Design Flaw of the Synthetic Control Method

Synthetic control method (SCM) identifies causal treatment effects by constructing a counterfactual treatment unit as a convex combination of donors in the control group, such that the weights of donors and predictors are jointly optimized during the pre-treatment period. This paper demonstrates that the true optimal solution to the SCM problem is typically a corner solution where all weight is assigned to a single predictor, contradicting the intended purpose of predictors. To address this inherent design flaw, we propose to determine the predictor weights and donor weights separately. We show how the donor weights can be optimized when the predictor weights are given, and consider alternative data-driven approaches to determine the predictor weights. Re-examination of the two original empirical applications to Basque terrorism and California's tobacco control program demonstrates the complete and utter failure of the existing SCM algorithms and illustrates our proposed remedies.