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On the inconsistency of the Malmquist-Luenberger index

Author

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  • Aparicio, Juan

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Pastor, Jesús

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Zofío, José Luis

    (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

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, Jesús & Zofío, José Luis, 2013. "On the inconsistency of the Malmquist-Luenberger index," Working Papers in Economic Theory 2013/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    • Handle: RePEc:uam:wpaper:201301
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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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    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.
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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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