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Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration

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  • Jean‐Philippe Boussemart
  • Walter Briec
  • Kristiaan Kerstens
  • Jean‐Christophe Poutineau

Abstract

This contribution establishes, from a theoretical viewpoint, the relations between the Malmquist productivity indices, that measure in either input or output orientations, and the Luenberger productivity indices, that can simultaneously contract inputs and expand outputs, but that can also measure in either input or output orientations. The main result is that a Malmquist productivity index overestimates productivity changes, since it provides productivity measures that are nearly twice those given by the Luenberger productivity index looking for simultaneous contractions of inputs and expansions of outputs. This relationship is empirically illustrated using data from 20 OECD countries over the 1974–97 period.

Suggested Citation

  • Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    • Handle: RePEc:bla:buecrs:v:55:y:2003:i:4:p:391-405
    DOI: 10.1111/1467-8586.00183
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    1. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    2. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    3. Chambers, Robert G & Fare, Rolf & Grosskopf, S, 1994. "Efficiency, Quantity Indexes, and Productivity Indexes: A Synthesis," Bulletin of Economic Research, Wiley Blackwell, vol. 46(1), pages 1-21, January.
    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. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    6. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    7. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
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