Spatial Panel Models with Heterogeneous Coefficients: A Scalable, Integrated Hamiltonian Monte Carlo Estimation Framework

Spatial panel models with heterogeneous coefficients provide a flexible framework for capturing region-specific spillovers, but their practical use is often constrained by two challenges: (i) existing estimators primarily justified under large-\(\:T\) asymptotics, leaving unit-specific effects imprecisely estimated in the short panels common in regional science; and (ii) allowing spatial dependence and slopes to vary across units yields a high-dimensional parameter space that is difficult to estimate efficiently. This paper proposes a hierarchical Bayesian spatial model with heterogeneous coefficients that addresses both issues through hierarchical priors and an integrated Hamiltonian Monte Carlo estimation framework. The hierarchical prior induces partial pooling across units, shifting inference toward low-dimensional population hyperparameters while stabilizing unit-level estimates in finite samples, particularly when \(\:N>T\). Furthermore, we develop scalable evaluation of the log-determinant term using a power-series expansion and Hutchinson stochastic trace estimation, and we exploit sparse matrix-vector multiplication and parallel computing to improve computational efficiency. Comprehensive simulation experiments demonstrate that the proposed Bayesian framework delivers reliable finite-sample inference and improved estimation accuracy relative to maximum likelihood in short panels. The results also show that heterogeneous spatial dependence is sensitive to the density of the spatial weights matrix than slope coefficients, offering practical guidance for applied research. JEL Classification : C11 · C13 · C23