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We study a business cycle model of the international monetary system featuring a time varying demand for safe dollar bonds, greater risk-bearing capacity in the United States than the rest of the world, and nominal rigidities. A flight to safety generates a dollar appreciation and decline in global output. Dollar bonds thus command a negative risk premium, and the United States holds a levered portfolio of capital finances in dollars. We quantify the effects of safety shocks and heterogeneity in risk-bearing capacity for global macroeconomic volatility, US external adjustment, and policy transmission, as of dollar swap lines.