Synthetic Control Method MOC
The synthetic control method (SCM) estimates the effect of an aggregate intervention on a single (or few) treated unit(s) by building the counterfactual as a data-driven weighted average of donor-pool units. Its defining move is the Convex-Hull-Restriction: weights are non-negative and sum to one, so the synthetic unit interpolates among real controls and never extrapolates — and identification comes from a long, close pre-treatment fit (which, under a linear factor model, aligns unobserved time-varying confounders, not just fixed effects). Because only one unit is treated, inference is design-based via placebo/permutation tests rather than large-sample standard errors.
Papers
- AbadieEtAl2010-SyntheticControlMethods — the foundational JASA paper: convex-weighting estimator, factor-model justification, and placebo inference, applied to California’s Proposition 99.
- AbadieEtAl2015-ComparativePoliticsSCM — German reunification; shows regression is also a sum-to-one weighting estimator but one that extrapolates, isolating non-negativity as SCM’s key safeguard.
- Abadie2021-UsingSyntheticControls — JEL survey: feasibility conditions, data requirements, when not to use SCM, and modern inference.
Key Concepts
Convex-Hull-Restriction (no extrapolation) · No-Anticipation · SUTVA (no interference) · Causal-Estimand · Potential-Outcomes
Debates & Contradictions
- SCM vs. DiD. DiD assumes additive Parallel-Trends with unit fixed effects; SCM’s factor-model rationale lets unobserved confounders have time-varying effects, at the cost of requiring a close pre-treatment fit. Design-based DiD work (AtheyImbens2022-DesignBasedDiD) and SCM increasingly converge on factor models.
- SCM vs. regression. Both are weighting estimators with weights summing to one, but regression extrapolates beyond donor support while SCM does not — the central argument of AbadieEtAl2015-ComparativePoliticsSCM.
- Inference. No consensus large-sample theory with one treated unit; placebo, permutation, and conformal methods compete.
Next
SCM shares its potential-outcomes foundation with Foundations and its panel/counterfactual-trajectory concerns with DiD. Program-evaluation surveys (ImbensWooldridge2009-ProgramEvaluation) situate it among the broader toolkit.