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

2025-06-26

AI Summary

In multilevel nested structures (e.g., nation–prefecture–municipality), conventional generalized entropy (GE) index decompositions suffer from hierarchical incompatibility—estimates at lower administrative levels often violate aggregate constraints imposed by higher-level benchmarks, undermining consistency across scales. Method: This paper proposes a constrained Bayesian multilevel estimation framework, the first to embed structural constraints directly into the GE decomposition architecture. By integrating the GE index with hierarchical Bayesian modeling, it ensures that subnational estimates strictly adhere to upper-level aggregates while preserving the intrinsic nested data structure. Contribution/Results: Applied to Japan’s three-tier administrative income data, the method delivers the first nationally scalable, cross-level, additive, and theoretically coherent decomposition of inequality. It precisely disentangles between- and within-region inequality components, enabling fine-grained measurement and policy-relevant attribution of regional inequality—establishing a novel paradigm for equitable development analysis.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Game Theory and Economic Paradigms: Fair Division

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Decompose generalized entropy measures across nested population levels
• Ensure compatibility between hierarchical GE estimates and benchmarks
• Apply method to Japanese income data for inequality analysis

Innovation

• Multilevel decomposition of generalized entropy measures
• Constrained Bayes estimation for hierarchical compatibility
• Application to nested Japanese regional income data