Robust inference for geographic regression discontinuity designs: assessing the impact of police precincts

Abstract

We study variation in policing outcomes attributable to differential policing practices in New York City (NYC) using geographic regression discontinuity designs (GeoRDDs). By focusing on small geographic windows near police precinct boundaries, we can estimate local average treatment effects of police precinct practices on arrest rates. We propose estimands and develop estimators for the GeoRDD when the data come from a spatial point process. Standard GeoRDDs rely on continuity assumptions of the potential outcome surface or a local randomization assumption within a window around the boundary. These assumptions, however, can easily be violated in real applications. We develop a novel and robust approach to testing whether there are differences in policing outcomes that are caused by differences in police precinct policies across NYC. Importantly, this approach is applicable to standard regression discontinuity designs with both numeric and point process data. This approach is robust to violations of traditional assumptions made and is valid under weaker assumptions. We use a unique form of resampling to provide a valid estimate of our test statistic’s null distribution even under violations of standard assumptions. This procedure gives substantially different results in the analysis of NYC arrest rates than those that rely on standard assumptions.