Problems of intergovernmental policy coordination can take many forms and are becoming increasingly important with continuing economic integration. In this paper we focus on the fiscal competition problem where the non-cooperative choice of taxes and transfers among governments typically leads to a suboptimal outcome. We look at the effect of two widely used corrective policies: revenue sharing and expenditure sharing (or intergovernmental matching grants). Our main result is that these two corrective policies have opposite effects depending on the form of competition between governments, namely whether governments compete in taxes or expenditures. More precisely, for any form of competition, revenue sharing is desirable exactly when expenditure sharing is not and vice versa. The implication is that the choice of the optimal corrective policy requires a complete understanding of the underlying non-cooperative behavior among governments. Our second main result is that neither revenue sharing or expenditure sharing can be sustained as a Nash equilibrium among governments, although all governments would benefit from one of these two corrective policies. Central intervention is therefore inevitable unless governments can pre-commit to the optimal corrective policy before setting their fiscal policies.