Debt Sustainability and the Range of Multiple Equilibria

We characterize the size of the range of multiple equilibria in sovereign debt markets. We show that the nature of the equilibrium depends crucially on the degree of uncertainty, which we formalize first as uncertainty about primary balances and later as uncertainty about the fiscal feedback rule. For low uncertainty, the range can be large, but it becomes smaller as uncertainty becomes larger. If uncertainty is large enough, the multiplicity disappears: the interest rate is unique and becomes a continuous function of the debt level. The source of these results is that larger uncertainty decreases the effect of the perceived probability of default on the actual probability of default, thus reducing and eventually eliminating the scope for multiplicity. Interpreting the source of an increase in the interest rate in actual situations is difficult, and complicates the use of intervention by central banks.