An Original Statistical Framework for Decomposing Multidimensional Inequality in Nigeria Using Generalised Entropy and Shapley Value Methods

Multidimensional inequality in Nigeria encompasses correlated deprivations across income, health, and education whose joint statistical structure requires decomposition methods that respect the multivariate nature of inequality rather than treating dimensions independently. This dissertation develops an original statistical framework for decomposing multidimensional inequality in Nigeria using generalised entropy measures and Shapley value decomposition, contributing to both inequality theory and distributional statistics methodology. A multivariate generalised entropy class of inequality indices is defined with desirable axiomatic properties, including decomposability by population subgroup and statistical component. Shapley value decomposition allocates total multidimensional inequality to contributions of individual dimensions and their pairwise correlations. Asymptotic distribution theory for the proposed indices and Shapley values is derived, enabling hypothesis testing and confidence interval construction. Bootstrap-based inference is implemented computationally. The framework was applied to the 2022 Nigeria Living Standards Survey microdata (n=22,110 households) with income, health expenditure, and education expenditure as the three inequality dimensions. Total multidimensional inequality exceeded the sum of marginal univariate inequalities by 18 percent, reflecting positive inter-dimensional correlation. Income inequality contributed 52 percent, health 28 percent, and education 20 percent of total multidimensional inequality by Shapley attribution, with 11 percent attributable to inter-dimensional correlation. Significant between-zone inequality was confirmed. The dissertation contributes theoretical and empirical inequality measurement methodology applicable to Nigerian National Bureau of Statistics welfare reporting. Keywords: multidimensional inequality, generalised entropy, Shapley decomposition, distributional statistics, Nigeria