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Scale Efficiency and Homotheticity: Equivalence of Primal and Dual Measures

  • Valentin Zelenyuk


    (CEPA - School of Economics, The University of Queensland)

We address the issue of equivalence of primal and dual measures of scale efficiency in general production theory framework. We find that particular types of homotheticity of technologies, which we refer to here as scale homotheticity, provide necessary and sufficient condition for such equivalence. We also identify the case when the scale homotheticity is equivalent to the homothetic structure from Shephard (1970).

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Paper provided by School of Economics, University of Queensland, Australia in its series CEPA Working Papers Series with number WP022013.

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Date of creation: Feb 2013
Date of revision:
Handle: RePEc:qld:uqcepa:85
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  1. Leopold Simar & Valentin Zelenyuk, 2008. "Stochastic FDH/DEA estimators for Frontier Analysis," Discussion Papers 8, Kyiv School of Economics.
  2. Simar, Leopold & Zelenyuk, Valentin, 2004. "On testing equality of distributions of technical efficiency scores," MPRA Paper 28003, University Library of Munich, Germany.
  3. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer, vol. 11(3), pages 629-641.
  4. 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.
  5. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series WP062011, School of Economics, University of Queensland, Australia.
  6. Fare, Rolf & Grosskopf, Shawna, 1985. " Nonparametric Cost Approach to Scale Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 87(4), pages 594-604.
  7. Léopold Simar & Valentin Zelenyuk, 2007. "Statistical inference for aggregates of Farrell-type efficiencies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1367-1394.
  8. Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
  9. Valentin Zelenyuk, 2013. "A Note on Equivalences in Measuring Returns to Scale," International Journal of Business and Economics, College of Business, and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 12(1), pages 85-89, June.
  10. Valentin Zelenyuk, 2012. "A Scale Elasticity Measure for Directional Distance Function and its Dual: Theory and DEA Estimation," CEPA Working Papers Series WP072012, School of Economics, University of Queensland, Australia.
  11. Chambers Robert G. & Fare Rolf, 1994. "Hicks' Neutrality and Trade Biased Growth: A Taxonomy," Journal of Economic Theory, Elsevier, vol. 64(2), pages 554-567, December.
  12. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
  13. Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
  14. Førsund, Finn R. & Hjalmarsson, Lennart, 1978. "Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Working Paper Series 17, Research Institute of Industrial Economics.
  15. Valentin Zelenyuk, 2011. "A Note on Equivalences in Measuring Returns to Scale in Multi-output-multi-input Technologies," CEPA Working Papers Series WP052011, School of Economics, University of Queensland, Australia.
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