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Generalised Commensurability Properties of Efficiency Measures: Implications for Productivity Indicators

Author

Listed:
  • Walter Briec

    (Universite de Perpignan, LAMPS, 52 Avenue Villeneuve, F-66000 Perpignan, France)

  • Audrey Dumas

    (Universite de Perpignan, CDED, 52 Avenue Villeneuve, F-66000 Perpignan, France)

  • Kristiaan Kerstens

    (IESEG School of Management, CNRS, Univ. Lille, UMR 9221-LEM, 3 rue de la Digue, F-59000 Lille, France)

  • Agathe Stenger

    (Universite de Perpignan, CDED, 52 avenue de Villeneuve, F-66000 Perpignan, France)

Abstract

We analyse the role of new weak and strong commensurability conditions on efficiency measures and especially on productivity measurement. If strong commensurability fails, then a productivity index (indicator) may exhibit a homogeneity bias yielding inconsistent and contradictory results. In particular, we show that the Luenberger productivity indicator (LPI) is sensitive to proportional changes in the input-output quantities, while the Malmquist productivity index is not affected by such changes. This is due to the homogeneity degree of the directional distance function under constant returns to scale. In particular, the directional distance function only satisfies the weak commensurability axiom in general. However, if the directional distance function is a diagonally homogeneous function of the technology, then the directional distance function satisfies strong commensurability. This explains why the direction of an arithmetic mean of the observed data works well. Numerical examples and an empirical illustration are proposed. Under a translation homothetic technology, the LPI is not affected by any additive directional transformation of the observations.

Suggested Citation

  • Walter Briec & Audrey Dumas & Kristiaan Kerstens & Agathe Stenger, 2021. "Generalised Commensurability Properties of Efficiency Measures: Implications for Productivity Indicators," Working Papers 2021-EQM-01, IESEG School of Management.
    • Handle: RePEc:ies:wpaper:e202101
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    References listed on IDEAS

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    Cited by:

    1. Tomas Balezentis & Kristiaan Kerstens & Zhiyang Shen, 2022. "Economic and Environmental Decomposition of Luenberger-Hicks-Moorsteen Total Factor Productivity Indicator: Empirical Analysis of Chinese Textile Firms With a Focus on Reporting Infeasibilities and Qu," Post-Print hal-03833245, HAL.
    2. Haiyan Deng & Ge Bai & Kristiaan Kerstens & Zhiyang Shen, 2023. "Comparing green productivity under convex and nonconvex technologies: Which is a robust approach consistent with energy structure?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(8), pages 4377-4394, December.

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    More about this item

    Keywords

    Malmquist and Luenberger productivity; Directional and proportional distance function; Weak and strong commensurability;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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