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Index Number Theory Using Differences Rather Than Ratios

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  • W. Erwin Diewert

Abstract

Traditional index number theory decomposes a value ratio into the product of a price index times a quantity index. The price (quantity) index is interpreted as an aggregate price (quantity) ratio. The present paper takes an alternative approach to index number theory, started by Bennet and Montgomery in the 1920s, which decomposes a value difference into the sum of a price difference plus a quantity difference. Axiomatic and economic approaches to this alternative branch of index theory are considered in the present paper. The analysis presented has some relevance to accounting theory in which revenue, cost, or profit changes need to be decomposed into price quantity components or where standard or budgeted performance is compared with actual performance (variance analysis). The methodology presented in the paper is also relevant for consumer surplus analysis.

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  • W. Erwin Diewert, 2005. "Index Number Theory Using Differences Rather Than Ratios," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 311-360, January.
    • Handle: RePEc:bla:ajecsc:v:64:y:2005:i:1:p:311-360
    DOI: 10.1111/j.1536-7150.2005.00365.x
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    References listed on IDEAS

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    1. 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 566-593, September.
    2. Diewert, W E, 1976. "Harberger's Welfare Indicator and Revealed Preference Theory," American Economic Review, American Economic Association, vol. 66(1), pages 143-152, March.
    3. Vartia, Yrjö O., . "Relative Changes and Index Numbers," ETLA A, The Research Institute of the Finnish Economy, number 4, June.
    4. repec:bla:revinw:v:42:y:1996:i:3:p:353-63 is not listed on IDEAS
    5. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    6. Bert M. Balk, 1996. "Consistency‐In‐Aggregation And Stuvel Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 42(3), pages 353-363, September.
    7. Harberger, Arnold C, 1971. "Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay," Journal of Economic Literature, American Economic Association, vol. 9(3), pages 785-797, September.
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