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The Augmented Synthetic Control Method
Open accessAbstract
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 pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pretreatment fit is infeasible. Analogous to bias correction for inexact matching, augmented SCM uses an outcome model to estimate the bias due to imperfect pretreatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pretreatment 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.
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“We followed standard practice for placebo tests, conducting in-space and in-time tests.40,42,43”
From The Peacemaker Fellowship and Urban Gun Violence in Richmond, California (2026) · cites this paper as [40]
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Cites
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“This underscores the importance of the recommendation in Abadie, Diamond, and Hainmueller (2010, 2015) to use SCM only in settings with excellent pretreatment fit.”
InfluentialThe economic costs of conflict: a case study of the Basque Country
Abadie, A., & Gardeazabal, J. (2003) · American Economic Review · doi:10.1257/000282803321455188 · Cited by 4,517 · cited 6×
“The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings with a modest number of control units and with many pre-treatment periods (Abadie and Gardeazabal, 2003; Abadie et al., 2010, 2015).”
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MethodComparative Politics and the Synthetic Control Method
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Comparative Politics and the Synthetic Control MethodPreprint
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“This underscores the importance of the recommendation in Abadie, Diamond, and Hainmueller (2010, 2015) to use SCM only in settings with excellent pretreatment fit.”
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“[20], who substitute the constraint with a penalty factor, the so-called hyperparameter, which penalises the dispersion of the weights following a suggestion by Abadie et al.”
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Swift, S. L., O’Donnell, L., Horn, B. P., Kezios, K., Elfassy, T., Reagan, J. K., Hazzouri, A. Z. A., & Collins, T. C. (2024) · Journal of Public Health Policy · doi:10.1057/s41271-024-00531-z · Cited by 3
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“…causal inference, emphasizing design-based approaches (Athey & Imbens, 2017), interactive unobserved effects (Xu, 2017), matrix completion (Athey et al., 2021), bias correction (Ben-Michael et al., 2021), and penalized estimators (Abadie & L’Hour 2021), among others (Arkhan-gelsky & Imbens, 2024).”
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“…fields such as labour economics (Castillo et al. 2017; Peri and Yasenov 2019), transportation (Tveter, Welde, and Odeck 2017; Xin et al. 2021), taxation (Biagi, Brandano, and Pulina 2017; Ben-Michael, Feller, and Rothstein 2021), and tourism (Addessi, Biagi, and Brandano 2019; Doerr et al. 2020).”
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Single proxy synthetic control
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Metadata
- Authors
- Ben-Michael, E., Feller, A., & Rothstein, J.
- Affiliations
- Department of Statistics, Institute for Quantitative Social Sciences, Harvard University
- University of California System (US)
- Corresponding author
- Feller, Avi
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2021-07-29
- Volume
- 116
- Issue
- 536
- Pages
- 1789-1803
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W3123564515
- Cited by
- 462
- References
- 42
- Citations by year
- 2026: 93 · 2025: 110 · 2024: 79 · 2023: 69 · 2022: 58 · 2021: 33
- FWCI
- 44.66
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Journal of the American Statistical Association (publishedVersion)
- National Bureau of Economic Research (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University) (submittedVersion)
- National Bureau of Economic Research (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University)
- Figshare (cc-by)
- Funders
- Institute of Education Sciences (R305D200010)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Social Sciences › Public Administration › Evaluation and Performance Assessment
- Keywords
- synthetic control method, treatment effect estimation, bias correction, ridge regression, factor models, regularization, overfitting, economic growth
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