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Primary Submission Category: Causal Inference and SUTVA/Consistencies Violations

A Spatial Extension of Synthetic Difference-in-Differences

Authors: Renan Serenini, Frantisek Masek, Renan Serenini,

Presenting Author: Renan Serenini*

We propose a spatial extension of the Synthetic Difference-in-Differences (SDiD) estimator of Arkhangelsky et al. (2021). Our estimator handles the situation of a possible violation of the Stable Unit Treatment Value Assumption (SUTVA) when treatment may spillover to control units included in the donor pool resulting in biased and inconsistent Average Treatment Effect (ATE) estimation. We build on the approach of the Spatial Difference-in-Differences estimator of Delgado and Florax (2015) and incorporate it into SDiD. Thus, the ATE can be disentangled into direct and indirect treatment effects. We compare our approach with the SDiD estimator using an example of a violation of the SUTVA. All the features presented in Arkhangelsky et al. (2021) related to the comparison of the SDiD towards conventional Difference-in-Differences (DiD) carry forward for the direct effect. Pertaining to the indirect treatment effect, we show that our estimator may be superior to Delgado and Florax (2015) in the case when directly and indirectly treated units are similar. However, this does not hold unconditionally. We suggest a fast quantitative check to compare the synthetic control unit with the control unit using uniform weights as in Delgado and Florax (2015) to decide which of the methods better satisfies the common trend assumption for the indirectly treated units in each specific case.