On Ponzi schemes in infinite horizon collateralized economies with default penalties

Araujo, Páscoa and Torres-Martínez (2002) showed that, without imposing any debt constraint, Ponzi schemes are ruled out in infinite horizon economies with limited commitment when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2009) presented two examples in which they argued that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. Moreover, they claimed that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is restored. This paper questions the validity of the claims made in Páscoa and Seghir (2009). First, we show that it is not true that harsh default penalties lead to Ponzi schemes in the examples they have proposed. A competitive equilibrium with no trade can be supported due to unduly pessimistic expectations on asset deliveries. We subsequently refine the equilibrium concept in the spirit of Dubey, Geanakoplos and Shubik (2005) in order to rule out spurious inactivity on asset markets due to irrational expectations. Our second contribution is to provide a specific example of an economy with moderate default penalties in which Ponzi schemes reappear when overpessimistic beliefs on asset deliveries are ruled out. Our finding shows that, contrary to what is claimed by Páscoa and Seghir (2009), moderate default penalties do not always prevent agents to run a Ponzi scheme.

In this document we consider an abstract infinite dimensional maximization problem and we present some necessary and sufficient conditions for optimality. These technical results play a crucial role in Section 3 and 4 of the associated paper.