I show that the majority of short-term nominal exchange rate fluctuations among large economies can be explained by changes in the relative stance of their monetary policies. Adapting recently developed instrumental variable techniques for shock identification, I find that monetary policy shocks of the US relative to the euro area account for 76 percent of the short-term fluctuations of the USD-EUR exchange rate over a one-month horizon? substantially more than previously documented. Similar results are obtained for exchange rates involving the British pound and Japanese yen. Relative monetary policy shocks explain a larger fraction of variability of the exchange rate than of interest rate differentials throughout the yield curve, and small changes in risk-free rates are associated with sizable jumps in the exchange rate. Identifying US and euro area shocks separately reveals that both are important for the USD-EUR rate. Taken together, these findings speak to the significance of (not only US) monetary policy in driving frictions in interest parity relations that have recently been found to be crucial for understanding exchange rate behavior from a theoretical perspective.