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.

翻译：本文将经典的不平等曲线与测度概念拓展至条件不平等曲线与测度，并引入了条件不平等测度曲线。这一拓展为结合协变量进行更细致的不平等分析提供了框架。特别地，该方法使得在不同协变量取值条件下比较子群体间的不平等成为可能。为估计这些曲线与测度，本文提出了一种估计条件分位数函数的新方法。该方法采用改进的分位数回归框架，结合等渗回归以确保分位数曲线无交叉。我们证明了所提估计量的一致性，并通过模拟研究评估了其有限样本表现，同时与现有分位数回归方法进行了比较。最后，通过分析不同年龄组员工的薪酬不平等问题，展示了条件不平等测度在实证研究中的应用潜力。本文结果所用代码已发布于GitHub代码库。