On Focused, Fit-For-Purpose Inequality Measurement

Many inequality indices are based on an aggregation of all individual outcome differences from some centrality measure or focus point, regardless of where that point is in the outcome spectrum. Often they are employed with normative intent, to highlight the lack of equality in outcomes, with equality generally viewed as a good thing wherever it occurs in the outcome spectrum. Yet, when outcomes are positively associated with well-being, while high inequality with respect to a high focus point, suggesting a preponderance of inferior outcomes, may be considered "bad", that same level of inequality measured with respect to a low focus point, suggesting a preponderance of superior outcomes, could be construed as relatively "good". In essence some inequality measures may be inappropriately focused. Here, a family of Focused Inequality indices, together with their sampling distributions, is introduced. While the indices are formulated for multivariate unordered and ordered categorical data environments, they are readily extended to the continuous paradigm. They are exemplified in a study of the evolution of health and loneliness inequalities over the ageing process in China.