A statistical model for the dynamics between two fuzzy states: theory and application to poverty analysis

Manifestations of a number of social and economic phenomena are commonly perceived as dichotomous: welfare-poverty, employment-unemployment, health-illness, etc.. However these phenomena are intrinsically fuzzy, therefore a statistical analysis with binary variables oversimplifies reality and tends to wipe out all the nuances that exist between the two opposite extremes. Such a problem is especially relevant in the case of dynamic analyses on panel data, where the use of binary variables is required if one of the available discrete states models is to be applied. In order to avoid such a rigid simplification it is possible to follow a fuzzy approach which is coherent with the intrinsic nature of the studied phenomenon. This paper deals with the dynamic model with fuzzy states recently proposed and developed in a series of papers (Cheli, 1995; Cheli and Betti, 1999; Betti, Cheli and Lemmi 2002). Here we basically aim to summarise its theory and to develop it by means of a series of theorems and by introducing two new statistical tools that we called Dynamic Indices and Average Transition Matrices. Although the scope of this paper is essentially methodological, we also present an application to the analysis of poverty dynamics in Great Britain from 1991 to 1997