The DOI matches its Crossref record; 50 of the 50 references it cites were found in a registry or an index.
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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Citations
Cites
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
Abadie, A., Diamond, A., & Hainmueller, J. (2010) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.ap08746 · Cited by 5,513 · cited 12×
“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).”
BackgroundMethodInfluentialLogistic Regression in Rare Events Data
King, G., & Zeng, L. (2001) · Political Analysis · doi:10.1093/oxfordjournals.pan.a004868 · Cited by 4,316 · cited 2×
“McCullagh and Nelder (1989) and King and Zeng (2001) show that the MLE for logistic regression can be badly biased when the response is a rare event.”
BackgroundEstimation of Regression Coefficients When Some Regressors Are Not Always Observed
Robins, J. M., Rotnitzky, A. G., & Zhao, L. P. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476818 · Cited by 2,943 · cited 1×
“Equation (10), by contrast, is analogous to standard doubly robust estimation (Robins, Rotnitzky, and Zhao 1994), which begins with the outcome model but then re-weights to balance residuals.”
MethodComparative Politics and the Synthetic Control Method
Abadie, A., Diamond, A., & Hainmueller, J. (2014) · American Journal of Political Science · doi:10.1111/ajps.12116 · Cited by 2,493
Comparative Politics and the Synthetic Control MethodPreprint
Abadie, A., Diamond, A., & Hainmueller, J. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.1950298 · Cited by 2,217 · cited 14×
“This underscores the importance of the recommendation in Abadie, Diamond, and Hainmueller (2010, 2015) to use SCM only in settings with excellent pretreatment fit.”
InfluentialOn the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9
Neyman, J., Dabrowska, D. M., & Speed, T. P. (1990) · Statistical Science · doi:10.1214/ss/1177012031 · Cited by 1,680
Synthetic Difference-in-Differences
Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021) · American Economic Review · doi:10.1257/aer.20190159 · Cited by 1,518
Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects
Abadie, A. (2021) · Journal of Economic Literature · doi:10.1257/jel.20191450 · Cited by 1,486
Research works printed but not linked: 3
- Ben-Michael, E., Feller, A., & Rothstein, J. (2019), “Synthetic Controls With Staggered Adoption,” Journal of the Royal Statistical Society, Series B, Forthcoming, arXiv: 1912.03290. · arXiv
- 10.1080/01621459.2021.1920957 · DOI · Paper page
- Vovk, V., Gammerman, A., & Shafer, G. (2005), Algorithmic Learning in a Random World, Boston, MA: Springer.
Cited by
Sorted by citations
What's trending in difference-in-differences? A synthesis of the recent econometrics literature
Roth, J., Sant’Anna, P. H. C., Bilinski, A., & Poe, J. (2023) · Journal of Econometrics · doi:10.1016/j.jeconom.2023.03.008 · Cited by 2,027
Synthetic Difference-in-Differences
Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021) · American Economic Review · doi:10.1257/aer.20190159 · Cited by 1,518
Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects
Abadie, A. (2021) · Journal of Economic Literature · doi:10.1257/jel.20191450 · Cited by 1,486
Matrix Completion Methods for Causal Panel Data Models
Athey, S., Bayati, M., Doudchenko, N., Imbens, G., & Khosravi, K. (2018) · doi:10.3386/w25132 · Cited by 497
Liu, L., Wang, Y., & Xu, Y. (2024) · American Journal of Political Science · doi:10.1111/ajps.12723 · Cited by 390
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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