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A superlative indicator for the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application

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  • Ang, Frederic
  • Kerstens, Pieter Jan

Abstract

Consisting of the difference between an output indicator and an input indicator, the Luenberger-Hicks-Moorsteen (LHM) productivity indicator allows straightforward interpretation. However, its computation requires estimating distance functions that are inherently unknown. This paper shows that a computationally simple Bennet indicator is a superlative indicator for the LHM indicator when one can assume profit-maximizing behavior and the input and output directional distance functions can be represented up to the second order by a quadratic functional form. We also show that the Luenberger- and LHM-approximating Bennet indicators coincide for an appropriate choice of directional vectors. Focusing on a large sample of Italian food and beverages companies for the years 1995−2007, we empirically investigate the extent to which this theoretical equivalence translates into similar estimates. We find that the Bennet indicator is a close empirical alternative to the LHM indicator for the sample.

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  • Ang, Frederic & Kerstens, Pieter Jan, 2020. "A superlative indicator for the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1161-1173.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:3:p:1161-1173
    DOI: 10.1016/j.ejor.2020.02.030
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    2. 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.
    3. Tomas Balezentis & Vaida Sapolaite, 2022. "Productivity surplus and its distribution in Lithuanian agriculture," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 49(3), pages 721-740, August.
    4. Frederic Ang & Pieter Jan Kerstens, 2023. "Robust nonparametric analysis of dynamic profits, prices and productivity: An application to French meat-processing firms," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 50(2), pages 771-809.
    5. Frederic Ang & Stephen J. Ramsden, 2024. "Analysing determinate components of an approximated Luenberger–Hicks–Moorsteen productivity indicator: An application to German dairy‐processing firms," Agribusiness, John Wiley & Sons, Ltd., vol. 40(2), pages 349-370, April.
    6. Zhiyang Shen & Kristiaan Kerstens & Tomas Baležentis, 2023. "An environmental Luenberger–Hicks–Moorsteen total factor productivity indicator: empirical analysis considering undesirable outputs either as inputs or outputs, and attention for infeasibilities," Post-Print hal-04273656, HAL.
    7. Chen, Xiaodong & Guo, Anda & Miao, Zhuang & Zhu, Pengyu, 2024. "Assessing the performance of the transport sector within the global supply chain context: Decomposition of energy and environmental productivity," Applied Energy, Elsevier, vol. 358(C).

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