Self-fulfilling Business Cycles with Production Networks

What is the role of production networks in inducing self-fulfilling business cycles? We build a continuous-time multisector business cycle model with input-output linkages and credit constraints to study this. Credit constraints faced by productive firms endogenously create self-fulfilling business cycles: an expected decline in firm value tightens constraints and further depresses equity value, generating a financial multiplier and thus self-fulfilling business cycles. Theoretically, we derive that the financial multiplier nests the input-output multiplier. We illustrate that the likelihood of self-fulfilling business cycles depends on intermediate input share through a "size effect" and a "diluting effect": the combination of two effects has a U-shaped relation with the financial multiplier. We also illustrate that the network structure has an important but ambiguous impact on self-fulfilling business cycles. Quantitatively, we demonstrate that tightening credit constraints in sectors with higher Domar weights in the production network is more likely to lead to a self-fulfilling equilibrium.