Financial Fragility, Systemic Risks and Informational Spillovers : Modelling Banking Contagion as State-Contingent Change in Cross-Bank Correlation

We consider banking panic transmission in a two-bank setting, in which the main propagator of a shock across banks is the informational spillover channel. Banks are perceived to be positively connected to some unobserved macroeconomic fundamental. Depositors in each bank are assumed to noisily observe their bank's idiosyncratic fundamental. The game takes a dynamic bayesian setting with depositors of one bank, making their decision to withdraw after observing the event in the other bank. We show that, if this public event is used for bayesian inference about the state of the common macroeconomic fundamental, then, in the equilibrium profile of the game, contagion and correlation both occur with positive probability, with contagion modeled as a state-contingent change in the cross-bank correlation. Such endogenous characterisation of probabilistic assessments of contagion and correlation, has the appealing feature that it enables us to distill between these two concepts as equilibrium phenomena and to assess their relative importance in a given banking panic transmission setting. We show that contagion is characterised by public informational dominance in depositors.decision set.