  Researchers who estimate treatment effects using a regression discontinuity
design (RDD) typically assume that there are no spillovers between the treated
and control units. This may be unrealistic. We characterize the estimand of RDD
in a setting where spillovers occur between units that are close in their
values of the running variable. Under the assumption that spillovers are
linear-in-means, we show that the 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. Specifically, 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. In the more
realistic regime where radius is of similar order as the bandwidth, the RDD
estimand is a mix of the above effects. To recover direct and spillover
effects, we propose incorporating estimated spillover terms into local linear
regression -- the local analog of peer effects regression. We also clarify the
settings under which the donut-hole RD is able to eliminate the effects of
spillovers.
