A contraction for sovereign debt models

Abstract

Using a dual representation, we show that the Markov equilibria of the one-period-bond Eaton and Gersovitz (1981) incomplete markets sovereign debt model can be represented as a fixed point of a contraction mapping, providing a new proof of the uniqueness and existence of equilibrium in the benchmark sovereign debt model. The arguments can be extended to incorporate re-entry probabilities after default when the shock process is iid. Our representation of the equilibrium bears many similarities to an optimal contracting problem. We use this to argue that commitment to budget rules has no value to a benevolent government. We show how the introduction of long-term bonds breaks the link to the constrained planning problem.