Operational identification of the complete class of superlative index numbers: an application of Galois theory
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 of creation:||Feb 2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (785) 864-3501
Fax: (785) 864-5270
Web page: http://www2.ku.edu/~kuwpaper/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
- Diewert, W E, 1992. "Exact and Superlative Welfare Change Indicators," Economic Inquiry, Western Economic Association International, vol. 30(4), pages 562-82, October.
- Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-28, May.
- Theil, Henri, 1973. "A New Index Number Formula," The Review of Economics and Statistics, MIT Press, vol. 55(4), pages 498-502, November.
- Lau, Lawrence J, 1979. "On Exact Index Numbers," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 73-82, February.
- Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-93, September.
- William Barnett & Ki-Hong Choi & Tara M. Sinclair, 2012.
"The Differential Approach to Superlative Index Number Theory,"
WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS
201234, University of Kansas, Department of Economics, revised Sep 2012.
- Barnett, William A. & Choi, Ki-Hong & Sinclair, Tara M., 2003. "The Differential Approach to Superlative Index Number Theory," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35.
- William A. Barnett & Ke- Hong Choi & Tara M. Sinclair, 2001. "The Differential Approach to Superlative Index Number Theory," Econometrics 0111002, EconWPA, revised 28 Dec 2001.
- Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
- Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
- Blackorby, C. & Davidson, R. & Schworm, W., 1990.
"Implicit Separability: Characterisation And Implications For Consumer Demands,"
90a16, Universite Aix-Marseille III.
- Blackorby, Charles & Davidson, Russell & Schworm, William, 1991. "Implicit separability: Characterisation and implications for consumer demands," Journal of Economic Theory, Elsevier, vol. 55(2), pages 364-399, December.
When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:200604. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jianbo Zhang)
If references are entirely missing, you can add them using this form.