Barnett, William A. and Choi, KiHong (2006): Operational identification of the complete class of superlative index numbers: an application of Galois theory.

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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 SatoVartia index, is within the superlative index number class.
Item Type:  MPRA Paper 

Original Title:  Operational identification of the complete class of superlative index numbers: an application of Galois theory 
Language:  English 
Subjects:  D  Microeconomics > D0  General C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology; Computer Programs E  Macroeconomics and Monetary Economics > E0  General 
Item ID:  416 
Depositing User:  William A. Barnett 
Date Deposited:  12. Oct 2006 
Last Modified:  18. Feb 2013 17:46 
References:  Exact index numbers, superlative index number class, Divisia line integrals, aggregator function space, Galois theory 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/416 