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Measuring scale efficiency from a parametric hyperbolic distance function

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  • Daehoon Nahm
  • Ha Vu

Abstract

This paper shows how scale efficiency can be measured from an arbitrary parametric hyperbolic distance function with multiple outputs and multiple inputs. It extends the methods introduced by Ray (J Product Anal 11:183–194, 1998 ), and Balk (J Product Anal 15:159–183, 2001 ) and Ray ( 2003 ) that measure scale efficiency from a single-output multi-input distance function and from a multi-output and multi-input distance function, respectively. The method developed in the present paper is different from Ray’s and Balk’s in that it allows for simultaneous contraction of inputs and expansion of outputs. Theorems applicable to an arbitrary parametric hyperbolic distance function are introduced first, and then their uses in measuring scale efficiency are illustrated with the translog functional form. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Daehoon Nahm & Ha Vu, 2013. "Measuring scale efficiency from a parametric hyperbolic distance function," Journal of Productivity Analysis, Springer, vol. 39(1), pages 83-88, February.
    • Handle: RePEc:kap:jproda:v:39:y:2013:i:1:p:83-88
    DOI: 10.1007/s11123-012-0269-z
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    References listed on IDEAS

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    1. Lau, Lawrence J, 1972. "Profit Functions of Technologies with Multiple Inputs and Outputs," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 281-289, August.
    2. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
    3. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701.
    4. 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.
    5. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    6. Rafael Cuesta & José Zofío, 2005. "Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks," Journal of Productivity Analysis, Springer, vol. 24(1), pages 31-48, September.
    7. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190.
    8. Subhash Ray, 2003. "Measuring Scale Efficiency from the Translog Multi-Input, Multi-Output Distance Function," Working papers 2003-25, University of Connecticut, Department of Economics.
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    Cited by:

    1. Mallikarjun, Sreekanth & Lewis, Herbert F. & Sexton, Thomas R., 2014. "Operational performance of U.S. public rail transit and implications for public policy," Socio-Economic Planning Sciences, Elsevier, vol. 48(1), pages 74-88.
    2. Bert Balk & Rolf Färe & Giannis Karagiannis, 2015. "On directional scale elasticities," Journal of Productivity Analysis, Springer, vol. 43(1), pages 99-104, February.
    3. McKillop, Donal G. & Quinn, Barry, 2017. "Irish credit unions: Differential regulation based on business model complexity," The British Accounting Review, Elsevier, vol. 49(2), pages 230-241.
    4. Qushim, Berdikul & Gillespie, Jeffrey & McMillin, Kenneth, 2014. "Productivity And Efficiency Of U.S. Meat Goat Farms," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162435, Southern Agricultural Economics Association.

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    More about this item

    Keywords

    Scale efficiency; Scale elasticity; Hyperbolic distance function; Almost homogeneity; Translog function; D24; C67;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models

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