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On the circularity of the Malmquist productivity index

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  • Finn R. Førsund

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Abstract

Circularity is a desirable property of a productivity index seldom satisfied in available bilateral indices, such as the Malmquist index. Within a setting of micro units belonging to groups with group-specific frontier technology, the bilateral Malmquist productivity index is investigated. Our setting can be interpreted as representing cross section data, but also cross section, time series by identifying groups as time periods. A general proposition giving the condition for the Malmquist index to be circular is presented. When the condition is not met, ways of making the index transitive are explored. Four strategies adopted from the literature is followed; using one group as base, taking an average over possible bases, developing a multilateral index, and chain-linking. An expression of the Malmquist multilateral index is developed giving the difference between the Malmquist bilateral- and multilateral indexes.

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers with number 29-2002.

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Length: 34 pages
Date of creation: Jun 2002
Date of revision:
Handle: RePEc:icr:wpicer:29-2002

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Keywords: Circularity; transitivity; Malmquist productivity index; multilateral index; chain-linking;

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References

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  1. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  2. 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.
  3. Berg, Sigbjorn Atle & Forsund, Finn R. & Hjalmarsson, Lennart & Suominen, Matti, 1993. "Banking efficiency in the Nordic countries," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 371-388, April.
  4. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
  5. Berg, Sigbjorn Atle & Forsund, Finn R & Jansen, Eilev S, 1992. " Malmquist Indices of Productivity Growth during the Deregulation of Norwegian Banking, 1980-89," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(0), pages S211-28, Supplemen.
  6. Chambers Robert G. & Fare Rolf, 1994. "Hicks' Neutrality and Trade Biased Growth: A Taxonomy," Journal of Economic Theory, Elsevier, vol. 64(2), pages 554-567, December.
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Cited by:
  1. Alexandra Daskovska & Léopold Simar & Sébastien Bellegem, 2010. "Forecasting the Malmquist productivity index," Journal of Productivity Analysis, Springer, vol. 33(2), pages 97-107, April.
  2. Tamini, Lota D. & Larue, Bruno, 2009. "Technical and Environmental efficiencies and Best Management Practices in Agriculture," MPRA Paper 18964, University Library of Munich, Germany.
  3. Edvardsen, Dag Fjeld & Forsund, Finn R., 2003. "International benchmarking of electricity distribution utilities," Resource and Energy Economics, Elsevier, vol. 25(4), pages 353-371, October.

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