Decomposing Lorenz and Concentration Curves*

Abstract

We decompose the Lorenz curve (LC) and its associated concentration curve (CC) by population subgroups. To illustrate these decompositions, we examine changes in earnings inequality among West Germans, East Germans, and foreign guest workers during the recent German unification. We show that East German earnings have become less concentrated in the lower deciles of the overall German earnings distribution, whereas the earnings of West Germans and foreign guest workers have become more concentrated in the lower deciles.

Gender Segregation in the Spanish Labor Market: An Alternative Approach

“…A decomposition of the local segregation curve is obtained when partitioning occupations into different classes, which is in line with the decomposition of the Lorenz curve by population subgroups proposed by Bishop et al (2003). An alternative decomposition of the local segregation curve according to a classification of the individuals of the target group is also offered.…”

Geographical Concentration of Unemployment: A Male–Female Comparison in Spain

“…The two types of measures seem reasonable and focus on different aspects of the distribution, so we have chosen to use both in the empirical section. Finally, we use the decomposition of the Lorenz curve by subgroups, proposed by BISHOP et al, 2003, to determine the contribution of municipalities, classified according to their size, at different points of the unemployment distribution. The decomposition of the Theil index is also used to determine the contribution of men and and women to the overall concentration of unemployment.…”

Measuring concentration: Lorenz curves and their decompositions

“…Second, additive decompositions of this curve by subsectors and by groups of locations are proposed, since even though additive decompositions of the generalized entropy family of indexes have been used to measure industrial concentration (Brülhart and Traeger 2005), as far as we know, no decompositions of the employment Lorenz curves have yet been suggested. One of the decompositions parallels that proposed by Bishop et al (2003) in a context of income distribution. Third, the employment Lorenz curves and their decompositions are finally used to analyze the concentration of manufacturing industries in Spain in 2008.…”

“…Following the decomposition of the standard Lorenz curve proposed by Bishop et al (2003) in an inequality context, in what follows, we offer two forms of decomposition of these curves: one by groups of locations, and the other by subsectors.…”

“…Proof Following the decomposition of the standard Lorenz curve by population subgroups proposed by Bishop et al (2003), we define indicator G k l so that G k l = 1 if location (region) l belongs to group (country) k and G k l = 0 otherwise (l = 1, . .…”