Consistency in Aggregation

Abstract

A price index number can be calculated either from the elementary commodities, or in two or more stages, by first computing subindex numbers for subsets of commodities, and from these subindex numbers, the index number for the total set. If both approaches generate the same number, the applied price index is consistent in aggregation. For official price statistics this is a fundamental requirement. 
In former studies it has been argued that prominent price indices like the Fisher, Törnqvist, and Marshall-Edgeorth index are not consistent in aggregation. However, these studies have a somewhat arbitrary focus which results in a too restrictive notion of consistency. In the present study this arbitrariness is removed and a less restrictive notion of consistency is introduced. It is examined whether this new approach results in additional price indices becoming consistent in aggregation.