Bank walks and options

Why did it takes so long?

Currency and deposits are imperfect substitutes. Currency is more convenient for some things, and deposits are more convenient for other things, so many people hold both.

If a banking system is working normally, deposits include the option to convert them into currency at a fixed exchange rate (par). (And banks are normally willing to convert your currency into deposits at par too.)

That option is a valuable asset, that will be exercised whenever the marginal valuation of currency exceeds the marginal valuation of deposits (plus the cost of visiting the ATM). The existence of that option makes the demand for deposits higher than it otherwise would be, and the demand for currency lower than it otherwise would be. But it may not be possible for everyone to exercise that option at once.

Let P(t) be the (subjective) probability that an individual will be able to exercise that option on the following day. So P(t) = 1 for all t in a bank that is always thought to be 100% safe. The smaller is P(t), the smaller the value of the option, and the less deposits (and the more currency) people will wish to hold.

We get a bank walk where P(t) declines slowly over time, and a bank run where P(t) drops discontinuously. But P(t) may be endogenous.

In a Diamond Dybvig type model, P(t) is endogenous, and has two equilibria: P(t)=1; and P(t)=0. A bank run is where we flip from the first to the second equilibrium. But introducing a lender of last resort eliminates the second equilibrium, by offering a guarantee that the option can be exercised.

To get a bank walk, we need to change the model so the lender of last resort may stop acting as lender of last resort in future. Let L(t) be the (subjective) probability that the lender of last resort will continue to act as lender of last resort on the following day. We know that P(t) cannot be less that L(t), but it might be greater than L(t).

Since P(t) can have multiple equilibria, for L(t)  strictly less than one, we cannot say precisely how P(t) depends on L(t). But it probably makes sense to assume that P(t) is an increasing function of L(t). If so, we get a bank walk if we assume that L(t) is exogenous, and is slowly declining over time when negotiations drag on and look less and less likely to be resolved satisfactorily.

Which is probably why it took so long.

Comments

[dlr]

I agree that L(t) has to be exogenous; otherwise it seems to be zero. I mean, what exactly is an endogenous lender of last resort? A lender of first resort?

[Nick Rowe]

dlr: you might have a lender of second resort, who has limited funds, and can only handle a bank run up to a certain size. That would fit Iceland maybe, but not the ECB and Greece. Or something like Crete, where it won't guarantee the deposits for 100% if the bank is insolvent.

[dlr]

Agreed, but the lender of 2nd resort doesn't solve the binary DD equilibria problem, which at least to me is the defining quality of the LOLR. A LO2ndR operates pretty much the same as an underlying banking system with a relatively stronger capital/liquidity profile: It holds the equilibrium at 1 for longer than it otherwise would, but it ultimately endogenous. So it's really a different beast altogether than a LOLR. You are either exogenous and solve the run externality (and create the bank-walk possibility) or you are a snooze button. That doesn't mean you are worthless, though; just not a DD compliant LOLR.

[dlr]

Nick, since I'm here, I want to ask you the same thing that I asked Scott. Why aren't guys like you screaming from the rooftops that both sides should be focused on finding a solution that tries to minimize disruption from "leaving" the Eurozone while crucially still helping Greece to leave the Euro. I am not saying this is easy, or even reasonably possible, either legally or politically. But because it is seems Pareto optimal to every other possible direction, someone still should be screaming it, even if in vain. It would be a lot easier, for example, for Greece to successfully overcome the Latin America de-dollarization problem and actually change the MOA if it did so forcefully with a detailed, troika-included, changeover plan that didn't represent some angry secession or expulsion into the unknown. The short term will be scary, but not as scary as being expelled from the Euro only to find that the economy remains de-factor Euro-ized in the same quasi equilibrium that has left 25-50% of the economy idle for six years while wages and prices grindingly lag in chase. Chaos plus nominal catastrophe. Argentina should be crying for Greece.

The debate Gadflys both within and without Greece are focused primarily about austerity and debt size and the morality of debt forigveness and all kinds of structural imperfections in Greece, but where are the nominalists reminding everyone that none of this stuff requires half a country to sit around doing nothing for a decade?

[Jacques René Giguère]

Nick: I can elecronically transfer deposits but not cash. It increases my demand for deposits and lower my gemand for currency. There is an option on both sides of the market.

[anon]

Nitpicking, but I think you mean Cyprus rather than Crete (which is part of Greece nowadays).

[David Andolfatto]

Nick,

The restriction to P(t) = 0 or 1 in the DD model applies only to the case where a bank-run equilibrium is expected to occur with zero probability. In general, one might think of the bank anticipating a run with probability 0 < 1-P(t) < 1, where P(t) is exogenous (e.g., sunspot). In this setting, the realization of P(t) will influence the bank's asset portfolio -- it will want to hold more cash reserves (and finance less capital spending) in a world where P(t) is declining over time. Basically, P(t) serves as a money-demand shock.

I like your idea of linking P(t) to L(t). Probably makes a lot of sense in the present (Greek) context. Although, according to the model I just described, the effect of this would be for Greek banks to load up on reserves and curtail lending.

To get the effect you want, I think you'd have to specify heterogeneous beliefs over L(t), with the marginal belief becoming progressively more pessimistic. I think Fostel and Geanakoplos have the type of set up that can formalize your idea: http://cowles.econ.yale.edu/~gean/art/p1430.pdf

[Nick Rowe]

anon: oops!

Jacques Rene: I expect you could call that an "option" (though I was thinking about the option to convert one asset into another at par). I would call that one of the reasons why deposits are sometimes more convenient than currency, and one of the things that makes them imperfect substitutes.

dlr and David: I am trying to think about a model where there are different types of sunspots, and not everybody sees all types of sunspot. I'm not sure if this gives me what I want, or if it makes sense. (Sunspots are a sort of theorist's fiction.)

dlr: we probably should be thinking and writing about that. But my first-best would be an unwinding of the Euro from the top down, beginning with Germany leaving. Which seems very unlikely to happen. It's hard to get your head around an n'th best scenario.

[louis]

Is it difficult for a Greek citizen to open a checking account at a foreign bank? Those deposits are a closer substitute to Greek bank deposits than currency is.