On the circularity of the Malmquist productivity index
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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- 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.
- 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.
- 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.
- 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.
- 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.
- Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
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