A Note on the Additive Decomposition of GEKS Indexes

It is often useful to decompose an index number into the contribution of each product toward the total index, and consequently there are several well-known decompositions for bilateral indexes. In this note, I extend these decompositions to cases where bilateral indexes are made into multilateral GEKS indexes. Although the result is primarily of theoretical interest, it shows how decompositions based on a bilateral index can be extended to a multilateral index, and highlights the challenge of decomposing GEKS indexes.