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Scale Efficiency: Equivalence of Primal and Dual Measures

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  • Valentin Zelenyuk

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

Abstract

In this paper we address an issue of equivalence of primal and dual measures of scale efficiency in general production theory framework. We find that particular types of homotheticity, which we refer to as scale homotheticity, provide necessary and sufficient condition for such equivalence. Specifically, we show that the input scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the input/cost oriented case. Similarly, the output scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the output/revenue oriented case. We also discuss the case when technology is both input scale homothetic and output scale homothetic, as well as indicate about some relationships of scale homotheticity with the homotheticity notions that have already been used in economic theory.

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File URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP092011.pdf
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Bibliographic Info

Paper provided by School of Economics, University of Queensland, Australia in its series CEPA Working Papers Series with number WP092011.

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Date of creation: 2011
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Handle: RePEc:qld:uqcepa:75

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  1. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 29(1), pages 62-98.
  2. Léopold Simar & Valentin Zelenyuk, 2007. "Statistical inference for aggregates of Farrell-type efficiencies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 22(7), pages 1367-1394.
  3. 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.
  4. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series, School of Economics, University of Queensland, Australia WP062011, School of Economics, University of Queensland, Australia.
  5. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, Springer, vol. 36(1), pages 33-53, August.
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Cited by:
  1. Valentin Zelenyuk, 2012. "Aggregation of Scale Efficiency," CEPA Working Papers Series, School of Economics, University of Queensland, Australia WP042012, School of Economics, University of Queensland, Australia.
  2. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, Springer, vol. 42(1), pages 15-24, August.

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