IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2202.08426.html
   My bibliography  Save this paper

Synthetic Control As Online Linear Regression

Author

Listed:
  • Jiafeng Chen

Abstract

This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow-The-Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference-in-differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.

Suggested Citation

  • Jiafeng Chen, 2022. "Synthetic Control As Online Linear Regression," Papers 2202.08426, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2202.08426
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2202.08426
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    3. 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.
    4. 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.
    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. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    7. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
    8. 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.
    9. 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.
    10. 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.
    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. Guido W. Imbens, 2022. "Causality in Econometrics: Choice vs Chance," Econometrica, Econometric Society, vol. 90(6), pages 2541-2566, November.
    2. Xiaomeng Zhang & Wendun Wang & Xinyu Zhang, 2022. "Asymptotic Properties of the Synthetic Control Method," Papers 2211.12095, arXiv.org.

    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. Rong J. B. Zhu, 2023. "Synthetic Regressing Control Method," Papers 2306.02584, arXiv.org, revised Oct 2023.
    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. 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.
    4. Matias D. Cattaneo & Yingjie Feng & Filippo Palomba & Rocio Titiunik, 2022. "scpi: Uncertainty Quantification for Synthetic Control Methods," Papers 2202.05984, arXiv.org, revised Oct 2022.
    5. 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.
    6. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    7. Xiaomeng Zhang & Wendun Wang & Xinyu Zhang, 2022. "Asymptotic Properties of the Synthetic Control Method," Papers 2211.12095, arXiv.org.
    8. Alberto Abadie & Jinglong Zhao, 2021. "Synthetic Controls for Experimental Design," Papers 2108.02196, arXiv.org, revised Dec 2023.
    9. Kim, Youngho, 2023. "Payments for Ecosystem Services Programs and Climate Change Adaptation in Agriculture," 2023 Annual Meeting, July 23-25, Washington D.C. 335971, Agricultural and Applied Economics Association.
    10. 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.
    11. 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.
    12. 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.
    13. Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    14. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    15. Billy, Alexander & Packard, Michael, 2022. "Crime and the Mariel Boatlift," International Review of Law and Economics, Elsevier, vol. 72(C).
    16. Dmitry Arkhangelsky & David Hirshberg, 2023. "Large-Sample Properties of the Synthetic Control Method under Selection on Unobservables," Papers 2311.13575, arXiv.org, revised Dec 2023.
    17. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2023. "Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data," Econometrica, Econometric Society, vol. 91(6), pages 2125-2154, November.
    18. Justin Wiltshire, 2021. "allsynth: Synthetic control bias-corrections utilities for Stata," 2021 Stata Conference 15, Stata Users Group.
    19. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    20. Claudia Shi & Dhanya Sridhar & Vishal Misra & David M. Blei, 2021. "On the Assumptions of Synthetic Control Methods," Papers 2112.05671, arXiv.org, revised Dec 2021.

    More about this item

    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:2202.08426. 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.