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Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies

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  • Walter Briec
  • Kristiaan Kerstens
  • Hervé Leleu
  • Philippe Eeckaut

Abstract

Thepurpose of this short article is to simplify goodness-of-fitmethods to obtain qualitative information about returns to scalefor individual observations. Traditional and new goodness-of-fitmethods developed for estimating returns to scale on nonparametricdeterministic reference technologies are reviewed. Using compositionrules for technologies with specific returns to scale assumptions,we show how these goodness-of-fit methods can be simplified inthe case of convex technologies (Data Envelopment Analysis (DEA)models). Copyright Kluwer Academic Publishers 2000

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  • Walter Briec & Kristiaan Kerstens & Hervé Leleu & Philippe Eeckaut, 2000. "Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies," Journal of Productivity Analysis, Springer, vol. 14(3), pages 267-274, November.
    • Handle: RePEc:kap:jproda:v:14:y:2000:i:3:p:267-274
    DOI: 10.1023/A:1026507205581
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    1. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
    2. Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    3. Benoit Dervaux & Gary Ferrier & Herve Leleu & Vivian Valdmanis, 2004. "Comparing French and US hospital technologies: a directional input distance function approach," Applied Economics, Taylor & Francis Journals, vol. 36(10), pages 1065-1081.
    4. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    5. Colin Glass, J. & McCallion, Gillian & McKillop, Donal G. & Rasaratnam, Syamarlah & Stringer, Karl S., 2006. "Implications of variant efficiency measures for policy evaluations in UK higher education," Socio-Economic Planning Sciences, Elsevier, vol. 40(2), pages 119-142, June.
    6. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
    7. Victor Podinovski, 2004. "Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only," Journal of Productivity Analysis, Springer, vol. 22(3), pages 227-257, November.
    8. Hirofumi Fukuyama & Hiroya Masaki & Kazuyuki Sekitani & Jianming Shi, 2014. "Distance optimization approach to ratio-form efficiency measures in data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 42(2), pages 175-186, October.
    9. Mehdiloo, Mahmood & Podinovski, Victor V., 2019. "Selective strong and weak disposability in efficiency analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1154-1169.
    10. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    11. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2019. "Cone extensions of polyhedral production technologies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 736-743.
    12. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    13. 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.
    14. Soleimani-damaneh, M. & Jahanshahloo, G.R. & Reshadi, M., 2006. "On the estimation of returns-to-scale in FDH models," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1055-1059, October.
    15. Trigo Gamarra, Lucinda, 2007. "Single- versus multi-channel distribution strategies in the German life insurance market: A cost and profit efficiency analysis," Thuenen-Series of Applied Economic Theory 81, University of Rostock, Institute of Economics.
    16. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    17. M Soleimani-damaneh, 2009. "A fast algorithm for determining some characteristics in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1528-1534, November.
    18. V V Podinovski, 2004. "Local and global returns to scale in performance measurement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 170-178, February.

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    Keywords

    Returns to scale; DEA; FDH;
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