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Temporal Technical and Profit Efficiency Measurement: Definitions, Duality and Aggregation Results

Author

Listed:
  • Walter Briec

    (JEREM, University of Perpignan)

  • Christine Comes

    (Groupe AZUR GMF, Paris)

  • Kristiaan Kerstens

    (CNRS-LABORES and IESEG School of Management)

Abstract

The shortage function, an important tool in production theory, measures potential increases in outputs and decreases in inputs for a given direction g at a given date. To develop a temporal version of technical efficiency measurement, we introduce the concept of a temporal shortage function. This temporal efficiency measure is easily computed using linear programming. We also establish a duality result stating that the temporal profit function and the temporal shortage function are dual to one another. This result has two consequences. First, one can derive a shadow price path via the shadow prices of the temporal shortage function. Second, transposing the classic Farrell inefficiency decomposition, temporal profit efficiency is decomposed into temporal technical and temporal allocative efficiency components. Finally, in line with the recent literature on aggregation over firms, this contribution treats the possibilities and limits of the aggregation of efficiency measures over time.

Suggested Citation

  • Walter Briec & Christine Comes & Kristiaan Kerstens, 2005. "Temporal Technical and Profit Efficiency Measurement: Definitions, Duality and Aggregation Results," Working Papers 2005-ECO-01, IESEG School of Management.
    • Handle: RePEc:ies:wpaper:e200501
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    References listed on IDEAS

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    1. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1, McMaster University Archive for the History of Economic Thought.
    2. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    3. Edward Jaenicke, 2000. "Testing for Intermediate Outputs in Dynamic DEA Models: Accounting for Soil Capital in Rotational Crop Production and Productivity Measures," Journal of Productivity Analysis, Springer, vol. 14(3), pages 247-266, November.
    4. Fare,Rolf & Grosskopf,Shawna & Lovell,C. A. Knox, 2008. "Production Frontiers," Cambridge Books, Cambridge University Press, number 9780521072069, September.
    5. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    6. Henry Tulkens & Philippe Eeckaut, 2006. "Nonparametric Efficiency, Progress and Regress Measures For Panel Data: Methodological Aspects," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 395-429, Springer.
    7. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    8. Sengupta, Jati K., 1999. "A dynamic efficiency model using data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 62(3), pages 209-218, September.
    9. Nishimizu, Mieko & Page, John M, Jr, 1982. "Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-78," Economic Journal, Royal Economic Society, vol. 92(368), pages 920-936, December.
    10. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2008. "Aggregation of Nerlovian profit indicator," Applied Economics Letters, Taylor & Francis Journals, vol. 15(11), pages 845-847.
    11. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 1993. "The Measurement of Productive Efficiency: Techniques and Applications," OUP Catalogue, Oxford University Press, number 9780195072181.
    12. Elvira Silva & Spiro Stefanou, 2003. "Nonparametric Dynamic Production Analysis and the Theory of Cost," Journal of Productivity Analysis, Springer, vol. 19(1), pages 5-32, January.
    13. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    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. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    16. Walter Briec & Benoit Dervaux & Hervé Leleu, 2003. "Aggregation of Directional Distance Functions and Industrial Efficiency," Journal of Economics, Springer, vol. 79(3), pages 237-261, July.
    17. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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    4. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.
    5. Leleu, Hervé & Briec, Walter, 2009. "A DEA estimation of a lower bound for firms' allocative efficiency without information on price data," International Journal of Production Economics, Elsevier, vol. 121(1), pages 203-211, September.
    6. Emile Blaise Siewe Pougoue & Ibrahim Manu & Innocent Adédédji Labiyi & Thiburce Bokossa, 2019. "Efficacité technique des exploitations avicoles productrices d’œufs au sud du Bénin," Post-Print halshs-01516234, HAL.
    7. Fu-bao Zhou & Xin-xin Wang & Ying-ke Liu, 2014. "Gas drainage efficiency: an input–output model for evaluating gas drainage projects," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(2), pages 989-1005, November.

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