  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 precincts
on arrest rates. We propose estimands and develop estimators for the GeoRDD
when the data come from a spatial point process. Additionally, 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 realistic applications. We
develop a novel and robust approach to testing whether there are differences in
policing outcomes that are caused by differences in police precincts 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.
