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The Differential Approach to Superlative Index Number Theory

Author

Listed:
  • 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.

Suggested Citation

  • William A. Barnett & Ke- Hong Choi & Tara M. Sinclair, 2001. "The Differential Approach to Superlative Index Number Theory," Econometrics 0111002, University Library of Munich, Germany, revised 28 Dec 2001.
    • Handle: RePEc:wpa:wuwpem:0111002
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    References listed on IDEAS

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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. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, University Library of Munich, Germany.
    3. Jean Ville & P. K. Newman, 1951. "The Existence-Conditions of a Total Utility Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 19(2), pages 123-128.
    4. W.A. Barnett & J.M. Binner, 2004. "The Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 79-97, Emerald Group Publishing Limited.
    5. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-593, September.
    6. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    7. Barnett, William A. & Lee, Yul W. & Wolfe, Michael D., 1985. "The three-dimensional global properties of the minflex laurent, generalized leontief, and translog flexible functional forms," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 3-31.
    8. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    9. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
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    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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    More about this item

    Keywords

    Theil Diewert superlative index numbers Divisia differential approach;

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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