Self-Enforcing Debt and Rational Bubbles

We analyze repayment incentives in an infinite horizon competitive economy where agents cannot commit to financial contracts. We follow Bulow and Rogoff (1989) by assuming that a defaulting agent is excluded from borrowing forever but keeps the ability to save. Hellwig and Lorenzoni (2009) proved that self-enforcing and not-too-tight debt limits can form a bubble (or discounted martingale) at equilibrium. They also show that when debt limits form a bubble, then the equilibrium outcomes (prices and consumption) are the same as in a model without private debt but with unbacked public debt. The contribution of this paper is to show that bubbles are the only debt limits that are self-enforcing and not too tight. Our characterization is obtained without imposing any ad-hoc boundedness assumption on the endogenous debt limits.