Multidimensional and Specific Inequalities

James E. Foster and Michael Lokshin

No 10748, Policy Research Working Paper Series from The World Bank

Abstract: Despite the multitude of measures of multidimensional inequality, none is regularly used in policymaking. This paper proposes multidimensional inequality measures that are easily implementable and transparent and overcome many deficiencies of existing measures. The measures follow a traditional two-stage format, which aggregates dimensions first and then applies a unidimensional measure like the Gini coefficient to the distribution of aggregates. A novel characterization result identifies the precise form of aggregation needed to obtain axiomatically sound measures. The paper derives an additive decomposition formula — breaking down multidimensional inequality into terms reflecting the average specific inequalities (within dimensions) and the joint distribution (across dimensions) — for any measure created using a standard unidimensional measure or the Lorenz curve. The paper also provides an approach to calibrating the measure for use with data over time, replacing the usual ad hoc normalization of variables with one that accounts for a policymaker’s normative weights. The technology is illustrated first using synthetic data to understand how the measure varies as the components are changed and then using data from Azerbaijan.

Date: 2024-04-04
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