Fuzzy Measures of Longitudinal Poverty in a Comparative Perspective

In this paper we present a methodology for the study of longitudinal aspects of monetary and multi-dimensional poverty, and apply this in a multi-country comparative context. The conventional poor/non-poor dichotomy is replaced by defining poverty as a matter of degree, determined by the place of the individual in the income distribution. The same methodology facilitates the inclusion of other dimensions of deprivation into the analysis: by appropriately weighting indicators of deprivation to reflect their dispersion and correlation, we can construct measures of non-monetary deprivation in its various dimensions. An important contribution of the paper is to identify rules for the intersection and union of fuzzy sets appropriate for the study of poverty and deprivation. These rules allow us to meaningfully study the persistence of poverty and deprivation over time. We establish the consistency of the approach when applied to a time sequence of any length. We can thus study longitudinally over time a whole range of indicators of poverty and deprivation, from cross-sectional monetary poverty rates to multi-dimensional indicators of deprivation: in particular, we propose the new “Fuzzy At-persistent-risk-of-poverty rate”, and compare it with the corresponding Laeken indicator adopted by Eurostat.