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On the inconsistency of the Malmquist–Luenberger index

Author

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  • Aparicio, Juan
  • Pastor, Jesus T.
  • Zofio, Jose L.
Abstract
Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist–Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad outputs. In particular, we show that the usual interpretation of the technical change component in terms of production frontier shifts can be inconsistent with its numerical value, thereby resulting in an erroneous interpretation of this component that passes on to the index itself. We illustrate this issue with a simple numerical example. Finally, we propose a solution for this inconsistency issue based on incorporating a new postulate for the technology related to the production of bad outputs.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesus T. & Zofio, Jose L., 2013. "On the inconsistency of the Malmquist–Luenberger index," European Journal of Operational Research, Elsevier, vol. 229(3), pages 738-742.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:3:p:738-742
    DOI: 10.1016/j.ejor.2013.03.031
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    References listed on IDEAS

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    1. Yoruk, BarIs K. & Zaim, Osman, 2005. "Productivity growth in OECD countries: A comparison with Malmquist indices," Journal of Comparative Economics, Elsevier, vol. 33(2), pages 401-420, June.
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    4. Pastor, Jesus T. & Lovell, C.A. Knox, 2005. "A global Malmquist productivity index," Economics Letters, Elsevier, vol. 88(2), pages 266-271, August.
    5. Dong-hyun Oh, 2010. "A global Malmquist-Luenberger productivity index," Journal of Productivity Analysis, Springer, vol. 34(3), pages 183-197, December.
    6. Rolf Färe & Shawna Grosskopf & Carl A Pasurka, Jr., 2001. "Accounting for Air Pollution Emissions in Measures of State Manufacturing Productivity Growth," Journal of Regional Science, Wiley Blackwell, vol. 41(3), pages 381-409, August.
    7. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, September.
    8. Henry Tulkens & Philippe Eeckaut, 2006. "Nonparametric Efficiency, Progress and Regress Measures For Panel Data: Methodological Aspects," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 395-429, Springer.
    9. Parakramaweera Sunil Dharmapala, 2010. "The issue of input/output slacks in validating data envelopment analysis-based Malmquist productivity index: an example from banking," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 2(3), pages 302-319.
    10. Kumar, Surender, 2006. "Environmentally sensitive productivity growth: A global analysis using Malmquist-Luenberger index," Ecological Economics, Elsevier, vol. 56(2), pages 280-293, February.
    11. Victoria Shestalova, 2003. "Sequential Malmquist Indices of Productivity Growth: An Application to OECD Industrial Activities," Journal of Productivity Analysis, Springer, vol. 19(2), pages 211-226, April.
    12. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl A., 2007. "Environmental production functions and environmental directional distance functions," Energy, Elsevier, vol. 32(7), pages 1055-1066.
    13. Chen, Yao, 2003. "A non-radial Malmquist productivity index with an illustrative application to Chinese major industries," International Journal of Production Economics, Elsevier, vol. 83(1), pages 27-35, January.
    14. E. Grifell-Tatjé & C. Lovell & J. Pastor, 1998. "A Quasi-Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 10(1), pages 7-20, July.
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    More about this item

    Keywords

    Data Envelopment Analysis; Malmquist–Luenberger productivity index; Technological change; Efficiency change; Directional distance function;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • Q55 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Technological Innovation

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