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A simple derivation of scale elasticity in data envelopment analysis

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  • Podinovski, Victor V.
  • Førsund, Finn R.
  • Krivonozhko, Vladimir E.

Abstract

In this paper, we suggest a simple derivation of the formulae for the scale elasticity in the variable returns-to-scale technology as used in data envelopment analysis. Our development is consistent with the existing literature but the proof is much shorter and applies to the general case without any simplifying conditions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:149-153
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    References listed on IDEAS

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    1. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    2. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
    3. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    4. Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    5. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    6. 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.
    7. 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.
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    Citations

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    Cited by:

    1. Amatatsu, Hirofumi & Ueda, Tohru, 2012. "Measurement of simultaneous scale and mix changes in inputs and outputs using DEA facets and RTS," European Journal of Operational Research, Elsevier, vol. 223(3), pages 752-761.
    2. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    3. Petros Hadjicostas & Andreas Soteriou, 2010. "Different orders of one-sided scale elasticities in multi-output production," Journal of Productivity Analysis, Springer, vol. 33(2), pages 147-167, April.
    4. Sahoo, Biresh K. & Zhu, Joe & Tone, Kaoru & Klemen, Bernhard M., 2014. "Decomposing technical efficiency and scale elasticity in two-stage network DEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 584-594.
    5. repec:eee:eneeco:v:70:y:2018:i:c:p:26-36 is not listed on IDEAS
    6. Sahoo, Biresh K & Khoveyni, Mohammad & Eslami, Robabeh & Chaudhury, Pradipta, 2016. "Returns to scale and most productive scale size in DEA with negative data," European Journal of Operational Research, Elsevier, vol. 255(2), pages 545-558.
    7. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    8. Michael Zschille, 2014. "Nonparametric measures of returns to scale: an application to German water supply," Empirical Economics, Springer, vol. 47(3), pages 1029-1053, November.
    9. Bert Balk & Rolf Färe & Giannis Karagiannis, 2015. "On directional scale elasticities," Journal of Productivity Analysis, Springer, vol. 43(1), pages 99-104, February.
    10. Atici, Kazim Baris & Podinovski, Victor V., 2012. "Mixed partial elasticities in constant returns-to-scale production technologies," European Journal of Operational Research, Elsevier, vol. 220(1), pages 262-269.
    11. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2012. "Returns-to-scale properties in DEA models: the fundamental role of interior points," Journal of Productivity Analysis, Springer, vol. 38(2), pages 121-130, October.
    12. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    13. Mahdi Mirjaberi & Reza Kazemi Matin, 2016. "On the Calculation of Directional Scale Elasticity in Data Envelopment Analysis," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-17, August.
    14. repec:eee:ejores:v:268:y:2018:i:1:p:268-280 is not listed on IDEAS

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