Synthetic Control Methods for Comparative Case Studies
Causal Question / Estimand
The effect of an aggregate intervention affecting a single treated unit (the treatment effect for California’s Proposition 99 tobacco-control program) when no single control region is a credible counterfactual and only one unit is treated.
Identification Strategy
Construct a synthetic control: a weighted average of donor-pool regions chosen so its pre-intervention outcomes and predictors track the treated unit. Weights are non-negative and sum to one — the Convex-Hull-Restriction — so the comparison is an interpolation among real units, not an extrapolation. Post-treatment, the gap between California and its synthetic counterpart estimates the effect. Identification rests on close pre-treatment fit over a long horizon (formalized via a linear factor model: matching many pre-periods controls for unobserved time-varying confounders, not just fixed effects).
Key Assumptions
Convex-Hull-Restriction (no extrapolation), close and long pre-treatment fit, No-Anticipation, SUTVA (no interference / spillovers to donor regions, no other contemporaneous shocks hitting only California), and donor units not themselves exposed.
Threats to Validity
Interpolation bias if California lies outside the donor convex hull; idiosyncratic shocks to donor units; over-fitting pre-treatment noise. Inference is non-standard (one treated unit), so they introduce placebo / permutation tests — reassign the intervention to each donor and compare the treated gap to the placebo distribution.
Setting / Data
California’s 1988 Proposition 99 tobacco program; per-capita cigarette sales, 38 control states, 1970–2000.
Key Claims
- A data-driven weighted average of controls is a more transparent and credible counterfactual than an ad hoc single comparison or unrestricted regression.
- Restricting weights to the convex hull makes the counterfactual’s reliance on each donor explicit and precludes extrapolation.
- Proposition 99 reduced cigarette consumption substantially; the effect exceeds the placebo distribution.
Connections
- Builds on: Potential-Outcomes; extends Abadie & Gardeazabal (2003).
- Foundational for: AbadieEtAl2015-ComparativePoliticsSCM, Abadie2021-UsingSyntheticControls
- Contrast: regression/Ignorability designs allow extrapolation; DiD assumes Parallel-Trends with fixed effects, whereas SCM’s factor model permits time-varying unobserved confounders. See also SCM
Citation
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.