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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.

Suggested Citation

  • Barnett, William A. & Choi, Ki-Hong & Sinclair, Tara M., 2003. "The Differential Approach to Superlative Index Number Theory," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35(Supplemen), pages 1-6.
    • Handle: RePEc:ags:joaaec:43279
    DOI: 10.22004/ag.econ.43279
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    1. 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.
    2. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    3. 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.
    4. 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.
    5. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
    6. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    7. 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.
    8. 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.
    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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