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Returms-to-scale Properties in DEA Models: The Fundamental Role of Interior Points

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  • Krivonozhko, Vladimir

    (Institute for Systems Analysis, Academy of Sciences, Moscow)

  • Førsund, Finn R.

    ()
    (Dept. of Economics, University of Oslo)

Abstract

Attempts can be found in the DEA literature to identify returns to scale at efficient interior points of the production possibility set on the basis of returns to scale at points of the corresponding reference sets. However, an opposite approach is put forward in this paper, advocating that returns-to-scale properties of efficient reference units should be found by identifying first returns to scale of an efficient interior unit that is a radial projection to the frontier of an inefficient unit. Returns-to-scale properties of both the corresponding reference units and units supporting the face in question can then be established.

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File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2009/Memo-15-2009.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 15/2009.

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Length: 22 pages
Date of creation: 04 Aug 2009
Date of revision:
Publication status: Published as Krivonozhko, Vladimir, Finn R. Førsund and Andrey V. Lychev, 'Returms-to-scale Properties in DEA Models: The Fundamental Role of Interior Points' in Journal of productivity analysis, 2012, pages 121-130.
Handle: RePEc:hhs:osloec:2009_015

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Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
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Web page: http://www.oekonomi.uio.no/indexe.html
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Keywords: Returns to scale; DEA; Interior points; Vertices;

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References

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  1. 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.
  2. 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.
  3. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
  4. 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.
  5. Panzar, John C & Willig, Robert D, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, MIT Press, vol. 91(3), pages 481-93, August.
  6. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
  7. 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.
  8. 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.
  9. 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.
  10. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
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Cited by:
  1. Krivonozhko, Vladimir & R. Førsund, Finn & V. Lychev, Andrey, 2011. "A Note on Imposing Strong Complementary Slackness Conditions in DEA," Memorandum 17/2010, Oslo University, Department of Economics.
  2. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2014. "Measurement of returns to scale using non-radial DEA models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 664-670.

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