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Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions

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  • Podinovski, Victor V.
  • Kuosmanen, Timo

Abstract

The treatment of undesirable (bad) outputs in models of efficiency and productivity analysis often requires replacing the assumption of free disposability of outputs by their weak disposability. In a recent publication the authors showed that the Kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs. In this paper we relax the assumption of full convexity and consider two further possibilities: the case in which only the output sets are assumed convex and the case in which no convexity is assumed at all. In the first case we show that, although the traditional Shephard technology of nonparametric production analysis satisfies the assumption of convex output sets, it is larger than necessary. Based on the minimum extrapolation principle, we develop a correct model that is based on the assumed axioms. The second case leads to the development of a weakly disposable analogue of the free disposable hull. To complete our study, we give a full axiomatic definition of the Shephard technology.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 211 (2011)
Issue (Month): 3 (June)
Pages: 577-585

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Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:577-585

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Data envelopment analysis Nonparametric productivity analysis Environmental performance Undesirable outputs Non-convex technologies;

References

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  1. Timo Kuosmanen & Laurens Cherchye & Timo Sipiläinen, 2003. "The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms," Microeconomics 0312006, EconWPA, revised 18 Dec 2003.
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  17. Kuosmanen, Timo, 2001. "DEA with efficiency classification preserving conditional convexity," European Journal of Operational Research, Elsevier, vol. 132(2), pages 326-342, July.
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Citations

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Cited by:
  1. Halkos, George & Tzeremes, Nickolaos, 2012. "Economic growth and environmental efficiency: Evidence from U.S. regions," MPRA Paper 42675, University Library of Munich, Germany.
  2. Bian, Yiwen & He, Ping & Xu, Hao, 2013. "Estimation of potential energy saving and carbon dioxide emission reduction in China based on an extended non-radial DEA approach," Energy Policy, Elsevier, vol. 63(C), pages 962-971.
  3. Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.
  4. 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.
  5. George Halkos & Nickolaos Tzeremes, 2013. "National culture and eco-efficiency: an application of conditional partial nonparametric frontiers," Environmental Economics and Policy Studies, Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(4), pages 423-441, October.
  6. Sueyoshi, Toshiyuki & Goto, Mika, 2012. "Environmental assessment by DEA radial measurement: U.S. coal-fired power plants in ISO (Independent System Operator) and RTO (Regional Transmission Organization)," Energy Economics, Elsevier, vol. 34(3), pages 663-676.
  7. Hervé Leleu, 2013. "Duality of Shephard’s weakly disposable technology under a directional output distance function," Working Papers 2013-ECO-03, IESEG School of Management.
  8. Halkos, George & Tzeremes, Nickolaos, 2012. "Regional economic growth and environmental efficiency in greenhouse emissions: A conditional directional distance function approach," MPRA Paper 40015, University Library of Munich, Germany.
  9. Thanassoulis, Emmanuel & Kortelainen, Mika & Allen, Rachel, 2012. "Improving envelopment in Data Envelopment Analysis under variable returns to scale," European Journal of Operational Research, Elsevier, vol. 218(1), pages 175-185.
  10. Mircea Epure & Esteban Lafuente, 2014. "Monitoring Bank Performance in the Presence of Risk," Working Papers 613, Barcelona Graduate School of Economics.
  11. Chang, Dong-Shang & Liu, Wenrong & Yeh, Li-Ting, 2013. "Incorporating the learning effect into data envelopment analysis to measure MSW recycling performance," European Journal of Operational Research, Elsevier, vol. 229(2), pages 496-504.
  12. Halkos, George & Sundström, Aksel & Tzeremes, Nickolaos, 2013. "Environmental performance and quality of governance: A non-parametric analysis of the NUTS 1-regions in France, Germany and the UK," MPRA Paper 48890, University Library of Munich, Germany.
  13. Sueyoshi, Toshiyuki & Goto, Mika, 2012. "Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry," European Journal of Operational Research, Elsevier, vol. 216(3), pages 668-678.

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