This paper shows that the outcome of trade wars for tariffs and welfare will be affected by the monetary policy regime. The key message is that trade policy interacts with monetary policy in a way that magnifies the welfare costs of discretionary monetary policy in an international setting. If countries follow monetary policies of flexible inflation targeting, trade wars are relatively mild, with low equilibrium tariffs and small welfare costs. Discretionary monetary policies imply much higher tariffs, high inflation rates, and substantially larger welfare costs. We quantify the effects of a global trade war among major economies using estimates of trade elasticities, economic size, net foreign assets and trade openness. We find large welfare benefits of an inflation targeting monetary policy for all countries.