The decompositions of rank-dependent poverty measures using ordered weighted averaging operators

This paper concerns with rank-dependent poverty measures and shows that an ordered weighted averaging, hereafter OWA, operator is underlying in the definition of these indices. The dual decomposition of an OWA operator into the self-dual core and the anti-self-dual remainder allows us to propose a decomposition for all the rank-dependent poverty measures in terms of incidence, intensity and inequality. In fact, in poverty fields it is well known that every poverty index should be sensitive to the incidence of poverty, the intensity of poverty and to the inequality among the poor individuals. However, the inequality among the poor can be analyzed in terms of either incomes or gaps of the distribution of the poor. And depending on the side we focus on, contradictory results can be obtained. Nevertheless, the properties inherited by the proposed decompositions from the OWA operators obliges the inequality components to measure equally the inequality of income and inequality of gap overcoming one of the main drawbacks in poverty and inequality measurement. Finally, we provide an empirical illustration showing the appeal of our decompositions for some European Countries in 2005 and 2011.