The Differential Approach to Superlative Index Number Theory
AbstractDiewert’s (1976) “superlative” index numbers, defined to be exact for second order aggregator functions, unify index number theory with aggregation theory, but have been difficult to identify. We present a new approach to finding elements of this class. This new approach, related to that advocated by Henri Theil (1973), transforms candidate index numbers into growth rate form and explores convergence rates to the Divisia index. Since the Divisia index in continuous time is exact for any aggregator function, any discrete time index number that converges to the Divisia index and that has a third order remainder term is superlative.
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Bibliographic InfoPaper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201234.
Length: 17 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Divisia; index numbers; superlative indexes;
Other versions of this item:
- 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.
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
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.
- Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
- Allen, Robert C & Diewert, W Erwin, 1981. "Direct versus Implicit Superlative Index Number Formulae," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 430-35, August.
- 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.
- Barnett, William A. & Choi, Ki-Hong, 2006. "Operational identification of the complete class of superlative index numbers: an application of Galois theory," MPRA Paper 416, University Library of Munich, Germany.
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