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Superlative Index Numbers and Consistency in Aggregation

W. E. Diewert

Abstract

Very often, an index number used in an economic model has been constructed in two or more stages. If the two stage procedure gives the same answer as a single stage procedure, then Vartia calls the index number formula "consistent in aggregation." Paasche and Laspeyres indexes have this consistency in aggregation property, but these index number formulae are consistent only with very restrictive functional forms for the underlying aggregator (i.e., utility or production) function. The present paper shows that the class of superlative index number formulae has an approximate consistency in aggregation property, where a superlative index number formula is one which is consistent with a flexible functional form for the underlying aggregator function. The paper also contains some empirical examples which both illustrate the main theorem and also indicate that the chain principle for constructing index numbers is preferable to the fixed base method. Finally, the paper proves some theorems about the class of pseudo-superlative index numbers.