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    • Seeking to solve these problems Cazals et al developed

    2018-10-25

    Seeking to solve these problems, Cazals et al. (2002) developed an alternative way to robustly estimate technical efficiency. That’s how the efficiency frontier method—m is born. Therefore, considering that public security offers different services, besides the possibility of the existence of measurement errors or outliers, we estimate the efficiency of public security in Brazilian states through the order—m production frontier method. In order to calculate technological gap levels, according to Wongchai et al. (2012), we apply the meta-frontier theory, defined as the envelopment of production functions for decision unit subgroups, as initially proposed by Hayami (1969) and Hayami and Ruttan (1970, 1971). The production functions envelopment is defined by the most efficient aspects of each specific technology, as explained by Ruttan et al. (1978). Besides this introduction, this work is organized as follows: Section 2 introduces and discusses the methodology used to calculate technical efficiency levels, technological gaps, TPF and its decomposition for Brazilian states. Section 3 discusses the construction of a database and develops a descriptive analysis. Section 4 introduces and discusses result obtained from the methods described in Section 2. Section 5 deals with the final considerations.
    Technical efficiency methodology There are several DEA formulations found in literature. The method proposed by Charnes et al. (1978), also known as CCR (constant returns to scale), evaluates production technical efficiency based on the find more information of constant returns to scale. However, this hypothesis is quite restrictive and consequently, inefficiency values may become biased. Alternatively, the Banker et al. model (1984) known as BCC, refers to the hypothesis of constant returns to scale assuming that these returns vary. Based on the hypothesis of variable returns to scale it is possible to separately estimate scale efficiency and technique for each decision unit. This model, although more flexible than the CCR, has been criticized for using a hypothetical value as efficiency calculation reference, which in reality is not observed, as it only existed in the constructed frontier. If the frontier value is not observed, there is no evidence that it can be reached. Therefore, a decision unit may be considered inefficient based on a reference that is impossible to reach. Besides, the BCC model is sensitive to the set of variables selected and to the existence of outliers. Deprins et al. (1984) developed a DEA model denominated FHD (Free Disposal Hull) based on a production frontier with variable non-convex scale returns assuming a free disposal. However, the DEA and FDH models have some important disadvantages: (a) results are strongly dependent on the set of variables and they can be biased with the simple inclusion or exclusion of an input and/or output; (b) the influence of stochastic factors or measurement errors completely alters the frontier position and biased results; (c) treating inputs and/or outputs as if they were homogeneous, when in general they are heterogeneous, may distort results; (d) the presence of outliers may completely alter results. Years later, Cazals et al. (2002) developed the order—m frontier approach. This approach, contrary to the DEA and FDH methods, does not include all points and dicots also requires much less information (data) than the previous methodologies. Its main advantage is that in the presence of significant measurement errors and a reasonable number of outliers, technical efficiency estimates are more robust if compared to the other parametric and non-parametric methods. Krüger (2012) demonstrated these properties through Monte Carlo simulations.
    Database and statistics Among many others, we can highlight the following studies: (a) Schull et al. (2014) use crime rates (intentional homicide, robbery, involuntary vehicular manslaughter, drug trafficking and rape) as a product and the expenses in security as an input; (b) Pereira Filho et al. (2010) estimate the public security efficiency based on a costs frontier. They use the wages of the military and civil policemen as inputs and the inverse homicide rate as product (cost); (c) Arantes et al. (2012) estimate the technical efficiency of public security in the Minas Gerais municipalities where the products are: the homicide rate, the rate of violent crimes against property, the rate of violent crimes against persons, the rate of less aggressive crimes and the rate of criminals arrested during violent crimes. The input applied was the expense per capita with public security; (d) Scalco et al. (2012) estimate the technical efficiency of the Minas Gerais military police. They used the following input variable: number of military policemen per each 1000 people. The outputs were: number of arrests registered due to violent crime acts against persons per policeman; number of arrests registered due to violent crimes against property per policemen, inverse violent crime rate against persons and inverse of violent crime rate against property.