Multilevel Decomposition Methods for Income Inequality Measures

This paper studies the multilevel decomposability of the respective income inequality measures proposed by Theil, Rao and Bahattacharya–Maharanobis. All the methods can be decomposed into multilevels if and only if each lower level subgroup belongs to only one particular higher level group. We found not only analytically but also empirically that the residual in the decomposed Bahattacharya–Maharanobis measure tends to increase when the decomposition levels increase. We conclude that Theil’s and Rao’s decompositions have advantages in empirical analysis and that the choice of the decomposition methods depends on the purpose of the analysis.