IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v12y2021i4p1197-1221.html
   My bibliography  Save this article

Synthetic controls with imperfect pretreatment fit

Author

Listed:
  • Bruno Ferman
  • Cristine Pinto

Abstract

We analyze the properties of the Synthetic Control (SC) and related estimators when the pre‐treatment fit is imperfect. In this framework, we show that these estimators are generally biased if treatment assignment is correlated with unobserved confounders, even when the number of pre‐treatment periods goes to infinity. Still, we show that a demeaned version of the SC method can improve in terms of bias and variance relative to the difference‐in‐difference estimator. We also derive a specification test for the demeaned SC estimator in this setting with imperfect pre‐treatment fit. Given our theoretical results, we provide practical guidance for applied researchers on how to justify the use of such estimators in empirical applications.

Suggested Citation

  • Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    • Handle: RePEc:wly:quante:v:12:y:2021:i:4:p:1197-1221
    DOI: 10.3982/QE1596
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE1596
    Download Restriction: no
    File URL: https://libkey.io/10.3982/QE1596?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurent Gobillon & Thierry Magnac, 2016. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 535-551, July.
    2. 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.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    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. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    6. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    7. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    8. Bruno Ferman, 2021. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1764-1772, October.
    9. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Muhammad Jehangir Amjad & Devavrat Shah & Dennis Shen, 2017. "Robust Synthetic Control," Papers 1711.06940, arXiv.org.
    15. Andrew Goodman-Bacon, 2018. "Difference-in-Differences with Variation in Treatment Timing," NBER Working Papers 25018, National Bureau of Economic Research, Inc.
    16. Irene Botosaru & Bruno Ferman, 2019. "On the role of covariates in the synthetic control method," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 117-130.
    17. 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.
    18. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    19. Cheng Hsiao & H. Steve Ching & Shui Ki Wan, 2012. "A Panel Data Approach For Program Evaluation: Measuring The Benefits Of Political And Economic Integration Of Hong Kong With Mainland China," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 705-740, August.
    20. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    21. 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.
    22. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    23. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2018. "A $t$-test for synthetic controls," Papers 1812.10820, arXiv.org, revised Jan 2024.
    24. Ding, Peng & Li, Fan, 2019. "A Bracketing Relationship between Difference-in-Differences and Lagged-Dependent-Variable Adjustment," Political Analysis, Cambridge University Press, vol. 27(4), pages 605-615, October.
    25. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    26. James Heckman & Jose Scheinkman, 1987. "The Importance of Bundling in a Gorman-Lancaster Model of Earnings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 243-255.
    27. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    28. 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.
    29. 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.
    30. Li, Kathleen T. & Bell, David R., 2017. "Estimation of average treatment effects with panel data: Asymptotic theory and implementation," Journal of Econometrics, Elsevier, vol. 197(1), pages 65-75.
    31. Carlos Viana de Carvalho & Ricardo Masini & Marcelo Cunha Medeiros, 2016. "The perils of Counterfactual Analysis with Integrated Processes," Textos para discussão 654, Department of Economics PUC-Rio (Brazil).
    32. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    33. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    34. Geng, Huayan & Zhou, Qiankun, 2019. "Estimation and Inference of Treatment Effects Using a New Panel Data Approach with Application to the Impact of US SYG Law on State Level Murder Rate," 2019 Annual Meeting, July 21-23, Atlanta, Georgia 291212, Agricultural and Applied Economics Association.
    35. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    36. 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.
    37. Kaul, Ashok & Klößner, Stefan & Pfeifer, Gregor & Schieler, Manuel, 2015. "Synthetic Control Methods: Never Use All Pre-Intervention Outcomes Together With Covariates," MPRA Paper 83790, University Library of Munich, Germany.
    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 Jun 2024.
    2. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    3. 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.
    4. Xiong, Ruoxuan & Pelger, Markus, 2023. "Large dimensional latent factor modeling with missing observations and applications to causal inference," Journal of Econometrics, Elsevier, vol. 233(1), pages 271-301.
    5. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2019. "Inference on average treatment effects in aggregate panel data settings," CeMMAP working papers CWP32/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2018. "A $t$-test for synthetic controls," Papers 1812.10820, arXiv.org, revised Jan 2024.
    7. 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.
    8. Jason Poulos & Andrea Albanese & Andrea Mercatanti & Fan Li, 2021. "Retrospective causal inference via matrix completion, with an evaluation of the effect of European integration on cross-border employment," Papers 2106.00788, arXiv.org.
    9. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    10. Viviano, Davide & Bradic, Jelena, 2023. "Synthetic Learner: Model-free inference on treatments over time," Journal of Econometrics, Elsevier, vol. 234(2), pages 691-713.
    11. Bai, Jushan & Wang, Peng, 2024. "Causal inference using factor models," MPRA Paper 120585, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. Bruno Ferman, 2021. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1764-1772, October.
    15. Klößner, Stefan & Pfeifer, Gregor, 2015. "Synthesizing Cash for Clunkers: Stabilizing the Car Market, Hurting the Environment," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113207, Verein für Socialpolitik / German Economic Association.
    16. 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.
    17. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    18. 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.
    19. Michael Funke & Kadri Männasoo & Helery Tasane, 2023. "Regional Economic Impacts of the Øresund Cross-Border Fixed Link: Cui Bono?," CESifo Working Paper Series 10557, CESifo.
    20. Daniel Albalate & Germà Bel & Ferran A. Mazaira-Font, 2021. "Decoupling synthetic control methods to ensure stability, accuracy and meaningfulness," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(4), pages 549-584, December.

    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:wly:quante:v:12:y:2021:i:4:p:1197-1221. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.