New Tests for Richness and Poorness:A Stochastic Dominance Analysis of Income Distributions in Hong Kong

In this paper, we develop the theory of descending stochastic dominance for application to income distribution analysis. We show that conclusions of dominance obtained using our new tests of richness and poorness offer more accurate and more in-depth characterization of welfare inequality in any population. The empirical application of our proposed approach shows that, for Hong Kong, the distribution of total incomes in 2001 has less proportion of poor units in relatively lower income levels compared to that of 2006 at the same time that the distribution of total incomes in 2006 has a higher proportion of rich units in relatively higher income levels. Our analysis also suggests that there exist lower levels of household welfare in 2011 compared to both 2001 and 2006. In terms of age groups, the application of our new methods showed that the younger age cohorts tended to have lesser proportions of poor units in relatively lower income levels compared to those in the 65+ age group, while at the same time, those in the 65+ age group tended to have a higher proportion of rich units in the relatively higher income levels. These extreme concentrations of income units at the ‘bottom end’ for the younger households and at the ‘top end’ for the older households may help explain the overall high inequality level that has persisted in Hong Kong for several years now.