Government Debt in an Intergenerational Model of Economic Growth, Endogenous Fertility, and Elastic Labor With an Application to Japan

We derive the social optimum and optimal government debt in an intergenerational model of growth with fertility, elastic labor, human capital externalities and a non-convex feasible set. Debt through lump-sum taxation increases leisure and labor, reduces fertility, and can achieve the social optimum with education subsidization. Debt and education subsidization through labor income taxation can generate similar effects on fertility and labor. Quantitatively, the model can yield changes in output growth, fertility, and labor resembling observations in Japan with rising debt since 1970. From this calibration, the optimal debt-output ratio is 12.3% and excessive debt causes substantial welfare losses.