On modelling endogenous default

Not only in the classic Arrow-Debreu model, but also in many mainstream macro models, an implicit assumption is that all agents honour their obligations, and thus there is no possibility of default. That leads to well-known problems in providing an essential role for either money or for financial intermediaries. So, in more realistic models, the introduction of minimal financial institutions, for example default and banks, becomes a logical necessity. But if default involved no penalties, everyone would do so. Hence there must be default penalties to allow for an equilibrium with partial default. What we show here is that there is an equivalence between a general equilibrium model with incomplete markets (GEI) and endogeneous default, and a model with exogenous probabilities of default (PD). The practical, policy implications are that a key function of regulators (via bankruptcy codes and default legislation), or the markets (through default premia) are broadly substitutable. The balance between these alternatives depends, however, on many institutional details, which are not modelled here, but should be a subject for future research.