Bounds on inequality with incomplete data

James Banks, Thomas Glinnan and Tatiana Komarova

Papers from arXiv.org

Abstract: We study inequality measures when outcomes are observed only in intervals, as in historical tabulations, privacy-protected grouped data, and modern surveys. We develop a nonparametric framework for sharp identification and inference with grouped and interval-valued data, covering brackets and overlapping intervals. For a class of inequality indices, sharp bounds are attained by discrete distributions with finite support, reducing the problem to optimization; linear-fractional indices, including the Gini and quantile ratios, yield linear or quadratic programs. Plug-in bound endpoints have a $\sqrt{n}$ asymptotic distribution, using an $m$-out-of-$n$ bootstrap. Applications to wealth and historical income data compare identified sets with imputation-based estimates.

Date: 2025-12, Revised 2026-08
New Economics Papers: this item is included in nep-ecm
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