Aggregate Demand Externality and Self-Fulfilling Default Cycles

We develop a model of self-fulfilling default cycles with demand externality a la Dixit- Stiglitz to explain the recurrent clustered defaults observed in the data. The literature reports that observable fundamental factors alone are insufficient to explain the cluster. A decline in aggregate output reduces the value of firms and increases their probability of default. As defaults take more firms out of production, aggregate output declines further, creating a positive feedback loop that generates multiple equilibria and self-fulfilling default cycles. Our global analysis using Bogdanov-Takens bifurcation reveals the existence of multiple or even infinite paths that satisfy all equilibrium conditions. Moreover, a family of periodic orbits can emerge in the perfect foresight equilibrium. Our model is consistent with the view that business cycles arise largely because the economy's internal forces tend to endogenously generate cyclical mechanisms (Beaudry et al., 2020)