Data Envelopment Analysis and hyperbolic efficiency measures: Extending applications and possibilities for between-group comparisons

Data Envelopment Analysis (DEA) is a widely used tool to estimate relative efficiencies. However, this methodology encounters issues when between-group comparisons with variable returns of scale (VRS) are of interest. In this specification efficiency scores can be undefined when the projection of the efficiency estimation of an observation from one group does not have an intersection with the frontier of the other group. To address this issue, a hyperbolic efficiency estimation can be used. Up to now, the literature lacks consideration of weight restrictions and non-discretionary variables in the hyperbolic DEA method. Weight restrictions allow redefining the production possibility set (PPS), while non-discretionary variables adjust the model's orientation. Considering these factors, it is possible to incorporate prior knowledge, substitution effects, and increase discriminatory power. This paper introduces the respective mathematical formulations and the practical implementation in statistical software. The estimation methods have been combined in an R-package called hyperbolicDEA in order to facilitate the application of hyperbolic DEA with weight restrictions, non-discretionary variables, and additional functionalities. An empirical example of fish farms illustrates the advantages of the introduced methodologies and the functionalities of the R-package.