Vector autoregressions (VARs) are
exible time series models that can capture
complex dynamic interrelationships among macroeconomic variables. Their
generality, however, comes at the cost of being very densely parameterized. As a
result, the estimation of VARs tends to deliver good in-sample t, but unstable
inference and inaccurate out- of-sample forecasts, particularly when the model includes
many variables. A potential solution to this problem is combining the richly
parameterized unrestricted model with parsimonious priors, which help controlling
estimation uncertainty. Unfortunately, however, the issue of how to optimally set
the weight of the prior relative to the likelihood information is largely unexplored.
In this paper, we propose a simple and theoretically founded methodology for prior
selection in Bayesian VARs. Our recommendation is to select priors by maximizing
(or integrating over) the likelihood function integrated over the model parameters.
The latter is known as the marginal data density and it only depends on the hyperparameters
that characterize the relative weight of the prior model and the information
in the data. We show that the out-of-sample forecasting accuracy of our
model not only is superior to that of VARs with
at priors, but is also comparable
to that of factor models.