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A Scale Elasticity Measure for Directional Distance Function and its Dual: Theory and DEA Estimation

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In this paper we focus on scale elasticity measure based on directional distance function for multi-output-multi-input technologies, explore its fundamental properties and show its equivalence with the input oriented and output oriented scale elasticity measures. We also establish duality relationship between the scale elasticity measure based on the directional distance function with scale elasticity measure based on the profit function. Finally, we discuss the estimation issues of the scale elasticity based on the directional distance function via the DEA estimator.

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File URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP072012.pdf
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Paper provided by School of Economics, University of Queensland, Australia in its series CEPA Working Papers Series with number WP072012.

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Date of creation: 2012
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Handle: RePEc:qld:uqcepa:83

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  1. Fukuyama, Hirofumi, 2003. "Scale characterizations in a DEA directional technology distance function framework," European Journal of Operational Research, Elsevier, Elsevier, vol. 144(1), pages 108-127, January.
  2. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 62(1), pages 74-84, October.
  3. Hanoch, Giora, 1975. "The Elasticity of Scale and the Shape of Average Costs," American Economic Review, American Economic Association, American Economic Association, vol. 65(3), pages 492-97, June.
  4. Valentin Zelenyuk, 2011. "A Note on Equivalences in Measuring Returns to Scale in Multi-output-multi-input Technologies," CEPA Working Papers Series, School of Economics, University of Queensland, Australia WP052011, School of Economics, University of Queensland, Australia.
  5. Banker, R. D. & Bardhan, I. & Cooper, W. W., 1996. "A note on returns to scale in DEA," European Journal of Operational Research, Elsevier, Elsevier, vol. 88(3), pages 583-585, February.
  6. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, Elsevier, vol. 168(2), pages 425-449, January.
  7. Golany, Boaz & Yu, Gang, 1997. "Estimating returns to scale in DEA," European Journal of Operational Research, Elsevier, Elsevier, vol. 103(1), pages 28-37, November.
  8. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, Elsevier, vol. 126(2), pages 469-492, June.
  9. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(2), pages 407-419, August.
  10. Fukuyama, Hirofumi, 2000. "Returns to scale and scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 125(1), pages 93-112, August.
  11. Førsund, Finn R. & Hjalmarsson, Lennart, 1978. "Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Working Paper Series, Research Institute of Industrial Economics 17, Research Institute of Industrial Economics.
  12. 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, Springer, vol. 28(1), pages 45-56, October.
  13. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  14. Panzar, John C & Willig, Robert D, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 91(3), pages 481-93, August.
  15. Petros Hadjicostas & Andreas Soteriou, 2010. "Different orders of one-sided scale elasticities in multi-output production," Journal of Productivity Analysis, Springer, Springer, vol. 33(2), pages 147-167, April.
  16. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 17(1), pages 35-44, July.
  17. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, INFORMS, vol. 30(9), pages 1078-1092, September.
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Cited by:
  1. Carvalho, Pedro & Marques, Rui Cunha, 2014. "Computing economies of vertical integration, economies of scope and economies of scale using partial frontier nonparametric methods," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(1), pages 292-307.

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