Synthetic Difference-in-Differences
Also known as: Synthetic DID, SDID
Synthetic Difference-in-Differences (SDID) combines synthetic control and difference-in-differences approaches to estimate treatment effects when a policy or intervention affects one unit (country, firm) at a point in time. Introduced by Arkhangelsky et al. (2021), it improves upon both methods alone by using weighted combinations of controls to match treated units' pre-treatment trends and levels. This yields more precise and robust estimates than classical DiD or synthetic control.
Key highlights
- Combines synthetic-control and DiD flexibility, improving precision
- Robust to violations of parallel-trends assumption within the weighted sample
- Naturally extends to multiple treatments and staggered adoption
- Computationally simple; weights have closed-form solutions
Intuition
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How it works
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When to use it
Use SDID when analyzing policy changes affecting a single unit (national policy, regional reform) and you have panel data with multiple pre- and post-treatment periods. It is valuable for studying international policy changes (Brexit, sanctions), firm-level interventions, or regional regulatory shifts. Requires N > 1 controls and T_0 > 1 pre-treatment periods.
Strengths & limitations
- Combines synthetic-control and DiD flexibility, improving precision
- Robust to violations of parallel-trends assumption within the weighted sample
- Naturally extends to multiple treatments and staggered adoption
- Computationally simple; weights have closed-form solutions
- Requires sufficient control units; performance degrades with few controls
- Assumes constant treatment effect over time (or allows time-varying effects with more structure)
- Sensitivity to choice of pre-treatment period length
- Inference can be conservative when weights concentrate on few controls
Common pitfalls
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Applications
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Frequently asked
How many pre-treatment periods do I need?
Minimum 2-3 periods to establish trends. Ideally 5-10 periods for robust matching. Longer pre-treatment windows reduce bias but may include earlier shocks affecting treated unit.
What if my controls are also partially treated?
SDID assumes controls are unaffected. If spillovers exist, they bias treatment-effect estimates downward. Use a truly untreated control group or instrument for spillovers.
How do I choose the pre-treatment window?
Theoretically: use the period before treatment announcement (if policy surprise) or actual implementation. Empirically: test sensitivity to window definition; results should be robust.
Can I use SDID with multiple treated units?
Yes. Arkhangelsky et al. (2021) extend to staggered treatment; modified SDID handles multiple treated units and treatment times simultaneously.
Sources
- 1.Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic difference-in-differences. American Economic Review, 111(12), 4088-4118.
- 2.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.
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Cite this page
ScholarGate. (2026, June 3). Synthetic Difference-in-Differences. ScholarGate. https://scholargate.app/econometrics/synthetic-difference-in-differences