Multiplicative Decompositions of GEKS-Type Indices into the Contribution of Individual Commodities

Price index decomposition allows the National Statistical Institute to break down aggregated price movements into contributions of individual commodities or product groups. In particular, decomposing multilateral indices, which combine many different time comparisons within the time window, can be useful in understanding and interpreting them by common users. This paper discusses multiplicative decompositions of multilateral GEKS-type indices, among which, currently, the GEKS-F and GEKS-T formulas are the most widely used. The paper also provides a multiplicative decomposition of the known GEKS-W index, as well as a decomposition of the GEKS-L, GEKS-GL, and GEKS-LM multilateral indices recently proposed in the literature. The paper also proposes normalized multiplicative decompositions of multilateral indices along with a relative commodity impact measure to enable comparisons of commodity contributions between products and across indices. The effects of these decompositions are demonstrated on two real scanner data sets from the food product segment.