UCLouvain Economics Seminar: Filipe Martins Da Rocha

Self-enforcing Debt Limits and Costly Default in General Equilibrium

Filipe Martins Da Rocha, Université Dauphine

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 Jerman (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 sufficiently 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-enforcing debt and costly default are equivalent to Arrow-Debreu equilibria with limited pledgeability, as defined by Gottardi and Kubler (2015).

Co-authors: Toan Phan and Yiannis Vailakis.