Decomposing indexes with Euler weights

<jats:p>I've always liked Hallerbach (2005)'s decomposition of the Fisher index. It's such a simple and straightforward way to decompose the Fisher index that generalizes to a wide range of index-number formulas. The latter has, to my knowledge, not been explored before, and Hallerbach's approach of using Euler weights to decompose an index number is instead associated with the Fisher index.</jats:p>