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.

翻译：合成控制方法通过将处理单元的结果与一组加权平均的控制单元进行比较来估计因果效应，这些控制单元在处理前的结果与其高度匹配，其假设是处理单元与控制单元潜在结果之间的关系在处理前后保持稳定。然而，当这些关系发生偏移或控制单元之间高度相关时，估计量可能变得不可靠。为应对这些挑战，我们提出了分布鲁棒合成控制（DRoSC）方法，该方法能够适应潜在的关系偏移，并处理控制单元间的高度相关性。DRoSC方法针对一种新颖的因果估计量，该估计量被定义为一个考虑所有与处理前期相容的可能权重的最坏情况优化问题的优化解。当经典合成控制方法的识别条件成立时，DRoSC方法的目标因果效应与合成控制相同；当这些条件被违反时，我们证明这一新的因果估计量是不可识别因果效应的一个保守代理。我们进一步表明DRoSC估计量的极限分布是非正态的，并提出了一种新颖的推断方法。我们通过数值研究以及对巴斯克地区恐怖主义经济影响的分析来展示其性能。