Working Paper 2006-32
When poverty is viewed as a matter of degree, i.e. as a fuzzy measure, two additional aspects are introduced into the analysis compared with the conventional poor/non-poor dichotomous approach: (i) the choice of membership functions i.e. quantitative specification of individuals’ or households’ degrees of poverty and deprivation; and (ii) the choice of rules for the manipulation of the resulting fuzzy sets, rules defining their complements, intersections, union and averaging. Specifically, for longitudinal analysis of poverty using the fuzzy set approach, we need joint membership functions covering more than one time period, which have to be constructed on the basis of the series of cross-sectional membership functions over those time periods. In this paper we propose a general rule for the construction of fuzzy set intersections, that is, rules for the construction of longitudinal poverty measures from a sequence of cross-sectional measures. On the basis of the results obtained, various fuzzy poverty measures over time can be constructed as consistent generalisations of the corresponding conventional (dichotomous) measures. Examples are rates of any-time, persistent and continuous poverty, distribution of persons and poverty spells according to duration, rates of exit and re-entry into the state of poverty, etc.
Authors: Gianni Betti, Bruno Cheli, Vijay Verma.