Measuring and analyzing class inequality with the Gini index informed by model-based clustering

The most widely used measure for studying social, economic, and health inequality is the Gini index/ratio. Whereas other measures of inequality possess certain useful characteristics, such as the straightforward decomposability of the generalized entropy measures, the Gini index has remained the most popular, at least in part due to its ease of interpretation. However, the Gini index has a limitation in measuring inequality. It is less sensitive to how the population is stratified than how individual values differ. The twin purposes of this paper are to explain the limitation and to propose a model-based method - latent class/clustering analysis for understanding and measuring inequality. The latent cluster approach has the major advantage of being able to identify potential "classes" of individuals who share similar levels of income or one or more other attributes and to assess the fit of the model-based classes to the empirical data, based on different cluster distributional assumptions and the number of latent classes. This paper distinguishes class inequality from individual inequality, the type that is better captured by the Gini. Once the classes are estimated, the membership of estimated classes obtained from the best fitting model facilitates the decomposition of the Gini index into individual and class inequality. Class inequality is then measured by two relative stratification indices based on either the relative size of the Gini between-class components or the relative number of stratified individuals. Therefore, the Gini index is extended and assisted by model-based clustering to measure class inequality, thereby realizing its great potential for studying inequality. Income data from France and Hungary are used to illustrate the application of the method.