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The Differential Approach to Superlative Index Number Theory

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  • Barnett, William A.
  • Choi, Ki-Hong
  • Sinclair, Tara M.

Abstract

Diewert’s “superlative†index numbers, defined to be exact for second-order aggregator functions, unify index number theory with aggregation theory but have been difficult to identify. We present a new approach to finding elements of this class. This new approach, related to that advocated by Henri Theil, transforms candidate index numbers into growth rate form and explores convergence rates to the Divisia index. Because the Divisia index in continuous time is exact for any aggregator function, any discrete time index number that converges to the Divisia index and that has a third-order remainder term is superlative.

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Bibliographic Info

Article provided by Southern Agricultural Economics Association in its journal Journal of Agricultural and Applied Economics.

Volume (Year): 35 (2003)
Issue (Month): ()
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Handle: RePEc:ags:joaaec:43279

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Keywords: Divisia; index numbers; superlative indexes;

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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. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
  3. Allen, Robert C & Diewert, W Erwin, 1981. "Direct versus Implicit Superlative Index Number Formulae," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 430-35, August.
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Cited by:
  1. Barnett, William A. & Choi, Ki-Hong, 2008. "Operational identification of the complete class of superlative index numbers: An application of Galois theory," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 603-612, July.

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