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Exponential environmental productivity index and indicators

Author

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  • Arnaud Abad

    (UPVD - Université de Perpignan Via Domitia, BETA - Bureau d'Économie Théorique et Appliquée - INRA - Institut National de la Recherche Agronomique - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

  • Paola Ravelojaona

    (UPVD - Université de Perpignan Via Domitia)

Abstract

The major contributions of this paper are twofold. First, it introduces an exponential environmental productivity indicator and its ratio-based counterpart constructed through an exponential distance function. These innovative exponential environmental productivity index and indicator inherit the basic structure of both Malmquist-Luenberger productivity index and environmental Luenberger productivity indicator. Thereafter, an exponential version of the environmental Luenberger-Hicks-Moorsteen productivity indicator is proposed. Such a specification allows to overcome the special issue of infeasabilities. Second, looking from a dynamical viewpoint, we propose an exponential generalized dynamical distance function. This new efficiency measure shows the degree of efficiency of an observation, taking into consideration its technical efficiency and/or technological variation adjustment path. A sample of 11 representative French airports is considered over the period 2008-2011, in order to implement these new exponential environmental productivity index and indicators.

Suggested Citation

  • Arnaud Abad & Paola Ravelojaona, 2017. "Exponential environmental productivity index and indicators," Post-Print hal-03025344, HAL.
    • Handle: RePEc:hal:journl:hal-03025344
    DOI: 10.1007/s11123-017-0513-7
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    1. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1, McMaster University Archive for the History of Economic Thought.
    2. Murty, Sushama, 2010. "Externalities and fundamental nonconvexities: A reconciliation of approaches to general equilibrium externality modeling and implications for decentralization," Journal of Economic Theory, Elsevier, vol. 145(1), pages 331-353, January.
    3. Murty, Sushama & Russell, R. Robert, 2010. "On modeling pollution-generating technologies," Economic Research Papers 271176, University of Warwick - Department of Economics.
    4. Picazo-Tadeo, Andrés J. & Castillo-Giménez, Juana & Beltrán-Esteve, Mercedes, 2014. "An intertemporal approach to measuring environmental performance with directional distance functions: Greenhouse gas emissions in the European Union," Ecological Economics, Elsevier, vol. 100(C), pages 173-182.
    5. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2014. "Measurement of returns to scale using non-radial DEA models," European Journal of Operational Research, Elsevier, vol. 232(3), pages 664-670.
    6. Dong-hyun Oh, 2010. "A global Malmquist-Luenberger productivity index," Journal of Productivity Analysis, Springer, vol. 34(3), pages 183-197, December.
    7. See, Kok Fong & Coelli, Tim, 2014. "Total factor productivity analysis of a single vertically integrated electricity utility in Malaysia using a Törnqvist index method," Utilities Policy, Elsevier, vol. 28(C), pages 62-72.
    8. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    9. Walter Briec & Kristiaan Kerstens, 2004. "A Luenberger-Hicks-Moorsteen productivity indicator: its relation to the Hicks-Moorsteen productivity index and the Luenberger productivity indicator," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(4), pages 925-939, May.
    10. Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
    11. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    12. Chambers, Robert G & Fare, Rolf & Grosskopf, S, 1994. "Efficiency, Quantity Indexes, and Productivity Indexes: A Synthesis," Bulletin of Economic Research, Wiley Blackwell, vol. 46(1), pages 1-21, January.
    13. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    14. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    15. Walter Briec & K. Kerstens, 2009. "Infeasibilities and directional distance functions: with application to the determinateness of the luenberger productivity indicator," Post-Print hal-00372560, HAL.
    16. Mehdiloozad, Mahmood & Sahoo, Biresh K. & Roshdi, Israfil, 2014. "A generalized multiplicative directional distance function for efficiency measurement in DEA," European Journal of Operational Research, Elsevier, vol. 232(3), pages 679-688.
    17. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    18. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    19. Kerstens, Kristiaan & Van de Woestyne, Ignace, 2014. "Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data," European Journal of Operational Research, Elsevier, vol. 233(3), pages 749-758.
    20. Saeideh Fallah-Fini & Konstantinos Triantis & Andrew Johnson, 2014. "Reviewing the literature on non-parametric dynamic efficiency measurement: state-of-the-art," Journal of Productivity Analysis, Springer, vol. 41(1), pages 51-67, February.
    21. Fare, R. & Grosskopf, S. & Hernandez-Sancho, F., 2004. "Environmental performance: an index number approach," Resource and Energy Economics, Elsevier, vol. 26(4), pages 343-352, December.
    22. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    23. Aiken, Deborah Vaughn & Pasurka, Carl Jr., 2003. "Adjusting the measurement of US manufacturing productivity for air pollution emissions control," Resource and Energy Economics, Elsevier, vol. 25(4), pages 329-351, October.
    24. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    25. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    26. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    27. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    28. Murty, Sushama & Robert Russell, R. & Levkoff, Steven B., 2012. "On modeling pollution-generating technologies," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 117-135.
    29. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2016. "Congestion in production correspondences," Journal of Economics, Springer, vol. 119(1), pages 65-90, September.
    30. Luenberger, David G, 1996. "Welfare from a Benefit Viewpoint," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 445-462, April.
    31. Nishimizu, Mieko & Page, John M, Jr, 1982. "Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-78," Economic Journal, Royal Economic Society, vol. 92(368), pages 920-936, December.
    32. Rajiv D. Banker & Ajay Maindiratta, 1986. "Piecewise Loglinear Estimation of Efficient Production Surfaces," Management Science, INFORMS, vol. 32(1), pages 126-135, January.
    33. David G. Luenberger, 1996. "Welfare from a benefit viewpoint (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 445-462.
    34. W. Erwin Diewert, 2005. "Index Number Theory Using Differences Rather Than Ratios," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 311-360, January.
    35. Pittman, Russell W, 1983. "Multilateral Productivity Comparisons with Undesirable Outputs," Economic Journal, Royal Economic Society, vol. 93(372), pages 883-891, December.
    36. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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    Cited by:

    1. 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.
    2. Shen, Zhiyang & Wu, Haitao & Bai, Kaixuan & Hao, Yu, 2022. "Integrating economic, environmental and societal performance within the productivity measurement," Technological Forecasting and Social Change, Elsevier, vol. 176(C).
    3. Briec, Walter & Fukuyama, Hirofumi & Ravelojaona, Paola, 2021. "Exponential distance function and duality theory," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1002-1014.
    4. Arnaud Abad & Paola Ravelojaona, 2021. "Pollution‐adjusted productivity analysis: The use of Malmquist and Luenberger productivity measures," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 635-648, April.
    5. Arnaud Abad & Paola Ravelojaona & Ziyi Shen, 2022. "An exponential analysis of total factor productivity," Working Papers hal-03419905, HAL.

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