Multilevel Decomposition of Generalized Entropy Measures Using Constrained Bayes Estimation: An Application to Japanese Regional Data

TL;DR

This paper introduces a multilevel decomposition method for generalized entropy measures that respects hierarchical population structures and ensures consistency across levels, demonstrated on Japanese income data.

Contribution

It presents a novel constrained Bayes estimation approach for multilevel GE decomposition, improving accuracy and hierarchical consistency over standard methods.

Findings

Successfully decomposed Japanese income inequality into multiple hierarchical levels.

Ensured compatibility of GE estimates across nested population layers.

Provided a practical framework for multilevel inequality analysis.

Abstract

We propose a method for multilevel decomposition of generalized entropy (GE) measures that explicitly accounts for nested population structures such as national, regional, and subregional levels. Standard approaches that estimate GE separately at each level do not guarantee compatibility with multilevel decomposition. Our method constrains lower-level GE estimates to match higher-level benchmarks while preserving hierarchical relationships across layers. We apply the method to Japanese income data to estimate GE at the national, prefectural, and municipal levels, decomposing national inequality into between-prefecture and within-prefecture inequality, and further decomposing prefectural GE into between-municipality and within-municipality inequality.