How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies

• Published in: European journal of operational research Vol. 240; no. 3; pp. 882 - 891
• Main Authors: Aparicio, Juan, Pastor, Jesus T., Zofio, Jose L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-02-2015; Elsevier Sequoia S.A
• Subjects: Allocative efficiency; Data Envelopment Analysis; Economic models; Economies of scale; Efficiency; Homotheticity; Overall efficiency; Production management; Resource allocation; Studies; Technical efficiency; Technology adoption; Overall efficiency; Homotheticity; Allocative efficiency; Technical efficiency; Data Envelopment Analysis
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2014.08.012

•We discuss the decomposition of economic efficiency under non-homotheticity.•Radial measures estimate true technical efficiency only for CRS with one output.•In a non-homothetic setting, we show how to correctly decompose economic efficiency.•We define a new directional distance function with endogenous direction.•We show that large differences arise using either the standard or the new approach.
We discuss how to properly decompose economic efficiency when the underlying technology is non-homothetic using alternative allocative and technical efficiency criteria. We first show that only under the production of one output and assuming the particular case of constant returns to scale homotheticity, we may claim that the standard radial models correctly measure pure technical efficiency. Otherwise, when non-homotheticity is assumed, we then show that these traditional estimations would measure an undetermined mix of technical and allocative efficiency. To restore a consistent measure of technical efficiency in the non-homothetic case we introduce a new methodology that takes as reference for the economic efficiency decomposition the preservation of the allocative efficiency of firms producing in the interior of the technology. This builds upon the so-called reversed approach recently introduced by Bogetoft et al. (2006) that allows estimating allocative efficiency without presuming that technical efficiency has been already accomplished. We illustrate our methodology within the Data Envelopment Analysis framework adopting the most simple non-homothetic BCC model and a numerical application. In this application we show that there are significant differences in the allocative and technical efficiency scores depending on the approach.