Operational identification of the complete class of superlative index numbers: an application of Galois theory
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 416.
Date of creation: 11 Feb 2006
Date of revision:
Other versions of this item:
- 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.
- William Barnett & Ki-Hong Choi, 2006. "Operational identification of the complete class of superlative index numbers: an application of Galois theory," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200604, University of Kansas, Department of Economics.
- D0 - Microeconomics - - General
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
- E0 - Macroeconomics and Monetary Economics - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-12-04 (All new papers)
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