Regression Discontinuity Design with Spillovers

This paper studies regression discontinuity designs (RDD) when linear-in-means spillovers occur between units that are close in their running variable. We show that the RDD estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. RDD estimates direct treatment effect when radius is of larger order than the bandwidth and total treatment effect when radius is of smaller order than the bandwidth. When the two are of similar order, the RDD estimand need not have a causal interpretation. To recover direct and spillover effects in the intermediate regime, we propose to incorporate estimated spillover terms into local linear regression. Our estimator is consistent and asymptotically normal and we provide bias-aware confidence intervals for direct treatment effects and spillovers. In the setting of Gonzalez (2021), we detect endogenous spillovers in voter fraud during the 2009 Afghan Presidential election. We also clarify when the donut-hole design addresses spillovers in RDD.