Additive decompositions for Fisher,Törnqvist and geometric mean indexes

Abstract

Users of a price or quantity index often want to know how much each item in the index contributes to its overall change. Consequently, statistical agencies generally publish items' contributions to changes in the indexes that they publish. For fixed basket index formulas, calculating contributions to index change that add up to the correct total is straightforward, but for Fisher, Törnqvist and geometric mean index formulas -- which statistical agencies are beginning to use -- it is not. We use economic and axiomatic approaches to derive additive decompositions of the change in a Fisher index, and we use an axiomatic approach to derive an additive decomposition of the change in a Törnqvist or geometric mean index.