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Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan
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Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan

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  • Pastor, Jesus T.
  • Zofio, Jose L.

Abstract

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 means of the Shephard 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. We show that both approaches yield different allocative (in)efficiency terms – unless technical efficiency is assumed, and how these terms are related. The practical implications of the multiplicative and additive approaches are discussed and illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:1:p:345-351
    DOI: 10.1016/j.ejor.2016.08.007
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    4. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    5. 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.
    6. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    7. Kapelko, Magdalena & Oude Lansink, Alfons & Zofío, José L., 2022. "Endogenous dynamic inefficiency and optimal resource allocation: An application to the European Dietetic Food Industry," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1444-1457.
    8. Rolf Färe & Xinju He & Sungko Li & Valentin Zelenyuk, 2019. "A Unifying Framework for Farrell Profit Efficiency Measurement," Operations Research, INFORMS, vol. 67(1), pages 183-197, January.

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