Distributionally Robust Synthetic Control: Ensuring Robustness Against Highly Correlated Controls and Weight Shifts

The synthetic control method estimates the causal effect by comparing the treated unit's outcomes to a weighted average of control units that closely match its pre-treatment outcomes, assuming the relationship between treated and control potential outcomes remains stable before and after treatment. However, the estimator may become unreliable when these relationships shift or when control units are highly correlated. To address these challenges, we introduce the Distributionally Robust Synthetic Control (DRoSC) method, which accommodates potential shifts in relationships and addresses high correlations among control units. The DRoSC method targets a novel causal estimand defined as the optimizer of a worst-case optimization problem considering all possible weights compatible with the pre-treatment period. When the identification conditions for the classical synthetic control method hold, the DRoSC method targets the same causal effect as the synthetic control; when these conditions are violated, we demonstrate that this new causal estimand is a conservative proxy for the non-identifiable causal effect. We further show that the DRoSC estimator's limiting distribution is non-normal and propose a novel inferential approach. We demonstrate its performance through numerical studies and an analysis of the economic impact of terrorism in the Basque Country.