The Informational Index of Inequality
Abstract
A new informational index of income inequality is proposed. Based on a combinatorial characterisation of entropy andon its generalisation by multivariate measures of co-information, the index addresses a limiting analytical choice
embedded in Theil’s two indices of income inequality. This yields a positive measure of inequality of opportunity in
income-generating processes, defined in relation to probabilities that the population-wide distribution
of income describes the set of possible income levels facing specified sub-groups of that population. Its measure
across a population is given when sub-groups consist of each individual. This can be successively decomposed
linearly by sub-groups defined by covariates of income. In those instances, the index also provides informational
measures of phenomenological association and interaction between income and those covariates. On those bases
the index improves on mean-log deviations as measures of “luck egalitarian” notions of equity; casts new light on and
uncovers new properties in the Theil-Finezza index of segregation; offers a non-parametric generalisation of
the Kitagawa-Oaxaca-Blinder decomposition; and lays new conceptual foundations for work on the determinants and
normative content of patterns of income differentiation in decentralised market economies.