FUZZY MEASURES OF THE INCIDENCE OF RELATIVE POVERTY AND DEPRIVATION: A LONGITUDINAL AND COMPARATIVE PERSPECTIVE

Gianni Betti (Italy) and Vijay Verma (Italy)

Received January 14, 2009

Abstract

In this paper, we present a methodology for the study of multi-dimensional and longitudinal aspects of poverty and deprivation, 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 allows us to meaningfully combine income and the diverse non-income deprivation indices at the micro-level and construct what we have termed ‘latent’ and ‘manifest’ indicators of deprivation. Mathematically the same approach is carried over for studying 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 ‘latent’ and ‘manifest’ indicators of deprivation.

Keywords and phrases: fuzzy sets, longitudinal and multi-dimensional poverty measures, comparative analysis.