Eficiência na segurança pública: uma abordagem com Análise Envoltória de Dados e índice Malmquist

Abstract

This research studies the efficiency of the use of resources in public security in the Brazilian states. The aim was to investigate the efficiency of the Federative Units (UF) in the allocation of resources destined to the public security’s State forces. Efficiency was estimated from a quantitative approach and the analysis was divided in two stages. In the first stage, Data Envelopment Analysis (DEA) was used considering variable returns of scales with output orientation. In the second phase, the Malmquist index was applied to analyze the longitudinal change in the level of efficiency, from 2011 to 2020. The analyzes were operationalized in the R Studio software, which is free. As a result of the cross-sectional analysis for the year 2020, the efficiency scores of the 27 FUs were estimated, as decision-making units, being twelve States classified as efficient, two had weak inefficiency, six states moderate inefficiency and seven states strong inefficiency. It was observed that the States with the highest per capta expenditures were inefficient, such as Amapá with R$872.91/inhabitant (strongly inefficient) and Mato Grosso with R$730.81/inhabitant (strongly inefficient). Conversely, States with the lowest per capta expenditures were considered efficient, being Piauí with R$239.47/inhabitant, São Paulo with R$257.85/inhabitant. This indicates that there is no exclusive direct relationship between spending and efficiency. In addition, the States of São Paulo, Santa Catarina, Paraíba, Piauí and Bahia formed the efficiency frontier and stood out as references for inefficient States. Regarding the longitudinal analysis, the Malmquist index analysis indicated efficiency gains in all states, when compared to previous years, with São Paulo and Santa Catarina being efficiency benchmarks and four states (Maranhão, Paraíba, Piauí, Rio Grande do Norte) never were benchmarking. In addition, in 2020, nineteen states presented Malmquist index it a value 1, indicating that their efficiency has improved compared to 2019 which also occurred in previous years.