A location discrete choice model of crime: Police elasticity and optimal deployment

Despite the common belief that police presence reduces crime, there is mixed evidence of such causal effects in major Latin America cities. In this work we identify the casual relationship between police presence and criminal events by using a large dataset of a randomized controlled police intervention in Bogotá D.C., Colombia. We use an Instrumental Variables approach to identify the causal effect of interest. Then we consistently estimate a Conditional Logit discrete choice model with aggregate data that allow us to identify agents' utilities for crime location using Two Stage Least Squares. The estimated parameters allow us to compute the police own and cross-elasticities of crime for each of the spatial locations and to evaluate different police patrolling strategies. The elasticity of crime to police presence is, on average across spatial locations, -0.26 for violent crime, -0.38 for property crime and -0.38 for total crime, all statistically significant. Estimates of cross-elasticities are close to zero; however, spillover effects are non-negligible. Counterfactual analysis of different police deployment strategies show, for an optimal allocating algorithm, an average reduction in violent crime of 7.09%, a reduction in property crimes of 8.48% and a reduction in total crimes of 5.15% at no additional cost. These results show the potential efficiency gains of using the model to deploy police resources in the city without increasing the total police time required.