IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

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

  • Kristof Witte


  • Rui Marques


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.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 35 (2011)
Issue (Month): 3 (June)
Pages: 213-226

in new window

Handle: RePEc:kap:jproda:v:35:y:2011:i:3:p:213-226
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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, 09.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  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. 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.
  14. 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.
  15. Sabbioni, Guillermo, 2008. "Efficiency in the Brazilian sanitation sector," Utilities Policy, Elsevier, vol. 16(1), pages 11-20, March.
  16. 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.
  17. 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.
  18. repec:cor:louvrp:-571 is not listed on IDEAS
  19. 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.
  20. W. Briec & K. Kerstens & P. Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Post-Print hal-00211174, HAL.
  21. 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.
  22. John Ashton, 2000. "Cost efficiency in the UK water and sewerage industry," Applied Economics Letters, Taylor & Francis Journals, vol. 7(7), pages 455-458.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:kap:jproda:v:35:y:2011:i:3:p:213-226. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.