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Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

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  • Kristof De Witte
  • Rui C. Marcques

Abstract

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7 to 10 million m3.

Suggested Citation

  • Kristof De Witte & Rui C. Marcques, 2008. "Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies," Working Papers of Department of Economics, Leuven ces0822, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:ces0822
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    Cited by:

    1. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    2. Guerrini, Andrea & Romano, Giulia & Leardini, Chiara, 2018. "Economies of scale and density in the Italian water industry: A stochastic frontier approach," Utilities Policy, Elsevier, vol. 52(C), pages 103-111.
    3. Massarutto, Antonio & Grassetti, Luca & Lambardi di San Miniato, Michele & Moletta, Mattia, 2023. "Efficient firms are all alike, but every inefficient firm is such in its own way: Heterogeneity of costs determinants in the Italian water sector," Utilities Policy, Elsevier, vol. 84(C).
    4. Jean-Paul Chavas & Kwansoo Kim, 2015. "Nonparametric analysis of technology and productivity under non-convexity: a neighborhood-based approach," Journal of Productivity Analysis, Springer, vol. 43(1), pages 59-74, February.
    5. Saal David S. & Arocena Pablo & Maziotis Alexandros & Triebs Thomas, 2013. "Scale and Scope Economies and the Efficient Vertical and Horizontal Configuration of the Water Industry: A Survey of the Literature," Review of Network Economics, De Gruyter, vol. 12(1), pages 93-129, March.
    6. Ferreira, D.C. & Marques, R.C. & Nunes, A.M., 2018. "Economies of scope in the health sector: The case of Portuguese hospitals," European Journal of Operational Research, Elsevier, vol. 266(2), pages 716-735.
    7. Brandon Pope & Andrew Johnson, 2013. "Returns to scope: a metric for production synergies demonstrated for hospital production," Journal of Productivity Analysis, Springer, vol. 40(2), pages 239-250, October.
    8. Andrea Guerrini & Giulia Romano & Bettina Campedelli, 2013. "Economies of Scale, Scope, and Density in the Italian Water Sector: A Two-Stage Data Envelopment Analysis Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4559-4578, October.
    9. Zschille, Michael, 2012. "Consolidating the Water Industry: An Analysis of the Potential Gains from Horizontal Integration in a Conditional Efficiency Fr," CEPR Discussion Papers 8737, C.E.P.R. Discussion Papers.
    10. 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.
    11. Diogo Cunha Ferreira & Rui Cunha Marques, 2020. "A step forward on order-α robust nonparametric method: inclusion of weight restrictions, convexity and non-variable returns to scale," Operational Research, Springer, vol. 20(2), pages 1011-1046, June.
    12. De Witte, Kristof & Mika, Kortelainen, 2009. "Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables," MPRA Paper 14034, University Library of Munich, Germany.
    13. Nickolaos G. Tzeremes, 2019. "Technological change, technological catch-up and export orientation: evidence from Latin American Countries," Journal of Productivity Analysis, Springer, vol. 52(1), pages 85-100, December.
    14. Michael Zschille, 2014. "Marktstrukturen in der Trinkwasserversorgung," DIW Roundup: Politik im Fokus 43, DIW Berlin, German Institute for Economic Research.
    15. Meihong Dai & Xianneng Li & Yuduo Lu, 2017. "How Urbanization Economies Impact TFP of R&D Performers: Evidence from China," Sustainability, MDPI, vol. 9(10), pages 1-17, September.
    16. Michael Zschille, 2015. "Consolidating the water industry: an analysis of the potential gains from horizontal integration in a conditional efficiency framework," Journal of Productivity Analysis, Springer, vol. 44(1), pages 97-114, August.
    17. Michael Zschille, 2016. "Cost Structure and Economies of Scale in German Water Supply," Discussion Papers of DIW Berlin 1576, DIW Berlin, German Institute for Economic Research.
    18. José Antonio Palomero-González & Vicent Almenar-Llongo & Ramón Fuentes-Pascual, 2021. "Evaluating the Efficiency of Water Distribution Network Sectors Using the DEA-Weight Russell Directional Distance Model: The Case of the City of Valencia (Spain)," Sustainability, MDPI, vol. 13(19), pages 1-21, September.
    19. Giulia Romano & Andrea Guerrini & Rui Cunha Marques, 2017. "European Water Utility Management: Promoting Efficiency, Innovation and Knowledge in the Water Industry," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(8), pages 2349-2353, June.
    20. Michael Zschille, 2012. "Consolidating the Water Industry: An Analysis of the Potential Gains from Horizontal Integration in a Conditional Efficiency Framework," Discussion Papers of DIW Berlin 1187, DIW Berlin, German Institute for Economic Research.
    21. Adel Hatami-Marbini & Zahra Ghelej Beigi & Jens Leth Hougaard & Kobra Gholami, 2014. "Estimating Returns to Scale in Imprecise Data Envelopment Analysis," MSAP Working Paper Series 07_2014, University of Copenhagen, Department of Food and Resource Economics.
    22. Chavas, Jean-Paul & Kim, Kwansoo, 2013. "Nonparametric Analysis of Technology and Productivity under Non-Convexity," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149684, Agricultural and Applied Economics Association.

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    More about this item

    Keywords

    Free Disposal Hull; economies of scale; optimal size; water sector;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • L33 - Industrial Organization - - Nonprofit Organizations and Public Enterprise - - - Comparison of Public and Private Enterprise and Nonprofit Institutions; Privatization; Contracting Out
    • L51 - Industrial Organization - - Regulation and Industrial Policy - - - Economics of Regulation
    • L95 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Gas Utilities; Pipelines; Water Utilities

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