IDEAS home Printed from https://ideas.repec.org/p/ies/wpaper/e201303.html
   My bibliography  Save this paper

Duality of Shephard’s weakly disposable technology under a directional output distance function

Author

Listed:
  • Hervé Leleu

    (CNRS-LEM and IESEG School of Management)

Abstract

In a recent paper Kuosmanen and Matin (2011) have developed a dual formulation of the weakly disposable Kuosmanen’s technology (Kuosmanen, 2005). Their work sheds new light on the economic interpretation of weak disposability and allows estimation of shadow prices for undesirable/bad outputs. More precisely, they have derived the multiplier formulation for the Kuosmanen weakly disposable technology and have found a ‘limited liability condition’ as the economic interpretation of weak disposability. Considering further the traditional Shephard technology, they argued that: “Obviously, the duality theory of linear programming does not apply to the classic Shephard technology because it is generally non-convex. This explains why the dual formulations of the weakly disposable technology are currently unavailable” (p.505). We prove here that by considering a directional output distance function there exists a duality for the Shephard weakly disposable technology. Moreover it turns out with a clear, intuitive and relevant economic interpretation of the weak disposability axiom. Thanks to our dual framework, we finally provide an original proof of the existing relationship between weak disposability and returns to scale.

Suggested Citation

  • 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.
  • Handle: RePEc:ies:wpaper:e201303
    as

