David Andolfatto has a very good post on "Monetary Policy Implications of Blockchain Technology". In passing (it's not a central point of his post), David says:
"However, it's worth pointing out that the leading economic theory of bank sector fragility, the Diamond and Dybvig model, does not rely on the existence of opacity in the financial market. In that model, the portfolios of banks are perfectly transparent. A bank run may nevertheless be triggered by the expectation of a mass redemption event, which subsequently becomes a self-fulfilling prophecy. It is also interesting to note that (in the same model) bank-runs can be eliminated if banks adopt a credible policy of suspending redemptions once they run out of cash (this commits the bank not to firesale assets to meet short-term debt obligations)."
I think that David is right about suspending redemptions. But I think that David would be wrong if we made a small change to the Diamond Dybvig model. We simply add an extra time period, or periods. It's a friendly amendment to the model.
[My own views on Diamond Dybvig-type models have been influenced by Morgan Ricks' "The Money Problem", but I am not 100% sure whether Morgan would agree with what I say here, though I think he will.]
Agents are ex ante identical. Each agent has an endowment of apples. There is a costless storage technology for apples. There is also an investment technology (planting apples in the ground) which gives a strictly positive rate of return at maturity, but a negative rate of return if you cancel the investment before maturity. Each agent has a 10% probability of becoming impatient (getting the munchies) and wanting to eat all his apples this period. Those probabilities are independent across agents, and there is a large number of agents, so exactly 10% of agents will become impatient each period. Getting the munchies is private information.
The standard Diamond Dybvig model has 3 periods: an initial period where agents lend their apples to the bank; a second period where 10% of agents get the munchies and ask for their apples back; and a third period when the investment matures. Banks exist to provide insurance against risk of munchies by pooling assets; normal insurance won't work because the information is private.
Let's instead make it a 4 period model: an initial period where agents lend their apples to the bank; a second period where 10% of agents get the munchies and ask for their apples back; a third period where another 10% of agents get the munchies and ask for their apples back; and a fourth period when the investment matures.
Suppose the bank credibly commits that it will never cancel an investment before maturity, and stores 20% of apples in reserve. In the good equilibrium there is no sunspot and only agents who get the munchies ask for their apples back. Now suppose there is a sunspot and a run on the bank in the second period of the 4-period model. An agent who does not have the munchies in the second period will rationally join that run on the bank, falsely claiming that he does have the munchies. The reason is that he might get the munchies in the third period, and if the bank suspends redemptions he will be unable to satisfy his future cravings, so he wants to join the line before the bank runs out of stored apples, so he can store apples at home.
Alternatively, we could make an infinite period model, with the good equilibrium being a steady state with the bank's assets staying constant over time because flows in equal flows out. All that is required for runs, despite suspension of redemptions, is that investments take more than 2 periods to mature. [And in a continuous time version of the model, the bank would not be able to prevent runs by committing to stop redemptions whenever X% of apples have been redeemed.]
Even if people are 100% confident that the bank is solvent, there can still be bank runs if people cannot predict their own future needs for liquidity, and fear that the bank might become illiquid in future. Having a deposit in an illiquid bank is functionally not the same as having a deposit in a liquid bank, even if both are solvent.
Even if deposit insurance guarantees that your deposit is safe, you might see a bank run if there is expected to be a delay in paying out that insurance. Liquid assets are more desirable than illiquid assets that pay the same rate of return.
But the real problem with the Diamond Dybvig model is, ummmm, that it's a real model, not a monetary model. If there really were only one bank that created money, the problem of bank runs due to fear of illiquidity would not arise. Because any money spent by one agent immediately goes into the account of another agent at the same bank.