It seems to be widely believed that the case for centralising revenue-raising is stronger than that for centralising expenditure decisions, so that federal governments should typically make transfers to lower level "state" governments. This paper argues, however, that pure efficiency considerations may plausibly point in exactly the opposite direction. This arises becauses of a "vertical" fiscal externality: the typical state may neglect the impact that its tax decisions have on the federal tax base. The optimal federal response is to internalise this distortion of state decisions by means of offsetting subsidy on the common tax base, the financing of which may plausibly require transfers from the states.