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The matching grant (the Pigovian tax) program from a central government to the jurisdictional governments is a strong instrument to solve the problem of an insufficiently provision of local public goods. The under-provision (over-provision) of public goods arises from different kinds of externalities, such as the benefit spillovers and the tax-exporting effect. This study introduces the spillover effect of public goods and the heterogeneity of jurisdictions to the capital tax competition literature using a two-period economy. It is assumed that the central government and the jurisdictional governments play a Stackelberg game with centralised leadership and that there is a unique Stackelberg equilibrium in each period. Meanwhile, the central government and the jurisdictional governments are assumed to be hyperopic and benevolent. A clear result is that the revision of a corrective device used by the central government in the first period to ensure an optimal level of a local public good which is provided by a hyperopic jurisdictional government, significantly depends on the relative size of the income and spill-in effects in the second period. When the income effect is larger than the spill-in effect in the second period, the optimal matching grant rate (the Pigovian tax rate) in the first period from the central government to a more hyperopic jurisdictional government should be increased (decreased). Conversely, when the spill-in effect is larger than the income effect in the second period, the optimal matching grant rate (the Pigovian tax rate) in the first period from the central government to a more hyperopic jurisdictional government should be decreased (increased). The relative size of the two effects, which work in opposite directions, is determined by the tastes and endowments of the jurisdictions, the form of their production functions and the degree of spillovers, among other factors. This result is quite different from the literature.

A Corrective Device for Large Heterogeneous Jurisdictions in a Two-Period Economy with Spillover Effects