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

Author

Listed:
  • Aparicio, Juan

    () (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Pastor, Jesús

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Zofío, José Luis

    () (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

Abstract

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 nonhomothetic BCC model and a numerical example. We show that there are significant differences in the allocative and technical efficiency scores depending on the approach.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesús & Zofío, José Luis, 2013. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," Working Papers in Economic Theory 2013/11, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  • Handle: RePEc:uam:wpaper:201311
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    References listed on IDEAS

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    1. repec:eee:enepol:v:107:y:2017:i:c:p:258-277 is not listed on IDEAS
    2. repec:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0512-8 is not listed on IDEAS
    3. Pastor, Jesus T. & Zofio, Jose L., 2017. "Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan," European Journal of Operational Research, Elsevier, vol. 257(1), pages 345-351.
    4. Xin ZHAO & Yong PENG & Yuemei XUE & Shun YUAN, 2016. "Spatial Patterns of Ocean Economic Efficiency and their Influencing Factors in Chinese Coastal Regions," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 35-49, December.
    5. Álvarez, Inmaculada & Barbero, Javier & Zofío, Jose Luis, 2016. "A Data Envelopment Analysis Toolbox for MATLAB," Working Papers in Economic Theory 2016/03, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    6. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.

    More about this item

    Keywords

    Data Envelopment Analysis; Overall efficiency; Technical efficiency; Allocative efficiency; Homotheticity.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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