Financial integration generates macroeconomic spillovers that may require international monetary policy coordination. We show that individual central banks may set nominal interest rates too low or too high relative to the cooperative outcome. We identify three sufficient statistics that determine whether the Nash equilibrium exhibits under-tightening or over-tightening: the output gap, sectoral differences in labor intensity, and the trade balance response to changes in nominal rates. Independently of the shocks hitting the economy, we find that under-tightening is possible during economic expansions or contractions. For large shocks, the gains from coordination can be substantial.