This paper considers the problem facing a central government which can transfer resources between regional governments by use of intergovernmental grants. Regions provide a public good and are subject to privately observed shocks either to income, or demand for, or cost of, the public good. There may be public good spillovers between regions. In this set-up, central government has an insurance role, and possibly also a role as co-ordinator of regional public good provision. When grants are chosen to maximise regional expected utility, notatble results are; (i) depending on the source of the shock, the grant may induce over- or undersupply of the public good relative to the Samuelson rule; (ii) with asymmetric information, and with spollovers, there is a two way distortion of public good supply - that is, qualitatively different distortions (relative to the Samuelson rule) at different points in the support of the distribution of the shock; (iii) with symmetric information, the optimal grant is always linear in the public good, but with asymmetric information, the grant will have a quasi-concave or quasi-convex, rather than an constant slope, depending on the source of the shock.
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