Sustainability of Euro-system along with the Stability and Growth Pact

We compute the probability of failure to comply with the Stability and Growth Pact (SGP) for the European countries by comparing the tax revenue requested by the SGP with that one which is socially admissible. Both are estimated with a logistic regression where the latter is represented by the corner point and the former is the latent variable satisfying both the efficiency criterion of the SGP, for the control of Public debt with tax revenue, and the rule of the balanced budget. We also take into account the effect of quantitative easing and of an exogenous stable public expenditure prefixed for policy purposes. We apply and adapt the Riccati equation to this stochastic setting in order to understand the stability properties of the benchmark model descending from the SGP.