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On directional scale elasticities

Author

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  • Bert Balk

    ()

  • Rolf Färe

    ()

  • Giannis Karagiannis

    ()

Abstract

In this paper we generalize the concept of scale elasticity to accommodate changes in any direction in the input–output space and not only in the radial input and output directions as was done so far with the conventional scale elasticity measure. Our departure point is that we view the scale elasticity as a directional derivative measure. Then for any functional representation of the technology and at a given point in the input–output space, the scale elasticity can be computed along any direction. By adjusting accordingly the direction vector we can measure appropriately factor returns with technologies exhibiting weak disposability of outputs and/or inputs. In addition, we do not have to restrict the analysis to only equi-proportional changes. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Bert Balk & Rolf Färe & Giannis Karagiannis, 2015. "On directional scale elasticities," Journal of Productivity Analysis, Springer, vol. 43(1), pages 99-104, February.
  • Handle: RePEc:kap:jproda:v:43:y:2015:i:1:p:99-104
    DOI: 10.1007/s11123-014-0399-6
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    References listed on IDEAS

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    1. W. Erwin Diewert & Takanobu Nakajima & Alice Nakamura & Emi Nakamura & Masao Nakamura, 2011. "Returns to scale: concept, estimation and analysis of Japan's turbulent 1964-88 economy," Canadian Journal of Economics, Canadian Economics Association, vol. 44(2), pages 451-485, May.
    2. Rolf Färe & Carlos Martins-Filho & Michael Vardanyan, 2010. "On functional form representation of multi-output production technologies," Journal of Productivity Analysis, Springer, vol. 33(2), pages 81-96, April.
    3. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.
    4. 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.
    5. John C. Panzar & Robert D. Willig, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, Oxford University Press, vol. 91(3), pages 481-493.
    6. Podinovski, Victor V. & Førsund, Finn R. & Krivonozhko, Vladimir E., 2009. "A simple derivation of scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 197(1), pages 149-153, August.
    7. 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.
    8. Robert Chambers & Rolf Färe, 2008. "A “calculus” for data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 30(3), pages 169-175, December.
    9. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    10. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    11. Jean-Paul Chavas & Kwansoo Kim, 2007. "Measurement and Sources of Economies of Scope: A Primal Approach," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 163(3), pages 411-427, September.
    12. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    13. Starrett, David A, 1977. "Measuring Returns to Scale in the Aggregate, and the Scale Effect of Public Goods," Econometrica, Econometric Society, vol. 45(6), pages 1439-1455, September.
    14. Hanoch, Giora, 1975. "The Elasticity of Scale and the Shape of Average Costs," American Economic Review, American Economic Association, vol. 65(3), pages 492-497, June.
    15. Fukuyama, Hirofumi, 2003. "Scale characterizations in a DEA directional technology distance function framework," European Journal of Operational Research, Elsevier, vol. 144(1), pages 108-127, January.
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    Cited by:

    1. Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.

    More about this item

    Keywords

    Scale elasticity; Technology; Radial distance function; Hyperbolic distance function; Directional distance function; Cost function; D21; D24;

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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