# Interval estimators for inequality measures using grouped data

## TL;DR

This paper develops methods to construct reliable confidence intervals for inequality measures using only grouped income data, demonstrating superior coverage compared to traditional methods, and applying these to real datasets.

## Contribution

It introduces bootstrap and Wald-type interval methods for quantile-based inequality measures with grouped data, utilizing the Generalized Lambda Distribution and linear interpolation.

## Key findings

- Bootstrap and Wald intervals achieve good coverage with grouped data.
- Methods outperform traditional intervals for measures like the Gini index.
- Application to real data demonstrates practical utility.

## Abstract

Income inequality measures are often used as an indication of economic health. How to obtain reliable confidence intervals for these measures based on sampled data has been studied extensively in recent years. To preserve confidentiality, income data is often made available in summary form only (i.e. histograms, frequencies between quintiles, etc.). In this paper, we show that good coverage can be achieved for bootstrap and Wald-type intervals for quantile-based measures when only grouped (binned) data are available. These coverages are typically superior to those that we have been able to achieve for intervals for popular measures such as the Gini index in this grouped data setting. To facilitate the bootstrapping, we use the Generalized Lambda Distribution and also a linear interpolation approximation method to approximate the underlying density. The latter is possible when groups means are available. We also apply our methods to real data sets.