  Model mis-specification in multivariate econometric models can strongly
influence quantities of interest such as structural parameters, forecast
distributions or responses to structural shocks, even more so if higher-order
forecasts or responses are considered, due to parameter convolution. We propose
a simple method for addressing these specification issues in the context of
Bayesian VARs. Our method, called coarsened Bayesian VARs (cBVARs), replaces
the exact likelihood with a coarsened likelihood that takes into account that
the model might be mis-specified along important but unknown dimensions.
Coupled with a conjugate prior, this results in a computationally simple model.
As opposed to more flexible specifications, our approach avoids overfitting, is
simple to implement and estimation is fast. The resulting cBVAR performs well
in simulations for several types of mis-specification. Applied to US data,
cBVARs improve point and density forecasts compared to standard BVARs, and lead
to milder but more persistent negative effects of uncertainty shocks on output.
