Rigidity and default in production networks

This paper studies the transmission of productivity shocks in general equilibrium production networks, when firms in different sectors operate under informational rigidity and rely on external debt. Rigidity breaks the Modigliani-Miller irrelevance of leverage and may generate default following shocks, even in equilibrium. The economy consists of firms, banks, and consumers. Under proportional shock transmission, we prove that a unique Walrasian rigid equilibrium exists and provide explicit expressions for equilibrium quantities, prices, and interest rates. We show that, on the one hand, Hulten's theorem fails under rigidity, even without leverage. On the other hand, we prove that welfare is smaller than in the first best if and only if both leverage and rigidity exist. The latter increase the total cost of debt and have inflationary effects on the levered sectors, which propagate downstream, and shift consumption and labor upstream. The occurrence of default depends solely on real shocks and the network structure, while the magnitude of the losses depends also on the connectedness of the economy and the cost of debt of the connected sectors. We provide conditions for default cascades to occur and study two examples of default propagation.