Intensive and Extensive Poverty: A Multidimensional Formulation

A fundamental difficulty for multidimentional poverty analysis is the identification of the poor. This paper proposes two multidimensional poverty indices: the intensive and extensive poverty, which correspond respectively to the most exclusive and inclusive definition of poverty defined according to multiple attributes. Bounds on the intensive and extensive poverty are provided. Drawing analogy from choice under uncertainty, we relate these indices to the minimin and minimax poverty criterion of a social planner. We also show that they can be used to establish sufficient conditions for the first order stochastic dominance of multivariate distributions. Since these conditions are rather demanding, we further propose an aggregate poverty index constructed as a convex combination of the intensive and extensive poverty, which explicitly accounts for the dimensionality effect. Because it effectively separates individual risk aversion and social poverty aversion, it can be used for socially optimal poverty policy that considers both individual welfare and poverty externality. An illustrative example on U.S. income and education distribution is presented.