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A Quasi-Malmquist Productivity Index

Author

Listed:
  • E. Grifell-Tatjé
  • C. Lovell
  • J. Pastor

Abstract

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of “one-sided” efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:10:y:1998:i:1:p:7-20
    DOI: 10.1023/A:1018329930629
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    References listed on IDEAS

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    1. Knox Lovell, C. A. & Pastor, Jesus T. & Turner, Judi A., 1995. "Measuring macroeconomic performance in the OECD: A comparison of European and non-European countries," European Journal of Operational Research, Elsevier, vol. 87(3), pages 507-518, December.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. Balk, Bert M, 1993. "Malmquist Productivity Indexes and Fisher Ideal Indexes: Comment," Economic Journal, Royal Economic Society, vol. 103(418), pages 680-682, May.
    4. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    5. Zieschang, Kimberly D., 1984. "An extended farrell technical efficiency measure," Journal of Economic Theory, Elsevier, vol. 33(2), pages 387-396, August.
    6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
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    Citations

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    Cited by:

    1. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    2. 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.
    3. E. Grifell-Tatjé & C. A. K. Lovell, 1999. "Profits and Productivity," Management Science, INFORMS, vol. 45(9), pages 1177-1193, September.
    4. Thijs Raa, 2008. "Debreu’s coefficient of resource utilization, the Solow residual, and TFP: the connection by Leontief preferences," Journal of Productivity Analysis, Springer, vol. 30(3), pages 191-199, December.
    5. Sueyoshi, Toshiyuki & Aoki, Shingo, 2001. "A use of a nonparametric statistic for DEA frontier shift: the Kruskal and Wallis rank test," Omega, Elsevier, vol. 29(1), pages 1-18, February.
    6. A. Camanho & R. Dyson, 2006. "Data envelopment analysis and Malmquist indices for measuring group performance," Journal of Productivity Analysis, Springer, vol. 26(1), pages 35-49, August.
    7. repec:gam:jsusta:v:9:y:2017:i:5:p:842-:d:98960 is not listed on IDEAS
    8. Krüger Jens J. & Cantner Uwe & Hanusch Horst, 2003. "Explaining International Productivity Differences / Erklärung internationaler Produktivitätsunterschiede," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 223(6), pages 659-679, December.
    9. repec:gam:jsusta:v:10:y:2018:i:2:p:397-:d:130100 is not listed on IDEAS
    10. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    11. repec:eee:jomega:v:83:y:2019:i:c:p:167-180 is not listed on IDEAS
    12. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2013. "Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA," European Journal of Operational Research, Elsevier, vol. 231(2), pages 443-451.
    13. Sahoo, Biresh K. & Acharya, Debashis, 2010. "An alternative approach to monetary aggregation in DEA," European Journal of Operational Research, Elsevier, vol. 204(3), pages 672-682, August.
    14. Pedro Cantos & José Pastor & Lorenzo Serrano, 1999. "Productivity, efficiency and technical change in the European railways: A non-parametric approach," Transportation, Springer, vol. 26(4), pages 337-357, November.
    15. repec:pal:jorsoc:v:55:y:2004:i:10:d:10.1057_palgrave.jors.2601787 is not listed on IDEAS
    16. Mohsen Afsharian & Heinz Ahn, 2015. "The overall Malmquist index: a new approach for measuring productivity changes over time," Annals of Operations Research, Springer, vol. 226(1), pages 1-27, March.
    17. Mei-Ying Huang & Jia-Ching Juo & Tsu-tan Fu, 2015. "Metafrontier cost Malmquist productivity index: an application to Taiwanese and Chinese commercial banks," Journal of Productivity Analysis, Springer, vol. 44(3), pages 321-335, December.
    18. Emrouznejad, Ali & Yang, Guo-liang, 2016. "CO2 emissions reduction of Chinese light manufacturing industries: A novel RAM-based global Malmquist–Luenberger productivity index," Energy Policy, Elsevier, vol. 96(C), pages 397-410.
    19. repec:eee:jomega:v:79:y:2018:i:c:p:9-20 is not listed on IDEAS

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