  Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on
the autoregressive coefficients. Introducing shrinkage on the error covariance
matrix is sometimes done but, in the vast majority of cases, without
considering the network structure of the shocks and by placing the prior on the
lower Cholesky factor of the precision matrix. In this paper, we propose a
prior on the VAR error precision matrix directly. Our prior, which resembles a
standard spike and slab prior, models variable inclusion probabilities through
a stochastic block model that clusters shocks into groups. Within groups, the
probability of having relations across group members is higher (inducing less
sparsity) whereas relations across groups imply a lower probability that
members of each group are conditionally related. We show in simulations that
our approach recovers the true network structure well. Using a US macroeconomic
data set, we illustrate how our approach can be used to cluster shocks together
and that this feature leads to improved density forecasts.
