Distributional synthetic controls

This article introduces a generalization of the widely-used synthetic controls estimator for evaluating causal effects of policy changes. The proposed method can be applied to settings with individual-level- or functional data and provides a geometrically faithful estimate of the entire counterfactual distribution or functional parameter of interest. The technical contribution is the development of a tensor-valued linear regression approach to efficiently compute the estimator in practice. It works as soon as the target distribution is absolutely continuous, but is also applicable in many settings where the target is discrete. The method can be applied to repeated cross-sections or panel data and works with as little as a single pre-treatment period. We introduce novel identification results by showing that any synthetic controls method, classical or our generalization, provides the correct counterfactual for causal models that are essentially affine in the unobserved heterogeneity. We also show that the optimal weights and the whole counterfactual distribution can be consistently estimated from data using this method.