Fast Two-Stage Variational Bayesian Approach to Estimating Panel Spatial Autoregressive Models with Unrestricted Spatial Weights Matrices

This paper proposes a fast two-stage variational Bayesian (VB) algorithm to estimat-
ing unrestricted panel spatial autoregressive models. Using Dirichlet-Laplace shrinkage
priors, we are able to uncover the spatial relationships between cross-sectional units
without imposing any a priori restrictions. Monte Carlo experiments show that our
approach works well for both long and short panels. We are also the first in the liter-
ature to develop VB methods to estimate large covariance matrices with unrestricted
sparsity patterns, which are useful for popular large data models such as Bayesian vec-
tor autoregressions. In empirical applications, we examine the spatial interdependence
between euro area sovereign bond ratings and spreads. We find marked differences
between the spillover behaviours of the northern euro area countries and those of the
south.