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Regulatory impact of environmental standards on the eco-efficiency of firms

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Journal of the Operational Research Society

Abstract

In this paper, we propose an approach to implement environmental standards into Data Envelopment Analysis (DEA) and in this way to measure their regulatory impact on eco-efficiency of firms. One standard feature of basic DEA models lies in the exogeneity of inputs, desirable and undesirable outputs. Taking into account the environmental constraints, we therefore apply the bounded variable DEA model. The regulatory impact is assessed as difference in eco-efficiency scores before and after fictive introduction of an environmental standard. Furthermore, we distinguish between weak and strong disposability of undesirable outputs and develop corresponding models. Assessing the regulatory impact of environmental standards in advance provides support for environmental policymakers in choosing appropriate instruments and in adjusting the intensity of regulation.

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Notes

  1. Korhonen and Luptacik (2004) define eco-efficiency according to Heinz Felsner: ‘We are looking for eco-efficient solutions such that the goods and services can be produced with less energy and resources and with less waste and emission’.

  2. For a survey of DEA studies in the area of energy and environment, see Zhou et al (2008).

  3. The same procedure can also be applied to derive the regulatory impact on allocative and overall efficiency, respectively.

  4. According to Shannon (1997), ‘there are several ways to describe the production possibility set of a firm, one refers to a transformation function f’.

  5. Limitation on absolute amount of undesirable outputs.

  6. Note that the regulatory impact can be computed for single firms (difference in single eco-efficiency scores) and the whole industry (difference in average eco-efficiency scores), given the sample remains unchanged.

  7. For a more detailed description of the analytical model framework the interested reader is referred to Korhonen and Luptacik (2004).

  8. The Undesirable Output Model from Cooper et al (2007) is provided in Appendix A.

  9. This condition was not specified by Shephard (1970), Kuosmanen (2005) and Podinovski and Kuosmanen (2011). We add it to describe the technology under weak disposability via inputs. Starting from a given technology (y g, y b)∈P(x), bad outputs need to be decreased to (θy b). Consequently, inputs need to be increased to ((1)/(θ)x).

  10. The advantage of a fictive sample is that the data can be used for all models presented in the paper and thus achieves comparability.

  11. For a graphical illustration, see Figure 2.

  12. DMU D is again projected on the intersection between efficiency frontier and environmental standard (). For a graphical illustration, see Figure 1.

  13. Recall that the environmental standard was set to (Emission/Output)⩽3.5.

  14. Moreover, it is interesting to compare the results of SBM Model B in Table 2 and SBM Model B weak in Table 4. Despite referring to the same firms and efficiency frontier, the average efficiency score decreased from 0.80 to 0.76 when taking into account weak disposability of undesirable outputs.

References

  • Ali A and Seiford L (1990). Translation invariance in data envelopment analysis. Operations Research Letters 9 (6): 403–405.

    Article  Google Scholar 

  • Charnes A, Cooper W and Rhodes E (1978). Measuring efficiency of decision making units. European Journal of Operational Research 2 (6): 429–444.

    Article  Google Scholar 

  • Cooper WW, Seiford LM and Tone K (2007). Data Envelopment Analysis: A Comprehensive Text With Models, Applications, References and DEA-Solver Software, 2nd edn. Springer: New York.

    Google Scholar 

  • Cropper M and Oates W (1992). Environmental economics: A survey. Journal of Economic Literature 30 (2): 675–740.

    Google Scholar 

  • Dudenhöffer F (1984). The regulation of intensities and productivities: Concepts in environmental policy. Journal of Institutional and Theoretical Economics 140 (2): 276–287.

    Google Scholar 

  • Dyson R, Allen R, Camanho A, Podinovski V, Sarrico C and Shale E (2001). Pitfalls and protocols in DEA. European Journal of Operational Research 132 (2): 245–259.

    Article  Google Scholar 

  • Färe R and Grosskopf S (2003). Nonparametric productivity analysis with undesirable outputs: Comment. American Journal of Agricultural Economics 85 (4): 1070–1074.

    Article  Google Scholar 

  • Färe R and Grosskopf S (2004). Modeling undesirable factors in efficiency evaluation: Comment. European Journal of Operational Research 157 (1): 242–245.

    Article  Google Scholar 

  • Färe R and Grosskopf S (2009). A comment on weak disposability in nonparametric production analysis. American Journal of Agricultural Economics 91 (2): 535–538.

    Article  Google Scholar 

  • Färe R and Logan J (1983). The rate-of-return regulated firm: Cost and production duality. The Bell Journal of Economics 14 (2): 405–414.

    Article  Google Scholar 

  • Färe R and Logan J (1992). The rate of return regulated version of Farrell efficiency. International Journal of Production Economics 27 (2): 161–165.

    Article  Google Scholar 

  • Färe R, Grosskopf S and Pasurka C (1986). Effects on relative efficiency in electric power generation due to environmental controls. Resources and Energy 8 (2): 167–184.

