Analyzing the Effects of Negative and Non-negative Values on Income Inequality: Evidence from the Survey of Household Income and Wealth of the Bank of Italy (2012)

Generally, inequality indices play a basic role in the analysis of welfare economics, also appearing as technical tools applied to income data. A good deal of findings in this research field is provided by the Gini coefficient, typically used for non-negative income values. Even if negative income is often an unfamiliar concept, its presence in real surveys may lead to difficulty in applying the classical Gini-based inequality measures, as they lie outside their standard ranges. In this paper, the more general issue of negative values is considered and a reformulation of the main Gini-based inequality measures adjusted for the problem of negative values is adopted with the purpose of providing theoretical extensions for the income decomposition approach by both income sources and area components. Investigations about the related inferential issues, conducted thorough simulation studies based on resampling techniques, highlight how the traditional approach of removing negative income values may yield different results in terms of inequality estimation, proving that the proposed approach, based on preserving negative values, is the more appropriate practice to follow to avoid the loss of data that really provide a coherent picture of the inequality condition.