Scale properties in data envelopment analysis
AbstractRecently 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 (Frisch 1965). 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 InfoPaper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 4/2011.
Length: 31 pages
Date of creation: 01 Jul 2011
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Find related papers by JEL classification:
- C00 - Mathematical and Quantitative Methods - - General - - - General
- C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
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- 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.
- 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.
- Zellner, A & Revankar, N S, 1969. "Generalized Production Functions," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 241-50, April.
- Olesen, Ole B. & Ruggiero, John, 2012. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," Discussion Papers of Business and Economics 2/2012, Department of Business and Economics, University of Southern Denmark.
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