Overview
This research introduces a framework for estimating conditional inequality curves and measures, designed to quantify the inequality or concentration within the conditional distribution of a specific feature. These measures pertain to the feature's relationship with certain continuous variables. To facilitate a visual representation of changes in the proposed conditional indices, a curve of conditional inequality measures is also presented. A primary contribution of this work is a novel methodology for estimating the conditional quantile function, which forms the basis for deriving these curves and measures.
Approach
The proposed method for estimating the conditional quantile function integrates two distinct regression techniques. Initially, it employs quantile regression to generate estimates for a predefined set of quantile orders. Following this, isotonic regression is applied to the estimated regression coefficients. The application of isotonic regression serves to ensure that the estimated conditional quantile function maintains a nondecreasing property. The theoretical soundness of this approach is supported by a proof of consistency for the proposed estimators.
Findings
- Conditional inequality curves and measures are proposed, which describe the inequality/concentration of a conditional distribution of a feature concerning continuous variables.
- A curve of conditional inequality measures is introduced for graphical illustration of changes in conditional indices.
- A new method for estimating the conditional quantile function is proposed, utilizing quantile regression estimates for given quantile orders.
- Isotonic regression is applied to the estimated regression coefficients to ensure the estimated conditional quantile function is nondecreasing.
- The consistency of the proposed estimators is proved.
- Finite sample performance of the estimators was evaluated through simulation studies and compared with existing approaches.
- Practical application of conditional curves and measures is demonstrated through determining estimated curves of conditional salary inequalities.
- Conditional salary inequalities were analyzed with respect to years of experience across different employee tenure groups.
- The analysis utilized real data.
Why This Matters
The development of conditional inequality curves and measures provides a mechanism for understanding how the distribution of a feature varies conditionally on continuous variables. The proposed estimation method, by combining quantile and isotonic regression, offers a way to rigorously quantify and visualize these conditional relationships. Its application to real salary data exemplifies its utility in analyzing complex distributional patterns within specific subgroups.
Potential Applications
The practical utility of the proposed conditional curves and measures is illustrated through an application in economics. Specifically, the method was used to estimate curves of conditional salary inequalities. This analysis focused on how salary inequality relates to years of experience, distinguishing between different employee tenure groups, using real-world data.
Research Resources
The code utilized to generate the simulation results presented in the paper is accessible to the public. It is available in a dedicated GitHub repository.