MULTILEVEL DECOMPOSITION METHODS FOR INCOME INEQUALITY MEASURES

Abstract

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. jere_447 333..344 Decomposition methods for income inequality measures are used in a number of empirical studies. Some researchers decompose the total income inequality into the inequalities of each factor component of individual or household income. Other researchers decompose the total income inequality into the inequalities between and within groups of individuals or households. In this paper, we focus on the latter case and the multilevel decomposition of the income inequality measures. Multilevel decomposition means that total inequality is decomposed not only into the inequalities between groups and within groups, but also between subgroups and within subgroups. For example, when considering regional income inequality in Japan, it would be better to see not only the contributions of the inequalities between regions (groups) and within regions but also the contributions of the inequalities between prefectures (subgroups) and within prefectures to income inequality at the same time. Many researchers discussed multilevel decomposition methods in the 1970s and 1980s. However, after Cowell (1985) detected the situation to which the multilevel decomposition for Theil’s decomposition (Theil, 1967) can be applied, there was no further discussion until recently. In 2002, Salas (2002) proposed a multilevel decomposition method for a general entropy measure, including Theil’s decomposition. In empirical analyses, other than the Theil decomposition, two other decomposition methods are applied for the single level decomposition proposed by Bahattacharya and Maharanobis (1967) and by Rao (1969). The Bahattacharya and Maharanobis (B–M) decomposition method decomposes the total inequality measured by the Gini coefficient into the inequality between groups and within groups. Rao’s decomposition measures only the contributions of the groups to the total inequality measured by the Gini coefficient.