In a continuous time model of two symmetric open economies, with a floating exchange rate, we find that the pay-off to macroeconomic policy coordination depends systematically on how heterogeneous is their inflation experience. While monetary policy coordination improves welfare in handling a common rate of underlying inflation, it exacerbates the "time consistency" problem arising when there are differences (as is illustrated diagrammatically). Since the principle of "certainty equivalence" applies to time consistent policy in linear quadratic models, we are also able to give a stochastic interpretation of the deterministic results.