Data envelopment analysis efficiency of public services: bootstrap simultaneous confidence region

Abstract

Public services, such as higher education, medical services, libraries or public administration offices, provide services to their customers. To obtain opinion-satisfaction indices of customers, it would be necessary to survey all the customers of the service (census), which is impossible. What is possible is to estimate the indices by surveying a random customer sample. The efficiency obtained with the classic data envelopment analysis models, considering the opinion indices of the customers of the public service as output data estimated with a user sample, will be an estimation of the obtained efficiency if the census is available. This paper proposes a bootstrap methodology to build a confidence region to simultaneously estimate the population data envelopment analysis efficiency score vector of a set of public service-producing units, with a fixed confidence level and using deterministic input data and estimated customer opinion indices as output data. The usefulness of the result is illustrated by describing a case study comparing the efficiency of libraries.