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Estimation and Inference for Synthetic Control Methods with Spillover Effects

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Document pages: 40 pages

Abstract: The synthetic control method is often used in treatment effect estimationwith panel data where only a few units are treated and a small number ofpost-treatment periods are available. Current estimation and inferenceprocedures for synthetic control methods do not allow for the existence ofspillover effects, which are plausible in many applications. In this paper, weconsider estimation and inference for synthetic control methods, allowing forspillover effects. We propose estimators for both direct treatment effects andspillover effects and show they are asymptotically unbiased. In addition, wepropose an inferential procedure and show it is asymptotically unbiased. Ourestimation and inference procedure applies to cases with multiple treated unitsor periods, and where the underlying factor model is either stationary orcointegrated. In simulations, we confirm that the presence of spilloversrenders current methods biased and have distorted sizes, whereas our methodsyield properly sized tests and retain reasonable power. We apply our method toa classic empirical example that investigates the effect of California stobacco control program as in Abadie et al. (2010) and find evidence ofspillovers.

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