IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v48y2017i2d10.1007_s11123-017-0512-8.html
   My bibliography  Save this article

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

Author

Listed:
  • Juan Aparicio

    () (Universidad Miguel Hernández de Elche)

  • José L. Zofío

    (Universidad Autónoma de Madrid)

Abstract

In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0512-8
    DOI: 10.1007/s11123-017-0512-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11123-017-0512-8
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

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

    Other versions of this item:

    References listed on IDEAS

    as
    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. Sato, Ryuzo, 1977. "Homothetic and Non-Homothetic CES Production Functions," American Economic Review, American Economic Association, vol. 67(4), pages 559-569, September.
    3. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    4. J.Ph. Boussemart & W. Briec & H. Leleu, 2010. "Linear programming solutions and distance functions under alpha-returns to scale," Post-Print hal-00573297, HAL.
    5. Zieschang, Kimberly D., 1983. "A note on the decomposition of cost efficiency into technical and allocative components," Journal of Econometrics, Elsevier, vol. 23(3), pages 401-405, December.
    6. 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.
    7. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    8. Manthos Delis & Maria Iosifidi & Efthymios G. Tsionas, 2014. "On the Estimation of Marginal Cost," Operations Research, INFORMS, vol. 62(3), pages 543-556, June.
    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. Raymond J. Kopp, 1981. "The Measurement of Productive Efficiency: A Reconsideration," The Quarterly Journal of Economics, Oxford University Press, vol. 96(3), pages 477-503.
    11. Schmidt, Peter & Knox Lovell, C. A., 1979. "Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers," Journal of Econometrics, Elsevier, vol. 9(3), pages 343-366, February.
    12. 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.
    13. 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.
    14. Fare, Rolf & Grosskopf, Shawna, 1997. "Profit efficiency, Farrell decompositions and the Mahler inequality1," Economics Letters, Elsevier, vol. 57(3), pages 283-287, December.
    15. Jean-Philippe Boussemart & Walter Briec & Nicolas Peypoch & Christophe Tavéra, 2009. "α-Returns to scale and multi-output production technologies," Post-Print halshs-00418883, HAL.
    16. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    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. J-P Boussemart & W Briec & H Leleu, 2010. "Linear programming solutions and distance functions under α-returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1297-1301, August.
    19. Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
    20. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    21. Mensah, Yaw M., 1994. "A simplification of the Kopp--Diewert method of decomposing cost efficiency and some implications," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 133-144.
    22. Kopp, Raymond J. & Diewert, W. Erwin, 1982. "The decomposition of frontier cost function deviations into measures of technical and allocative efficiency," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 319-331, August.
    23. Kumbhakar, Subal C., 1997. "Modeling allocative inefficiency in a translog cost function and cost share equations: An exact relationship," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 351-356.
    24. Blackorby, Charles & Diewert, W E, 1979. "Expenditure Functions, Local Duality, and Second Order Approximations," Econometrica, Econometric Society, vol. 47(3), pages 579-601, May.
    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. Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Orea, Luis & Zofío, José L., 2017. "A primer on the theory and practice of efficiency and productivity analysis," Efficiency Series Papers 2017/05, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).

    More about this item

    Keywords

    Non-homotheticity; Technical efficiency; Allocative efficiency; Directional distance function;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    Statistics

    Access and download statistics

    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:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0512-8. 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: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    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.