Mixture models and poverty measurement

Classifying agents into “poor”, “middle class” or “rich” subgroups for the purpose of analysis is commonplace in economics, unfortunately the identification of class boundaries is contentious and beset with problems. From a more general perspective, the entire population can be viewed a collection of a small number of classes k = 1, 2, á , K determined by inherent circumstances, such that an individual belonging to class k faces outcome opportunities described by a distribution fk. Since classes are not defined a priori, finite mixture models (FMM) can be used to estimate the parameters of the sub-distributions making up the population distribution. Articulated this way, poverty analysis is about identifying and measuring various aspects of the sub-distributions in the mixture together with their mixing coefficients with a focus on the poorest subgroup. It is also straightforward to calculate sub-group inequality and polarization measures as well as the extent the sub- distributions differ. As a substantive illustration, the anatomy of income distribution in Kyrgyzstan is analyzed.