Mean Reverting Debt/GDP Dynamics in a General Equilibrium Model

The choice of financing public expenditure with taxes or debt (or both) have been widely investigated by the literature, without finding an ultimate solution. In this article, we take a different point of view and compute the dynamics of the optimal debt/GDP ratio to study under which conditions it converges towards a finite equilibrium that is endogenous to the model. We show that the convergence exists if the capital growth rate is higher than the (constant) interest rate paid on the public debt. When the interest rate is allowed to depend on the debt itself, the convergence exists if the deficit/GDP is sufficiently small. Thus, a policy of deficit control/reduction is needed in order to prevent the debt from exploding and this justify some super-national policies implemented, for instance, at the EU level.