A rank-dependent multidimensional deprivation index (MDI) for binary data

This paper first shows how to extend the Sen-Shorrocks poverty index to the analysis of multidimensional deprivation, when only dichotomous variables are available to assess deprivation in various domains, the most common case in the literature. More precisely, it introduces the first rank-dependent multidimensional poverty index in the literature, using a counting approach. The resulting multidimensional deprivation index, or MDI in short, has a nice graphical representation (“PUB curve†) that turns out to be an extension of the so-called TIP curve of Jenkins and Lambert to the case of multiple deprivations. This graphical representation is similar to the SD curve introduced by Lasso de la Vega (2010), but additionally emphasizes the third “I †of multidimensional deprivation: inequality. The MDI is sensitive to inequality and satisfies quite nice properties, but it cannot be broken down by population subgroups, when a standard decomposition is used, and it does not have the property of dimensional breakdown, as the latter is usually defined in the literature. The paper proves, however, that there exists an alternative decomposition by population subgroups that can be applied to the MDI; it also derives a decomposition by deprivation domain, analogous to the breakdown of the Gini index by factor components. A simple empirical illustration based on deprivation data from four Central American countries (Guatemala, El Salvador, Honduras, and Nicaragua) shows the usefulness of the MDI.