The FDIC Center for Financial Research released the study Deposit Inflows and Outflows in Failing Banks: The Role of Deposit Insurance as part of their Working Paper Series.
From the Conclusion:
In this paper we use a highly granular and unique dataset to identify important new findings related to deposit inflows and outflows in a failing bank. Our most important finding is that gross deposit inflows are of first order impact in failing banks’ balance sheets, despite the banks’ elevated default risk and supervisory actions meant to prevent costly and rapid deposit acquisition. This result strongly supports the notion that deposit insurance increases the willingness of depositors to fund banks, as it supports cheap lending to a highly leveraged firm.
The whole study can be found here.