The U.S. dollar holds a dominant place in the invoicing of international trade. In addition to a direct role for most U.S. exports and imports, it plays a global role for trade flows outside the United States. Using a simple center–periphery model, we show that this global role magnifies the exposure of periphery countries to the U.S.'s monetary policy even when trade flows with the U.S. are limited. This generates gains from coordinated monetary policy, as U.S. policy leads to inefficient movements in intra-periphery relative prices. Despite this inefficiency, flexible exchange rates remain valuable.