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Multi-equation modelling of desirable and undesirable outputs satisfying the materials balance

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  • Finn R. Førsund

    (University of Oslo)

Abstract

The key feature when modelling joint production of intended outputs and unintended residuals is that the latter stem from the use of material inputs. A multi-equation model building on the factorially determined multi-output model of classical production theory satisfies the materials balance that tells us that the mass contained in inputs cannot disappear, but must turn up in the desirable outputs or end up as residuals. In this model, potentially complex technical relationships are simplified to express each of the intended outputs and the residuals as functions of the same set of inputs. Serious problems with the single-equation models most often found in the literature are demonstrated. Abatement activity in the form of end of pipe is added, and an optimal planning solution is derived using the concept of an environmental damage function for the impact of discharge of residuals into the natural environment. It is shown that the traditional environmental policy instruments, like direct regulation restricting the amount of undesirable residuals discharged to the environment, a Pigou tax on pollutants, and cap and trade, all function well. Extending the multi-equation model to allow for inefficiency, three efficiency measures are introduced: desirable output efficiency, residuals efficiency, and abatement efficiency. It is conjectured that these measures can be estimated independently using the DEA model.

Suggested Citation

  • Finn R. Førsund, 2018. "Multi-equation modelling of desirable and undesirable outputs satisfying the materials balance," Empirical Economics, Springer, vol. 54(1), pages 67-99, February.
  • Handle: RePEc:spr:empeco:v:54:y:2018:i:1:d:10.1007_s00181-016-1219-9
    DOI: 10.1007/s00181-016-1219-9
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    3. Yicheol Han & Stephan J. Goetz & Claudia Schmidt, 2021. "Visualizing Spatial Economic Supply Chains to Enhance Sustainability and Resilience," Sustainability, MDPI, vol. 13(3), pages 1-15, February.
    4. Li, Hai-ling & Zhu, Xue-hong & Chen, Jin-yu & Jiang, Fei-tao, 2019. "Environmental regulations, environmental governance efficiency and the green transformation of China's iron and steel enterprises," Ecological Economics, Elsevier, vol. 165(C), pages 1-1.
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    7. Fang, Lei, 2020. "Opening the “black box” of environmental production technology in a nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 769-780.
    8. Jean-Philippe Boussemart & Hervé Leleu & Zhiyang Shen & Vivian Valdmanis, 2020. "Performance analysis for three pillars of sustainability," Journal of Productivity Analysis, Springer, vol. 53(3), pages 305-320, June.
    9. Xian, Yujiao & Wang, Ke & Wei, Yi-Ming & Huang, Zhimin, 2019. "Would China’s power industry benefit from nationwide carbon emission permit trading? An optimization model-based ex post analysis on abatement cost savings," Applied Energy, Elsevier, vol. 235(C), pages 978-986.
    10. Juan Aparicio & Magdalena Kapelko & Lidia Ortiz, 2021. "Modelling environmental inefficiency under a quota system," Operational Research, Springer, vol. 21(2), pages 1097-1124, June.
    11. Andreas Eder, 2021. "Environmental efficiency measurement when producers control pollutants under heterogeneous conditions: a generalization of the materials balance approach," Working Papers 752021, University of Natural Resources and Life Sciences, Vienna, Department of Economics and Social Sciences, Institute for Sustainable Economic Development.
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    14. Alexander Alexeev & Mikhail Sokolov, 2011. "A Note on Indices of Return," EUSP Department of Economics Working Paper Series Ec-02/11, European University at St. Petersburg, Department of Economics, revised 21 Feb 2011.
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    More about this item

    Keywords

    Desirable and undesirable outputs; Materials balance; Factorially determined multi-output production; Abatement; Efficiency measures; DEA;
    All these keywords.

    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General

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