Multiplicative Decomposition and Index Number Theory: An Empirical Application of the Sato–vartia Decomposition

In de Boer (2008), additive decompositions of aggregate changes in a variable into its factors were considered. We proposed using the ‘ideal’ Montgomery decomposition, developed in index number theory as an alternative to 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 we consider multiplicative decompositions and show that the method proposed by D&L of taking the geometric mean of all elementary decompositions is ‘ideal’. However, it requires the computation of an ever-increasing number of decompositions when the number of factors increases. As an alternative, we propose using the Sato–Vartia decomposition, which is also ‘ideal’, but requires the computation of only one decomposition. Application to the example of D&L reveals that the two methods yield results that are very close to each other.