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This paper investigates how the economic performance of four economies with floating exchange rates is affected by shocks in domestic and US economic policy uncertainty. We estimate a Bayesian VAR model describing the dynamics of ten local and US variables for each of the four countries and use it to evaluate the response of the system to structural shocks. The analysis reveals that increased economic uncertainty in the US reduces industrial output in all the countries analysed, while the effect of increased domestic uncertainty varies across the economies. A key finding concerns the role of the exchange rate. Whereas the real effective exchange rate amplifies the effect of uncertainty shocks in the US, it typically helps absorb shocks in the open economies. This asymmetry may reflect the role of the US as a safe haven in times of increased uncertainty. Supplementary Information The online version contains supplementary material available at 10.1007/s11079-021-09656-0.