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Russell and slack-based measures of efficiency: A unifying framework

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  • Zelenyuk, Valentin
  • Zhao, Shirong

Abstract

Some of the popular technical efficiency measures are not able to account for potential slacks in inputs or outputs and may misrepresent the degree of inefficiency pertinent to firms, industries, and countries when compared to their peers. A wide range of methods have been proposed in the literature over the last four decades to address this important issue. The precise relationship among many of these methods is not always clear. In this paper we briefly review this literature and propose a unifying framework for such measures, one which embraces many other important approaches in efficiency measurement (including slack-based measures, Russell efficiency measures, etc.) as special cases in this general framework. A numerical example is also presented to illustrate the differences among the special cases of the efficiency measures, complemented with the computational code in R for practitioners interested in using these models.

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  • Zelenyuk, Valentin & Zhao, Shirong, 2024. "Russell and slack-based measures of efficiency: A unifying framework," European Journal of Operational Research, Elsevier, vol. 318(3), pages 867-876.
    • Handle: RePEc:eee:ejores:v:318:y:2024:i:3:p:867-876
    DOI: 10.1016/j.ejor.2024.06.014
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    1. Dmitruk, Andrei V. & Koshevoy, Gleb A., 1991. "On the existence of a technical efficiency criterion," Journal of Economic Theory, Elsevier, vol. 55(1), pages 121-144, October.
    2. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Manh Pham & Léopold Simar & Valentin Zelenyuk, 2024. "Statistical Inference for Aggregation of Malmquist Productivity Indices," Operations Research, INFORMS, vol. 72(4), pages 1615-1629, July.
    4. Färe, Rolf & Zelenyuk, Valentin, 2020. "Profit efficiency: Generalization, business accounting and the role of convexity," Economics Letters, Elsevier, vol. 196(C).
    5. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    6. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    7. Léopold Simar & Valentin Zelenyuk, 2018. "Central Limit Theorems for Aggregate Efficiency," Operations Research, INFORMS, vol. 66(1), pages 137-149, January.
    8. Ruggiero, John, 1996. "Efficiency of Educational Production: An Analysis of New York School Districts," The Review of Economics and Statistics, MIT Press, vol. 78(3), pages 499-509, August.
    9. Thanassoulis, E. & Dyson, R. G., 1992. "Estimating preferred target input-output levels using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 56(1), pages 80-97, January.
    10. Ruggiero, John & Bretschneider, Stuart, 1998. "The weighted Russell measure of technical efficiency," European Journal of Operational Research, Elsevier, vol. 108(2), pages 438-451, July.
    11. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    12. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2015. "When Bias Kills The Variance: Central Limit Theorems For Dea And Fdh Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 31(2), pages 394-422, April.
    13. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    14. Rolf Färe & Xinju He & Sungko Li & Valentin Zelenyuk, 2019. "A Unifying Framework for Farrell Profit Efficiency Measurement," Operations Research, INFORMS, vol. 67(1), pages 183-197, January.
    15. Zieschang, Kimberly D., 1984. "An extended farrell technical efficiency measure," Journal of Economic Theory, Elsevier, vol. 33(2), pages 387-396, August.
    16. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2015. "Decomposing profit efficiency using a slack-based directional distance function," European Journal of Operational Research, Elsevier, vol. 247(1), pages 335-337.
    17. Sickles,Robin C. & Zelenyuk,Valentin, 2019. "Measurement of Productivity and Efficiency," Cambridge Books, Cambridge University Press, number 9781107036161, September.
    18. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    19. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    20. Färe, Rolf & Grosskopf, Shawna, 2010. "Directional distance functions and slacks-based measures of efficiency," European Journal of Operational Research, Elsevier, vol. 200(1), pages 320-322, January.
    21. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    22. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    23. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    More about this item

    Keywords

    Russell efficiency; Slack-based efficiency; Non-parametric efficiency estimators; Data Envelopment Analysis;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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