Infinite Debt Rollover in Stochastic Economies

This paper shows that there is more scope for a borrower to engage in a sustainable infinite debt rollover (a “Ponzi scheme”) when interest/growth rates are stochastic. In this context, I prove that the relevant “r vs. g” comparison uses the yield r_{long} to an infinite-maturity zero-coupon bond. I show that r_{long} is lower than the (risk-neutral) expectation of the short-term yield when it is variable, and that r_{long} is close to the minimal realization of the short-term yield when it is highly persistent. The paper applies these results to illustrative heterogeneous agent dynamic stochastic general equilibrium models to obtain weak sufficient conditions for the existence of public debt bubbles.