Public capital stocks in dynamic fiscal competition

We study dynamic fiscal competition when mobile capital responds to the stock of public infrastructure, not contemporaneous expenditure flows. Two governments choose taxes and public investment in a differential game with gradual accumula-tion and investment frictions. In the unique Nash equilibrium, long-run dynamics depend on discounting, erosion of advantages, the share of public investment that effectively adds to infrastructure, the private productivity effects of infrastructure, and adjustment/acquisition costs on public investment. The model delivers conver-gence to a symmetric steady state, and “invest–then–stop” behavior. Large initial gaps can rationally delay the laggard’s investment, generating distinct transition paths and persistent asymmetries.

Keywords: Fiscal competition; public capital stock; infrastructure investment; differential games; mobile capital.

JEL classification: F21; F23; H25; H54; H73; C73.