IDEAS home Printed from https://ideas.repec.org/p/ies/wpaper/e200501.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=44045475_2005-ECO-1_Briec_Comes_KK.pdf
    File Function: First version, 2005
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Fare,Rolf & Grosskopf,Shawna & Lovell,C. A. Knox, 2008. "Production Frontiers," Cambridge Books, Cambridge University Press, number 9780521072069.
    3. 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.
    4. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2008. "Aggregation of Nerlovian profit indicator," Applied Economics Letters, Taylor & Francis Journals, vol. 15(11), pages 845-847.
    5. Fare,Rolf & Grosskopf,Shawna & Lovell,C. A. Knox, 1993. "Production Frontiers," Cambridge Books, Cambridge University Press, number 9780521420334.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    12. 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.
    13. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    14. 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.
    15. 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.
    16. 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.
    17. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    18. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kerstens, Kristiaan & Mazza, Paolo & Ren, Tiantian & Van de Woestyne, Ignace, 2022. "Multi-Time and Multi-Moment Nonparametric Frontier-Based Fund Rating: Proposal and Buy-and-Hold Backtesting Strategy," Omega, Elsevier, vol. 113(C).
    2. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.
    3. Autant-Bernard, Corinne & Guironnet, Jean-Pascal & Massard, Nadine, 2011. "Agglomeration and social return to R&D: Evidence from French plant productivity changes," International Journal of Production Economics, Elsevier, vol. 132(1), pages 34-42, July.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    2. Deng, Zhongqi & Jiang, Nan & Pang, Ruizhi, 2021. "Factor-analysis-based directional distance function: The case of New Zealand hospitals," Omega, Elsevier, vol. 98(C).
    3. 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.
    4. A. Abad & P. Ravelojaona, 2017. "Exponential environmental productivity index and indicators," Journal of Productivity Analysis, Springer, vol. 48(2), pages 147-166, December.
    5. Mauricio Benegas & Emerson Marinho, 2008. "Duality, Net Supply, and The Directional Distance Function," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807211656140, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. Dairo Estrada & Poldy Osorio, 2004. "Effects of Financial Capital on Colombian Banking Efficiency," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, vol. 22(47), pages 162-201, December.
    7. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2016. "Congestion in production correspondences," Journal of Economics, Springer, vol. 119(1), pages 65-90, September.
    8. Silva, Elvira & Lansink, Alfons Oude & Stefanou, Spiro E., 2015. "The adjustment-cost model of the firm: Duality and productive efficiency," International Journal of Production Economics, Elsevier, vol. 168(C), pages 245-256.
    9. Abad, Arnaud & Briec, Walter, 2019. "On the axiomatic of pollution-generating technologies: Non-parametric production analysis," European Journal of Operational Research, Elsevier, vol. 277(1), pages 377-390.
    10. Manh D. Pham & Valentin Zelenyuk, 2017. "Convexity, Disposability and Returns to Scale in Production Analysis," CEPA Working Papers Series WP042017, School of Economics, University of Queensland, Australia.
    11. Arnaud Abad, 2020. "Environmental Efficiency and Productivity Analysis," Working Papers hal-03032038, HAL.
    12. Briec, Walter & Kerstens, Kristiaan & Prior, Diego & Van de Woestyne, Ignace, 2010. "Tangency capacity notions based upon the profit and cost functions: A non-parametric approach and a general comparison," Economic Modelling, Elsevier, vol. 27(5), pages 1156-1166, September.
    13. Martin Bod’a & Martin Dlouhý & Emília Zimková, 2018. "Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 813-846, December.
    14. Dupont, Diane P. & Grafton, R. Quentin & Kirkley, James & Squires, Dale, 2002. "Capacity utilization measures and excess capacity in multi-product privatized fisheries," Resource and Energy Economics, Elsevier, vol. 24(3), pages 193-210, June.
    15. Yaryna Kolomiytseva, 2018. "Revisiting Transformation and Directional Technology Distance Functions," Papers 1812.10108, arXiv.org.
    16. Walter Briec & Kristiaan Kerstens & Diego Prior, 2009. "Tangency Capacity Notions Based upon the Pro?t and Cost Functions: A Non-Parametric Approach and a Comparison," Working Papers 2009-ECO-05, IESEG School of Management.
    17. Walter Briec & Laurence Lasselle, 2022. "On some relations between a continuous time Luenberger productivity indicator and the Solow model," Bulletin of Economic Research, Wiley Blackwell, vol. 74(2), pages 484-502, April.
    18. Briec, Walter & Mussard, Stéphane, 2014. "Efficient firm groups: Allocative efficiency in cooperative games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 286-296.
    19. Briec, Walter & Mussard, Stéphane, 2020. "Improvement of technical efficiency of firm groups," European Journal of Operational Research, Elsevier, vol. 283(3), pages 991-1001.
    20. R H Green & W D Cook, 2004. "A free coordination hull approach to efficiency measurement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1059-1063, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ies:wpaper:e200501. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lies BOUTEN (email available below). General contact details of provider: https://edirc.repec.org/data/iesegfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.