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Duality of weakly disposable technology

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  • Kuosmanen, Timo
  • Kazemi Matin, Reza

Abstract

The axiom of weak disposability is frequently imposed in data envelopment analysis (DEA) models involving undesirable outputs such as pollution. This paper sheds new light on the economic interpretation of weak disposability by developing dual formulations of the weakly disposable DEA technology. We find that the economic implications of weak disposability on the multiplier DEA problem are two-fold: (1) the shadow prices of the undesirable outputs can be positive or negative, and (2) the economic loss of the benchmark cannot exceed the suck cost of the inputs. We interpret the second implications as a limited liability condition. The dual formulations developed in this paper enable one to estimate shadow prices of the undesirable outputs using the weakly disposable technology. The insights gained are illustrated by a numerical example and an empirical application to the US power plants.

Suggested Citation

  • Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:5:p:504-512
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    Cited by:

    1. Arabi, Behrouz & Munisamy, Susila & Emrouznejad, Ali, 2015. "A new slacks-based measure of Malmquist–Luenberger index in the presence of undesirable outputs," Omega, Elsevier, vol. 51(C), pages 29-37.
    2. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "Economic growth and environmental efficiency: Evidence from US regions," Economics Letters, Elsevier, vol. 120(1), pages 48-52.
    3. Berre, David & Boussemart, Jean-Philippe & Leleu, Hervé & Tillard, Emmanuel, 2013. "Economic value of greenhouse gases and nitrogen surpluses: Society vs farmers’ valuation," European Journal of Operational Research, Elsevier, vol. 226(2), pages 325-331.
    4. Zuoren Sun & Rundong Luo & Dequn Zhou, 2015. "Optimal Path for Controlling Sectoral CO 2 Emissions Among China’s Regions: A Centralized DEA Approach," Sustainability, MDPI, Open Access Journal, vol. 8(1), pages 1-20, December.
    5. Leleu, Hervé, 2013. "Shadow pricing of undesirable outputs in nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 231(2), pages 474-480.
    6. George Halkos & Nickolaos Tzeremes, 2012. "Measuring German regions’ environmental efficiency: a directional distance function approach," Letters in Spatial and Resource Sciences, Springer, vol. 5(1), pages 7-16, March.
    7. Fang, Lei, 2015. "Congestion measurement in nonparametric analysis under the weakly disposable technology," European Journal of Operational Research, Elsevier, vol. 245(1), pages 203-208.
    8. Jeanneaux, Philippe & Latruffe, Laure, 2016. "Modelling pollution-generating technologies in performance benchmarking: Recent developments, limits and future prospects in the nonparametric frameworkAuthor-Name: Dakpo, K. Hervé," European Journal of Operational Research, Elsevier, vol. 250(2), pages 347-359.
    9. Boussemart, Jean-Philippe & Leleu, Hervé & Shen, Zhiyang, 2017. "Worldwide carbon shadow prices during 1990–2011," Energy Policy, Elsevier, vol. 109(C), pages 288-296.
    10. Bretholt, Abraham & Pan, Jeh-Nan, 2013. "Evolving the latent variable model as an environmental DEA technology," Omega, Elsevier, vol. 41(2), pages 315-325.
    11. George Halkos & George Papageorgiou, 2016. "Spatial environmental efficiency indicators in regional waste generation: a nonparametric approach," Journal of Environmental Planning and Management, Taylor & Francis Journals, vol. 59(1), pages 62-78, January.
    12. Rødseth, Kenneth Løvold, 2013. "Capturing the least costly way of reducing pollution: A shadow price approach," Ecological Economics, Elsevier, vol. 92(C), pages 16-24.
    13. Picazo-Tadeo, Andrés J. & Beltrán-Esteve, Mercedes & Gómez-Limón, José A., 2012. "Assessing eco-efficiency with directional distance functions," European Journal of Operational Research, Elsevier, vol. 220(3), pages 798-809.
    14. Li, Tianxiang & Baležentis, Tomas & Makutėnienė, Daiva & Streimikiene, Dalia & Kriščiukaitienė, Irena, 2016. "Energy-related CO2 emission in European Union agriculture: Driving forces and possibilities for reduction," Applied Energy, Elsevier, pages 682-694.
    15. Liu, Wenbin & Zhou, Zhongbao & Ma, Chaoqun & Liu, Debin & Shen, Wanfang, 2015. "Two-stage DEA models with undesirable input-intermediate-outputs," Omega, Elsevier, vol. 56(C), pages 74-87.
    16. Xu, Jiuping & Li, Zongmin, 2012. "A review on Ecological Engineering based Engineering Management," Omega, Elsevier, vol. 40(3), pages 368-378.
    17. Halkos, George & Tzeremes, Nickolaos, 2013. "An additive two-stage DEA approach creating sustainability efficiency indexes," MPRA Paper 44231, University Library of Munich, Germany.
    18. repec:gam:jsusta:v:8:y:2015:i:1:p:28:d:61444 is not listed on IDEAS
    19. repec:eee:eneeco:v:66:y:2017:i:c:p:279-289 is not listed on IDEAS
    20. repec:wut:journl:v:3:y:2017:p:5-20:id:1309 is not listed on IDEAS
    21. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    22. Chen, Lei & Wang, Ying-Ming & Lai, Fujun, 2017. "Semi-disposability of undesirable outputs in data envelopment analysis for environmental assessments," European Journal of Operational Research, Elsevier, vol. 260(2), pages 655-664.
    23. Zhou, P. & Ang, B.W. & Wang, H., 2012. "Energy and CO2 emission performance in electricity generation: A non-radial directional distance function approach," European Journal of Operational Research, Elsevier, vol. 221(3), pages 625-635.

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