Decomposing Multilateral Price Indexes into the Contributions of Individual Commodities

This article describes methods for decomposing price indexes into contributions from individual commodities, to help understand the influence of each commodity on aggregate price index movements.Previous authors have addressed the decomposition of bilateral price indexes, which aggregate changes in commodity prices from one time period to another. Our focus is the decomposition of multilateral price indexes, which aggregate commodity prices across more than two time periods or countries at once. Multilateral indexes have historically been used for spatial comparisons, and have recently received attention from statistical agencies looking to produce temporal price indexes from large and high frequency price data sets, such as scanner data. Methods for decomposing these indexes are of practical relevance.We present decompositions of three multilateral price indexes. We also review methods proposed by other researchers for extending multilateral indexes without revising previously published index levels, and show how to decompose the extended indexes they produce. Finally, we use a data set of seasonal prices and quantities to illustrate how these decomposition methods can be used to understand the influence of individual commodities on multilateral price index movements, and to shed light on the relationships between various multilateral and extension methods.