Estimation of conditional inequality curves and measures via estimating the conditional quantile function

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in relation to covariates. In particular, this enables comparison of inequalities between subpopulations, conditioned on certain values of covariates. To estimate the curves and measures, a novel method for estimating the conditional quantile function is proposed. The method incorporates a modified quantile regression framework that employs isotonic regression to ensure that there is no quantile crossing. The consistency of the proposed estimators is proved while their finite sample performance is evaluated through simulation studies and compared with existing quantile regression approaches. Finally, practical application is demonstrated by analysing salary inequality across different employee age groups, highlighting the potential of conditional inequality measures in empirical research. The code used to prepare the results presented in this article is available in a dedicated GitHub repository.