Bayesian Spatially Clustered Compositional Regression: Linking intersectoral GDP contributions to Gini Coefficients

TL;DR

This paper introduces a Bayesian spatially clustered compositional regression model to analyze how intersectoral GDP contributions influence income inequality, capturing spatial heterogeneity and clustering effects.

Contribution

It develops a novel nonparametric Bayesian framework with spatially clustered coefficients for compositional regression, enabling detection of heterogeneous spatial effects.

Findings

Model effectively identifies spatial clusters of economic effects.

Simulation studies show superior performance over existing methods.

Application reveals distinct regional patterns linking GDP contributions to Gini coefficients.

Abstract

The Gini coefficient is an universally used measurement of income inequality. Intersectoral GDP contributions reveal the economic development of different sectors of the national economy. Linking intersectoral GDP contributions to Gini coefficients will provide better understandings of how the Gini coefficient is influenced by different industries. In this paper, a compositional regression with spatially clustered coefficients is proposed to explore heterogeneous effects over spatial locations under nonparametric Bayesian framework. Specifically, a Markov random field constraint mixture of finite mixtures prior is designed for Bayesian log contrast regression with compostional covariates, which allows for both spatially contiguous clusters and discontinous clusters. In addition, an efficient Markov chain Monte Carlo algorithm for posterior sampling that enables simultaneous inference on both cluster configurations and cluster-wise parameters is designed. The compelling empirical performance of the proposed method is demonstrated via extensive simulation studies and an application to 51 states of United States from 2019 Bureau of Economic Analysis.