In this work, we study the transmission of shocks (e.g. financial, monetary) between countries by developing a novel approach which relies on Bayesian techniques in order to estimate the GVAR model as a system of simultaneous equations, which we call Bayesian System GVAR (BSGVAR), while providing two procedures to select the dominant economies. Also, we use endogenously determined time varying weights with random coefficients. In this context, we utilize the proposed model to a selected panel of world economies that account for more than 90% of global production. Our work identifies and estimates the link between countries based on the global variables of trade and finance, which act as the transmission channels that have been documented in the literature as being important. To this end, we investigate how the dominant economies of USA and EU17 will be affected by a potential slowdown in the BRICs. Consistent with international evidence, the empirical findings show that both monetary and financial variables, such as interest rates and total credit, have a significant impact on the transmission of shocks. According to our findings, the EU17 economy seems to be more vulnerable than the US economy to shocks from the BRICs.