Estimating Difference-in-Differences in the Presence of Spillovers

I propose a method for difference-in-differences (DD) estimation in situations where the stable unit treatment value assumption is violated locally. This is relevant for a wide variety of cases where spillovers may occur between quasi-treatment and quasi-control areas in a (natural) experiment. A flexible methodology is described to test for such spillovers, and to consistently estimate treatment effects in their presence. This spillover-robust DD method results in two classes of estimands: treatment effects, and “close” to treatment effects. The methodology outlined describes a versatile and non-arbitrary procedure to determine the distance over which treatments propagate, where distance can be defined in many ways, including as a multi-dimensional measure. This methodology is illustrated by simulation, and by its application to estimates of the impact of state-level text-messaging bans on fatal vehicle accidents. Extending existing DD estimates, I document that reforms travel over roads, and have spillover effects in neighbouring non-affected counties. Text messaging laws appear to continue to alter driving behaviour as much as 30 km outside of affected jurisdictions.