TY - JOUR

T1 - Data Envelopment Analysis and hyperbolic efficiency measures

T2 - Extending applications and possibilities for between-group comparisons

AU - Öttl, Alexander

AU - Asmild, Mette

AU - Gulde, Daniel

N1 - Funding Information: We would like to express our thanks to Takibur Rahmen and Rasmus Nielsen for providing exemplary data. Special appreciation goes to Lorenz Aigner and the anonymous reviewers for proofreading and offering helpful comments. Lastly, we are grateful to Sofia Lavin for her motivation in initiating the project. Publisher Copyright: © 2023 The Author(s)

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - DEA software

KW - Efficiency analysis

KW - Hyperbolic Data Envelopment Analysis

KW - Non-discretionary variables

KW - Weight restrictions

U2 - 10.1016/j.dajour.2023.100343

DO - 10.1016/j.dajour.2023.100343

M3 - Journal article

AN - SCOPUS:85181888928

VL - 9

JO - Decision Analytics Journal

JF - Decision Analytics Journal

SN - 2772-6622

M1 - 100343

ER -