Fast and order-invariant inference in Bayesian VARs with nonparametric shocks

The shocks that 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 that uses a Dirichlet process mixture (DPM) to model the reduced-form shocks. However, we do not follow the obvious strategy of simply modeling the VAR errors with a DPM as 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 that allows for computationally fast and order-invariant inference in large VARs with nonparametric shocks. Our empirical results with nonparametric VARs of various dimensions show that nonparametric treatment of the VAR errors often improves forecast accuracy and can be used to analyze the changing transmission of US monetary policy.