IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2012.15367.html
   My bibliography  Save this paper

Assessing the Sensitivity of Synthetic Control Treatment Effect Estimates to Misspecification Error

Author

Listed:
  • Billy Ferguson
  • Brad Ross

Abstract

We propose a sensitivity analysis for Synthetic Control (SC) treatment effect estimates to interrogate the assumption that the SC method is well-specified, namely that choosing weights to minimize pre-treatment prediction error yields accurate predictions of counterfactual post-treatment outcomes. Our data-driven procedure recovers the set of treatment effects consistent with the assumption that the misspecification error incurred by the SC method is at most the observable misspecification error incurred when using the SC estimator to predict the outcomes of some control unit. We show that under one definition of misspecification error, our procedure provides a simple, geometric motivation for comparing the estimated treatment effect to the distribution of placebo residuals to assess estimate credibility. When we apply our procedure to several canonical studies that report SC estimates, we broadly confirm the conclusions drawn by the source papers.

Suggested Citation

  • Billy Ferguson & Brad Ross, 2020. "Assessing the Sensitivity of Synthetic Control Treatment Effect Estimates to Misspecification Error," Papers 2012.15367, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2012.15367
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2012.15367
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tamara Broderick & Ryan Giordano & Rachael Meager, 2020. "An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?," Papers 2011.14999, arXiv.org, revised Jul 2023.
    2. 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.
    3. George J. Borjas, 2021. "The Wage Impact Of The Marielitos: A Reappraisal," World Scientific Book Chapters, in: Foundational Essays in Immigration Economics, chapter 12, pages 375-408, World Scientific Publishing Co. Pte. Ltd..
    4. Iavor Bojinov & Neil Shephard, 2019. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1665-1682, October.
    5. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    6. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
    7. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2018. "A $t$-test for synthetic controls," Papers 1812.10820, arXiv.org, revised Jan 2024.
    8. Maxwell Kellogg & Magne Mogstad & Guillaume Pouliot & Alexander Torgovitsky, 2020. "Combining Matching and Synthetic Control to Trade off Biases from Extrapolation and Interpolation," NBER Working Papers 26624, National Bureau of Economic Research, Inc.
    9. 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.
    10. Giovanni Peri & Vasil Yasenov, 2019. "The Labor Market Effects of a Refugee Wave: Synthetic Control Method Meets the Mariel Boatlift," Journal of Human Resources, University of Wisconsin Press, vol. 54(2), pages 267-309.
    11. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    12. Charles F. Manski & John V. Pepper, 2018. "How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 232-244, May.
    13. 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.
    14. Alberto Abadie & Alexis Diamond & Jens Hainmueller, 2015. "Comparative Politics and the Synthetic Control Method," American Journal of Political Science, John Wiley & Sons, vol. 59(2), pages 495-510, February.
    15. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    16. Andreas Hagemann, 2020. "Inference with a single treated cluster," Papers 2010.04076, arXiv.org.
    17. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    Full references (including those not matched with items 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. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    2. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2022. "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data," Papers 2207.14481, arXiv.org, revised Oct 2022.
    3. Giovanni Peri & Derek Rury & Justin C. Wiltshire, 2020. "The Economic Impact of Migrants from Hurricane Maria," NBER Working Papers 27718, National Bureau of Economic Research, Inc.
    4. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    5. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    6. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    7. Lea Bottmer & Guido Imbens & Jann Spiess & Merrill Warnick, 2021. "A Design-Based Perspective on Synthetic Control Methods," Papers 2101.09398, arXiv.org, revised Jul 2023.
    8. Demirci, Murat, 2023. "Youth responses to political populism: Education abroad as a step toward emigration," Journal of Comparative Economics, Elsevier, vol. 51(2), pages 653-673.
    9. Bruno Ferman & Cristine Pinto & Vitor Possebom, 2020. "Cherry Picking with Synthetic Controls," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 39(2), pages 510-532, March.
    10. Peter Backus & Thien Nguyen, 2021. "The Effect of the Sex Buyer Law on the Market for Sex, Sexual Health and Sexual Violence," Economics Discussion Paper Series 2106, Economics, The University of Manchester.
    11. Gharehgozli, Orkideh, 2021. "An empirical comparison between a regression framework and the Synthetic Control Method," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 70-81.
    12. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    13. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    14. Jason Poulos, 2019. "State-Building through Public Land Disposal? An Application of Matrix Completion for Counterfactual Prediction," Papers 1903.08028, arXiv.org, revised Dec 2023.
    15. Jason Poulos & Shuxi Zeng, 2021. "RNN‐based counterfactual prediction, with an application to homestead policy and public schooling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 1124-1139, August.
    16. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    17. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    18. Guillaume Allaire Pouliot & Zhen Xie, 2022. "Degrees of Freedom and Information Criteria for the Synthetic Control Method," Papers 2207.02943, arXiv.org.
    19. Masahiro Kato & Akari Ohda & Masaaki Imaizumi & Kenichiro McAlinn, 2023. "Synthetic Control Methods by Density Matching under Implicit Endogeneity," Papers 2307.11127, arXiv.org, revised Jul 2023.
    20. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.

    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:2012.15367. 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.