Operational identification of the complete class of superlative index numbers: an application of Galois theory

William Barnett and Ki-Hong Choi
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Ki-Hong Choi: National Pension Research Institute

No 200604, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: We provide an operational identification of the complete class of superlative index numbers to track the exact aggregator functions of economic aggregation theory. If an index number is linearly homogeneous and a second order approximation in a formal manner that we define, we prove the index to be in the superlative index number class of nonparametric functions. Our definition is mathematically equivalent to Diewert°Øs most general definition. But when operationalized in practice, our definition permits use of the full class, while Diewert°Øs definition, in practice, spans only a strict subset of the general class. The relationship between the general class and that strict subset is a consequence of Galois theory. Only a very small number of elements of the general class have been found by Diewert°Øs method, despite the fact that the general class contains an infinite number of functions. We illustrate our operational, general approach by proving for the first time that a particular family of nonparametric functions, including the Sato-Vartia index, is within the superlative index number class.

Keywords: Exact index numbers; superlative index number class; Divisia line integrals; aggregator function space; Galois theory. (search for similar items in EconPapers)
JEL-codes: C8 D E01 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2006-02
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Related works:
Journal Article: Operational identification of the complete class of superlative index numbers: An application of Galois theory (2008)
Working Paper: Operational identification of the complete class of superlative index numbers: an application of Galois theory (2006)
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