Synthetic controls

Joaquim Estopinan | June 23, 2025

This method also belongs to Adjusted methods (Backdoor C.).

Table of Contents

1. Description & principle
2. Reference articles
3. Packages
4. Assessment table

Description & principle

The synthetic control (SC) method originates from the early 2000s, with its first introduction in the influential Abadie & Gardeazabal (2003) article. It consists in combining a selection of control sites to best mimick the treatment site’s counterfactual, based on the pre-intervention similarity of their respective outcome and covariates. It is an effect estimation method shifting the causal sufficiency assumption (no unobserved confounders) to the good pre-intervention fit condition, still assuming no time-varying unobserved confoundinfing after the intervention.

Major variants

The success of this method has also led to numerous variants. We can cite among others:

• Robust SC from Amjad, Shah, & Shen (2018): Adds de-noising, uncertainty estimation and handles missing data
• Augmented SC from Ben-Michael, Feller, & Rothstein (2020) (2022): Relaxes constraints on the synthetic control combination to improve pre-treatment fit and allows staggered adoption of treatment between various units
• Sparse SC from Quistorff, Goldman, & Thorpe (2021): Helps pre-treatment variables selection and add regularization to meet big data context needs
• Penalized SC from Abadie (2021): An adaptation of the SC method to deal with disaggregated data gathering varied treated units
• Finally, a number of recent developement merge the SC method with other approaches:
  • Generalized SC relaxes the parallel trend assumption and unifies the SC method with linear fixed effects models (Xu, 2016)
  • Synthetic Diff-in-diffs combines SCs with the difference-in-differences estimator (Arkhangelsky et al., 2021)
  • Chernozhukov, Wüthrich, & Zhu (2021) exploit conformal prediction and structural breaks in conjunction with SCs
  • Imai, Kim, & Wang (2023) developped a flexible estimation procedure combining matching and SCs ideas with diff-and-diffs.

Further online resources

• A pedagocial blog decomposing the method: 15 - Synthetic Control
• On the covariate selection: Botosaru & Ferman (2019)
• Discussion on the violation of the parallel trends assumption and its consequences: Cross Validated

Reference articles

Method

An updated review paper positioning the method by its original author: Abadie & L’Hour (2021)

Research applications

With RS data in Ecology / Biodiversity

• Fick et al. (2021)
• Sharma et al. (2023)
• Rana & Miller (2019)
• West et al. (2020)

Without RS data (Ecology domain)

• Lépissier & Mildenberger (2021)
• Nakanishi et al. (2022)
• Kaiser, Dee, & Resasco (2025)

Packages

Python

• pysyncon

R

• Synth
• augsynth
• tidysynth
• microsynth
• gsynth
• SparseSC

Assessment table

Category	Criteria	Assessment
Outcome	Objective	Effect estimation, Scenario projection, Detection
	Estimand	ATT, ATE, Maps & generalisations
	Validity	Varying
Data compatibility	Type	Panel data (many samples)
	Required TS length	≥ 10
	Handles few samples	10 to 100
	Handles huge datasets (n)	Yes
	Handles missing data	Partially
	RS-data proven	Yes
Assumptions	Functional form	Assumption-free
	No unobserved confounders	Desirable
	No interference	Required
	Well-defined treatments	Required
	Common support (positivity)	Required
	Causal Markov Condition	Recommended
	Faithfulness	Recommended
	IDD	Required
	Model specific assumption	Good pretreatment fit, B/A treatment obs.
Model properties	Requires explicit processes	Agnostic
	Exposure type	Binary, Categorical
	Number of variables	Multivariate
	Handles lag effects	Yes
	Propagates uncertainty	Model-specific tools
	Parametric nature	Non-parametric
Packages	Language	R, Python
	Usage	Technical but well documented

