Eurosystem stability: A stochastic dynamic optimization approach to public debt

In this paper we focus on the dynamics of tax revenue and debt that should be necessary for the European countries to comply with the rules on which the Stability and Growth Pact (SGP) is founded, when public budgets are expounded to unexpected expenses. We specify a stochastic control model with infinite horizon formalizing the optimal rules implied by the SGP and compute tax revenue and debt satisfying the model. We find that, even though in long run equilibrium, they are non-stationary processes. From a technical point of view, we make use of a matrix discounted Riccati equation and show that, even in the presence of a unitary root, a real solution exists. The implementation of the optimal model with real data initial conditions suggests for European countries a more intense use of debt rather than tax revenue to finance the public budget in the absence of financial turmoil. Furthermore, there emerge also some small margins for this policy during the Covid-19 period.