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.
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. 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.
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Identification results are derived
A basic representation of the barycenter provides a computationally efficient implementation via a straightforward tensor-variate regression approach. In addition, identification results are provided
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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.
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.