    Download full text from publisher

    File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=439255387_2013-ECO-03_Leleu.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rolf Färe & Shawna Grosskopf, 2007. "A Comment on Weak Disposability in Nonparametric Production Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(2), pages 535-538.
    2. F J Arcelus & P Arocena, 2005. "Productivity differences across OECD countries in the presence of environmental constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1352-1362, December.
    3. William L. Weber & Bruce Domazlicky, 2001. "Productivity Growth and Pollution in State Manufacturing," The Review of Economics and Statistics, MIT Press, vol. 83(1), pages 195-199, February.
    4. M. Murty & Surender Kumar & Kishore Dhavala, 2007. "Measuring environmental efficiency of industry: a case study of thermal power generation in India," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 38(1), pages 31-50, September.
    5. Kuosmanen, Timo & Post, Thierry, 2001. "Measuring economic efficiency with incomplete price information: With an application to European commercial banks," European Journal of Operational Research, Elsevier, vol. 134(1), pages 43-58, October.
    6. Jens Kjærsgaard & Niels Vestergaard & Kristiaan Kerstens, 2009. "Ecological Benchmarking to Explore Alternative Fishing Schemes to Protect Endangered Species by Substitution: The Danish Demersal Fishery in the North Sea," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 43(4), pages 573-590, August.
    7. Timo Kuosmanen & Victor Podinovski, 2008. "Weak Disposability in Nonparametric Production Analysis: Reply to Färe and Grosskopf," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(2), pages 539-545.
    8. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    9. Byung M. Jeon & Robin C. Sickles, 2004. "The role of environmental factors in growth accounting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(5), pages 567-591.
    10. Zhou, P. & Ang, B.W. & Poh, K.L., 2008. "Measuring environmental performance under different environmental DEA technologies," Energy Economics, Elsevier, vol. 30(1), pages 1-14, January.
    11. Atakelty Hailu & Terrence S. Veeman, 2001. "Non-parametric Productivity Analysis with Undesirable Outputs: An Application to the Canadian Pulp and Paper Industry," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(3), pages 605-616.
    12. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
    13. H Leleu, 2009. "Mixing DEA and FDH models together," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1730-1737, December.
    14. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    15. Rolf Färe & Shawna Grosskopf, 2003. "Nonparametric Productivity Analysis with Undesirable Outputs: Comment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1070-1074.
    16. Atakelty Hailu, 2003. "Nonparametric Productivity Analysis with Undesirable Outputs: Reply," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1075-1077.
    17. Isabelle Piot-Lepetit & Monique Moing, 2007. "Productivity and environmental regulation: the effect of the nitrates directive in the French pig sector," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 38(4), pages 433-446, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leleu, Hervé, 2013. "Shadow pricing of undesirable outputs in nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 231(2), pages 474-480.
    2. 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.
    3. Boussemart, Jean Philippe & Leleu, Hervé & Shen, Zhiyang, 2015. "Environmental growth convergence among Chinese regions," China Economic Review, Elsevier, vol. 34(C), pages 1-18.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leleu, Hervé, 2013. "Shadow pricing of undesirable outputs in nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 231(2), pages 474-480.
    2. George Halkos & Nickolaos Tzeremes, 2013. "National culture and eco-efficiency: an application of conditional partial nonparametric frontiers," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(4), pages 423-441, October.
    3. Halkos, George & Tzeremes, Nickolaos, 2013. "An additive two-stage DEA approach creating sustainability efficiency indexes," MPRA Paper 44231, University Library of Munich, Germany.
    4. 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.
    5. 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.
    6. 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.
    7. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, vol. 227(1), pages 182-189.
    8. Manh D. Pham & Valentin Zelenyuk, 2017. "Convexity, Disposability and Returns to Scale in Production Analysis," CEPA Working Papers Series WP042017, School of Economics, University of Queensland, Australia.
    9. Hervé Leleu & Albane Tarnaud, 2016. "The duality of Shephard’s weakly disposable technology," Working Papers 2016-EQM-06, IESEG School of Management.
    10. Dakpo, K & Jeanneaux, Philippe & Latruffee, Laure, 2015. "Empirical comparison of pollution generating technologies in nonparametric modelling: The case of greenhouse gas emissions in French sheep meat farming," 2015 Conference, August 9-14, 2015, Milan, Italy 211557, International Association of Agricultural Economists.
    11. Halkos, George & Tzeremes, Nickolaos, 2011. "Regional environmental efficiency and economic growth: NUTS2 evidence from Germany, France and the UK," MPRA Paper 33698, University Library of Munich, Germany.
    12. Halkos, George & Tzeremes, Nickolaos, 2011. "Measuring regional environmental efficiency: A directional distance function approach," MPRA Paper 32934, University Library of Munich, Germany.
    13. 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.
    14. Cherchye, Laurens & Rock, Bram De & Walheer, Barnabé, 2015. "Multi-output efficiency with good and bad outputs," European Journal of Operational Research, Elsevier, vol. 240(3), pages 872-881.
    15. Chu, Junfei & Shao, Caifeng & Emrouznejad, Ali & Wu, Jie & Yuan, Zhe, 2021. "Performance evaluation of organizations considering economic incentives for emission reduction: A carbon emission permit trading approach," Energy Economics, Elsevier, vol. 101(C).
    16. Juan Aparicio & Javier Barbero & Magdalena Kapelko & Jesus T. Pastor & Jose L. Zofio, 2016. "Environmental Productivity Change in World Air Emissions: A new Malmquist-Luenberger Index Approach," JRC Research Reports JRC104083, Joint Research Centre (Seville site).
    17. Halkos, George & Tzeremes, Nickolaos, 2011. "Kuznets curve and environmental performance: evidence from China," MPRA Paper 34312, University Library of Munich, Germany.
    18. Abad, Arnaud & Briec, Walter, 2019. "On the axiomatic of pollution-generating technologies: Non-parametric production analysis," European Journal of Operational Research, Elsevier, vol. 277(1), pages 377-390.
    19. 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.
    20. Qingxian An & Haoxun Chen & Jie Wu & Liang Liang, 2015. "Measuring slacks-based efficiency for commercial banks in China by using a two-stage DEA model with undesirable output," Annals of Operations Research, Springer, vol. 235(1), pages 13-35, December.

    More about this item

    Keywords

    DEA; Efficiency; Environmental studies; Resource management;
    All these keywords.

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ies:wpaper:e201303. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lies BOUTEN (email available below). General contact details of provider: https://edirc.repec.org/data/iesegfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.