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On the calculation of the scale elasticity in DEA models

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Abstract

An issue in the multiple-output case within the literature on piecewise linear frontier production functions has been how to determine the nature of the scale properties. It is shown that knowledge of scale efficiency does not permit calculation of scale elasticity or vice versa. For inefficient units there is a relationship between input-saving and output-increasing efficiency measures through the average value of the scale elasticity between the two different reference points on the frontier. A direct approach to determine the scale properties is to calculate the scale elasticity from the dual problem to the calculation of Farrell efficiency measures.

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References

  • Al-Ayat, R., and R. Färe. (1979). “On the Existence of Joint Production Functions,” Naval Research Logistics Quarterly 26, 627–630.

    Google Scholar 

  • Banker, R.D. (1984). “Estimating Most Productive Scale Size Using Data Envelopment Analysis,” European Journal of Operational Research 17, 35–44.

    Google Scholar 

  • Banker, R.D., Charnes, A., and W.W. Cooper. (1984). “Some Models for Estimating Technical and Scale Inefficiencies,” Management Science 39, 1261–1264.

    Google Scholar 

  • Banker, R.D. and R.M. Thrall (1992). “Estimation of Returns to Scale Using Data Envelopment Analysis,” European Journal of Operational Research 62, 74–84.

    Google Scholar 

  • Caves, D.W., L.R. Christensen and W.E. Diewert (1982). “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity,” Econometrica 50, 1293–1414.

    Google Scholar 

  • Charnes, A., W.W. Cooper, A.Y. Lewin and L.M. Seiford (eds.). (1994). Data Envelopment Analysis: Theory, Methodology, and Applications, Boston/Dordrecht/London: Kluwer Academic Publishers.

    Google Scholar 

  • Charnes, A., W.W. Cooper and E. Rhodes. (1978). “Measuring the Efficiency of Decision-Making Units,” European Journal of Operational Research 2, 429–444.

    Google Scholar 

  • Färe, R. (1975). “Efficiency and the Production Function,” Zeitschrift für Nationalökonomie 35, 317–324.

    Google Scholar 

  • Färe, R., S. Grosskopf, and C.A.K. Lovell. (1985). The Measurement of Efficiency of Production. Boston: Kluwer-Nijhoff.

    Google Scholar 

  • Färe, R., S. Grosskopf and C.A.K. Lovell. (1986). “Scale Economies and Duality,” Journal of Economics (Zeitschrift für Nationalökonomie) 46(2), 175–182.

    Google Scholar 

  • Färe, R., S. Grosskopf, and C.A.K. Lovell. (1988). “Scale Elasticity and Scale Efficiency.” Journal of Institutional and Theoretical Economics (JITE) 144, 721–729.

    Google Scholar 

  • Färe, R., S. Grosskopf, and C.A.K. Lovell. (1994). Production Frontiers. Cambridge: Cambridge University Press.

    Google Scholar 

  • Färe, R. and C.A.K. Lovell. (1978). “Measuring the Technical Efficiency of Production,” Journal of Economic Theory 19, 150–162.

    Google Scholar 

  • Färe, R. and S. Grosskopf. (1994). “Estimation of Returns to Scale Using Data Envelopment Analysis: A Comment,” European Journal of Operations Research 79, 379–382.

    Google Scholar 

  • Farrell, M.J. (1957). “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society, Series A (General), 120 (III), 253–281 (290).

    Google Scholar 

  • Førsund, F.R. (1971). “A Note on the Technically Optimal Scale in Inhomogeneous Production Functions,” Swedish Journal of Economics 73, 225–240.

    Google Scholar 

  • Førsund, F.R. (1995). “Engineering Production Functions: Chocolate Production Revisited.” Paper presented at the centennial for Ragnar Frisch, March 3–5, 1995, published as Memorandum from Department of Economics, University of Oslo, No. 31, November 1995.

  • Førsund, F.R. and E. Hernaes. (1994). “A Comparative Analysis of Ferry Transport in Norway.” In A. Charnes, W.W. Cooper, A.Y. Lewin, and L.M. Seiford (eds.), Data Envelopment Analysis: Theory, Methodology, and Applications. Boston: Kluwer Academic Publishers, 285–311.

    Google Scholar 

  • Førsund, F.R. and L. Hjalmarsson. (1974). “On the Measurement of Productive Efficiency,” Swedish Journal of Economics 76, (2), 141–154.

    Google Scholar 

  • Førsund, F.R. and L. Hjalmarsson. (1979). “Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants.” Economic Journal 89, 294–315.

    Google Scholar 

  • Førsund, F.R. and L. Hjalmarsson. (1987). Analyses of Indusrial Structure: A Putty-Clay Approach. Stockholm: Almqvist & Wiksell International.

    Google Scholar 

  • Førsund, F.R. and L. Hjalmarsson. (1995). “Exploring Scale Elasticity Values of Piecewise Linear Technologies.” Paper presented at the New England Conference on Efficiency and Productivity, November 23–24, 1995, University of New England, Armidale, Australia.

    Google Scholar 

  • Frisch, R. (1965). Theory of Production. Dordrecht: D. Reidel.

    Google Scholar 

  • Panzar, J.C. and R.D. Willig. (1977). “Economies of Scale in Multi-Output Production,” Quarterly Journal of Economics XLI, 481–493.

    Google Scholar 

  • Rangan, N., R. Grabowski, H.Y. Aly, and C. Pasurka. (1988). “The Technical Efficiency of U.S. Banks,” Economics Letters 28, 169–175.

    Google Scholar 

  • Shephard, R.W. (1970). Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Starrett, D.A. (1977). “Measuring Returns to Scale in the Aggregate, and the Scale Effect of Public Goods,” Econometrica 45, 1439–1455.

    Google Scholar 

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Førsund, F.R. On the calculation of the scale elasticity in DEA models. J Prod Anal 7, 283–302 (1996). https://doi.org/10.1007/BF00157045

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