We develop a locally robust semiparametric framework for estimating conditional Theil and mean log deviation indices. The proposed series-based estimators allow aggregate inequality and its evolution to be decomposed into within-group, between-group, and reallocation components. We apply the methodology to Portuguese matched employer–employee data to study the roles of worker, job, and firm characteristics in the evolution of wage inequality from 2011 to 2019.

We propose a parametric model for the conditional Gini index, in the spirit of mean and quantile regression. We derive the moment condition for a general parametric specification and develop the econometric theory for the linear case: identification results, including under model misspecification, a loss function for the conditional Gini index, an R²-type goodness-of-fit measure, a Gini Index Regression (GIR) estimator, and bootstrap-based inference. An empirical application to U.S. labor market data reveals substantially higher inequality among non-union workers and shows that, among the college-educated and controlling for characteristics, occupation, and industry, inequality is modest at labor market entry — consistent with the skill-biased technical change hypothesis — but rises sharply with experience.

We derive the influence functions for functionals of conditional distributions to propose locally robust estimation and inference for Gini Index Regression (GIR) models. We consider three alternative model specifications as leading examples, and the resulting procedures are robust to first-stage, nonparametric kernel estimation of the conditional distribution function. We illustrate our theoretical findings via Monte Carlo experiments and an empirical application.