Nonparametric tests of optimizing behavior in public service provision: Methodology and an application to local safety

We develop a positive non-parametric model of public sector production that allows us to test whether an implicit procedure of cost minimization at shadow prices can rationalize the outcomes of public sector activities. The basic model focuses on multiple C-outputs and does not imply any explicit or implicit assumption regarding the trade-offs between the different inputs (in terms of relative shadow prices) or outputs (in terms of relative valuation). The proposed methodology is applied to a cross-section sample of 546 Belgian municipal police forces. Drawing on detailed task-allocation data and controlling, among others, for the presence of state police forces, the cost minimization hypothesis is found to provide a good fit of the data. Imposing additional structure on output valuation, derived from available ordinal information, yields equally convincing goodness-of-fit results. By contrast, we find that aggregating the labor input over task specializations, a common practice in efficiency assessments of police departments, entails a significantly worse fit of the data.