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The Differential Approach to Superlative Index Number Theory

Author Info

Listed author(s):
  • 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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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
Note: Type of Document - Word; prepared on IBM PC; to print on HP;
Contact details of provider: Web page: http://econwpa.repec.org

Keywords: Theil Diewert superlative index numbers Divisia differential approach;

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Find related papers by JEL classification:
  • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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  1. 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 430-435, August.
  2. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
  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, 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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