    Article  Google Scholar 

  • Färe R, Grosskopf S, Lovell K and Pasurka C (1989). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics 71 (1): 90–98.

    Article  Google Scholar 

  • Forsund F (2008). Good Modelling of Bad Outputs: Pollution and Multiple-Output Production. Memorandum, Department of Economics, University of Oslo.

    Google Scholar 

  • Golany B and Roll Y (1989). An application procedure for DEA. Omega: The International Journal of Management Science 17 (3): 237–250.

    Article  Google Scholar 

  • Golany B and Roll Y (1994). Incorporating standards via DEA. In: Charnes A, Cooper WW, Lewin AY and Seiford LM (eds). Data Envelopment Analysis: Theory, Methodology, And Applications. Kluwer: Boston, MA, pp 313–328.

    Chapter  Google Scholar 

  • Hailu A (2003). Nonparametric productivity analysis with undesirable outputs: Reply. American Journal of Agricultural Economics 85 (4): 1075–1077.

    Article  Google Scholar 

  • Hailu A and Veeman T (2001). Non-parametric productivity analysis with undesirable outputs: An application to the Canadian pulp and paper industry. American Journal of Agricultural Economics 83 (3): 605–616.

    Article  Google Scholar 

  • Helfand G (1991). Standards versus standards: The effects of different pollution restrictions. American Economic Review 81 (3): 622–634.

    Google Scholar 

  • Koopmans T (1951). Analysis of production as an efficient combination of activities. In: Koopmans T (ed). Activity Analysis of Production and Allocation. Wiley: New York, pp 33–97.

    Google Scholar 

  • Korhonen P and Luptacik M (2004). Eco-efficiency analysis of power plants: An extension of data envelopment analysis. European Journal of Operational Research 154 (2): 437–446.

    Article  Google Scholar 

  • Kuosmanen T (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics 87 (4): 1077–1082.

    Article  Google Scholar 

  • Lozano S and Gutierrez E (2011). Slacks-based measure of efficiency of airports with airplanes delays as undesirable outputs. Computers and Operations Research 38 (1): 131–139.

    Article  Google Scholar 

  • Luptacik M (2009). Mathematical Optimization and Economic Analysis. Springer: New York.

    Google Scholar 

  • Ouellette P and Vigeant S (2001). On the existence of a regulated production function. Journal of Economics 73 (2): 193–200.

    Article  Google Scholar 

  • Ouellette P, Quesnel J-P and Vigeant S (2009). Measuring Returns to Scale in DEA Models when the Firm is Regulated, http://www.wise.xmu.edu.cn/Master/News/NewsPic/201063092839104.pdf, accessed 13 December 2013.

  • Podinovski VV and Kuosmanen T (2011). Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions. European Journal of Operational Research 211 (3): 577–585.

    Article  Google Scholar 

  • Sahoo B, Luptacik M and Mahlberg B (2011). Alternative measures of environmental technology structure in DEA: An application. European Journal of Operational Research 215 (3): 750–762.

    Article  Google Scholar 

  • Scheel H (2001). Undesirable outputs in efficiency evaluations. European Journal of Operational Research 132 (2): 400–410.

    Article  Google Scholar 

  • Shannon C (1997). Increasing returns in infinite-horizon economies. Review of Economic Studies 64 (1): 73–96.

    Article  Google Scholar 

  • Shephard R (1970). Theory of Cost and Production Functions. Princeton University Press: Princeton, NJ.

    Google Scholar 

  • Tyteca D (1996). On the measurement of the environmental performance of firms—A literature review and a productive efficiency perspective. Journal of Environmental Management 46 (3): 281–308.

    Article  Google Scholar 

  • Yang H and Pollitt M (2010). The necessity of distinguishing weak and strong disposability among undesirable outputs in DEA: Environmental performance of Chinese coal-fired power plants. Energy Policy 38 (8): 4440–4444.

    Article  Google Scholar 

  • Zhou P, Ang B and Poh K (2008). A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research 189 (1): 1–18.

    Article  Google Scholar 

  • Zofio JL and Prieto AM (2001). Environmental efficiency and regulatory standards: The case of CO2 emissions from OECD industries. Resource and Energy Economics 23: 63–83.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful for helpful comments of the participants of the EWEPA 2011 Conference in Verona and the International Conference on Operations Research 2011 in Zurich.

