Bayesian vector autoregression with applications on panel data and small area estimation

We present a Bayesian vector autoregressive (BVAR) model designed for panel data. In small-area applications, traditional vector autoregressive (VAR) models quickly become overparameterized, and standard BVARs often rely on aggressive global shrinkage, risking over-shrinking meaningful regional dynamics. To address these challenges, we develop a spatial BVAR-CAR framework that combines global regularization with flexible local shrinkage. We introduce a conditional autoregressive prior on region-specific intercepts to capture spatial dependance and a hierarchical shrinkage (horseshoe-type) prior on autoregressive coefficients to borrow strength across regions, stabilizing estimation in high-dimensional settings. This setup eliminates redundant parameters while retaining heterogeneous dynamics across local areas. We evaluate forecasting performance using two annual panel datasets: average hourly earnings of production employes in California Metropolitan Statistical Areas (small areas) and gender unemployment gaps in African countries. Our BVAR-CAR model outperforms three benchmarks – a univariate AR(1) model, a restricted VAR model with shared hyperparameters, and an unrestricted BVAR without spatial and global-local shrinkage priors – in both panels. The results highlight the benefits of spatial pooling in Bayesian models when time series are short. By integrating cross-sectional structure with temporal dependance, our approach provides a flexible and interpretable solution for forecasting and small-area estimation in regional economic analysis.