An Alternative Decomposition Of The Fisher Index

Aside from the aggregated information provided by price and quantity indexes, there is growing interest in index decompositions that reveal the contribution of each index component to overall index change. In this paper, we derive a “natural” decomposition of the Fisher price index that is directly implied by its linear homogeneity in price relatives. The proposed “Euler” weights not only indicate the total contribution of each component to total index change but also reveal which component had the highest or lowest marginal impact. Our results can readily be generalized to any index that satisfies the linear homogeneity property.