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

  • Kristof De Witte
  • Rui C. Marcques

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.

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Paper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces0822.

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Date of creation: Aug 2008
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Handle: RePEc:ete:ceswps:ces0822
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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. 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.
  3. Sabbioni, Guillermo, 2008. "Efficiency in the Brazilian sanitation sector," Utilities Policy, Elsevier, vol. 16(1), pages 11-20, March.
  4. 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.
  5. 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.
  6. 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, 04.
  7. 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.
  8. H. Leleu, 2006. "A linear programming framework for free disposal hull technologies and cost functions: primal and dual models," Post-Print hal-00204497, HAL.
  9. Cinzia Daraio & Leopold Simar, 2003. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," LEM Papers Series 2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  10. Fare, Rolf & Grosskopf, Shawna & Lovell, C A Knox, 1983. " The Structure of Technical Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 85(2), pages 181-90.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Fumitoshi Mizutani & Takuya Urakami, 2001. "articles: Identifying network density and scale economies for Japanese water supply organizations," Papers in Regional Science, Springer, vol. 80(2), pages 211-230.
  16. KERSTENS, Kristiaan & VANDEN EECKAUT, Philippe, 1997. "Estimating returns to scale using nonparametric deterministic technologies : a new method based on goodness-of-fit," CORE Discussion Papers 1997013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. John Ashton, 2000. "Cost efficiency in the UK water and sewerage industry," Applied Economics Letters, Taylor & Francis Journals, vol. 7(7), pages 455-458.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. repec:cor:louvrp:-571 is not listed on IDEAS
  23. 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, 02.
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