On the Gini coefficient normalization when attributes with negative values are considered

Abstract

Typically, inequality indices appear both as basic concepts in the analysis of welfare economics and as technical tools applied to income or other transferable attributes. Several findings in such research fields are provided by the standard Gini coefficient, traditionally introduced for incomes taking non-negative values. Even if negative income can appear as an unfamiliar concept, it can arise in real surveys, especially when assessing families’ financial assets. The main troubles associated with the treatment of negative income regards the violation of the normalization principle. The inclusion of income taking negative values can yield for the standard Gini coefficient achieving values $$>$$ 1. The Gini coefficient then has to be adjusted in order to ensure that its range is bounded between 0 and 1. In this paper, a reformulation of the Gini coefficient with respect to that proposed in the literature is presented and discussed in light of the negative income issue. In particular, a new definition of the Gini coefficient normalization term, revealing more coherence with the classical situation of maximum inequality, is provided. Finally, an empirical application based on the Survey of Household Income and Wealth data of the Bank of Italy (2012) further validates the actual attitude of the new Gini coefficient in catching inequality in the distribution of the attribute.