Journal of Productivity Analysis

, Volume 48, Issue 2–3, pp 133–146 | Cite as

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

  • Juan Aparicio
  • José L. Zofío


In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.


Non-homotheticity Technical efficiency Allocative efficiency Directional distance function 

JEL Classification

C61 D21 D24 



We would like to express our gratitude to two anonymous referees for their helpful comments, as well as to the Spanish Ministry for Economy and Competitiveness for supporting this research under grant MTM2013-43903-P.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Center of Operations Research (CIO)Universidad Miguel Hernández de ElcheElcheSpain
  2. 2.Departamento de Análisis Económico: Teoría Económica e Historia EconómicaUniversidad Autónoma de MadridMadridSpain

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