Public investment, public debt, and population aging under the golden rule of public finance

This paper develops an overlapping generations model with debt-financed public investment. The model assumes that government is subject to the golden rule of public finance and that households are finitely lived in the sense of Yaari–Blanchard. It is shown that the growth-maximizing tax rate is not equivalent to the welfare-maximizing one; in addition, both tax rates are lower than the output elasticity of public capital. This paper also derives the threshold value of public debt to GDP ratio that maximizes the equilibrium growth rate and social welfare, i.e., the inverted-U relation between the public debt to GDP ratio and the economic growth rate suggested by empirical studies. Furthermore, this paper shows that both tax rates and the public debt to GDP ratio positively depend on longevity. This result provides a possible explanation for the rising tendency of the public debt to GDP ratio under population aging in countries such as the United Kingdom, Germany, and Japan.