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During the post-crisis period, economic performance has been highly heterogenous across the euro area. While some economies rebounded quickly after the 2009 output collapse, others are undergoing a protracted further decline as part of an extensive deleveraging process. At the same time, inflation has been subdued throughout the whole of the euro area and intra-euro-area exchange rates have hardly moved. We interpret these facts through the lens of a two-country model of a currency union. We find that deleveraging in one country generates deflationary spillovers which cannot be contained by monetary policy, as it becomes constrained by the zero lower bound. As a result, the real exchange rate response becomes muted, and the output collapse—concentrated in the deleveraging economies.