Examining Inequality in Subpopulations Using the Gini Index

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Chaitra Nagaraja*+
• Companies: Fordham University
• Keywords: Gini index ; inequality

Abstract

We often hear claims that our unequal societies are progressively becoming more inequitable. To illustrate this, one can draw Lorenz curves which use order statistics to show how, for instance, wealth is distributed cumulatively across a population. From such curves, one can compute the Gini index for inequality. This index allows one to quantify inequality in a population with a single statistic. While variables such as income or housing price are frequently divided into lower, middle, and upper classes, changes in the economy can impact these subgroups differently. Therefore, it can be more illuminating to examine Gini indices for such subgroups as well. In this paper, we build a theoretical foundation for examining Gini indices for subpopulations computed from observations drawn from a common distribution. In particular, we show how the theoretical Gini index for non-overlapping subpopulations defined by quantile ranges relate to both the overall population index and to each other. Asymptotic distributions are derived for subpopulation Gini index estimators using the mean difference formulation. To conclude, examples using the gamma distribution are provided.