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

TL;DR

This paper extends classical inequality measures to a conditional context, introducing a new estimation method for conditional quantile functions that accounts for covariates, and demonstrates its practical application in salary inequality analysis.

Contribution

It proposes a novel isotonic regression-based method for estimating conditional quantile functions, ensuring no quantile crossing and enabling nuanced inequality analysis conditioned on covariates.

Findings

The method provides consistent estimators for conditional inequality measures.

Simulation studies show improved finite sample performance over existing methods.

Application to salary data reveals insights into inequality across age groups.

Abstract

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.