Private policing is an explicit effort to creat...private policing is an explicit effort to create visible agents and equipment of crime control by nongovernmental institutions. it is a service provided by meaningful markets in many countries. for example, nowadays the ratio between private security guards and policemen is close to 2.4 in brazil, 2.3 in australia, 1.9 in japan and in china, 1.5 in england and 1.4 in the usa. in economics, researchers have analyzed this issue from two main perspectives. first there have been attempts to measure average treatment effects of private policing on crime using quasi experiments to compare victimization indicators among neighborhoods with different intensities of the service. invariably, these studies found evidence that private policing reduces crime locally, but say little about its net effect across cities . second, there is a line of research investigating the complementarity/substitutability between public and private security. nevertheless, it also reports few points about net effects across spaces larger than a neighborhood. these papers frequently use as baseline the theoretical model of clotfelter, possibly because it was the first to analyze the externalities generated by private policing on crime among neighborhoods. in this framework, there are two reaction curves interacting in a crime-security plane. the crime reaction curve has an undefined slope, because the intensity of private security on one side of the city can significantly distort criminal payoffs in other neighborhoods. on the other hand, the security reaction curve would be positively sloped. in short, if "c" and "s" represent continuous indicators of crime and private security in some city, the theory suggests that, ceteris paribus: more "s" reduces crimes in some neighborhoods, but would have an ambiguous effect on "c" considering all the city; and, more "c" improves "s". curiously we have found few attempts to evaluate this model, maybe because it involves two econometric challenges. first, researchers may remove zero cases from the sample, and occasionally no informative result is observed in the regressions because of this data elimination. second, a regression "c" on "s" demands instruments to control the endogeneity caused by the simultaneity, whose availability can be problematic. these challenges can be solved from a system of simultaneous equations with dependent variables truncated or censored at zero, and it can be estimated by limited information maximum likelihood (liml) or by full information maximum likelihood (fiml). succinctly, with liml each equation is estimated separately, using instrumental variables; while with fiml all equations are estimated at same time, using constraints to allow the identifiability and to simulate instruments. in this context, we intend to contribute to the literature when concomitantly: (i) there are many zeros outcomes; (ii) the researcher does not wish to discard information; and, (iii) instruments are not clearly available. thus, our strategy is: to estimate bivariate copulas in tobit marginals, solving (i) and (ii); and, to apply fiml over these copulas in a structural system, imposing constrained parameters to mitigate the challenge (iii).