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A Unifying Framework for Farrell Profit Efficiency Measurement

Author

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  • Rolf Färe

    (Department of Economics, Oregon State University, Corvallis, Oregon 97331)

  • Xinju He

    (Department of Economics, Hong Kong Baptist University, Kowloon Tong, Hong Kong)

  • Sungko Li

    (Department of Economics, Hong Kong Baptist University, Kowloon Tong, Hong Kong)

  • Valentin Zelenyuk

    (School of Economics and Centre for Efficiency and Productivity Analysis, University of Queensland, St. Lucia, Queensland 4072, Australia)

Abstract

Measuring profit efficiency is a challenging task, and many different approaches have been suggested. This paper synthesizes existing approaches and develops a general Farrell-type approach of the profit efficiency measurement. Our derivations unveil new and useful relationships between existing measures and the proposed new Farrell-type measures. In addition, this helps us establish a generalized and unifying framework for studying efficiency behavior of firms, where the profit efficiency measure satisfies desirable properties and contains the conventional Farrell measures of technical efficiency and allocative efficiency as multiplicative components. A new component of the decomposition of profit efficiency, which we call the revenue-efficient allocative efficiency measure , is introduced to identify the necessary changes of input scale and input mix in addition to output changes. The proposed new approach also encompasses and is coherent with profit-maximizing behavior as a benchmark case.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:1:p:183-197
    DOI: 10.1287/opre.2018.1770
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    Cited by:

    1. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Färe, Rolf & Zelenyuk, Valentin, 2020. "Profit efficiency: Generalization, business accounting and the role of convexity," Economics Letters, Elsevier, vol. 196(C).
    3. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.
    4. Robin C. Sickles & Valentin Zelenyuk, 2021. "Response to Review Article by Bert Balk on Measurement of Productivity and Efficiency: Theory and Practice," International Productivity Monitor, Centre for the Study of Living Standards, vol. 41, pages 153-156, Fall.
    5. 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.
    6. Zhou, Xun & Kuosmanen, Timo, 2020. "What drives decarbonization of new passenger cars?," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1043-1057.
    7. Wen, Yao & An, Qingxian & Gong, Yeming & Wu, Pengkun, 2024. "Structural rearrangement of the network system from an efficiency perspective: A silver lining of profit improvement," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1001-1011.
    8. Rolf Färe & Valentin Zelenyuk, 2021. "Sequential data envelopment analysis," Annals of Operations Research, Springer, vol. 300(1), pages 307-312, May.
    9. 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.
    10. Zhichao Wang & Valentin Zelenyuk, 2021. "Performance Analysis of Hospitals in Australia and its Peers: A Systematic Review," CEPA Working Papers Series WP012021, School of Economics, University of Queensland, Australia.
    11. Bao Hoang Nguyen & Robin C. Sickles & Valentin Zelenyuk, 2022. "Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 129-171, Springer.
    12. Ayouba, Kassoum & Boussemart, Jean-Philippe & Lefer, Henri-Bertrand & Leleu, Hervé & Parvulescu, Raluca, 2022. "An indirect, Luenberger approach to price performance," International Journal of Production Economics, Elsevier, vol. 244(C).
    13. Rolf Färe & Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Sequences in Hilbert Spaces," CEPA Working Papers Series WP132019, School of Economics, University of Queensland, Australia.
    14. Valentin Zelenyuk, 2021. "Performance Analysis: Economic Foundations & Trends," CEPA Working Papers Series WP162021, School of Economics, University of Queensland, Australia.
    15. Camanho, Ana Santos & Silva, Maria Conceicao & Piran, Fabio Sartori & Lacerda, Daniel Pacheco, 2024. "A literature review of economic efficiency assessments using Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 315(1), pages 1-18.
    16. Valentin Zelenyuk, 2018. "Profit Efficiency, DEA, FDH and Big Data," CEPA Working Papers Series WP042018, School of Economics, University of Queensland, Australia.
    17. Kok Fong See & Shawna Grosskopf & Vivian Valdmanis & Valentin Zelenyuk, 2021. "What do we know from the vast literature on efficiency and productivity in healthcare? A Systematic Review and Bibliometric Analysis," CEPA Working Papers Series WP072021, School of Economics, University of Queensland, Australia.
    18. Bao Hoang Nguyen & Valentin Zelenyuk, 2021. "Aggregate efficiency of industry and its groups: the case of Queensland public hospitals," Empirical Economics, Springer, vol. 60(6), pages 2795-2836, June.
    19. Zhichao Wang & Bao Hoang Nguyen & Valentin Zelenyuk, 2024. "Performance analysis of hospitals in Australia and its peers: a systematic and critical review," Journal of Productivity Analysis, Springer, vol. 62(2), pages 139-173, October.
    20. Mike Tsionas & Valentin Zelenyuk, 2021. "Goodness-of-fit in Optimizing Models of Production: A Generalization with a Bayesian Perspective," CEPA Working Papers Series WP182021, School of Economics, University of Queensland, Australia.
    21. Cheng, Louis T.W. & Lee, Shu Kam & Li, Sung Ko & Tsang, Chun Kei, 2023. "Understanding resource deployment efficiency for ESG and financial performance: A DEA approach," Research in International Business and Finance, Elsevier, vol. 65(C).
    22. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2020. "A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system," Omega, Elsevier, vol. 95(C).
    23. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    24. Ram Pratap Sinha, 2021. "Profit Benchmarking of Indian General Insurance Companies," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 7, pages 73-92.
    25. Rolf Färe & Valentin Zelenyuk, 2020. "Profit Efficiency and its Estimation," CEPA Working Papers Series WP072020, School of Economics, University of Queensland, Australia.

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