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Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit

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  • Kerstens, Kristiaan
  • Vanden Eeckaut, Philippe

Abstract

The purpose of this note is to define a new and more general method to obtain qualitative information about returns to scale for individual observations. In a second section the traditional methods developed for estimating returns to scale on nonparametric deterministic reference technologies (Data Envelopment Analysis (DEA) models) are reviewed. Section 3 provides a new and more general method that is suitable for all reference technologies. Its usefulness is illustrated by considering variations on an existing non-convex production model, known as the Free Disposal Hull (FDH). When different returns to scale assumptions are introduced into the FDH, then previous methods for determining returns to scale do no longer apply.
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Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:113:y:1999:i:1:p:206-214
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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. repec:bla:scandj:v:87:y:1985:i:4:p:594-604 is not listed on IDEAS
    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. Bauer, Paul W. & Hancock, Diana, 1993. "The efficiency of the Federal Reserve in providing check processing services," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 287-311, April.
    5. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
    6. Chavas, Jean-Paul & Cox, Thomas L, 1990. "A Non-parametric Analysis of Productivity: The Case of U.S. and Japanese Manufacturing," American Economic Review, American Economic Association, vol. 80(3), pages 450-464, June.
    7. Fare,Rolf & Grosskopf,Shawna & Lovell,C. A. Knox, 2008. "Production Frontiers," Cambridge Books, Cambridge University Press, number 9780521072069, October.
    8. repec:bla:scandj:v:85:y:1983:i:2:p:181-90 is not listed on IDEAS
    9. Kerstens, K., 1996. "Technical efficiency measurement and explanation of French urban transit companies," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(6), pages 431-452, November.
    10. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    11. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    12. Knox Lovell, C. A., 1995. "Measuring the macroeconomic performance of the Taiwanese economy," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 165-178, April.
    13. C. Lovell & Shawna Grosskopf & Eduardo Ley & Jesús Pastor & Diego Prior & Philippe Eeckaut, 1994. "Linear programming approaches to the measurement and analysis of productive efficiency," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 175-248, December.
    14. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    15. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    16. Banker, R. D. & Bardhan, I. & Cooper, W. W., 1996. "A note on returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 88(3), pages 583-585, February.
    17. Niels Christian Petersen, 1990. "Data Envelopment Analysis on a Relaxed Set of Assumptions," Management Science, INFORMS, vol. 36(3), pages 305-314, March.
    18. Chang, Kuo-Ping & Guh, Yeah-Yuh, 1991. "Linear production functions and the data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 52(2), pages 215-223, May.
    19. 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.
    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. Löthgren, Mickael & Tambour, Magnus, 1996. "Alternative Approaches to Estimate Returns to Scale in DEA- Models," SSE/EFI Working Paper Series in Economics and Finance 90, Stockholm School of Economics.
    22. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
    23. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 1993. "The Measurement of Productive Efficiency: Techniques and Applications," OUP Catalogue, Oxford University Press, number 9780195072181.
    24. 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.
    25. Fare, Rolf & Grosskopf, Shawna, 1995. "Nonparametric tests of regularity, Farrell efficiency, and goodness-of-fit," Journal of Econometrics, Elsevier, vol. 69(2), pages 415-425, October.
    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. Fried, H. O. & Knox Lovell, C.A. & Vanden Eeckaut, P., 1995. "Service productivity in U.S. credit unions," LIDAM Reprints CORE 1169, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    28. Joe Zhu & Zhao-Han Shen, 1995. "A discussion of testing DMUs' returns to scale," European Journal of Operational Research, Elsevier, vol. 81(3), pages 590-596, March.
    29. Fare, Rolf & Grosskopf, Shawna, 1994. "Estimation of returns to scale using data envelopment analysis: A comment," European Journal of Operational Research, Elsevier, vol. 79(2), pages 379-382, December.
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    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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