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On the inconsistency of the Malmquist–Luenberger index

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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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    11. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl A., 2007. "Environmental production functions and environmental directional distance functions," Energy, Elsevier, vol. 32(7), pages 1055-1066.
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    More about this item

    Keywords

    Data Envelopment Analysis; Malmquist–Luenberger productivity index; Technological change; Efficiency change; Directional distance function;

    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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