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Marginal Rates and Elasticities of Substitution with Additive Models in DEA

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  • W. Cooper
  • Dr. Park
  • Professor Ciurana

Abstract

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency—as in standard versions of additive models. Copyright Kluwer Academic Publishers 2000

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  • W. Cooper & Dr. Park & Professor Ciurana, 2000. "Marginal Rates and Elasticities of Substitution with Additive Models in DEA," Journal of Productivity Analysis, Springer, vol. 13(2), pages 105-123, March.
    • Handle: RePEc:kap:jproda:v:13:y:2000:i:2:p:105-123
    DOI: 10.1023/A:1007896629828
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    References listed on IDEAS

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    1. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    2. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
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    Cited by:

    1. Amineh Ghazi & Farhad Hosseinzadeh Lotfı & Masoud Sanei, 2022. "Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming," Operational Research, Springer, vol. 22(1), pages 165-198, March.
    2. Cooper, W. W. & Seiford, Lawrence M. & Thanassoulis, Emmanuel & Zanakis, Stelios H., 2004. "DEA and its uses in different countries," European Journal of Operational Research, Elsevier, vol. 154(2), pages 337-344, April.
    3. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    4. Patrick Brockett & William Cooper & Honghui Deng & Linda Golden & T. Ruefli, 2004. "Using DEA to Identify and Manage Congestion," Journal of Productivity Analysis, Springer, vol. 22(3), pages 207-226, November.
    5. Chia-Yen Lee, 2017. "Directional marginal productivity: a foundation of meta-data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 544-555, May.
    6. 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.
    7. Giovanni Dosi & Marco Grazzi & Luigi Marengo & Simona Settepanella, 2016. "Production Theory: Accounting for Firm Heterogeneity and Technical Change," Journal of Industrial Economics, Wiley Blackwell, vol. 64(4), pages 875-907, December.
    8. Brockett, Patrick L. & Cooper, W.W. & Golden, Linda L. & Kumbhakar, Subal C. & Kwinn Jr., Michael J. & Layton, Brian & Parker, Barnett R., 2008. "Estimating elasticities with frontier and other regressions in evaluating two advertising strategies for US Army recruiting," Socio-Economic Planning Sciences, Elsevier, vol. 42(1), pages 1-17, March.
    9. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    10. A. Ghazi & F. Hosseinzadeh Lotfi, 2023. "Marginal rates in DEA using defining hyperplanes of PPS with CRS technology," Operational Research, Springer, vol. 23(1), pages 1-37, March.
    11. Sueyoshi, Toshiyuki & Yuan, Yan, 2016. "Marginal Rate of Transformation and Rate of Substitution measured by DEA environmental assessment: Comparison among European and North American nations," Energy Economics, Elsevier, vol. 56(C), pages 270-287.
    12. Prior, Diego & Surroca, Jordi, 2006. "Strategic groups based on marginal rates: An application to the Spanish banking industry," European Journal of Operational Research, Elsevier, vol. 170(1), pages 293-314, April.
    13. Vigeant, Stéphane, 2016. "From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scaleAuthor-Name: Ouellette, Pierre," European Journal of Operational Research, Elsevier, vol. 253(3), pages 880-887.
    14. Sueyoshi, Toshiyuki & Goto, Mika, 2012. "Returns to Scale, Damages to Scale, Marginal Rate of Transformation and Rate of Substitution in DEA Environmental Assessment," Energy Economics, Elsevier, vol. 34(4), pages 905-917.
    15. Asmild, Mette & Paradi, Joseph C. & Reese, David N., 2006. "Theoretical perspectives of trade-off analysis using DEA," Omega, Elsevier, vol. 34(4), pages 337-343, August.
    16. Ramón Sala-Garrido & Manuel Mocholí-Arce & María Molinos-Senante & Alexandros Maziotis, 2021. "Comparing Operational, Environmental and Eco-Efficiency of Water Companies in England and Wales," Energies, MDPI, vol. 14(12), pages 1-14, June.
    17. Cooper, William W. & Ruiz, Jose L. & Sirvent, Inmaculada, 2007. "Choosing weights from alternative optimal solutions of dual multiplier models in DEA," European Journal of Operational Research, Elsevier, vol. 180(1), pages 443-458, July.
    18. Kaoru Tone & Biresh Sahoo, 2006. "Re-examining scale elasticity in DEA," Annals of Operations Research, Springer, vol. 145(1), pages 69-87, July.
    19. Sala-Garrido, Ramon & Mocholi-Arce, Manuel & Maziotis, Alexandros & Molinos-Senante, María, 2023. "The carbon and production performance of water utilities: Evidence from the English and Welsh water industry," Structural Change and Economic Dynamics, Elsevier, vol. 64(C), pages 292-300.
    20. Adler, Nicole & Volta, Nicola, 2016. "Accounting for externalities and disposability: A directional economic environmental distance function," European Journal of Operational Research, Elsevier, vol. 250(1), pages 314-327.
    21. Usman Akbar & Muhammad Asif Khan & Marryum Akmal & Éva Zsuzsanna Tóth Naárné & Judit Oláh, 2020. "Trade-Offs for the Optimal Energy Efficiency of Road Transportation: Domestic Cases in Developing Countries," Energies, MDPI, vol. 13(24), pages 1-14, December.

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