Lorenz regression analysis of inequality of opportunity and explained inequality

Working Paper 2026-699

Abstract

Inequality of opportunity (IOp) is typically operationalized as explained inequality: inequality in the conditional expectation of an advantage given circumstances. Existing methods work in two stages, first estimating a model for the outcome, and then applying an inequality index to the fitted values. Any bias in the first stage can therefore propagate to the second stage. By contrast, this paper builds instead on Lorenz regressions which optimize the object of interest directly — explained inequality — under a flexible single-index model. We show that this provides a robust and unified framework adapted to both continuous and binary outcomes and illustrate the method for income- and education-based IOp, where it integrates naturally into existing work while improving estimation stability, interpretability, and robustness.

Authors: Alexandre Jacquemain, Cédric Heuchenne, Philippe Van Kerm.