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

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.