This paper characterizes strongly stable networks under general threshold contagion. Among other applications, the theory is applied to interbank lending and financial contagion wherein a government can intervene to stop contagion. In the absence of intervention, banks form disjoined clusters to minimize contagion. In the presence of intervention, banks become less concerned with the counterparties of their counterparties, which we dub network hazard. Network hazard allows some banks to become systemically important and gives the network a core-periphery structure. The counterparty risk of a large part of the economy becomes correlated through the core banks’ solvency. Core banks serve as a buffer against contagion when solvent and an amplifier of contagion when insolvent. As such, bailouts create welfare volatility and increase systemic risk via network hazard. It is shown that network hazard is a novel force distinct from moral hazard. Results are historically relevant to the pyramiding of reserves and the establishment of the Federal Reserve.
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