Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States
Abstract
We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear individual-level interactions. DSP-BART-HS is the best or statistically indistinguishable from the best estimator in every scenario. Conventional region-time-aggregate comparators suffer severe performance degradation -- trailing by a factor of three or more -- whenever individual-level non-linearity drives outcome variance, a limitation this framework's tree-ensemble design directly addresses. The model also maintains strong predictive accuracy under a zero-training-region spatial holdout via its spatial diffusion mechanism. We demonstrate practical utility across two U.S. county-level panel applications -- intergenerational economic mobility and geographic income inequality -- under genuine unseen-region, random, and temporal holdouts, with results validated through repeated-split uncertainty quantification and paired significance testing against every comparator. One clear limitation emerges: under temporal extrapolation specifically, a lighter per-region autoregressive specification (MTS-CAR-X) achieves a robust, and consistent advantage. DSP-BART-HS nonetheless establishes strong predictive performance, automated variable selection, and flexible inference for hierarchical spatio-temporal panel data.
Related
- The reverse Hölder inequality for 𝒜p(·) weights with applications to matrix weights
- A priori bounds for geodesic diameter. Part III. A Sobolev–Poincaré inequality and applications to a variety of geometric variational problems
- Applications of Royen's Gaussian Correlation Inequality in high-dimensional testing
- A Reilly-Type Inequality for CR Dirac Operators on CR Manifolds and Applications
- Pólya--Szegö Inequality on Submanifolds of Riemannian Manifolds with Nonnegative Curvature and Applications
BibTeX
@misc{olayinka2026dynamic,
title = {{Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States}},
author = {Hammed A. Olayinka and Saheed O. Olayemi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00072},
eprint = {2610.00072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00072},
}
RIS
TY - UNPB
TI - Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States
AU - Hammed A. Olayinka
AU - Saheed O. Olayemi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00072
UR - https://arxiv.org/abs/2610.00072
AB - We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear individual-level interactions. DSP-BART-HS is the best or statistically indistinguishable from the best estimator in every scenario. Conventional region-time-aggregate comparators suffer severe performance degradation -- trailing by a factor of three or more -- whenever individual-level non-linearity drives outcome variance, a limitation this framework's tree-ensemble design directly addresses. The model also maintains strong predictive accuracy under a zero-training-region spatial holdout via its spatial diffusion mechanism. We demonstrate practical utility across two U.S. county-level panel applications -- intergenerational economic mobility and geographic income inequality -- under genuine unseen-region, random, and temporal holdouts, with results validated through repeated-split uncertainty quantification and paired significance testing against every comparator. One clear limitation emerges: under temporal extrapolation specifically, a lighter per-region autoregressive specification (MTS-CAR-X) achieves a robust, and consistent advantage. DSP-BART-HS nonetheless establishes strong predictive performance, automated variable selection, and flexible inference for hierarchical spatio-temporal panel data.
ER -