We develop a framework to analyze the consequences of alternative designs for interbank networks, in which a failure of one bank may lead to others. Earlier work had suggested that, provided shocks were not too large (or too correlated), denser networks were preferred to more sparsely connected networks because they were better able to absorb shocks. With large shocks, especially when systems are non-conservative, the likelihood of costly bankruptcy cascades increases with dense networks. Governments, worried about the cost of bailouts, have proposed bail-ins, where creditors of defaulting banks voluntarily contribute to rescue their debtors.
However, credibility and enforceability were again at issue.  How can the government enforce private sector involvement when the private sector knows that in the absence of its cooperation, the government would nonetheless proceed with a bailout? While a few bail-ins have been observed in practice, it has not been understood until recently under which conditions they exist.

We answer in the affirmative the key question of whether credible bail-in strategies exist, showing that this strongly depends on the network structure. We model the coordination of a rescue consortium between a social planner and the banks as a sequential game. We show that the equilibrium welfare losses are generically unique, and characterize the subgame perfect equilibrium of the game yielding the optimal intervention plan.

Our findings reverse the presumptions in earlier works and promote sparsely connected networks over densely connected ones because (i) the no-intervention threat exhibits a phase transition and becomes more credible for large shocks and (ii) banks’ contributions to the coordinated bail-in plan are larger.

This is joint work with Benjamin Bernard and Joseph Stiglitz.