A comment on the MPI index

Abstract

Sabina Alkire and James Foster [3]’s review of their approach to multidimensional poverty measurement is a clear presentation of ideas they have presented and defended previously. Their AF index, especially its simplest form which they call “adjusted multidimensional headcount ratio” and which is the multidimensional poverty index used by Alkire and Santos [2] in their empirical paper, has certainly the advantage of clarity and simplicity, when compared to other multidimensional poverty indices. This is indeed what makes it extremely attractive, in addition to the fact that it has quite a nice number of appealing properties. As emphasized by Rippin [8] there is however at least one (debatable) feature which the MPI index (and actually any AF index) does not have: it violates the axiom of Non-Increasingness under a Strong Inequality Decreasing Switch. In other words the MPI index will not decrease when the number of dimensions in which the poorer individual is deprived decreases. An additional missing property is that Alkire and Foster ignore substitutability and complementarity between dimensions, although in footnote 25 they explain why they disregarded this feature. Taking into account this element when there are more than two dimensions is in fact not a simple task but it may have very important policy implications. Duclos et al. [5], when discussing the case of complementarity between two dimensions, thus wrote that “better nourished children learn better” so that “overall poverty would decline by more if we were to transfer education from the poorly nourished to the better nourished.” To simplify the analysis of multidimensional poverty but keep its policy relevance, it could be useful to make a clear distinction between the number of dimensions to take into account when measuring deprivation and the number of variables to include when attempting to derive an index for each poverty dimension. Alkire [1] had stressed this point when she listed some of the questions that have to be raised