Journal of Productivity Analysis

, Volume 40, Issue 3, pp 257–266

The directional profit efficiency measure: on why profit inefficiency is either technical or allocative


DOI: 10.1007/s11123-012-0292-0

Cite this article as:
Zofio, J.L., Pastor, J.T. & Aparicio, J. J Prod Anal (2013) 40: 257. doi:10.1007/s11123-012-0292-0


The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement.


Directional distance function Profit efficiency Technical efficiency Allocative efficiency 

JEL Classification

C61 D21 D24 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jose L. Zofio
    • 1
  • Jesus T. Pastor
    • 2
  • Juan Aparicio
    • 2
  1. 1.Departamento de Analisis Economico: Teoria Economica e Historia EconomicaUniversidad Autonoma de MadridMadridSpain
  2. 2.Center of Operations Research (CIO)Universidad Miguel Hernandez de ElcheElcheSpain

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