CONSISTENCY-IN-AGGREGATION AND STUVEL INDEXES

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