 Operational identification of the complete class of superlative index numbers: An application of Galois theoryWilliam Barnett and Ki-Hong Choi Journal of Mathematical Economics, 2008, vol. 44, issue 7-8, 603-612 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's most general definition. But when operationalized in practice, our definition permits use of the full class, while Diewert's 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's 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. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:44:y:2008:i:7-8:p:603-612 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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