  This paper proposes a fast two-stage variational Bayesian (VB) algorithm to
estimate unrestricted panel spatial autoregressive models. Using
Dirichlet-Laplace 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 literature to develop VB methods to
estimate large covariance matrices with unrestricted sparsity patterns, which
are useful for popular large data models such as Bayesian vector
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.
