Cited by 462Advanced Causal Inference TechniquesSpatial and Panel Data AnalysisEvaluation and Performance Assessment

The Augmented Synthetic Control Method

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Ben-Michael, Eli, Feller, Avi, Rothstein, Jesse·2021·Journal of the American Statistical Association

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 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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  • Standard practice for placebo tests was followed by conducting in-space and in-time tests.

    “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]

    Section 2.3 describes placebo checks as part of synthetic-control practice, and the appendix discussion of Figures F.10–F.12 reports in-time placebo tests. The passages do not establish in-space tests as part of the practice attributed to this source. Whether the citing authors conducted either test is their own report, not something this source can verify. (LLM, conf=0.83)

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Research works printed but not linked: 12

  1. Abadie, A., A. Diamond, and J. Hainmueller (2010). Synthetic Control Methods for Com- parative Case Studies: Estimating the E↵ect of California's Tobacco Control Program. Journal of the American Statistical Association 105 (490), 493-505.
  2. Abadie, A. and G. W. Imbens (2011). Bias-corrected matching estimators for average treat- ment e↵ects. Journal of Business & Economic Statistics 29 (1), 1-11.
  3. Arkhangelsky, D., S. Athey, D. A. Hirshberg, G. W. Imbens, and S. Wager (2019). Synthetic di↵erence in di↵erences. arXiv preprint arXiv:1812.09970 . · arXiv
  4. Ben-Michael, E., A. Feller, and J. Rothstein (2019). Synthetic controls and weighted event studies with staggered adoption. arXiv preprint arXiv:1912.03290 . · arXiv
  5. Doudchenko, N. and G. W. Imbens (2017). Di↵erence-In-Di↵erences and Synthetic Control Methods: A Synthesis. arxiv 1610.07748 . · arXiv
  6. Vovk, V., A. Gammerman, and G. Shafer (2005). Algorithmic learning in a random world. Springer.
  7. Athey, S., G. W. Imbens, and S. Wager (2018). Approximate residual balancing: debiased inference of average treatment e↵ects in high dimensions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 (4), 597-623.
  8. Cassel, C. M., C.-E. Sarndal, and J. H. Wretman (1976). Some results on generalized di↵erence estimation and generalized regression estimation for finite populations. Biometrika 63 (3), 615- 620.
  9. Chattopadhyay, A., Christopher H. Hase, and J. R. Zubizarreta (2020). Balancing Versus Modeling Approaches to Weighting in Practice. Statistics in Medicine in press.
  10. Chernozhukov, V., K. Wuthrich, and Y. Zhu (2018). Inference on average treatment e↵ects in aggregate panel data settings. arXiv preprint arXiv:1812.10820 . · arXiv
  11. Doudchenko, N. and G. W. Imbens (2017). Di↵erence-In-Di↵erences and Synthetic Control Meth- ods: A Synthesis. arxiv 1610.07748 . · arXiv
  12. Robbins, M., J. Saunders, and B. 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 112 (517), 109-126.

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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
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 · 2020: 14 · 2019: 5 · 2018: 1
FWCI
44.66
Type
journal article
Language
en
Open access
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 › Decision Sciences › Management Science and Operations Research › 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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