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Synthetic learner: model-free inference on treatments over time

Understanding the effect of a particular treatment or a policy pertains to many areas of interest, ranging from political economics, marketing to healthcare. In this paper, we develop a non-parametric algorithm for detecting the effects of treatment over time in the context of Synthetic Controls. The method builds on counterfactual predictions from many algorithms without necessarily assuming that the algorithms correctly capture the model. We introduce an inferential procedure for detecting treatment effects and show that the testing procedure is asymptotically valid for stationary, beta mixing processes without imposing any restriction on the set of base algorithms under consideration. We discuss consistency guarantees for average treatment effect estimates and derive regret bounds for the proposed methodology. The class of algorithms may include Random Forest, Lasso, or any other machine-learning estimator. Numerical studies and an application illustrate the advantages of the method.