IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v165y2015icp19-28.html
   My bibliography  Save this article

Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited

Author

Listed:
  • Aparicio, Juan
  • Borras, Fernando
  • Pastor, Jesus T.
  • Vidal, Fernando

Abstract

Overall inefficiency measurement and decomposition are important for firms facing a world of changing prices since the resultant loss has implications on managers׳ decision making. In this paper, we draw attention to some problems within existing approaches to decompose overall inefficiency into its sources and propose new revenue and cost inefficiency measures based on the well-known Russell measures. Specifically, the technical inefficiency component is calculated by the Russell output (input) measure, which is able to incorporate all sources of inefficiency corresponding to the output (input) side, specifically output (input) slacks, whereas allocative inefficiency is retrieved residually. All our results are derived from a new Fenchel–Mahler inequality using the theory of convex conjugates. This paper has several implications in theory and practice. From a theoretical point of view, we establish a natural dual relationship between the revenue (cost) function and the Russell output (input) measure; despite the previous unsuccessful attempts in the literature to provide such duality result. From a practical point of view, we provide a way of decomposing revenue (cost) inefficiency into allocative inefficiency and a component that measures technical inefficiency in the sense of Pareto, contrasting with the usual approaches for decomposing revenue (cost) inefficiency, such as those based on Shephard׳s output (input) distance function and the directional output (input) distance function.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:proeco:v:165:y:2015:i:c:p:19-28
    DOI: 10.1016/j.ijpe.2015.03.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527315000869
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dmitruk, Andrei V. & Koshevoy, Gleb A., 1991. "On the existence of a technical efficiency criterion," Journal of Economic Theory, Elsevier, vol. 55(1), pages 121-144, October.
    2. R. Russell & William Schworm, 2009. "Axiomatic foundations of efficiency measurement on data-generated technologies," Journal of Productivity Analysis, Springer, vol. 31(2), pages 77-86, April.
    3. Chambers, Robert G. & Fare, Rolf, 2004. "Additive decomposition of profit efficiency," Economics Letters, Elsevier, vol. 84(3), pages 329-334, September.
    4. Rolf Fare & Daniel Primont, 2006. "Directional duality theory Directional duality theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 239-247, September.
    5. Kopp, Raymond J., 1981. "Measuring the technical efficiency of production: A comment," Journal of Economic Theory, Elsevier, vol. 25(3), pages 450-452, December.
    6. Alfons Oude Lansink & Christien Ondersteijn, 2006. "Energy Productivity Growth in the Dutch Greenhouse Industry," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(1), pages 124-132.
    7. Fare, Rolf & Grosskopf, Shawna & Zelenyuk, Valentin, 2002. "Finding Common Ground: Efficiency Indices," MPRA Paper 28004, University Library of Munich, Germany, revised Jan 2005.
    8. R. Robert Russell & William Schworm, 2009. "Axiomatic Foundations of Inefficiency Measurement on Space," Discussion Papers 2009-07, School of Economics, The University of New South Wales.
    9. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, December.
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
    12. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    13. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017, December.
    14. Kuosmanen, Timo & Kortelainen, Mika & Sipiläinen, Timo & Cherchye, Laurens, 2010. "Firm and industry level profit efficiency analysis using absolute and uniform shadow prices," European Journal of Operational Research, Elsevier, vol. 202(2), pages 584-594, April.
    15. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    16. 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.
    17. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    18. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    19. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    20. Bol, Georg, 1986. "On technical efficiency measures: A remark," Journal of Economic Theory, Elsevier, vol. 38(2), pages 380-385, April.
    21. 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.
    22. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
    23. Russell, R. Robert, 1985. "On the Axiomatic Approach to the Measurement of Technical Efficiency," Working Papers 85-33, C.V. Starr Center for Applied Economics, New York University.
    24. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    25. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    26. 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.
    27. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    28. Fukuyama, Hirofumi & Maeda, Yasunobu & Sekitani, Kazuyuki & Shi, Jianming, 2014. "Input–output substitutability and strongly monotonic p-norm least distance DEA measures," European Journal of Operational Research, Elsevier, vol. 237(3), pages 997-1007.
    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. 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.
    2. Aparicio, Juan & Kapelko, Magdalena & Zofío, José L., 2020. "The measurement of environmental economic inefficiency with pollution-generating technologies," Resource and Energy Economics, Elsevier, vol. 62(C).
    3. Ayouba, Kassoum & Boussemart, Jean-Philippe & Lefer, Henri-Bertrand & Leleu, Hervé & Parvulescu, Raluca, 2019. "A measure of price advantage and its decomposition into output- and input-specific effects," European Journal of Operational Research, Elsevier, vol. 276(2), pages 688-698.
    4. Aparicio, Juan & Ortiz, Lidia & Pastor, Jesus T., 2017. "Measuring and decomposing profit inefficiency through the Slacks-Based Measure," European Journal of Operational Research, Elsevier, vol. 260(2), pages 650-654.
    5. Aparicio, Juan & Borras, Fernando & Pastor, Jesús T. & Zofio, Jose Luis, 2015. "Loss Distance Functions and Profit Function: General Duality Results," Working Papers in Economic Theory 2015/06, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    6. Halická, Margaréta & Trnovská, Mária, 2018. "The Russell measure model: Computational aspects, duality, and profit efficiency," European Journal of Operational Research, Elsevier, vol. 268(1), pages 386-397.

    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:eee:proeco:v:165:y:2015:i:c:p:19-28. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.