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Scale efficiency and homotheticity: equivalence of primal and dual measures

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  • Valentin Zelenyuk

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Abstract

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 structures from Shephard (Theory of cost and production functions, Princeton studies in mathematical economics. Princeton University Press, Princeton, 1970 ). Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:42:y:2014:i:1:p:15-24
    DOI: 10.1007/s11123-013-0361-z
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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. Valentin Zelenyuk, 2013. "A Note on Equivalences in Measuring Returns to Scale," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 12(1), pages 85-89, June.
    3. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    4. 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.
    5. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    6. 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.
    7. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.
    8. Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
    9. Fare, Rolf & Li, Sung Ko, 2001. "A nonparametric test of translation homotheticity," Economics Letters, Elsevier, vol. 72(3), pages 341-345, September.
    10. Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 629-641.
    17. 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. Diewert, Erwin & Fox, Kevin J., 2014. "Decomposing Bjurek Productivity Indexes into Explanatory Factors," Economics working papers erwin_diewert-2014-32, Vancouver School of Economics, revised 30 Jun 2014.
    2. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2016. "Cost decompositions and the efficient subset," Omega, Elsevier, vol. 62(C), pages 123-130.
    3. Hideyuki Mizobuchi, 2017. "Productivity indexes under Hicks neutral technical change," Journal of Productivity Analysis, Springer, vol. 48(1), pages 63-68, August.
    4. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    5. Barnabé Walheer, 2019. "Disaggregation for efficiency analysis," Journal of Productivity Analysis, Springer, vol. 51(2), pages 137-151, June.
    6. Diewert, W. Erwin & Fox, Kevin J., 2017. "Decomposing productivity indexes into explanatory factors," European Journal of Operational Research, Elsevier, vol. 256(1), pages 275-291.
    7. Antonio Peyrache, 2014. "Hicks-Moorsteen versus Malmquist: a connection by means of a radial productivity index," Journal of Productivity Analysis, Springer, vol. 41(3), pages 435-442, June.
    8. Manh D. Pham & Léopold Simar & Valentin Zelenyuk, 2019. "Statistical Inference for Aggregation of Malmquist Productivity Indices," CEPA Working Papers Series WP082019, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    Production theory; Scale efficiency; Homotheticity; Duality theory; D24;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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