This paper decomposes the time-varying effect of exogenous exchange rate shocks on euro area countries inflation into country-specific (idiosyncratic) and region-wide (common) components. To do so, we propose a flexible empirical framework based on dynamic factor models subject to drifting parameters and exogenous information. We show that exogenous shocks to the EUR/USD exchange rate account for over 50% of nominal EUR/USD exchange rate fluctuations in more than a third of the quarters of the past six years, especially in turning point periods. Our main results indicate that headline inflation in euro area countries, and in particular its energy component, has become significantly more affected by these exogenous exchange rate shocks since the early 2010s, in particular for the region‘s largest economies. While in the case of headline inflation this increasing sensitivity is solely reliant on a sustained surge in the degree of comovement, for energy inflation it is also based on a higher region-wide effect of the shocks. By contrast, purely exogenous exchange rate shocks do not seem to have a significant impact on the core component of headline inflation, which also displays a lower degree of comovement across euro area countries.