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The Augmented Synthetic Control Method

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  • Eli Ben-Michael
  • Avi Feller
  • Jesse Rothstein

Abstract

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The "synthetic control" is a weighted average of control units that balances the treated unit's pre-treatment outcomes as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package.

Suggested Citation

  • Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2018. "The Augmented Synthetic Control Method," Papers 1811.04170, arXiv.org, revised Jul 2020.
  • Handle: RePEc:arx:papers:1811.04170
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    References listed on IDEAS

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    Cited by:

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    2. Mónica Amador-Jiménez & Naomi Millner & Charles Palmer & R. Toby Pennington & Lorenzo Sileci, 2020. "The Unintended Impact of Colombia’s Covid-19 Lockdown on Forest Fires," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 1081-1105, August.
    3. Rieger, Matthias & Wagner, Natascha & Mebratie, Anagaw & Alemu, Getnet & Bedi, Arjun, 2019. "The impact of the Ethiopian health extension program and health development army on maternal mortality: A synthetic control approach," Social Science & Medicine, Elsevier, vol. 232(C), pages 374-381.
    4. Lea Bottmer & Guido Imbens & Jann Spiess & Merrill Warnick, 2021. "A Design-Based Perspective on Synthetic Control Methods," Papers 2101.09398, arXiv.org.
    5. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2019. "Synthetic Controls with Staggered Adoption," Papers 1912.03290, arXiv.org, revised Jan 2021.
    6. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org.
    7. Bennett, Magdalena, 2021. "All things equal? Heterogeneity in policy effectiveness against COVID-19 spread in chile," World Development, Elsevier, vol. 137(C).
    8. Robert J. R. Elliott & Ingmar Schumacher & Cees Withagen, 2020. "Suggestions for a Covid-19 Post-Pandemic Research Agenda in Environmental Economics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 1187-1213, August.
    9. Brantly Callaway & Sonia Karami, 2020. "Treatment Effects in Interactive Fixed Effects Models," Papers 2006.15780, arXiv.org.
    10. Roy Cerqueti & Raffaella Coppier & Alessandro Girardi & Marco Ventura, 2021. "The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy," Papers 2101.11901, arXiv.org.

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