Tax policy coordination, vertical externalities, and optimal taxation in a system of hierarchical governments

Tax policies of two levels of government (state and federal) with overlapping tax bases are considered. This overlap leads to "vertical" fiscal externalities are considered when several different commodities are in the tax base and the tax bases of the two levels of government may not be identical. When the governments share a tax base, the mix of combined taxes is optimal. With different tax bases, combined taxes are no longer optimal as federal tax rates are adjusted to reflect state public service levels. When grants are available, a welfare-maximizing mix of taxes and public services is obtained.