Bank runs and multiple equilibria

When I was flying to Portugal on Friday for a short holiday (more of that in a later post) I faced the small but not zero probability that the banking system might have collapsed. Why? Because the previous day the newspapers were full of stories about withdrawals of cash from Greek banks. The amount was in the region of €1 bn, barely 1% of total Greek bank deposits, but bank runs are a matter of rational contagion. Let’s say Greeks who had not thought of pulling their money out, having read the papers, decided they should too, just to be on the safe side. If that view spread fast enough it would lead to a collapse of the Greek banks. Depositors in other weak Eurozone countries (Portugal and Ireland being top of the list) might then decide that, again to be on the safe side, they should take their cash out too, bringing about bank collapses elsewhere and leading to the destruction of most of the European banking system.

Most economists I’ve spoken to about this are puzzled why such a scenario hasn’t happened, because it is surely rational individually to take your money out. What are the owners of the other 99% of Greek deposits thinking? I realise that something like €20-25bn has already been stuffed under Greek mattresses but the pernicious quality of a bank run is that is rational to take part and get in early. Perhaps this shows that Greeks are more sensible that we economists think, though I rather fear it is more a matter of time.

Banks are inherently risky because they mis-match short term, liquid liabilities (your bank deposits) against longer term, illiquid loans (mortgages, car loans etc). This maturity transformation is very valuable economically but history and theory tell us that they can catastrophically fail if this mis-match gives rise to concerns among the depositors. This is an example of a fairly common phenomenon in the social world, that of multiple equilibria.

When what you should optimally do depends on what others should optimally do, including their and your expectations of that behaviour, we need to use game theory, the theory of interdependent decision making. This is widely applied in the social sciences and in biology, where it helps to explain social behaviour in flocks of birds, shoals of fish and so on. The key concept to solving a game theoretic problem is the Nash equilibrium, named after John Nash (of the film “A Beautiful Mind”). A Nash equilibrium is a set of strategies (decision/behaviours) which are rationally optimal given every other player’s optimal strategy. A trivial example is driving on one side of the road. It is unimportant whether it’s the left or right hand side, so long as we all agree. If we all agree or coordinate on the left hand side we have a Nash equilibrium. But the right hand side is also a Nash equilibrium.

Similarly, if we all trust the bank to repay our deposits when we need them, we have a Nash equilibrium. But if for some reason we are in doubt and we think other people are also doubting, then the rational thing to do is pull your money out. Since everyone else will optimally do the same thing, there is a second but economically far worse Nash equilibrium in which the bank collapses, proving to everyone that it was indeed rational to get your money out early. The problem is compounded in Greece and other Eurozone economies by the currency devaluation risk. A depositor might not think the bank is actually going to be allowed to go bust (or at least may believe the depositors will be protected by the government). But if you fear that your deposits will be turned into New Drachma, and therefore worth far less, you might rationally take out the cash in the form of Euro notes that you can then take over the border and deposit in another country’s banking system. (This is why, if Greece leaves the Euro, the borders will need to be closed and possibly martial law imposed, while all existing Euro notes are stamped to turn them into Drachma. It would be very ugly).

Two articles in today’s Financial Times mention the classic economic theory of bank runs and multiple equilibria, which is by Douglas Diamond and Philip Dybvig (available here). Diamond and Dybvig is in the noble tradition of economics articles which tell us in an analytically precise and rigorous way that which we largely already knew. If you want a simple but vivid example of how to start a bank run, I suggest the Walt Disney film “Mary Poppins” about a strange and magical nanny to the children of a bank manager in early twentieth century London. The little boy, under pressure to put his pocket money into an account at his father’s bank,  demands it back. Other customers, hearing him shouting “give me my money!” conclude (a bit too readily perhaps) that the bank hasn’t got the money to repay him and demand their own money, thus bringing about a run which does indeed ruin the bank (and the boy’s father). Their initially incorrect conjecture about the bank’s inability to repay them becomes a self-fulfilling prophecy. They move from a good equilibrium to a bad one. (There is also a bank run in the classic American film “It’s A Wonderful Life“, drawing on the very strong folk memory of the collapse of US banks during the 1930s) .You don’t need Nash equilibria or Diamond and Dybvig to see the risk of something similar happening in Greece.