  This paper develops a simple two-stage variational Bayesian algorithm to
estimate panel spatial autoregressive models, where N, the number of
cross-sectional units, is much larger than T, the number of time periods
without restricting the spatial effects using a predetermined weighting matrix.
We use Dirichlet-Laplace priors for variable selection and parameter shrinkage.
Without imposing any a priori structures on the spatial linkages between
variables, we let the data speak for themselves. Extensive Monte Carlo studies
show that our method is super-fast and our estimated spatial weights matrices
strongly resemble the true spatial weights matrices. As an illustration, we
investigate the spatial interdependence of European Union regional gross value
added growth rates. In addition to a clear pattern of predominant country
clusters, we have uncovered a number of important between-country spatial
linkages which are yet to be documented in the literature. This new procedure
for estimating spatial effects is of particular relevance for researchers and
policy makers alike.
