Modeling the Great Recession as a Bank Panic : Challenges

We consider bank panic models in which, depending on the configuration of fundamentals, there can be a positive probability of a bank panic. A crucial assumption in these models is that new equity cannot enter in a panic. We quantify the importance of this assumption by computing the minimal entry cost that justifies the no-entry assumption. We find that that cost is implausibly high across the several models considered. We also show that small changes in assumptions about entry have a qualitative impact on equilibria: a panic may not be possible or there could be several equilibria with different levels of panic. The economic reasons for this sensitivity are clarified by transforming the market economy into a game and studying banker best response functions. A second, additional result, is displayed in a three-period version of the panic model of Gertler and Kiyotaki (2015). That model naturally suggests the idea that welfare can be improved by imposing a restriction on bank leverage. We compute the Ramsey-optimal leverage restriction but find that there is an implementation problem: the restriction can be associated with more than one equilibrium, not just the desired one. We discuss one way to address the implementation problem