Estimation of quantile ratios of the Dagum distribution

Inequality measures based on ratios of quantiles are frequently applied in economic research, especially to the analysis of income distributions in different divisions. Simple quantile ratios or quantile dispersion ratios, which can be considered supplementary to the popular Gini and Zenga indices, are often applied in comparison of incomes for various subpopulations or to assess inequality changes over time. They have the advantage of being focused on extremal income groups that are especially interesting from the point of view of economic inequality and polarization. In the paper a confidence interval for such measures, assuming the Dagum distribution, is constructed. The ends of the confidence interval depend on an unknown shape parameter of the underlying income distribution model. In applications this parameter must be estimated from the data. The constructed confidence interval, applied to decile and quintile ratios, was implemented to the analysis of income inequaity in Poland. The quantile-based inequality measures have been estimated for the Polish macro-regions (NUTS1) and for the whole country, on the basis of micro-data coming from the Household Budget Survey 2015.