References

1. Abadie, A., & Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93, 113–132. https://doi.org/10.1257/000282803321455188
2. Amjad, M., Shah, D., & Shen, D. (2018). Robust Synthetic Control. Journal of Machine Learning Research, 19, 1–51. http://jmlr.org/papers/v19/17-777.html
3. Ben-Michael, E., Feller, A., & Rothstein, J. (2020). The Augmented Synthetic Control Method. arXiv. http://arxiv.org/abs/1811.04170
4. Ben-Michael, E., Feller, A., & Rothstein, J. (2022). Synthetic Controls with Staggered Adoption. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84, 351–381. https://doi.org/10.1111/rssb.12448
5. Quistorff, B., Goldman, M., & Thorpe, J. (2021). Sparse Synthetic Controls: Unit-Level Counterfactuals from High-Dimensional Data.
6. Abadie, A. (2021). Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects. Journal of Economic Literature, 59, 391–425. https://doi.org/10.1257/jel.20191450
7. Xu, Y. (2016). Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models [SSRN Scholarly Paper]. https://doi.org/10.2139/ssrn.2584200
8. Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic Difference-in-Differences. The American Economic Review, 111, 4088–4118. https://www.jstor.org/stable/27086719
9. Chernozhukov, V., Wüthrich, K., & Zhu, Y. (2021). An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls. Journal of the American Statistical Association, 116, 1849–1864. https://doi.org/10.1080/01621459.2021.1920957
10. Imai, K., Kim, I. S., & Wang, E. H. (2023). Matching Methods for Causal Inference with Time-Series Cross-Sectional Data. American Journal of Political Science, 67, 587–605. https://doi.org/10.1111/ajps.12685
11. Botosaru, I., & Ferman, B. (2019). On the Role of Covariates in the Synthetic Control Method. The Econometrics Journal, 22, 117–130. https://doi.org/10.1093/ectj/utz001
12. Abadie, A., & L’Hour, J. (2021). A Penalized Synthetic Control Estimator for Disaggregated Data. Journal of the American Statistical Association, 116, 1817–1834. https://doi.org/10.1080/01621459.2021.1971535
13. Fick, S. E., Nauman, T. W., Brungard, C. C., & Duniway, M. C. (2021). Evaluating Natural Experiments in Ecology: Using Synthetic Controls in Assessments of Remotely Sensed Land Treatments. Ecological Applications, 31, e02264. https://doi.org/10.1002/eap.2264
14. Sharma, R., Jones, S., Robinson, D., & Gordon, A. (2023). Evaluating the Impact of Private Land Conservation with Synthetic Control Design. Conservation Biology, 37, e14150. https://doi.org/10.1111/cobi.14150
15. Rana, P., & Miller, D. C. (2019). Explaining Long-Term Outcome Trajectories in Social–Ecological Systems. PLOS ONE, 14, e0215230. https://doi.org/10.1371/journal.pone.0215230
16. West, T. A. P., Börner, J., Sills, E. O., & Kontoleon, A. (2020). Overstated Carbon Emission Reductions from Voluntary REDD+ Projects in the Brazilian Amazon. Proceedings of the National Academy of Sciences, 117, 24188–24194. https://doi.org/10.1073/pnas.2004334117
17. Lépissier, A., & Mildenberger, M. (2021). Unilateral Climate Policies Can Substantially Reduce National Carbon Pollution. Climatic Change, 166, 31. https://doi.org/10.1007/s10584-021-03111-2
18. Nakanishi, K., Yokomizo, H., Fukaya, K., Kadoya, T., Matsuzaki, S.-ichiro S., Nishihiro, J., Kohzu, A., & Hayashi, T. I. (2022). Inferring Causal Impacts of Extreme Water-Level Drawdowns on Lake Water Clarity Using Long-Term Monitoring Data. Science of The Total Environment, 838, 156088. https://doi.org/10.1016/j.scitotenv.2022.156088
19. Kaiser, A., Dee, L., & Resasco, J. (2025). Synthetic Control Methods Enable Stronger Causal Inference Using Participatory Science Data in Cities. In Review. https://doi.org/10.21203/rs.3.rs-6213868/v1