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- W2771966644 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 Diewerti¯s most general definition. But when operationalized in practice, our definition permits use of the full class, while Diewerti¯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 Diewerti¯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." @default.
- W2771966644 created "2017-12-22" @default.
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- W2771966644 date "2006-02-11" @default.
- W2771966644 modified "2023-09-23" @default.
- W2771966644 title "Operational identification of the complete class of superlative index numbers: an application of Galois theory" @default.
- W2771966644 hasPublicationYear "2006" @default.
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