Tests of Significance for Lorenz Partial Orders

Abstract

One approach to the study of inequality and the applied welfare economics of income distributions involves using household level micro data from surveys to construct statistically significant partial orders of entire income distributions. The approach is referred to as the dominance method and can be applied to rank income distributions across time, make comparisons among countries, and study the convergence and divergence of regional income distributions and welfare. The methods can also be adapted to study poverty, mobility and other income redistribution issues including tax progressivity, horizontal inequity and tax evasion. In recent years a number of studies applying the dominance approach to inequality and income distributions have been conducted and this emerging literature demonstrates the capacity of the methodology to yield very general conclusions concerning inequality and welfare. The dominance method relies upon developments in three areas — inequality measurement, the theoretical foundations of applied welfare economics as they relate to income distributions, and statistical inference procedures for partially ordering entire distributions. The theoretical developments are surveyed in detail elsewhere in this volume (see chapter 6). This chapter focuses on Lorenz dominance and provides statistical inference procedures that can be applied to rank income inequality using sample estimates based upon survey data. While the discussion and analysis center on relative inequality, we emphasize that the methodology is very general and can be applied in other contexts. In particular, dominance techniques can be used to rank distributions of absolute incomes, generalized Lorenz curves, and the concentration curves that are associated with Lorenz and generalized Lorenz curves.¹