Bounds on inequality with incomplete data

James Banks; Thomas Glinnan; Tatiana Komarova

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arXiv · 2512.07709

Bounds on inequality with incomplete data

James Banks·Thomas Glinnan·Tatiana Komarova

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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.

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BibTeX RIS

James Banks, Thomas Glinnan, Tatiana Komarova. 2025-12-08. Bounds on inequality with incomplete data. https://arxiv.org/abs/2512.07709

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