Beyond the Gini index: a poverty-normalized spatial Bayesian model for assessing territorial inequality

The Gini index is one of the most widely used measures of income inequality. However, it has limitations in allowing reliable comparisons across areas with different socio-economic structures, particularly in small populations, where the index can be highly unstable. This study explores a simple modification of the Gini index that can overcome some of these limitations.

We propose a modification of the original Gini index that incorporates the poverty rate as an offset. Combined with Bayesian spatial modelling, this approach improves the precision and comparability of small-area estimates, by providing measures of inequality conditional on local poverty levels. To illustrate it, income data from 8,043 Spanish municipalities for the year 2022 were used, and the spatial patterns of the normalized Gini index were compared with those obtained from the original index.

The normalized Gini index revealed spatial inequality patterns that were overlooked by the original index. The new approach identified municipalities with higher levels of inequality than expected given their poverty rates in Andalusia, Extremadura, and Murcia, in contrast to lower inequality in Catalonia, Basque Country, Madrid, and Balearic Islands. In addition, while the original Gini index increased with population density and urbanization, the normalized version showed an opposite trend, with higher relative inequality observed in rural and low-density municipalities after accounting for local poverty levels.

Given its simplicity, reliance on widely available indicators, and adaptability to different territorial scales, the proposed method offers a useful measure for describing income inequality conditional on a region's poverty level and informing local redistributive policies.