A subgroup decomposition of the inequality change over time

Abstract

This article proposes a subgroup decomposition of the determinants of the change in the Gini index over time. The decomposition allows one to explain the link between inequality change, reranking and income growth for the various subgroup components of the inequality index.

Keywords:

• inequality change
• Gini index
• subgroup decomposition
• reranking
• income growth

JEL Classification:

• D31
• D63
• C43

Notes

¹ Detailed manipulations of Equation 11(11) can be found in Vernizzi (2009, p. 5). The author fully discussed the use of the Hadamard product and permutation matrices for calculating and decomposing indices of redistribution and reranking.

² Since weights for longitudinal analysis were not produced, we followed Quintano et al. (2006) and used 2010 cross-sectional weights for both 2008 and 2010 incomes. We rescaled the weights assigned to the retained households to ensure that the sum of the weights equals the number of households.