A Unidimensional Representation of Multidimensional Inequality: An Econometric Analysis of Inequalities in the Arab Region

Abstract

This paper introduces a novel approach for analyzing multidimensional inequality. We use a counting-based approach and a transformed survival function to capture the impact of inequality at the individual level. We then define indices of multidimensional inequality as aggregations of these individual impacts and introduce two new graphical tools. These graphical tools leverage the unidimensional representation to provide an intuitive representation of multidimensional inequality. Through this representation we derive dominance conditions that allow for the identification of robust rankings of multidimensional inequality. This paper also pushes boundaries in stochastic dominance estimation and inference showcasing new estimation and statistical methods related to our new graphical tools and dominance conditions. As a practical demonstration, we apply our method to analyze data from the Harmonized Household Income and Expenditure Surveys for three Arab countries and the Arab Barometer survey for ten Arab countries.