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On the inconsistency of the Malmquist-Luenberger index

  • 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.)

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.

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Paper provided by Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History) in its series Working Papers in Economic Theory with number 2013/01.

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Length: 19 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:uam:wpaper:201301
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  1. 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.
  2. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  3. Barros, Carlos Pestana, 2008. "Efficiency analysis of hydroelectric generating plants: A case study for Portugal," Energy Economics, Elsevier, vol. 30(1), pages 59-75, January.
  4. 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.
  5. Kumar, Surender, 2006. "Environmentally sensitive productivity growth: A global analysis using Malmquist-Luenberger index," Ecological Economics, Elsevier, vol. 56(2), pages 280-293, February.
  6. Tulkens, H. & Vanden Eeckaut, P., . "Non-parametric efficiency, progress and regress measures for panel data: Methodological aspects," CORE Discussion Papers RP -1132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Dong-hyun Oh, 2010. "A global Malmquist-Luenberger productivity index," Journal of Productivity Analysis, Springer, vol. 34(3), pages 183-197, December.
  8. Pastor, Jesus T. & Lovell, C.A. Knox, 2005. "A global Malmquist productivity index," Economics Letters, Elsevier, vol. 88(2), pages 266-271, August.
  9. William L. Weber & Bruce Domazlicky, 2001. "Productivity Growth and Pollution in State Manufacturing," The Review of Economics and Statistics, MIT Press, vol. 83(1), pages 195-199, February.
  10. 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.
  11. 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.
  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. 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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