Abstract: Poverty measurement and the analysis of the progress (or otherwise) of the poor is
beset with difficulties and controversies surrounding the definition of a poverty line or
frontier. Here, using ideas from the partial identification literature and mixture models,
a new approach to poverty measurement is proposed which avoids specifying a frontier,
the price is that an agent's poverty status is only partially identified. Invoking variants
of Gibrat's law to give structure to the distribution of outcomes for homogeneous
subgroups of a population within the context of a finite mixture model of societal
outcomes facilitates calculation of the probability of an agent's poverty status. From
this it is straightforward to calculate all the usual poverty measures as well as other
characteristics of the poor and non poor subgroups in a society. These ideas are
exemplified in a study of 47 countries in Africa over the recent quarter century which
reveals among other things a growing poverty rate and a growing disparity between
poor and non poor groups not identified by conventional methods.
Keywords: Poverty Frontiers, Mixture Models, Gibrat\'s law, Partial Identification
JEL Classification: C14; I32; O1