Distributional synthetic controls
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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.
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