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)

Abstract

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.

Rural household income distribution and inequality in China: Effects of payments for ecosystem services policies and other factors

“…Given k sources of total income, the concentration coefficient (C k ), also known as the "pseudo-Gini" coefficient, is an important indicator for revealing the inequality of income from source k. The "pseudo-Gini" mimics the Gini coefficient calculation but re-orders source k income according to the household rank in total income (Raffinetti et al, 2017). When C k is greater than (overall) G, income from source k expands (worsens) total income inequality.…”

Group size increases inequality in cooperative behaviour

“…We added a correction for small sample bias of the Gini index [27] and an adjustment to allow negative values [25], which is needed to examine inequality in weight gains (that can be negative), resulting in the revised formula:…”

“…Our analyses use data from a long-term study of meerkats in the southern Kalahari that provides extensive records of cooperative behaviour and body weight in large numbers of recognizable individuals of known age across different group sizes [24]. To measure the extent of inequality in contributions among the helpers within groups, we used the Gini index, which quantifies the extent to which the distribution of a given value deviates from a state of complete equality [25]. We also examined some other indices of inequality to validate our results, as recommended by Kokko [26], but the Gini index was our primary index as it provides a straightforward measure, which is the most widely used one for inequality ( particularly in economics [25]) and also has a simple correction for small sample size bias [27] that was useful for us (see Methods).…”

“…To measure the extent of inequality in contributions among the helpers within groups, we used the Gini index, which quantifies the extent to which the distribution of a given value deviates from a state of complete equality [25]. We also examined some other indices of inequality to validate our results, as recommended by Kokko [26], but the Gini index was our primary index as it provides a straightforward measure, which is the most widely used one for inequality ( particularly in economics [25]) and also has a simple correction for small sample size bias [27] that was useful for us (see Methods). Our aim was to determine: (i) whether inequality in cooperative contributions and the frequency of free riders (defined below) is higher in larger groups, (ii) whether sex and age-related differences in individual contributions increase with group size; and (iii) whether increased inequality in workload among group members is associated either with reductions in the total amount of care provided to dependent juveniles or with reductions in their growth and survival.…”

Measuring income inequality based on unequally distributed income

“…Bellù and Liberati (2006) advise replacing zero incomes with arbitrarily small positive incomes. Raffinetti et al (2016) study the effects of these remedial adjustments on the Gini coefficient.…”