Estimation and Inference for Synthetic Control Methods with Spillover Effects

The synthetic control method is often used in treatment effect estimation with panel data where only a few units are treated and a small number of post-treatment periods are available. Current estimation and inference procedures for synthetic control methods do not allow for the existence of spillover effects, which are plausible in many applications. In this paper, we consider estimation and inference for synthetic control methods, allowing for spillover effects. We propose estimators for both direct treatment effects and spillover effects and show they are asymptotically unbiased. In addition, we propose an inferential procedure and show it is asymptotically unbiased. Our estimation and inference procedure applies to cases with multiple treated units or periods, and where the underlying factor model is either stationary or cointegrated. In simulations, we confirm that the presence of spillovers renders current methods biased and have distorted sizes, whereas our methods yield properly sized tests and retain reasonable power. We apply our method to a classic empirical example that investigates the effect of California's tobacco control program as in Abadie et al. (2010) and find evidence of spillovers.