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Public Debt in a Descriptive Endogenous Growth Model

In this paper we analyze a descriptive endogenous growth model with public debt. The government can run into debt, but, the primary surplus is a positive function of the debt to GDP ratio such that the debt ratio becomes a mean-reverting process. We show that a balanced budget scenario yields a higher long-run growth rate than a scenario with permanent deficits if and only if the public deficit exceeds the net saving out of government bonds. As regards the dynamics, the analysis shows that multiple balanced growth paths can arise. Further, reducing the reaction of the primary surplus to a higher public debt can generate endogenous cycles via a Hopf bifurcation and, for a sufficiently low reaction coefficient, the economy becomes unstable.