We apply ideas from fiscal federalism to derive new results on how fiscal authority should be delegated within a monetary union. We consider a monetary-economy model, in which governments finance their expenditures with nominal debt and inflation has a negative effect on productivity. If the monetary authority has commitment, then a version of Oates's (1999) decentralization result holds. By contrast, when the monetary authority lacks commitment, the resulting time-inconsistency problem generates an indirect endogenous fiscal externality. In this case, when a country-level fiscal authority chooses a higher level of nominal debt, it induces the monetary authority to inflate more. Since the country-level fiscal authority does not take into account this adverse indirect effect of its actions on inflation, a negative fiscal externality arises, which becomes more severe as the number of countries in the monetary union increases. Hence, a decentralized regime is optimal for small monetary unions, whereas a fiscal union is optimal for sufficiently large ones. Our key new result is that as the size of a monetary union increases, it becomes relatively more desirable to centralize fiscal authority.