Is there a need for international coordination of monetary policies within the current system of floating exchange rates? In a recent paper, Obstfeld and Rogoff (1995) argue that in an environment of sticky prices, under floating exchange rates monetary policy shocks will generate positive welfare spillovers across countries. This leads to the conclusion that international monetary policy coordination is unnecessary, and may in fact be undesirable, since it nurtures a bias toward high inflation. Our paper shows that these conclusions are dependent on the manner in which prices are set. When firms engage in "pricing-to-market" (PTM), setting prices in the currency of the buyer, monetary policy tends to have negative welfare spillovers. This gives an incentive to engage in "competitive depreciation." In a noncooperative equilibrium, world inflation will be higher, the greater the importance of PTM. With a high degree of PTM, it follows that the case for international monetary policy coordination is restored. If PTM is at an intermediate range, however, international monetary coordination may have no consequences at all.