Dynamic Synthetic Control Method
Dynamic Synthetic Control Method for Multi-Period Treatment Evaluation · Also known as: Dynamic SCM, Time-varying synthetic control, Multi-period synthetic control, DSC
The Dynamic Synthetic Control Method extends the classic synthetic control framework to evaluate treatments that unfold over multiple periods or change in intensity over time. It constructs a weighted combination of untreated units that matches the treated unit in pre-treatment outcomes, then traces the full time path of treatment effects period by period after the intervention — capturing not just an average effect but how the effect evolves dynamically.
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When to use it
Use Dynamic Synthetic Control when: you have one or a few treated aggregate units (countries, states, cities, firms) and a larger pool of untreated comparators; you want to trace how treatment effects evolve over multiple periods rather than estimating a single average; and you have a sufficiently long pre-treatment window (generally at least ten periods) to credibly fit the synthetic match. It is particularly suited for policy shocks — trade agreements, legislation, large-scale programmes — where impact timing and trajectory matter. Do not use it with many treated units (where difference-in-differences is more appropriate), when the pre-treatment fit is poor, when the donor pool is too small (fewer than five units), or when outcomes are only observed at a single point in time.
Strengths & limitations
- Produces a transparent, interpretable counterfactual that visually shows how the treated unit diverges from its synthetic twin over time.
- Captures the full dynamic trajectory of treatment effects rather than a single average, revealing onset, build-up, and decay.
- Does not require parallel-trends assumptions — matching is done directly on outcome levels and predictors.
- Permutation-based inference is valid even with very few units, making it suitable for aggregate data settings where asymptotics fail.
- Extrapolation is limited by the convex weighting constraint, preventing the synthetic control from moving far outside the support of donor outcomes.
- Requires a good pre-treatment fit; a poor match means the post-treatment counterfactual is unreliable regardless of the weight optimisation.
- With a very small donor pool (fewer than five units), inference via permutation tests has low power and poor coverage.
- The method is designed for a small number of treated units; it does not naturally scale to many simultaneous treatment adoptions.
- Weights are constant over the post-treatment period, which may be unrealistic if the composition of good comparators changes over time.
- The approach does not directly model spillover effects from the treated unit to donor units, which would contaminate the counterfactual.
Frequently asked
How does Dynamic SCM differ from standard Synthetic Control?
Standard SCM typically focuses on the average treatment effect over the post-treatment period or a single post-treatment observation. Dynamic SCM explicitly tracks the treatment effect at each post-treatment period, revealing the time path of impact. The weight estimation is the same, but the emphasis shifts from a summary effect to the full dynamic trajectory.
How do I assess whether my pre-treatment fit is good enough?
Plot the treated unit's outcome and the synthetic control side by side over the pre-treatment window. The paths should be close throughout — not just at the endpoint. A common rule is that the root mean squared prediction error (RMSPE) in the pre-treatment period should be small relative to the scale of the outcome. Also run in-time placebo tests to check that the method does not produce spurious gaps before the treatment.
How many pre-treatment periods do I need?
A longer pre-treatment window improves the quality of the synthetic match and the credibility of the counterfactual. As a practical guideline, at least ten pre-treatment periods are recommended, though this depends on the variance of the outcome and the size of the donor pool.
What if no donor receives zero weight?
Synthetic control often assigns positive weights to only a subset of donors — this is a feature, not a bug. Donors with zero weight are simply not part of the synthetic comparator. If all donors receive roughly equal positive weights, it may indicate a poor match or a very homogeneous donor pool.
Can I use Dynamic SCM with multiple treated units?
The original method handles one treated unit at a time. With multiple treated units adopting treatment at different times, staggered synthetic control approaches or synthetic difference-in-differences (Arkhangelsky et al., 2021) are more appropriate, as they aggregate unit-specific synthetic controls in a principled way.
Sources
- Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program. Journal of the American Statistical Association, 105(490), 493-505. DOI: 10.1198/jasa.2009.ap08746 ↗
- Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic Difference-in-Differences. American Economic Review, 111(12), 4088-4118. DOI: 10.1257/aer.20190159 ↗
How to cite this page
ScholarGate. (2026, June 3). Dynamic Synthetic Control Method for Multi-Period Treatment Evaluation. ScholarGate. https://scholargate.app/en/causal-inference/dynamic-synthetic-control-method
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Counterfactual Impact EvaluationCausal inference↔ compare
- Difference-in-DifferencesEconometrics↔ compare
- Dynamic Difference-in-DifferencesCausal inference↔ compare
- Panel Data Synthetic Control MethodCausal inference↔ compare
- Synthetic Control MethodCausal inference↔ compare