What is the synthetic control method for causal analysis?

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AcadiFi · Accepted Answer

Synthetic control (Abadie-Gardeazabal 2003, Abadie-Diamond-Hainmueller 2010) constructs a weighted combination of control units to match the pre-treatment trajectory of a treated unit, then attributes post-treatment divergence to the intervention. Ideal for case studies with one or few treated units.

Procedure: (1) select a donor pool of unaffected units (e.g., other US states); (2) choose weights W = (w_1, ..., w_J) on donors to minimize ||X_1 - X_0*W|| subject to w_j >= 0 and sum(w_j) = 1, where X_1 are pre-treatment outcome predictors of the treated unit and X_0 are donor predictors; (3) the synthetic control unit's outcome is Y_synth_t = sum(w_j * Y_j,t); (4) treatment effect is Y_1,t - Y_synth_t post-treatment.

For Kaleido's analysis of Oregon's corporate tax change with donor pool of 40 unaffected states matching on pre-period GDP, employment, and industry mix: weights might be 35% Washington, 25% Colorado, 20% Minnesota, 15% Nevada, 5% Utah. If Oregon's post-treatment business formation diverges -8% from synthetic Oregon, that's the estimated effect.

Inference uses placebo tests: apply the procedure to each donor as if it were treated, generate a distribution of 'placebo effects,' then compute a pseudo p-value as the fraction of placebos with effect magnitude exceeding the actual treatment. If Oregon's -8% is larger than 38/40 placebos, p ≈ 2.5%.

Advantages: transparent (weights are published), data-driven counterfactual, handles single-treatment cases that DiD struggles with. Limitations: only works with enough pre-treatment data to match trajectories, sensitive to donor pool selection, no clear asymptotic inference. Widely used for policy evaluation of tobacco taxes, trade liberalization, and natural experiments.

What is the synthetic control method for causal analysis?

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