Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States

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.