Bank Runs

I don't want to discuss current events here, but current events do influence my choice of topic. Mencius has made an interesting argument that bank runs and similar phenomena are caused by "maturity transformation", which is borrowing short-term in order to lend long-term at a higher rate. I think this is fundamentally mistaken, The possibility of something like a bank run is always present whenever an entity has fixed obligations that must be fulfilled upon demand.

To see why this is so, consider a world in which it is understood that fundamentally money is gold. In this world, people can and do make purchases with gold coins, but because of the danger of being robbed, people frequently instead make purchases using "checks" drawn on "banks". These "banks" are rather different from those of our world. They don't make loans, they don't pay interest, all they do is hold and transfer gold. There genuinely is physical gold in the bank vaults backing the value of depositors' accounts. If A writes B a check and they are both patrons of the same bank, unless B chooses to withdraw his gold, no gold actually moves. The amount of gold in the vault stays the same, but more is owned by B and less by A. There is some sort of clearinghouse system by which banks can cancel their reciprocal obligations, so it is only occasionally necessary to transfer the net balance of payments in physical gold from one bank to another by heavily armored truck. Bank shareholders make their profits from fees charged for holding and transferring funds. How could a run on a bank be possible in such a system?

In the rare event of a successful robbery of a truck or vault, whose gold is stolen? Who bears the cost? Well, if the amount is small, so that the bank still has sufficient gold to repay all deposits, the the answer is "the shareholders". Even if holdings of gold in the vault temporarily dip slightly below the total value of deposits, the bank might be able to continue operations, suspending dividends to the shareholders until the fees collected make the bank once again sound. But if depositors become aware that the amount of gold in the vaults has become less than the amount nominally deposited, it will be quite rational for them to immediately withdraw their funds or transfer them to a safe bank. The fact that the bank can probably weather the storm if they do not is irrelevant to them; why should they undertake risk for the shareholders' benefits?

There are two key points. The first is that there are always risks. If one is relying on the ability to make loans, one may find it has become impossible to borrow money, at least at the rates to which one is accustomed. If one makes loans, there is always a risk of default. And even if all one does is hold money, there is a real nontrivial risk of robbery. The second is that if one has multiple fixed obligations which must be fulfilled on demand, then if there is any risk at all that one will be unable to fulfill all one's obligations, fulfilling one obligation increases the probability that one will be unable to fulfill others. This makes it quite rational for creditors to insist on immediate payment whenever there is a nontrivial risk of default.