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Imposing the Regular Ultra Passum law in DEA models

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  • Olesen, Ole Bent
  • Petersen, Niels Christian
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    Abstract

    Recently there has been some discussion in the literature concerning the nature of scale properties in the Data Envelopment Model (DEA). It has been argued that DEA may not be able to provide reliable estimates of the optimal scale size. We argue in this paper that DEA is well suited to estimate optimal scale size, if DEA is augmented with two additional maintained hypotheses which imply that the DEA-frontier is consistent with smooth curves along rays in input and in output space that obey the Regular Ultra Passum (RUP) law, i.e. monotonically decreasing scale elasticities. A necessary condition for a smooth curve passing through all vertices to obey the RUP-law is presented. If this condition is satisfied then upper and lower bounds for the marginal product at each vertex are presented. It is shown that any set of feasible marginal products will correspond to a smooth curve passing through all points with a monotonic decreasing scale elasticity. The proof is constructive in the sense that an estimator of the curve is provided with the desired properties. A typical DEA based return to scale analysis simply reports whether or not a DMU is at the optimal scale based on point estimates of scale efficiency. A contribution of this paper is that we provide a method which allows us to determine in what interval optimal scale is located.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 41 (2013)
    Issue (Month): 1 ()
    Pages: 16-27

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    Handle: RePEc:eee:jomega:v:41:y:2013:i:1:p:16-27

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    Keywords: DEA; Efficiency; Regular Ultra Passum (RUP) law; Optimal scale size;

    References

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    1. Rajiv D. Banker & Ajay Maindiratta, 1986. "Erratum to: "Piecewise Loglinear Estimation of Efficient Production Surfaces"," Management Science, INFORMS, vol. 32(3), pages 385-385, March.
    2. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    3. 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.
    4. Førsund, Finn R. & Hjalmarsson, Lennart, 2002. "Are all Scales Optimal in DEA? Theory and Empirical Evidence," Working Papers in Economics 66, University of Gothenburg, Department of Economics.
    5. Rajiv D. Banker & Ajay Maindiratta, 1986. "Piecewise Loglinear Estimation of Efficient Production Surfaces," Management Science, INFORMS, vol. 32(1), pages 126-135, January.
    6. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
    7. 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.
    8. Zellner, A & Revankar, N S, 1969. "Generalized Production Functions," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 241-50, April.
    9. 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.
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    Cited by:
    1. Kaoru Tone & Miki Tsutsui, 2013. "How to deal with S-shaped curve in DEA," GRIPS Discussion Papers 13-10, National Graduate Institute for Policy Studies.
    2. Olesen, Ole B. & Ruggiero, John, 2014. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 235(3), pages 798-809.

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