This article extends the method of synthetic controls to probability measures. The distribution of the synthetic control group is obtained as the optimally weighted barycenter in Wasserstein space of the distributions of the control groups which minimizes the distance to the distribution of the treatment group. 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. An efficient practical implementation along with novel inference results and a minimum wage empirical illustration are provided .
This article extends the method of synthetic controls to probability measures. The distribution of the synthetic control group is obtained as the optimally weighted barycenter in Wasserstein space of the distributions of the control groups which minimizes the distance to the distribution of the treatment group. 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. Identification results are derived that also shed new light on the classical synthetic controls estimator. In order to obtain the correct weights in practice, a simple tensor-variate regression expression is developed. In addition, inference results for Wasserstein barycenters are derived and a minimum wage empirical illustration is given .
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An efficient practical implementation along with novel inference results
Identification results are derived that also shed new light on the classical synthetic controls estimator. In order to obtain the correct weights in practice, a simple tensor-variate regression expression is developed. In addition, inference results for Wasserstein barycenters are derived
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are provided
is given