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The Differential Approach to Superlative Index Number Theory

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  • William A. Barnett

    (Washington University in St. Louis)

  • Ke- Hong Choi

    (National Pension Research Center in Seoul, Korea)

  • Tara M. Sinclair

    (Washington University in St. Louis)

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 (1973), transforms candidate index numbers into growth rate form and explores convergence rates to the Divisia index. Since 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

Paper provided by EconWPA in its series Econometrics with number 0111002.

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Date of creation: 07 Nov 2001
Date of revision: 28 Dec 2001
Handle: RePEc:wpa:wuwpem:0111002

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Web page: http://128.118.178.162

Related research

Keywords: Theil Diewert superlative index numbers Divisia differential approach;

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  1. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
  2. 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.
  3. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
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Cited by:
  1. Barnett, William A. & Choi, Ki-Hong, 2006. "Operational identification of the complete class of superlative index numbers: an application of Galois theory," MPRA Paper 416, University Library of Munich, Germany.

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