Health Inequality Gini Decomposition

The Gini measures pure inter-individual inequality: how unequally health is distributed across all people, ranked by their own health. The concentration index measures socioeconomic inequality: how health is distributed across people ranked by income or another social variable. As Wagstaff and van Doorslaer stress, these answer different questions. A population can have substantial total health inequality (high Gini) with little socioeconomic gradient (near-zero concentration index), or vice versa. They are complements, and which to report depends on whether the concern is overall dispersion or the social gradient.

It captures whether a component is distributed in line with the overall health ranking. In the Lerman-Yitzhaki decomposition each source contributes its share of the mean times its own Gini times its Gini correlation with the total. A component can be very unequal on its own yet contribute little to total inequality if it does not track who is healthy overall — for example if it is high for some healthy and some unhealthy people alike. Ignoring the Gini correlation and reading only the component's own Gini badly misattributes the sources of inequality.

Not directly. The Gini requires a ratio scale with a meaningful zero, because it is defined relative to mean health and rests on the Lorenz curve. Ordinal categories like excellent/good/fair/poor have no defensible ratios, so a raw Gini on coded categories is uninterpretable and the result depends arbitrarily on the coding. Options are to map categories to a cardinal health-utility scale with external valuation, or to use measures designed for ordinal data. For purely ordinal socioeconomic-gradient questions, rank-based indices such as the concentration index are generally more appropriate.