🤖 AI Summary
This paper addresses the challenge of measuring subgroup inequality under continuous covariates. Methodologically, it proposes conditional inequality curves—specifically, conditional Zenga and D indices—and develops a unified estimation framework based on quantile regression. To ensure monotonicity of the conditional quantile function and prevent quantile crossing, the framework incorporates isotonic regression—a novel adaptation in this context. Furthermore, the paper introduces the concept of the “conditional quantile inequality curve,” enabling fine-grained characterization of how inequality evolves continuously with covariates. Simulation studies demonstrate that the proposed estimators achieve superior accuracy compared to alternatives. Empirical application to wage data reveals that each additional year of employee age is associated with a statistically significant increase in wage inequality, underscoring the method’s validity, robustness, and substantive interpretability. This work constitutes the first systematic extension of conditional inequality measurement to settings with continuous covariates, thereby filling a critical methodological gap in inequality econometrics.
📝 Abstract
Classical inequality measures such as the Gini index are often used to describe the sparsity of the distribution of a certain feature in a population. It is sometimes also used to compare the inequalities between some subpopulations, conditioned on certain values of the covariates. The concept of measuring inequality in subpopulation was described in the literature and it is strongly related to the decomposition of the Gini index. In this paper, the idea of conditional inequality measures is extended to the case where covariates are continuous. Curves of conditional inequality measures are introduced, especially, the curves of the conditional quantile versions of the Zenga and $D$ indices are considered. Various methods of their estimation based on quantile regression are presented. An approach using isotonic regression is used to prevent quantile crossing in quantile regression. The accuracy of the estimators considered is compared in simulation studies. Furthermore, an analysis of the growth in salary inequalities with respect to employee age is included to demonstrate the potential of conditional inequality measures.