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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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    References listed on IDEAS

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    1. Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, vol. 40(3), pages 257-266, December.
    2. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2015. "Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited," International Journal of Production Economics, Elsevier, vol. 165(C), pages 19-28.
    3. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    4. Walter Briec & Kristiaan Kerstens & Nicolas Peypoch, 2012. "Exact Relations Between Four Definitions Of Productivity Indices And Indicators," Bulletin of Economic Research, Wiley Blackwell, vol. 64(2), pages 265-274, April.
    5. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    6. Cooper, W.W. & Pastor, Jesus T. & Aparicio, Juan & Borras, Fernando, 2011. "Decomposing profit inefficiency in DEA through the weighted additive model," European Journal of Operational Research, Elsevier, vol. 212(2), pages 411-416, July.
    7. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    8. 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.
    9. Aparicio, Juan & Pastor, Jesus T. & Zofio, Jose L., 2015. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," European Journal of Operational Research, Elsevier, vol. 240(3), pages 882-891.
    10. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2015. "Decomposing profit efficiency using a slack-based directional distance function," European Journal of Operational Research, Elsevier, vol. 247(1), pages 335-337.
    11. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    12. Bert Balk & Rolf Färe & Shawna Grosskopf & Dimitris Margaritis, 2008. "Exact relations between Luenberger productivity indicators and Malmquist productivity indexes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 187-190, April.
    13. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    14. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    15. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2013. "Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA," European Journal of Operational Research, Elsevier, vol. 231(2), pages 443-451.
    16. Fare, Rolf & Grosskopf, Shawna, 1997. "Profit efficiency, Farrell decompositions and the Mahler inequality1," Economics Letters, Elsevier, vol. 57(3), pages 283-287, December.
    17. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    18. Zalinescu, C., 2010. "On the duality between the profit and the indirect distance functions in production theory," European Journal of Operational Research, Elsevier, vol. 207(1), pages 30-36, November.
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    Cited by:

    1. 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.
    2. Ferrier, Gary D. & Johnson, Andrew L. & Layer, Kevin & Sickles, Robin C., 2018. "Direction Selection in Stochastic Directional Distance Functions," Working Papers 18-010, Rice University, Department of Economics.
    3. Magdalena Kapelko, 2019. "Measuring productivity change accounting for adjustment costs: evidence from the food industry in the European Union," Annals of Operations Research, Springer, vol. 278(1), pages 215-234, July.
    4. 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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