How to determine the optimal level of deposit insurance
Deposit insurance is a crucial pillar of financial regulation as it has significantly reduced the number of bank failures ever since it was instituted in 1934 in the US. Nevertheless, it is also associated with moral hazard i.e. it affects the ex-ante behavior of market participants. The question then is what is the optimal level of deposit insurance coverage and which variables should be used for the determination of that level.
In this paper, Dávila and Goldstein provide a general framework that incorporates the most relevant tradeoffs and can be used to provide explicit guidance to policymakers when facing these questions.
We show that the welfare impact of changes in the level of deposit insurance coverage can be generally expressed in terms of a small number of sufficient statistics, which include the level of losses in specific scenarios and the probability of bank failure. We characterize the wedges that determine the optimal ex-ante regulation, which map to asset- and liability-side regulation. We demonstrate how to employ our framework in an application to the most recent change in coverage, which took place in 2008.

Optimal Deposit Insurance
Authors: Eduardo Dávila, Itay Goldstein
From: Yale University, University of Pennsylvania
When depositors are not well informed
In this paper Blicke et al. study the behavior of depositors in a financial crisis by looking at the run on the German banking system from May through July of 1931. There are two reasons for selecting this incident: a) at the time there were no capital and liquidity requirements, nor deposit insurance in Germany, which implies that depositors expected to incur losses if a bank were to fail; and b) a large number of German banks failed – 15 out of 123. This way the authors can identify which type of depositors withdraw from failing banks in the absence of deposit insurance. They granular balance sheet data for commercial banks as well as the central bank, and find that:
The average bank loses around 25% of its overall deposit funding over the two months from the start of the run to the end, when the government intervened. There is no difference in total deposit outflows between failing and surviving banks. This implies that, on average, depositors seem unable to successfully identify which banks will fail.

Who Can Tell Which Banks Will Fail?
Authors: Kristian Blickle, Markus Brunnermeier, Stephan Luck
From: Federal Reserve Bank of New York, Princeton University