CONSISTENCY‐IN‐AGGREGATION AND STUVEL INDICES

Bert Balk

Review of Income and Wealth, 1996, vol. 42, issue 3, 353-363

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.

Date: 1996
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