Endogenous debt constraints in collateralized economies with default penalties

Preprint submitted to Journal of Mathematical Economics. Final version to be published by ElsevierThe objective of the paper is to propose endogenous debt constraints that rule out Ponzi schemes and ensure existence of equilibria in a model with limited commitment and (possible) default. We appropriately modify the definition of finitely effective debt constraints, introduced by Levine and Zame (1996) (see also Levine and Zame (2002)), to encompass models with limited commitment, default penalties and collateral. Along this line, we introduce in the setting of Araujo, Pascoa and Torres-Martınez (2002), Kubler and Schmedders (2003) and Pascoa and Seghir (2009) the concept of actions with finite equivalent payoffs. We show that, independently of the level of default penalties, restricting plans to have finite equivalent payoffs rules out Ponzi schemes and guarantees the existence of an equilibrium that is compatible with the minimal ability to borrow and lend that we expect in our model. An interesting feature of our debt constraints is that they give rise to budget sets that coincide with the standard budget sets of economies having a collateral structure but no penalties (as defined in Araujo, Pascoa and Torres-Martinez (2002)). This illustrates the hidden relation between finitely effective debt constraints and collateral requirements