Coarsened Bayesian VARs: Correcting BVARs for incorrect specification

Model misspecification in multivariate econometric models can strongly influence estimates of 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 misspecified along important but unknown dimensions. Since endogenous variables in a VAR can feature different degrees of misspecification, our model allows for this and automatically detects the degree of misspecification. The resulting cBVARs perform well in simulations for several types of misspecification. Applied to US data, cBVARs improve point and density forecasts compared to standard BVARs.