Measuring Inequality by Asset Indices: A general approach with application to South Africa

Asset indices have become widely used in a number of areas of social research, particularly in the analysis of Demographic and Health Surveys. Indeed the calculation of "wealth indexes" is now routine practice in the DHSs. Asset indices have been externally validated in a number of contexts. While these indices have been shown to work well as proxy measures of poverty, they are not suited to investigate inequality. In this paper we will show that, in fact, typical asset indices also fail an internal validity test: they frequently rank individuals in ways which violate the basic principle that individuals that have more (of anything) should be ranked higher than individuals that have less. We consider from first principle what sort of indexes might make sense, given the predominantly dummy variable nature of asset schedules. We show that there is, in fact, a way to construct an asset index which does not violate some basic principles and which also has the virtue that it can be used to construct "asset inequality" measures. However, there is a need to pay careful attention to the components of the index. We illustrate this by discussing the asset indices released publicly with South African DHS data and then a South African case study of changes over time. Both situations show the perils of mechanical approaches to calculating indexes. When calculating inequality using asset indices on South African data we find high inequality in the DHS data but that inequality has decreased markedly between 1993 and 2008. This contrasts with findings derived from income data which suggest that inequality has hardly changed at all.