Subgroup Consistent Poverty Indices

Abstract

It seems desirable that the overall level of poverty should fall whenever poverty decreases within some of the population and is unchanged outside that group. Yet this simple and attractive property, which we call subgroup consistency, is violated by many of the poverty indices suggested in recent years. This paper characterizes the class of consistent poverty iindices, and identifies the special features associated with this property. ONE OF THE MOST APPEALING PROPERTIES of poverty indices suggested in recent years is a simple consistency axiom which requires the overall level of poverty to fall if a of the population experiences a reduction in poverty, while poverty in the rest of the population remains unchanged.2 This property-which we term subgroup consistency-is desirable for a number of reasons. From a practical point of view, it is needed- to coordinate the effects of a decentralized strategy towards poverty alleviation. For a decentralized strategy typically in- volves a collection of activities targeted at specific subgroups or regions of the country. If the poverty indicator is not consistent, we may be faced with a situation in which each local effort achieves its objective of reducing poverty within its targeted group, and yet the level of poverty in the population as a whole increases. Subgroup consistency may therefore be viewed as an essential counterpart to a coherent poverty program. Subgroup consistency may also be regarded as a natural analogue of the monotonicity condition of Sen (1976), since monotonicity requires that aggre- gate poverty fall (or, at least, does not increase) if one person's poverty is reduced, ceteris paribus, while consistency demands that aggregate poverty fall if one subgroup's poverty is reduced, ceteris paribus. Furthermore, consistency is closely related to the property of decomposability, which allows aggregate poverty to be expressed as a population-share weighted average of poverty levels, and hence facilitates the disaggregated- analysis of poverty by region or ethnic group of the type undertaken by Anand (1983). As it happens, the traditional poverty indices used by Anand and others -the headcount ratio (the fraction of the population that is poor) and the 1 Earlier versions of this paper were presented at a conference on Measurement and Modelling