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Is the directional distance function a complete generalization of the Farrell approach?


  • 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.)


Cost or revenue efficiency measurement based on the approach initiated by Farrell has received great attention from academics and practitioners since the fifties. Farrell’s approach decomposes cost efficiency into two different sources, viz. technical efficiency and allocative efficiency. Technical efficiency is estimated by the implementation of the Shephard’s input or output distance functions, while allocative efficiency is derived as a residual between cost or revenue efficiency and its corresponding technical efficiency component. The directional distance function (DDF) was introduced later in the literature to complete duality theory with respect to the profit function and as a generalization of the Shephard input and output distance functions. Considering the case of cost efficiency we show that, although the DDF correctly encompasses the technical efficiency component of the Farrell approach, this is not true for the allocative component. Additionally, we show that allocative inefficiency is underestimated when the DDF-additive approach is used for decomposing cost inefficiency unless technical efficiency is assumed.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesús & Zofío, José Luis, 2014. "Is the directional distance function a complete generalization of the Farrell approach?," Working Papers in Economic Theory 2014/05, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  • Handle: RePEc:uam:wpaper:201405

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    References listed on IDEAS

    1. Fare, Rolf & Grosskopf, Shawna, 1997. "Profit efficiency, Farrell decompositions and the Mahler inequality1," Economics Letters, Elsevier, vol. 57(3), pages 283-287, December.
    2. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, Southern Economic Association, vol. 66(2), pages 294-318, October.
    3. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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    Technical efficiency; Allocative efficiency; Directional Distance Functions;

    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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