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Scale Efficiency: Equivalence of Primal and Dual Measures

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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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  • Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:75
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    1. Fare, Rolf & Grosskopf, Shawna, 1985. " Nonparametric Cost Approach to Scale Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 87(4), pages 594-604.
    2. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
    3. 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.
    4. 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.
    5. Wesley D. Seitz, 1970. "The Measurement of Efficiency Relative to a Frontier Production Function," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(4), pages 505-511.
    6. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
    7. Kathy Hayes & Rolf Färe & Shawna Grosskopf & Finn R. Førsund & Almas Heshmati, 2001. "A note on decomposing the Malmquist productivity index by means of subvector homotheticity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 239-245.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

    1. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    2. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.

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