Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis
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In a seminal paper Abadie et al (2010) develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units.The method constructs a set of weights such that covariates and pre-treatment outcomes of the treated unit are approximately matched by a weighted average of control units.The weights are restricted to be nonnegative and sum to one, which allows the procedure to obtain the weights even when the number of lagged outcomes is modest relative to the number of control units, a setting that is not uncommon in applications.In the current paper we propose a more general class of synthetic control estimators that allows researchers to relax some of the restrictions in the ADH method.We allow the weights to be negative, do not necessarily restrict the sum of the weights, and allow for a permanent additive difference between the treated unit and the controls, similar to difference-in-difference procedures.The weights directly minimize the distance between the lagged outcomes for the treated and the control units, using regularization methods to deal with a potentially large number of possible control units.
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Recent work has begun to try to combine insights from the difference-in-differences and synthetic control literatures.
“Recent work has begun to try to combine insights from the two literatures (e.g., Arkhangelsky, Athey, Hirshberg, Imbens and Wager, 2021; Ben-Michael, Feller and Rothstein, 2021, 2022; Doudchenko and Imbens, 2016).”
From What's trending in difference-in-differences? A synthesis of the recent econometrics literature (2023) · cites this paper as Doudchenko and Imbens, 2016
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Shaikh, A. M., & Toulis, P. (2021) · Journal of the American Statistical Association · doi:10.1080/01621459.2021.1974458 · Cited by 19 · see citing works
Samartsidis, P., Seaman, S. R., Presanis, A. M., Hickman, M., & Angelis, D. D. (2019) · Apollo (University of Cambridge) · doi:10.17863/cam.40086 · Cited by 18 · see citing works
Synthetic Learner: Model-free inference on treatments over time
Viviano, D., & Bradić, J. (2022) · Journal of Econometrics · doi:10.1016/j.jeconom.2022.07.006 · Cited by 18 · see citing works
Synthetic InterventionsPreprint
Agarwal, A., Devavrat Shah, B., & Shen, D. (2020) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.2006.07691 · Cited by 18 · see citing works
Inference for Factor Model Based Average Treatment EffectsPreprint
Li, K. Y. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3112775 · Cited by 18 · see citing works
Perilous Flood Risk AssessmentsPreprint
Weill, J. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4143914 · Cited by 18 · see citing works
Are IMF rescue packages effective? A synthetic control analysis of macroeconomic crises
Kuruc, K. (2022) · Journal of Monetary Economics · doi:10.1016/j.jmoneco.2022.02.002 · Cited by 17 · see citing works
Of the first five US states with food waste bans, Massachusetts alone has reduced landfill waste
Anglou, F. Z., Sanders, R. E., & Stamatopoulos, I. (2024) · Science · doi:10.1126/science.adn4216 · Cited by 17 · see citing works
The emergence of social soft skill needs in the post COVID-19 era
Gnecco, G., Landi, S., & Riccaboni, M. (2023) · Quality & Quantity · doi:10.1007/s11135-023-01659-y · Cited by 16 · see citing works
Focused Deterrence and Program Fidelity: Evaluating the Impact of Detroit Ceasefire
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Estimating the effects of a California gun control program with multitask Gaussian processes
Ben‐Michael, E., Arbour, D. T., Feller, A., Franks, A. M., & Raphael, S. P. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1654 · Cited by 17 · see citing works
Bayesian Method for Causal Inference in Spatially-Correlated Multivariate Time Series
Ning, B., Subhashis Ghosal, B., & Thomas, J. (2018) · Bayesian Analysis · doi:10.1214/18-ba1102 · Cited by 16 · see citing works
- Authors
- Doudchenko, N., & Imbens, G.
- Affiliations
- National Bureau of Economic Research (US)
- Stanford University (US)
- ORCID
- Imbens, Guido
- Venue
- National Bureau of Economic Research
- Publisher
- National Bureau of Economic Research
- Published
- 2016-10
- OpenAlex
- W2540009304
- Cited by
- 410
- References
- 22
- Citations by year
- 2026: 32 · 2025: 54 · 2024: 51 · 2023: 44 · 2022: 44 · 2021: 72 · 2020: 41 · 2019: 34 · 2018: 23 · 2017: 11 · 2016: 3 · 2014: 1
- Type
- report
- Language
- en
- Open access
- green
- doi.org
- Locations
- National Bureau of Economic Research (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- SSRN Electronic Journal (submittedVersion)
- National Bureau of Economic Research (submittedVersion)
- arXiv (Cornell University)
- 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, regularization, difference-in-differences, regression discontinuity design
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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