The Gini index decomposition and the overlapping between population subgroups

A century after the introduction of the Gini index, topics related to inequality measurement are central in the political and economic debate. Financial crises have resolved all around the world, aggregate production and income are at the pre-crisis levels, and stock markets indexes hit new records, but the mood is far from the enthusiasm which usually characterizes post-crises periods. A persistent gloom hampers entire countries, insecurity is a global and dominant feeling, protectionism reshapes world trade, nationalism is rising, and countries like United Kingdom prefer an individual to a common path. Rising inequality is the key that reconciles these two situations. Production, income, and wealth have grown, but their growth is unequally shared. If we look only at the GDP, or at the Dow Jones index, we don’t get a fully informative picture. The basic information set should be improved by adding an inequality measure. The debate about GDP, the contributions by the Sarkozy commission or similar committees, and the proposals related to alternative GDP evaluation systems are an important, but still insufficient step. Starting from the daily public information provided by newspapers and televisions, moving to all the actors of society, up to the targets of the national and supranational political strategies and to the data elaborated by the statistical agencies, we need to include inequality at the top of our priorities. An increase in GDP is a good news only if its growth is not too unequally shared, while the combination of an increase of both GDP and inequality would represent a bad news for most people. If the overall inequality level represents a fundamental reference, the information included in it can be successfully exploited by means of inequality decomposition. Inequality decomposition allows us to provide insights about the inequality structure, rank the different inequality factors, and assess their relevance. In this regard the aspect of interest refers to the measurement of inequality between subgroups, for which the literature presents many contributions, thus requiring a critical comparison. An issue strictly connected to the inequality between subgroups is the overlap between subgroups, a topic which Gini studied with his usual strong interest and determined motivation. While we do not encounter particular difficulties in the absence of overlapping, its presence complicates the measure of the contribution to the overall inequality related to the differences between the subgroups. Here we propose a joint analysis of Gini index decomposition and overlapping by developing a comparison between two different approaches: from one side methods based on the subgroup means, and from the other evaluations performed on the basis of all the characteristics of the subgroup distributions. The combination of the two approaches overcomes the disadvantages of the single proposals, thus avoiding the risk of underestimating the real effect of the inequality factors under study.