Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty

Abstract

We develop an approach for making welfare comparisons between populations with multidimensional discrete well-being indicators observed at the micro level. The approach is rooted in the concept of multidimensional first order dominance. It assumes that, for each indicator, the levels can be ranked ordinally from worse to better, however no assumptions are made about relative importance of any dimension nor about complementarity/substitutability relationships between dimensions. We also introduce an efficient algorithm for determining dominance and employ a bootstrap approach that permits cardinal rankings of populations. These approaches are applied to household survey data from Vietnam and Mozambique.

Poverty Mapping Based on First‐Order Dominance with an Example from Mozambique

“…The FOD criterion, in specific, corresponds to what in probability theory is referred to as the usual (stochastic) order (Lehmann, 1955). 5 This implies that the FOD approach does not depend on a weighting scheme or on strongly simplifying assumptions about the second order and cross derivatives of the social welfare function (Arndt et al, 2012b). Instead, for the case of binary welfare indicators where individuals or households are either deprived or not deprived in each specific welfare dimension, the FOD criterion simply asserts that it is better to be not deprived than deprived in any given dimension.…”

Poverty mapping based on first order dominance with an example from Mozambique

“…1 The idea of applying multidimensional techniques to rank welfare in small areas has been advanced by Arndt et al (2012b), in a UNU-WIDER working paper version of this study by Arndt et al (2013), and by Permanyer…”

Spatial and temporal multidimensional poverty in Nigeria

“…In this context, where consumption poverty estimates do not provide a clear perspective on poverty levels and trends, triangulating poverty analysis with alternative measures could be particularly informative. Ajakaiye et al (2014) advance the discussion by estimating multidimensional, non-income poverty within Nigeria's six geopolitical zones and rural and urban areas between 1999 and 2008 using the first-order dominance (FOD) method developed by Arndt et al (2012). Their analysis lends support to the view that poverty reduction in Nigeria has not kept pace with the rapid economic growth attained in the last decade.…”

“…Thus, while the welfare indicators are ordinal in nature, the application of bootstrap sampling produces probabilities of one population performing better than another does. For greater detail on the FOD methodology, see Arndt et al (2012).…”