Restricted and Unrestricted Hierarchy of Weights

The increasing interest in multidimensional poverty and well-being analysis added complexity to the way these phenomena are conceptualised and measured. A further source of arbitrariness typically derives from the choice of the ‘weights’ to be attached to poverty dimensions. In the literature there has not been thus far a specific attempt to conceptualise the nature of the desired hierarchy among the selected poverty dimensions: That is, the possible meanings of the statement “dimension h is more important than dimension k” have not critically been searched for. The aim of this paper is to move a first step into that direction. We envisage two simple and highly alternative ways in which such a statement can be understood, restricted and unrestricted hierarchy. The analytical conditions allowing to incorporate them into a poverty index are derived and their implications in terms of the understanding of poverty are discussed. An empirical application shows how the choice of the hierarchical scheme for poverty dimensions can lead to opposite conclusions on the trend of poverty.

Citation: Esposito, L. and Chiappero-Martinetti, E. (2008). 'Restricted and unrestricted hierarchy of weights', OPHI Working Paper 22, Oxford Poverty and Human Development Initiative (OPHI), University of Oxford.

Also published in Journal of Applied Economics, 2010, Vol. 13(2), pp. 181–204.