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Malmquist Productivity Index

Efficiency Change over Time
  • Kaoru Tone
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 71)

Abstract

The Malmquist index (MI) evaluates the efficiency change over time. In the non-parametric framework, it is measured as the product of catch-up (or recovery) and frontier-shift (or innovation) terms, both coming from the DEA technologies. We introduce three different approaches for measuring the Malmquist index along with scale efficiency related subjects.

Key words

Malmquist index catch-up recovery frontier-shift innovation radial non-radial slacks-based measure oriented non-oriented 

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References

  1. 1.
    Andersen, P. and Petersen, N.C., 1993, A procedure for ranking efficient units in data envelopment analysis, Management Science 39, 1261–1264.CrossRefGoogle Scholar
  2. 2.
    Balk, B.M., 2001, Scale efficiency and productivity change, Journal of Productivity Analysis 15, 159–183.CrossRefGoogle Scholar
  3. 3.
    Banker, R.D., 1984, Estimating the most productive scale size using data envelopment analysis, European Journal of Operational Research 17, 35–44.zbMATHCrossRefGoogle Scholar
  4. 4.
    Banker, R.D., Charnes, A. and Cooper, W.W., 1984, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30, 1078–1092.CrossRefGoogle Scholar
  5. 5.
    Bjurek, H., 1996, The Malmquist total factor productivity index, Scandinavian Journal of Economics 98, 303–313.CrossRefGoogle Scholar
  6. 6.
    Caves, D.W., Christensen, L.R. and Diewert, W.E., 1982, The economic theory of index numbers and the measurement of input, output and productivity, Econometrica 50, 1393–1414CrossRefGoogle Scholar
  7. 7.
    Chen, Y., 2003, Non-radial Malmquist productivity index with an illustrative application to Chinese major industries, International Journal of Production Economics 83,No. 1, 27–35.CrossRefADSGoogle Scholar
  8. 8.
    Cooper, W.W., Seiford, M.L. and Tone, K., 1999, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Boston, Kluwer Academic Publishers.Google Scholar
  9. 9.
    DEA-Solver Pro Version 4.0, 2003, Saitech-Inc, www.saitech-inc.com.Google Scholar
  10. 10.
    Färe, R. and Grosskopf, S., 1992, Malmquist indexes and Fisher ideal indexes, The Economic Journal 102, 158–160.CrossRefGoogle Scholar
  11. 11.
    Färe, R., Grosskopf, S, Lindgren, B. and Roos, P., 1989, 1994, Productivity change in Swedish hospitals: a Malmquist output index approach, in Charnes, A., Cooper, W.W., Lewin, A.Y. and Seiford, M.L. (eds.) Data Envelopment Analysis: Theory, Methodology and Applications, Boston, Kluwer Academic Publishers.Google Scholar
  12. 12.
    Färe, R., Grosskopf, S, Norris, M. and Zhang, Z., 1994, Productivity growth, technical progress, and efficiency change in industrialized countries, The American Economic Review 84, 66–83.Google Scholar
  13. 13.
    Färe, R., Grosskopf, S. and Roos, P., 1998a, Malmquist productivity indexes: a survey of theory and practice, in Index Numbers: Essays in Honour of Sten Malmquist, Kluwer Academic Publishers, 127–190.Google Scholar
  14. 14.
    Färe, R., Grosskopf, S. and Russell, R., 1998b, Index Numbers: Essays in Honour of Sten Malmquist, Kluwer Academic Publishers.Google Scholar
  15. 15.
    Lovell, CA.K. and Grifell-Tatje, E., 1994, A generalized Malmquist productivity index, Paper presented at the Georgia Productivity Workshop at Athens, GA, October 1994.Google Scholar
  16. 16.
    Malmquist, S., 1953, Index numbers and indifference surfaces, Trabajos de Estadistica 4, 209–242.zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Ray, S.C. and Delsi, E., 1997, Productivity growth, technical progress, eiticiency change in industrialized countries: comment, The American Economic Review 87, 1033–1039.Google Scholar
  18. 18.
    Seiford, M.L. and Zhu, J., 1999, Infeasibility of super-efficiency data envelopment analysis, INFOR 37, 174–187.Google Scholar
  19. 19.
    Thrall, R.M., 2000, Measures in DEA with an application to the Malmquist index, Journal of Productivity Analysis 13, 125–137.CrossRefGoogle Scholar
  20. 20.
    Tone, K., 2001, A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research 130, 498–509.zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Tone, K., 2002, A slacks-based measure of super-efficiency in data envelopment analysis, European Journal of Operational Research 143, 32–41.zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Zhu, J., 1996, Data envelopment analysis with preference structure, Journal of the Operational Research Society 47, 136–150.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Kaoru Tone
    • 1
  1. 1.National Graduate Institute for Policy StudiesTokyoJapan

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