What is Synthetic Control Method?
Synthetic Control Method is a comparative-case design that estimates a treated unit's counterfactual outcome path using a weighted combination of untreated donor units chosen to reproduce its pre-treatment outcomes and predictors.
Quick Facts
| Specification | Official Specification |
|---|
How It Works
Convex donor weights create a transparent counterfactual
The classic estimator selects weights w_j>=0 with sum(w_j)=1 to minimize distance between treated and weighted-donor pre-treatment predictors and outcomes. It then computes Y_treated,t-sum(w_j Y_j,t) after treatment. The convex constraint makes interpolation visible and limits extrapolation, but it can also prevent adequate fit when the treated unit lies outside the donor hull. Abadie, Diamond, and Hainmueller formalize this comparative-case approach.
Donor-pool design comes before optimization
Exclude donors exposed to the same intervention, anticipation, spillovers, major measurement changes, or incompatible structural shocks. Declare outcome and predictor windows before inspecting post-treatment gaps; otherwise donor selection becomes outcome-driven researcher discretion. Report every donor weight, predictor balance, pre-treatment path, RMSPE, and whether one donor dominates.
Inference relies on placebos and sensitivity, not one fitted line
In-space placebos reassign treatment to donors and compare post/pre-fit deterioration; in-time placebos test false treatment dates, and leave-one-out fits expose dependence on influential donors. Small donor pools limit the resolution of permutation evidence, while poor pre-fit makes post-period gaps hard to interpret. Use conformal or model-based intervals only with their stated residual assumptions, and distinguish base SCM from augmented, generalized, or synthetic DiD variants.
Key Characteristics
- Constructs a counterfactual from weighted untreated donor units
- Uses pre-treatment outcomes and predictors to choose weights
- Often constrains weights to a nonnegative convex combination
- Produces a time path of treated-minus-synthetic effects
- Makes pre-fit and donor influence directly auditable
- Requires placebo, sensitivity, and design-based credibility checks
Common Use Cases
- Evaluating a policy introduced in one state or country
- Estimating the impact of a product change launched to one market
- Constructing a comparison for a firm exposed to a unique intervention
- Studying an aggregate shock with a long pre-treatment history
- Testing whether results depend on one donor or treatment date
Example
Loading code...Frequently Asked Questions
How is Synthetic Control different from Difference-in-Differences?
Canonical DiD uses a comparison group's change under parallel trends. SCM chooses a weighted donor combination to reproduce the treated unit's pre-period path and predictors. Both need credible untreated counterfactual evolution, but their weighting, diagnostics, and standard inference procedures differ.
What does poor pre-treatment fit mean in Synthetic Control?
It means the donor pool cannot closely reproduce the treated unit before intervention under the chosen specification, weakening the claim that it will approximate the missing post-treatment counterfactual. Report the mismatch and consider redesigning the donor pool or using a justified alternative method.
How should the donor pool be selected?
Use substantive comparability and pre-treatment eligibility rules set without inspecting post-treatment outcomes. Exclude donors exposed to the intervention, spillovers, anticipation, incompatible measurement, or unique shocks. Sensitivity to donor inclusion should be reported rather than silently optimized away.
What do placebo tests prove in Synthetic Control?
They show whether the treated unit's gap or post/pre MSPE ratio is unusual relative to analogous fake interventions in the donor pool or pre-period. They do not prove the design assumptions, and a small donor pool yields coarse empirical probabilities and weak resolution.
Can classic Synthetic Control handle many treated units?
The classic formulation is strongest for one treated unit and many untreated donors. Multiple or staggered treatments usually require generalized or augmented synthetic control, synthetic Difference-in-Differences, matrix completion, or another panel design with matching estimands and inference.