Monetary Union Dynamics with Unsustainable Public Debt

There have been many attempts at solving the problem of determining the “fundamental value” of the credit spread of a government bond. This is particularly important in the case of Eurozone, where the ECB intervention on the government bonds' market is allowed only if the “spread” paid by the sovereign issuer is higher than the one justified by “fundamentals”. The complication in determining what is a fair level of the spread stems from the fact that public debt sustainability depends on many factors, among them the level of interest rates paid. This sort of circularity between debt sustainability and interest rate paid by the sovereign issuer is the major source of complexity. This paper highlights a possible solution inside a simplified framework resembling the peculiar institutional settings of the Eurozone: no possibility of money-financing, the famous Maastricht Treaty 3%-60% parameters, availability of financial assistance program subordinated to the acceptance of consolidation plans for public finances. We obtain the possibility of multiple equilibria for the credit spread, whose stability can be analyzed through a phase diagram. The dynamics of the model is derived from probabilistic assumptions about the public debt process. It does not depend on “loss” functions devised to model the strategic relationship between debtors and creditors, as in previous literature on public debt sustainability. Dynamic properties of equilibria can be used to gain insight on what does it mean “good” or “bad” equilibrium from the perspective of the ECB