An Ergodic Theory of Sovereign Default

We present the conditions under which the dynamics of a sovereign default model of private external debt are stationary, ergodic and globally stable. As our results are constructive, the model can be used for the accurate computation of global long run stylized facts. We show that default can be used to derive a stable unconditional distribution (i.e., a stable stochastic steady state), one for each possible event, which in turn allows us to characterize globally positive probability paths. We show that the stable and the ergodic distribution are actually the same object. We found that there are 3 type of paths: non-sustainable and sustainable; among this last category trajectories can be either stable or unstable. In the absence of default, non-sustainable and unstable paths generate explosive trajectories for debt. By deriving the notion of stable state space, we show that the government can use the default of private external debt as a stabilization policy