El ICEI no comparte necesariamente las opiniones expresadas en este trabajo, que son de exclusiva responsabilidad de sus autores.The divergence in sovereign yields has been presented as a reason for the lack of traction of monetary policy. We use a GVAR framework to assess the transmission of monetary policy in the period 2005-2016. We identify sovereign yield divergence as a key mechanism by which the leverage channel of monetary policy worked. Unconventional monetary policy was successful in mitigating this effect. When exploring the channels through which yields may affect the heterogeneous transmission of monetary policy, we find that the reaction of bank leverage depended substantially on where the sovereign yield originated, thus providing a mechanism that explains this heterogeneity. Second, large spillover effects meant that yield divergence decreased the traction of monetary policy even in anchor countries. Third, the heterogeneity in the transmission mechanism can be in part attributed to contagion from euro area wide sovereign stress. Fiscal credibility, therefore, may be an appropriate tool to enhance the output effect of monetary policy. Given the importance of spillovers, this credibility may be achieved by changes in the institutional make-up and policies in the euro area.