  The shocks which hit macroeconomic models such as Vector Autoregressions
(VARs) have the potential to be non-Gaussian, exhibiting asymmetries and fat
tails. This consideration motivates the VAR developed in this paper which uses
a Dirichlet process mixture (DPM) to model the shocks. However, we do not
follow the obvious strategy of simply modeling the VAR errors with a DPM since
this would lead to computationally infeasible Bayesian inference in larger VARs
and potentially a sensitivity to the way the variables are ordered in the VAR.
Instead we develop a particular additive error structure inspired by Bayesian
nonparametric treatments of random effects in panel data models. We show that
this leads to a model which allows for computationally fast and order-invariant
inference in large VARs with nonparametric shocks. Our empirical results with
nonparametric VARs of various dimensions shows that nonparametric treatment of
the VAR errors is particularly useful in periods such as the financial crisis
and the pandemic.