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Authors and Affiliations

  1. Vienna University of Economics and Business, Vienna, Austria

    Christoph Bremberger, Francisca Bremberger, Mikulas Luptacik & Stephan Schmitt

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  1. Christoph Bremberger
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  2. Francisca Bremberger
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  3. Mikulas Luptacik
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Appendices

Appendix A

Undesirable Output Model from Cooper et al (2007)

In the original formulation from Cooper et al (2007), the index k for good outputs was replaced by r. We modified this notation to be able to include separable as well as non-separable bad outputs in our framework.

s.t.:

Appendix B

SBM Model B bounded

In Table B1, the second column gives the eco-efficiency scores using the standard SBM Model B. Columns 3–7 present the eco-efficiency scores using SBM Model B bounded for different emission per unit of output regulations ((Emission/Output)⩽α 2). The heading gives the respective value of α 2. The regulatory impact is computed as the deviation of eco-efficiency scores from the average eco-efficiency score of SBM Model B. Note that DMUs A, F, G and H are not affected by the environmental standard. This is because DMU A is eco-efficient under all analysed regulations and each of the remaining DMUs is projected in A. For DMUs D and E, the eco-efficiency score is constantly decreasing, indicating that stricter environmental standards cost eco-efficiency. DMU C is projected on the efficiency frontier between A and B. Since DMU B does also not fulfil the environmental standard of α 2=1.5, the regulatory constraint cuts the efficiency frontier between these two points. However, as the eco-efficiency score of DMU C is not changing, the cut must appear between the projection point of DMUs C and B. Summing up, the regulatory impact for the whole industry is increasing with the strength of regulation.

Table B1 Eco-efficiency scores—Emission per unit of output regulation
Full size table

Appendix C

Undesirable Output Model bounded

In Table C1, the second column gives the eco-efficiency scores using the standard Undesirable Output Model from Cooper et al (2007). Columns 3–7 present the eco-efficiency scores using the Undesirable Output Model bounded for different intensity regulations (Emission)/(Input)⩽α 1. The heading gives the respective value of α 1. The regulatory impact is computed as the deviation of eco-efficiency scores from the average eco-efficiency score of the Undesirable Output Model from Cooper et al (2007). Note that for DMUs D and E, the eco-efficiency score is constantly decreasing, whereas the eco-efficiency scores of DMU F, G and H are increasing as soon as DMU B is no longer eco-efficient. This is because each of the three firms is projected on the efficiency frontier between A and B. If the environmental standard cuts the efficiency frontier between these two points, the firms face a shorter projection way and thus gain in eco-efficiency. Consequently, the regulatory impact for the whole industry is constant beyond a certain strength of regulation.

Table C1 Eco-efficiency scores—Intensity regulation
Full size table

Appendix D

SBM Model B bounded and weak

In Table D1, the second column gives the eco-efficiency scores using SBM Model B weak. Columns 3–7 present the eco-efficiency scores using SBM Model B extended for different emission per unit of output regulations (Emission/Output)⩽α 2. The heading gives the respective value of α 2. The regulatory impact is computed as the deviation of eco-efficiency scores from the average eco-efficiency score of SBM Model B weak. Note that DMUs A, F, G and H are not affected by the environmental standard. This is because DMU A is eco-efficient under all analysed regulations and each of the remaining DMUs is projected in A. For DMUs D and E, the eco-efficiency score is constantly decreasing, indicating that stricter environmental standards cost eco-efficiency. DMU C is projected on the efficiency frontier between A and B. As DMU B also has to be projected for α 2=1.5, the environmental standard cuts the efficiency frontier between A and B. More precisely, the variation in eco-efficiency scores of DMU C indicates that the efficiency frontier is intersected between the projection point of DMUs C and A. Summing up, the regulatory impact for the whole industry is increasing with strength of regulation on. Owing to the weak disposability assumption, the eco-efficiency decrease is higher than under strong disposability of undesirable outputs.

Table D1 Eco-efficiency scores—Emission per unit of output regulation
Full size table

Appendix E

Undesirable Output Model bounded and weak

In Table E1, the second column gives the eco-efficiency scores using the Undesirable Output Model weak. Columns 3–7 present the eco-efficiency scores using the Undesirable Output Model extended for different intensity regulations ((Emission/Input)⩽α 1). The heading gives the respective value of α 1. The regulatory impact is computed as the deviation of eco-efficiency scores from the average eco-efficiency score of the Undesirable Output Model weak. Note that for DMUs D and E, the eco-efficiency score is constantly decreasing, whereas the eco-efficiency scores of DMUs F and Gare increasing as soon as DMU B is no longer eco-efficient. This is because both firms are projected on the efficiency frontier between A and B. If the environmental standard cuts the efficiency frontier between these two points, the firms face a shorter projection way and thus gain in eco-efficiency. The eco-efficiency score of DMU H under weak disposability is not affected, because DMU H is projected on DMU A from the beginning on. Summing up, the regulatory impact for the whole industry is increasing with stricter regulation, this is because of the weak disposability assumption.

Table E1 Eco-efficiency scores—Intensity regulation
Full size table

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Bremberger, C., Bremberger, F., Luptacik, M. et al. Regulatory impact of environmental standards on the eco-efficiency of firms. J Oper Res Soc 66, 421–433 (2015). https://doi.org/10.1057/jors.2013.176

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