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Consistency‐In‐Aggregation And Stuvel Indices

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  • Bert M. Balk

Abstract

In the National Accounts framework a frequent use is made of value, price, and quantity indices. Three requirements appear to be of vital importance. (i) For each aggregate the price index multiplied by the quantity index must be equal to the value index. (ii) The indices must be consistent‐in‐aggregation (which means something more than that a single‐step calculation yields the same outcome as a two‐or‐more‐step calculation). (iii) The indices must satisfy the equality test (defined in this paper). In this paper it is shown that the only indices satisfying these three requirements are the generalized Stuvel (1957) indices. These indices satisfy the Eichhorn and Voeller (1983) axioms for price and quantity indices. However, if one also requires that the indices be linearly homogeneous in current period prices and quantities then the only admissible indices are those of Laspeyres and Paasche.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:revinw:v:42:y:1996:i:3:p:353-363
    DOI: 10.1111/j.1475-4991.1996.tb00187.x
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    Cited by:

    1. W. Erwin Diewert, 2002. "Harmonized Indexes of Consumer Prices: Their Conceptual Foundations," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(IV), pages 547-637, December.
    2. Ludwig von Auer & Jochen Wengenroth, 2019. "Consistent Aggregation With Superlative and Other Price Indices," Research Papers in Economics 2019-13, University of Trier, Department of Economics.
    3. 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.

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