Before revision:  It can be applied to settings with disaggregated- or aggregated (functional ) data . The method produces a generically unique counterfactual distribution when the data are continuously distributed. A basic representation of the barycenter provides a computationally efficient implementation via a straightforward tensor-variate regression approach . In addition, identification results are provided that also shed new light on the classical synthetic controls estimator. As an illustration the approach estimates the aggregate effect of the legalization of cannabis on the distribution of household income in Colorado one year after Amendment 64.
After revision:  It 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.