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Distributional synthetic controls

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Document pages: 51 pages

Abstract: This article introduces a generalization of the widely-used syntheticcontrols estimator for evaluating causal effects of policy changes. Theproposed method can be applied to settings with individual-level- or functionaldata and provides a geometrically faithful estimate of the entirecounterfactual distribution or functional parameter of interest. The technicalcontribution is the development of a tensor-valued linear regression approachto efficiently compute the estimator in practice. It works as soon as thetarget distribution is absolutely continuous, but is also applicable in manysettings where the target is discrete. The method can be applied to repeatedcross-sections or panel data and works with as little as a single pre-treatmentperiod. We introduce novel identification results by showing that any syntheticcontrols method, classical or our generalization, provides the correctcounterfactual for causal models that are essentially affine in the unobservedheterogeneity. We also show that the optimal weights and the wholecounterfactual distribution can be consistently estimated from data using thismethod.

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