This paper puts forward a Bayesian Global Vector Autoregressive Model with Common Stochastic Volatility (B-GVAR-CSV). We assume that Country specific volatility is driven by a single latent stochastic process, which simplifies the analysis and implies significant computational gains. Apart from computational advantages, this is also justified on the ground that the volatility of most macroeconomic quantities considered in our application tends to follow a similar pattern. Furthermore, Minnesota priors are used to introduce shrinkage to cure the curse of dimensionality. Finally, this model is then used to produce predictive densities for a set of macroeconomic aggregates. The dataset employed consists of quarterly data spanning from 1995:Q1 to 2012:Q4 and includes 45 economies plus the Euro Area. Our results indicate that stochastic volatility specifications influences accuracy along two dimensions: First, it helps to increase the overall predictive fit of our model. This result can be seen for some variables under scrutiny, most notably for real GDP and short-term interest rates. Second, it helps to make the model more resilient with respect to outliers and economic crises. This implies that when evaluated over time, the log predictive scores tend to show significantly less variation as compared to homoscedastic models. (author's abstract) / Series: Department of Economics Working Paper Series