Modelling simultaneously censored outcomes of private policing and crime

Private policing is generally used to curb crime in certain neighbourhoods. The impact of an increase in these services on the city as a whole is unclear, as crime could shift from protected to unprotected targets, causing greater social harm. In practice, estimating this effect at the city level encounters at least two problems. First, the simultaneity between the demand for private policing and criminal activity requires appropriate instrumental variables to mitigate endogeneity biases. Second, the dependent and endogenous variables can have an excessive number of zeros at the same time, requiring the use of more specialized econometric models. In this paper, I combine Clotfelter's theoretical model for private policing and crime with Amemiya's econometric model for simultaneously censored outcomes, linking structural and reduced forms and discussing identification issues. Then, a regular Bitobit is modified to estimate reduced forms with many zeros outcomes in a set of copulas to improve censoring specifications with endogeneity. Finally, I conduct an empirical study examining an exclusive database from Brazil to discuss the copula approach, and the hypothesis that more private policing reduces crime at the city level is not rejected.