What is a bank run
The Diamond-Dybvig model, however, is constructed on a gold-standard model of banking where institutions were reserve constrained, and thus does not apply to banking today. I have no issues with the model, just as I have no issues with carburetor design. It just isn't applicable when talking about fuel injected vehicles.
So, in the days of FDIC, reserve accounts, and fiat currency, what is a bank run?
1) When depositors take out their money, the bank debits its liability account, and also debits its reserve account. Let's say that the deposits are being transferred straight to another bank so we don't have to worry about inventory issues with physical cash. That other bank credits its deposit and liability accounts.
2) The first bank now has a lower reserve position, and it may be so low that the bank cannot make its reserve requirements. No worries, it can borrow the excess reserve it needs on the overnight interbank market -- but only if other banks are willing to make the loan. This then, is a "modern" bank run. A bank is below its reserve requirement, and other banks are not willing to lend them their excess reserves overnight.
3) The bank short on reserves can always go to the discount window and borrow directly from the Fed. The Fed, howerever, has asset requirements it demands for collateral, and the bank may or may not have those assets.
4) If the bank cannot borrow at the overnight market, nor at the discount window, then functionally it is reserve constrained. It can no longer operate as a bank.
Three interesting observations:
1) The Fed's mechanism for setting the FFR, a number which it could simply declare by fiat the way McDonalds prices its hamburgers, is susceptible to credit risk. If this looks like a broken design to you, it should, because it's terrible.
2) Over the past 12 months, the Fed has taken on ever crummier assets as collateral to lend against at the discount window. If you're asking yourself "why is the Fed asking for collateral at all, as Treasury money is the ultimate backstop anyway?" you are asking yourself an excellent question. This collateralized lending is terrible as well.
3) Note how a bank operationally is only constrained by the Fed's rules for collateral at the discount window, and capital requirements. If the Fed chose to lend uncollateralized, and simply ignored capital requirements, then a bank could operate UNIMPAIRED even if it had massive negative reserves ("liquidity constrained") and massive negative equity ("insolvent"). When someone assets that the Govt could not let Goldman et. al go under, simply say that the Fed could lend unsecured (as it ended up doing anyway) and ignore capital requirements (as it ended up doing anyway) and bank operations would be unimpaired, but the capital structure would be maintained. You can keep a bank running, but let the equity investors "go under" without any problems.