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

Author

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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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    1. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    2. 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.
    3. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    4. Pablo Arocena, 2005. "The measurement of scope, scale and diversification economies: How (in)efficient is electricity restructuring and unbundling?," Working Papers 2005/1, Institut d'Economia de Barcelona (IEB).
    5. 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.
    6. Pablo Arocena, 2005. "The measurement of scope, scale and diversification economies: How (in)efficient is electricity restructuring and unbundling?," Working Papers 2005/1, Institut d'Economia de Barcelona (IEB).
    7. repec:bla:scandj:v:85:y:1983:i:2:p:181-90 is not listed on IDEAS
    8. Fumitoshi Mizutani & Takuya Urakami, 2001. "articles: Identifying network density and scale economies for Japanese water supply organizations," Papers in Regional Science, Springer;Regional Science Association International, vol. 80(2), pages 211-230.
    9. 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.
    10. Torres, Marcelo & Morrison Paul, Catherine J., 2006. "Driving forces for consolidation or fragmentation of the US water utility industry: A cost function approach with endogenous output," Journal of Urban Economics, Elsevier, vol. 59(1), pages 104-120, January.
    11. Garcia, Serge & Moreaux, Michel & Reynaud, Arnaud, 2007. "Measuring economies of vertical integration in network industries: An application to the water sector," International Journal of Industrial Organization, Elsevier, vol. 25(4), pages 791-820, August.
    12. Steven Renzetti, 1999. "Municipal Water Supply and Sewage Treatment: Costs, Prices and Distortions," Canadian Journal of Economics, Canadian Economics Association, vol. 32(3), pages 688-704, May.
    13. 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.
    14. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    15. Antonioli, B. & Filippini, M., 2001. "The use of a variable cost function in the regulation of the Italian water industry," Utilities Policy, Elsevier, vol. 10(3-4), pages 181-187.
    16. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    17. 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.
    18. repec:cor:louvrp:-571 is not listed on IDEAS
    19. Walter Briec & Kristiaan Kerstens & Philippe Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity (Journal of Economics 81(2):155–192)," Journal of Economics, Springer, vol. 87(3), pages 307-308, April.
    20. 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.
    21. Arnaud Reynaud & Serge Garcia & Michel Moreaux, 2004. "Measuring Economies of Vertical Integration in Network," Econometric Society 2004 North American Summer Meetings 184, Econometric Society.
    22. Serge Garcia & Alban Thomas, 2001. "The Structure of Municipal Water Supply Costs: Application to a Panel of French Local Communities," Journal of Productivity Analysis, Springer, vol. 16(1), pages 5-29, July.
    23. Sabbioni, Guillermo, 2008. "Efficiency in the Brazilian sanitation sector," Utilities Policy, Elsevier, vol. 16(1), pages 11-20, March.
    24. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    25. Seiford, Lawrence M. & Zhu, Joe, 1999. "An investigation of returns to scale in data envelopment analysis," Omega, Elsevier, vol. 27(1), pages 1-11, February.
    26. Banker, Rajiv D. & Chang, Hsihui & Cooper, William W., 1996. "Equivalence and implementation of alternative methods for determining returns to scale in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 89(3), pages 473-481, March.
    27. Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2000. "What Is the Economic Meaning of FDH? A Reply to Thrall," Journal of Productivity Analysis, Springer, vol. 13(3), pages 263-267, May.
    28. Cubbin, John & Tzanidakis, George, 1998. "Regression versus data envelopment analysis for efficiency measurement: an application to the England and Wales regulated water industry," Utilities Policy, Elsevier, vol. 7(2), pages 75-85, June.
    29. John Ashton, 2000. "Cost efficiency in the UK water and sewerage industry," Applied Economics Letters, Taylor & Francis Journals, vol. 7(7), pages 455-458.
    30. Sergio Destefanis & Giuseppe Storti, 2002. "Measuring cross-country technological catch-up through variable-parameter FDH," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(1), pages 109-125, February.
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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. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Michael Zschille, 2014. "Marktstrukturen in der Trinkwasserversorgung," DIW Roundup: Politik im Fokus 43, DIW Berlin, German Institute for Economic Research.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.

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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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