Shocks and Defaults in Production Networks: a Theoretical and Simulation-Based Analysis

Modern economies are highly interconnected, as shocks in one sector can spill over across the entire network, generating aggregate fluctuations and increasing the systemic risk. In theory, such shocks would be less disruptive if industries could instantly adjust their decisions, optimizing their profits and avoiding defaults. In practice, however, production and investment choices cannot be costlessly or immediately adapted. This thesis analyzes an economic equilibrium model in which firms make rigid, state-independent decisions prior to the realization of shocks, under imperfect information. In the considered model, firms rely partly on external debts financed by a bank and aim to maximize their conditional expected profit. In this context, a unique rigid Walrasian equilibrium can be proven to exist, whereby defaults occur when equilibrium profit realizations are negative and loans remain partly unpaid. The main contribution of this work is the use of the properties of the exponentially tilted distribution, its density function and moments, to characterize the default condition for a firm hit by a single node shock transmitted through one supplier. Sufficient moment based conditions are derived to ensure the existence of at most one default interval. We show that such an interval is always unique for exponential and Bernoulli shock distributions, while for gamma shock distributions the default interval is unique only for a range of the parameters that we characterize. Extending the analysis to a single node shock propagated through two suppliers, the results indicate that default intervals are still determined by the tilted moments of the distribution and coincide with those of the single supplier case. Another key aspect is the implementation of numerical simulations on different network structures to compute equilibrium quantities, default probabilities and profit variances. Simulations show that shocks are more disruptive when they strike all nodes simultaneously, and may also affect firms not directly connected to the source. In simple structures, as line or DAG, shocks propagate only to consumers, with effects decreasing along the chain, while in cycles or real world networks they can also reach suppliers. Default probabilities remain unaffected by the presence of the bank, since they are only influenced by realized shocks. By contrast, profit variances depend on both firm centrality, determined by the debt cost, itself driven by the choice of the bank interest rates, and shock realizations. Consequently, industries with the highest centrality do not necessarily exhibit the largest profit variance.