2011. "For the few not the many? The effects of affirmative action on presence, prominence, and social capital of women directors in Norway," Scandinavian Journal of Management, Elsevier, vol. 27(1), pages 44-54, March.
    4. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
    5. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    6. Andrews, Donald W.K. & Kim, Jae-Young, 2006. "Tests for Cointegration Breakdown Over a Short Time Period," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 379-394, October.
    7. Firpo Sergio & Possebom Vitor, 2018. "Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets," Journal of Causal Inference, De Gruyter, vol. 6(2), pages 1-26, September.
    8. Michael W. Robbins & Jessica Saunders & Beau Kilmer, 2017. "A Framework for Synthetic Control Methods With High-Dimensional, Micro-Level Data: Evaluating a Neighborhood-Specific Crime Intervention," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 109-126, January.
    9. Cristian L. Dezsö & David Gaddis Ross, 2012. "Does female representation in top management improve firm performance? A panel data investigation," Strategic Management Journal, Wiley Blackwell, vol. 33(9), pages 1072-1089, September.
    10. Eduardo Cavallo & Sebastian Galiani & Ilan Noy & Juan Pantano, 2013. "Catastrophic Natural Disasters and Economic Growth," The Review of Economics and Statistics, MIT Press, vol. 95(5), pages 1549-1561, December.
    11. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    12. 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.
    13. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    14. Noémi Kreif & Richard Grieve & Dominik Hangartner & Alex James Turner & Silviya Nikolova & Matt Sutton, 2016. "Examination of the Synthetic Control Method for Evaluating Health Policies with Multiple Treated Units," Health Economics, John Wiley & Sons, Ltd., vol. 25(12), pages 1514-1528, December.
    15. Xu, Yiqing, 2017. "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models," Political Analysis, Cambridge University Press, vol. 25(1), pages 57-76, January.
    16. 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.
    17. D. W. K. Andrews, 2003. "End-of-Sample Instability Tests," Econometrica, Econometric Society, vol. 71(6), pages 1661-1694, November.
    18. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2018. "Debiasing and $t$-tests for synthetic control inference on average causal effects," Papers 1812.10820, arXiv.org, revised May 2025.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Eli Ben‐Michael & Avi Feller & Jesse Rothstein, 2022. "Synthetic controls with staggered adoption," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 351-381, April.
    2. Youngho Kim, 2024. "Payments for Ecosystem Services Programs and Climate Change Adaptation in Agriculture," Economics Series Working Papers 1054, University of Oxford, Department of Economics.
    3. repec:ags:aaea22:335971 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eli Ben‐Michael & Avi Feller & Jesse Rothstein, 2022. "Synthetic controls with staggered adoption," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 351-381, April.
    2. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    3. Andrii Melnychuk, 2024. "Synthetic Controls with spillover effects: A comparative study," Papers 2405.01645, arXiv.org.
    4. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    5. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    6. Arne Henningsen & Guy Low & David Wuepper & Tobias Dalhaus & Hugo Storm & Dagim Belay & Stefan Hirsch, 2024. "Estimating Causal Effects with Observational Data: Guidelines for Agricultural and Applied Economists," IFRO Working Paper 2024/03, University of Copenhagen, Department of Food and Resource Economics.
    7. Justin C. Wiltshire, 2023. "Walmart Supercenters and Monopsony Power: How A Large, Low-Wage Employer Impacts Local Labor Markets," Department Discussion Papers 2304, Department of Economics, University of Victoria.
    8. Nyborg, Kjell G. & Woschitz, Jiri, 2025. "Robust difference-in-differences analysis when there is a term structure," Journal of Financial Economics, Elsevier, vol. 170(C).
    9. Joakim Weill, 2023. "Flood Risk Mapping and the Distributional Impacts of Climate Information," Working Papers 2023.10, FAERE - French Association of Environmental and Resource Economists.
    10. Joakim A. Weill, 2023. "Flood Risk Mapping and the Distributional Impacts of Climate Information," Finance and Economics Discussion Series 2023-066, Board of Governors of the Federal Reserve System (U.S.).
    11. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    12. Damm, Yannic & Cisneros, Elías & Börner, Jan, 2024. "Beyond Deforestation Reductions: Public Disclosure, Land-Use Change and Commodity Sourcing," World Development, Elsevier, vol. 175(C).
    13. Wu, Libo & Zhou, Yang, 2025. "Social norms and energy conservation in China," Resource and Energy Economics, Elsevier, vol. 82(C).
    14. Hao, Shiming, 2021. "True structure change, spurious treatment effect? A novel approach to disentangle treatment effects from structure changes," MPRA Paper 108679, University Library of Munich, Germany.
    15. Girma, Sourafel & Paton, David, 2022. "Is assisted suicide a substitute for unassisted suicide?," European Economic Review, Elsevier, vol. 145(C).
    16. 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.
    17. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2024. "Revisiting Event-Study Designs: Robust and Efficient Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3253-3285.
    18. Hans-Bernd Schaefer & Rok Spruk, 2024. "Islamic Law, Western European Law and the Roots of Middle East's Long Divergence: a Comparative Empirical Investigation (800-1600)," Papers 2401.14435, arXiv.org, revised Mar 2024.
    19. Tomasz Serwach, 2022. "The European Union and within-country income inequalities. The case of the New Member States," Working Papers hal-03548416, HAL.
    20. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1912.06320. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.