Poverty severity in a multidimensional framework : the issue of inequality between dimensions

This paper contributes to the axiomatic foundation of multidimensional poverty measures. A well-known problem in the multidimensional framework is that the identification method used in the one-dimensional framework, the union method, leads to exaggerated poverty rates. So far, this problem has been addressed by either changing the identification method itself or by introducing different weighting schemes - which all have in common that they assume attributes to be substitutes. In our paper we claim that the exaggeration problem is first of all an issue of how distribution sensitivity is accounted for and thus ought to be addressed at the aggregation instead of the identification level. In fact, we provide evidence that the way in which the Transfer principle, which accounts for distribution sensitivity in the one-dimensional framework, has been extended to the multidimensional framework is incomplete. We demonstrate that by solving this aggregation problem with the introduction of an additional axiom, the exaggeration problem at the identification level is, as a direct consequence, automatically solved as well. Finally, we derive a family of poverty measures whose specific, axiomatically implied weighting structure solves the exaggeration problem for ordinal as well as cardinal data while at the same time allowing for an independent relationship between attributes. We demonstrate that some of the most well-known poverty measures like the Multidimensional Poverty Index are special cases of this family.