Multiplicative decomposition and index number theory: an empirical application of the Sato-Vartia decomposition

In De Boer (2006) the additive decomposition of the aggregate change in a variable into its factors was considered. I proposed to use the "ideal" Montgomery decomposition, developed in index number theory, rather than the commonly used methods in structural decomposition analysis and applied it to the example analyzed by Dietzenbacher and Los (1998) (D&L). In this paper I consider the multiplicative decomposition and argue that from a theoretical point of view the "ideal" Sato-Vartia decomposition is to be preferred to the geometric average of the polar decompositions and that from a computational point of view it is to be preferred to the geometric average of all elementary decompositions. Application to the example of D&L reveals that the three methods yield results that are very close to each other.