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Marginal Values and Returns to Scale for Nonparametric Production Frontiers

Author

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  • Victor V. Podinovski

    (School of Business and Economics, Loughborough University, Loughborough LE11 3TU, United Kingdom)

  • Robert G. Chambers

    (Department of Agricultural and Resource Economics, University of Maryland, College Park, Maryland 20742)

  • Kazim Baris Atici

    (Department of Business Administration, Hacettepe University, Ankara 06800, Turkey)

  • Iryna D. Deineko

    (Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom)

Abstract

We present a unifying linear programming approach to the calculation of various directional derivatives for a very large class of production frontiers of data envelopment analysis (DEA). Special cases of this include different marginal rates, the scale elasticity, and a spectrum of partial and mixed elasticity measures. Our development applies to any polyhedral production technology including, to name a few, the conventional variable and constant returns-to-scale DEA technologies, their extensions with weight restrictions, technologies with weakly disposable undesirable outputs, and network DEA models. Furthermore, our development provides a general method for characterization of returns to scale (RTS) in any polyhedral technology. The new approach effectively removes the need to develop bespoke models for the RTS characterization and calculation of marginal rates and elasticity measures for each particular technology.

Suggested Citation

  • Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:1:p:236-250
    DOI: 10.1287/opre.2015.1457
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    Cited by:

    1. Victor V. Podinovski & Ole Bent Olesen & Cláudia S. Sarrico, 2018. "Nonparametric Production Technologies with Multiple Component Processes," Operations Research, INFORMS, vol. 66(1), pages 282-300, January.
    2. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    3. Alireza Amirteimoori & Biresh K. Sahoo & Saber Mehdizadeh, 2023. "Data envelopment analysis for scale elasticity measurement in the stochastic case: with an application to Indian banking," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-36, December.
    4. Noah J Miller & Jason S Bergtold & Allen M Featherstone, 2019. "Economic elasticities of input substitution using data envelopment analysis," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-15, August.
    5. Mehdiloozad, Mahmood & Podinovski, Victor V., 2018. "Nonparametric production technologies with weakly disposable inputs," European Journal of Operational Research, Elsevier, vol. 266(1), pages 247-258.
    6. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Production technologies with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1164-1178.
    7. Lin, Winston T. & Chen, Yueh H. & Hung, TingShu, 2019. "A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology," European Journal of Operational Research, Elsevier, vol. 272(2), pages 766-779.
    8. Chen, Lei & Wang, Ying-Ming, 2020. "DEA target setting approach within the cross efficiency framework," Omega, Elsevier, vol. 96(C).
    9. Jean-Philippe Boussemart & Walter Briec & Raluca Parvulescu & Paola Ravelojaona, 2022. "$\Lambda$-Returns to Scale and Individual Minimum Extrapolation Principle," Papers 2212.04724, arXiv.org, revised Dec 2023.
    10. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    11. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2021. "Optimal solutions of multiplier DEA models," Journal of Productivity Analysis, Springer, vol. 56(1), pages 45-68, August.
    12. Mehdiloo, Mahmood & Podinovski, Victor V., 2019. "Selective strong and weak disposability in efficiency analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1154-1169.
    13. Silva, Elvira & Magalhães, Manuela, 2023. "Environmental efficiency, irreversibility and the shadow price of emissions," European Journal of Operational Research, Elsevier, vol. 306(2), pages 955-967.
    14. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "The structure of production technologies with ratio inputs and outputs," Journal of Productivity Analysis, Springer, vol. 57(3), pages 255-267, June.
    15. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2019. "Cone extensions of polyhedral production technologies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 736-743.
    16. Seda Busra Sarac & Kazim Baris Atici & Aydin Ulucan, 2022. "Elasticity measurement on multiple levels of DEA frontiers: an application to agriculture," Journal of Productivity Analysis, Springer, vol. 57(3), pages 313-324, June.
    17. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    18. Pham, Manh D. & Zelenyuk, Valentin, 2019. "Weak disposability in nonparametric production analysis: A new taxonomy of reference technology sets," European Journal of Operational Research, Elsevier, vol. 274(1), pages 186-198.
    19. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    20. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Multicomponent production technologies with restricted allocations of shared inputs and outputs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 274-289.
    21. Song, Malin & Wang, Jianlin & Zhao, Jiajia, 2023. "Effects of rising and extreme temperatures on production factor efficiency: Evidence from China's cities," International Journal of Production Economics, Elsevier, vol. 260(C).
    22. Podinovski, Victor V., 2019. "Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs," European Journal of Operational Research, Elsevier, vol. 279(1), pages 258-276.
    23. Afsharian, Mohsen & Podinovski, Victor V., 2018. "A linear programming approach to efficiency evaluation in nonconvex metatechnologies," European Journal of Operational Research, Elsevier, vol. 268(1), pages 268-280.

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