Conditions for the Most Robust Poverty Comparisons Using the Alkire-Foster Family of Measures

In the burgeoning literature on multidimensional poverty indices, the Alkire-Foster (AF) measures stand out for their resilience in identifying the multidimensionally poor with cut-off criteria covering the spectrum from the union approach to the intersection approach. The intuitiveness and easy applicability of the measures’ identification and aggregation methods are reflected in the increasing use of the AF measures in poverty measurement, as well as in other fields. This paper extends the dominance results derived by Lasso de la Vega (2009) and Alkire and Foster (2010) for the adjusted headcount ratio and develops a new condition whose fulfillment ensures the robustness of comparisons using the adjusted headcount ratio for any choice of multidimensional cut-off and for any weights and poverty lines. The paper then derives a first-order dominance condition for the whole Alkire-Foster family (that is, for continuous variables). 

** Please note: As of September 2011, this paper has been revised and updated, and replaces Working Paper 44, published in July 2011 with the same title and using ISBN 978-1-907194-28-3.** 

Citation: Yalonetzky, G. (2011). 'Conditions for the most robust poverty comparisons using the Alkire-Foster family of measures (revised and updated)', OPHI Working Papers 44b,  Oxford Poverty and Human Development Initiative (OPHI), University of Oxford.

This paper is also published in Social Choice Welfare, 2014, Vol. 43(3), pp. 773–807.

A more general version of this paper is published as ECINEQ Working Paper 2012-257.