Klick and Tabarrok previously used terror alert status changes to identify the effect of police numbers on crime in Washington, DC. This time, MacDonald, Klick and Grunwald use a geographic regression discontinuity design to identify effects where, on one side of the line, you have only regular policing and, on the other, you also have policing by the University of Pennsylvania.
Personnel estimates from both the Philadelphia Police Department and the UPPD indicate that approximately twice as many officers patrol the Outer Penn Zone than the surrounding University City District. The area covered by Philadelphia Police in the relevant area is twice as large as that covered by the Penn Police, suggesting an effective increase in police presence on the order of 200 percent. Our estimate that UPPD activity is associated with a 60 percent reduction in crime suggests that the elasticity of crime with respect to police is about -0.30 for both violent and property crimes. These elasticity estimates are strikingly similar to those found in the modern literature on police and crime. Chalfin and McCrary (2012)'s recent paper provides a helpful summary of these previous estimates. Klick and Tabarrok (2005), Draca, Machin, and Witt (2011), and Di Tella and Schargrodsky (2004)—all of which use an exogenous shock in police deployment resulting from terrorism-related events—find an elasticity of approximately -0.30. Our results are also similar to those presented in Berk and MacDonald (2010) who examine a police crackdown in Los Angeles and find similar elasticities. The results from our investigation respond to concerns that short-term gains from police crackdowns are not sustainable. Instead, our results suggest that these crackdown studies may be generalizable if increased police presence becomes a permanent tactic in specific areas.A ten percent increase in the number of police reduces crime by about 3 percent. I expect that the American estimates would be a lower bound on the elasticity of crime with respect to police presence in New Zealand. If crime reduces with policing but at a decreasing rate, then places with fewer officers (per population) will see stronger effects from additional hiring.
The back-of-the-envelope estimates I'd run for my current policy issues class a few years back had a dollar in new police expenditure saving about two dollars in crime costs.
I expect you could find similar benefits in shifting police out of policing cannabis and into policing real crimes; it looks like that may already be under way.