Estimating income inequality : large sample inference in finite populations

Abstract: During the last decades the interest in measuring income inequality has substantially increased. In this work we consider measures related to the Lorenz Curve, e g the Gini coefficient. These measures are decomposable^ g the inequality in disposable income can be assigned to various income sources. These components are ratios of linear functions of order and/or concomitant statistics. The asymptotic normality of these inequality measures is demonstrated. This theory makes it possible to make inference about the inequality in infinite populations. But the principal aim is to make inference about the finite population inequality. In a design approach it seems necessary to introduce assumptions on the asymptotic properties on the inclusion probabilities. To avoid this, we introduce a superpopulation model within which the inference of the finite population inequalities is supposed to be made. Within this model we have to consider the linear functions of order and/or concomitant statistics as functionals of weighted empirical distribution functions. The measures considered are shown to be asymptotically normal. In appendices the effect of tied observations is discussed.