2025/12/08 by Banks, James, Glinnan, Thomas, Komarova, Tatiana
Decision Sciences · Mathematics · Social Sciences · #Advanced Statistical Methods and Models #Computation (stat.CO) #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Income, Poverty, and Inequality #Methodology (stat.ME) #Risk and Portfolio Optimization
paper · doi:10.48550/arxiv.2512.07709
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all Schur-convex inequality measures, and show that sharp bounds are attained by distributions with finite support. This reduces the computational problem to finite-dimensional optimization, and for indices admitting linear-fractional representations after suitable ordering of the data (including the Gini coefficient and quantile ratios), we express the bound problems as linear or quadratic programs. We then establish √(n) inference for the upper and lower bounds using a directional delta method and bootstrap confidence intervals. In applications, we compute sharp Gini bounds from household wealth data with mixed point and interval observations and use historical U.S. grouped income tables to bound time series for the Gini and quantile ratios.