Self-enforcing debt limits and costly default in general equilibrium

Abstract

We establish a novel determination of self-enforcing debt limits at the present value of default cost in a general competitive equilibrium. Agents can trade state-contingent debt but cannot commit to repay. If an agent defaults, she loses a fraction of her current and future endowments. Moreover, she is excluded from borrowing but is still allowed to save, as in Bulow and Rogoff (1989). Competition implies that debt limits are not-too-tight, as in Alvarez and Jermann (2000). Under a mild condition that the endowment loss from default is bounded away from zero, we show that the equilibrium interest rates must be suffciently high that the present value of aggregate endowments is finite. We show that equilibrium debt limits are exactly equal to the present value of endowment loss due to default. The determination of competitive debt limits based on endowment loss is isomorphic to the determination of public debt sustainable by tax revenues. We also show that competitive equilibria with self-enforcingdebt and costly default are equivalent to Arrow-Debreu equilibria with limitedpledgeability, as defined by Gottardi and Kubler (2015).