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On the Assumptions of Synthetic Control Methods

Author

Listed:
  • Claudia Shi
  • Dhanya Sridhar
  • Vishal Misra
  • David M. Blei
Abstract
Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit's counterfactual outcomes using a weighted combination of some other units' observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of the analysis from "large units" (e.g., states) to "small units" (e.g., individuals in states). Under this re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We highlight two implications of the reformulation: (1) it clarifies where "linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model, and (2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2112.05671
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    References listed on IDEAS

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    1. 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.
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    3. Kathleen T. Li, 2020. "Statistical Inference for Average Treatment Effects Estimated by Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2068-2083, December.
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    6. 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.
    7. 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.
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    10. 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.
    11. Ferman, Bruno & Pinto, Cristine, 2017. "Placebo Tests for Synthetic Controls," MPRA Paper 78079, University Library of Munich, Germany.
    12. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
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    14. 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:

    1. Aniket Kesari, 2022. "Do data breach notification laws reduce medical identity theft? Evidence from consumer complaints data," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 19(4), pages 1222-1252, December.
    2. Yiping Lu & Jiajin Li & Lexing Ying & Jose Blanchet, 2022. "Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls," Papers 2211.15241, arXiv.org.

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