# Estimation and inference for area-wise spatial income distributions from grouped data

## TL;DR

This paper introduces a Bayesian spatial state-space model for simultaneous estimation of area-wise income distributions from grouped data, enabling inference for both sampled and unsampled areas, demonstrated with Japanese data.

## Contribution

It develops a novel Bayesian spatial state-space approach for joint estimation of multiple area income distributions from grouped data, accounting for geographical information.

## Key findings

- The method accurately estimates income measures for all areas.
- It outperforms conventional separate estimation approaches.
- Demonstrated effectively on Japanese municipality data.

## Abstract

Estimating income distributions plays an important role in the measurement of inequality and poverty over space. The existing literature on income distributions predominantly focuses on estimating an income distribution for a country or a region separately and the simultaneous estimation of multiple income distributions has not been discussed in spite of its practical importance. In this work, we develop an effective method for the simultaneous estimation and inference for area-wise spatial income distributions taking account of geographical information from grouped data. Based on the multinomial likelihood function for grouped data, we propose a spatial state-space model for area-wise parameters of parametric income distributions. We provide an efficient Bayesian approach to estimation and inference for area-wise latent parameters, which enables us to compute area-wise summary measures of income distributions such as mean incomes and Gini indices, not only for sampled areas but also for areas without any samples thanks to the latent spatial state-space structure. The proposed method is demonstrated using the Japanese municipality-wise grouped income data. The simulation studies show the superiority of the proposed method to a crude conventional approach which estimates the income distributions separately.