Modelling spatial heterogeneity in the effects of area-level covariates on income distributions using Bayesian nonparametric methods

TL;DR

This paper introduces a Bayesian nonparametric model to analyze how income distribution varies across space and covariates, providing flexible inference on latent income factors and their spatial-temporal effects.

Contribution

The authors develop the NLMFM-C model with an adaptive Gibbs sampler and rotation method, enabling automatic inference of latent factors and comparability across datasets.

Findings

Latent income factors correspond to low, medium, and high income levels.

The model reveals spatial and temporal variations in covariate effects.

Application to U.S. microdata demonstrates the model's interpretability and flexibility.

Abstract

Understanding the how the distribution of an economic outcome, such as income, changes with respect to space and covariates is a key concern for policy makers. To address this, we develop a Bayesian nonparametric model, the Normalised Latent Measure Factor Model with Covariates (NLMFM-C), which expresses a large collection of related densities as mixtures of latent factor densities and allows for spatial and covariate effects. We propose an adaptive Gibbs sampler to automatically infer the number of latent factor distributions, and a rotation method to make posterior inference on different data sets comparable. We apply the NLMFM-C model to Public Use Microdata Sample (PUMS) data, focusing on income distributions for sub-areas of four U.S. states over to different years, 2016 and 2020. We show that the latent factor distributions can be interpreted by income level (e.g., low, medium, and high) and investigate the spatially- and time-changing impact of three covariates: gender, race and educational attainment.