Working Paper 2015-361
When measuring poverty with counting measures, it is worth inquiring into the conditions prompting poverty reduction which not only reduce the average poverty score further but also decrease deprivation inequality among the poor, thereby emphasizing improvements among the poorest of the poor. For comparisons of cross-sectional datasets of the same society in different periods of time (i.e. an anonymous assessment), Lasso de la Vega (2010) and Alkire and Foster (2011) developed a first-order dominance condition based on counting poverty headcounts, whose fulfillment ensures that multidimensional poverty decreases for a broad family of counting poverty measures. Further, Chakravarty and Zoli (2009) and Lasso de la Vega (2010) derived a second-order dominance condition based on reverse generalized Lorenz curves, whose fulfillment ensures that multidimensional poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive poverty measures. However, both conditions hold for a predetermined vector of weights for the poverty dimensions. In this paper we refine the second-order conditions in order to obtain necessary and sufficient conditions whose fulfillment ensures that multidimensional poverty reduction is robust to a broad array of weighting vectors and inequality-sensitive poverty measures. We illustrate these methods with an application to multidimensional poverty in Peru before and after the 2008 world financial crisis.
Authors: José V. Gallegos, Gaston Yalonetzky.