Plate v in print

The Run

Diamond and Dybvig; the promise to pay on demand, and the panic that proves it empty when confidence fails.

A bank promises each depositor his money on demand, though it cannot pay them all at once; let each fear the rest will come first, and all will come at once — and the fear will have made itself true.

— the argument of this plate, after Douglas Diamond and Philip Dybvig, 1983

The loan showed that a bank creates money by promising to pay — that the deposit which is most people's money is the bank's promise to hand over cash on demand. This plate shows what that promise conceals: that the bank cannot keep it to everyone at once. A bank holds far less cash than it owes its depositors; its promise to pay all of them on demand is one it can honor only so long as they do not all ask together. Most days they do not, and the promise holds. But let them come to doubt it, and the run that follows will prove the promise empty — not because the bank was unsound, but because they doubted it. The bank run is the sharpest demonstration of what money is: a promise that holds only on confidence, and fails when confidence fails.

To see why the bank cannot pay everyone, consider what a bank does with the money deposited in it. It does not keep the cash in a vault, idle; it lends most of it out — for years, in mortgages and business loans that cannot be called back on a day's notice — keeping only a small reserve of cash against the daily ebb and flow of withdrawals. This is the bank's essential function and its essential fragility: it borrows short and lends long, taking in deposits that can be withdrawn at any moment and turning them into loans that will not be repaid for years. The transformation is useful — it lets the public hold their wealth in liquid, spendable deposits while their savings fund long, illiquid investment — but it means the bank's promise to pay every depositor on demand is, at any moment, a promise it physically cannot keep: the cash to redeem all the deposits is not there, having been lent out long ago. The promise works only because, on any ordinary day, only a few depositors want their cash, and the bank's small reserve suffices to pay them. The bank is solvent — its loans are good, and will be repaid in time — but it is not liquid: it cannot turn those loans into cash fast enough to pay everyone who might demand it at once.1

1. Banks perform maturity transformation: they borrow short (deposits withdrawable on demand) and lend long (multi-year loans not callable quickly), holding only a small cash reserve. This lets the public hold liquid, spendable deposits while savings fund illiquid long-term investment — but it means the bank cannot pay all depositors at once: the cash isn't there, having been lent. A solvent bank (good loans) can still be illiquid (unable to convert them to cash fast enough to meet a mass demand).

Douglas Diamond and Philip Dybvig captured the danger in a model of startling simplicity, which showed that a bank of this kind has not one outcome but two, and that which one occurs depends on nothing but what depositors believe. In the good outcome, depositors are confident the bank is sound, so only those with a real need for cash withdraw it; their number is small, the bank's reserve covers them, and the bank carries on, its loans maturing in time to repay the rest. In the bad outcome, depositors fear a run — fear that others will withdraw and the cash will run out — and so each rushes to withdraw first, before the reserve is exhausted; the reserve is quickly drained, the bank must dump its long loans at a loss to raise cash, and it fails, unable to pay those at the back of the line. The terrible feature is that the bad outcome needs no bad news: the bank is exactly as sound in both cases; what differs is only belief. The run is a self-fulfilling prophecy — if each depositor expects the others to run, it is rational for each to run too, and the running makes the failure real; if each expects the others to stay calm, it is rational to stay calm, and the bank survives. The bank's fate hangs not on its assets but on a belief that confirms itself, and that can tip from confidence to panic on a rumor, a failure elsewhere, a loss of nerve.2

2. Diamond and Dybvig (1983) modeled the bank as having two equilibria, selected purely by depositor beliefs. Good: all believe the bank sound, so only those needing cash withdraw; the reserve covers them; the bank survives. Bad: all fear a run, so each withdraws first before the cash runs out; the reserve drains, the bank dumps loans at a loss and fails. The bank is equally sound in both — only belief differs. The run is self-fulfilling: expecting others to run makes running rational, causing the failure. No bad news is needed; a rumor suffices.
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The bank run is the mirror image of the thing the first plate found at money's root. Menger showed that money is accepted because each expects others to accept it — a self-fulfilling belief that sustains money's value. The run is that same self-fulfilling belief running in reverse: the bank's deposit is money because each depositor is confident he can convert it to cash, and that confidence holds only because each believes the others share it; let the belief falter, let each come to doubt that the promise will be honored, and the doubt destroys the very thing it fears — the deposit becomes unredeemable precisely because depositors feared it would. The run is the promise doubted, and the doubt made true by being held. And this exposes the deepest fact about money, the one toward which the whole volume builds: money rests on confidence, and confidence is a belief about what others believe, which can collapse as suddenly as it formed. The deposit was money so long as it was trusted; the moment it was doubted, it ceased to be money, reverting to what it always was beneath — a promise the bank could not keep to everyone. The run does not destroy a sound thing; it reveals that the thing was never solid, only trusted.3

3. The run mirrors, in reverse, money's root (The Barter): money is accepted because each expects others to accept it (self-fulfilling confidence); the run is that belief collapsing — each doubts the promise will be honored, and the doubt makes it unredeemable. The run is the promise doubted, made true by being doubted. It exposes the volume's central fact: money rests on confidence (a belief about others' beliefs), which can collapse as suddenly as it formed. The deposit is money while trusted; doubted, it reverts to an unkeepable promise.

If the run is a failure of confidence rather than of soundness, then its cure is not more cash but restored confidence — and two devices restore it. The first is the lender of last resort, the principle Walter Bagehot set down for a central bank in a panic: when a sound but illiquid bank faces a run, the central bank should lend it cash freely, against the bank's good loans as collateral, at a penalty rate — so that the bank can pay every depositor who demands cash, the run has nothing to feed on, and the panic subsides. The central bank, able to create cash without limit, can supply the liquidity the bank lacks, turning its good-but-illiquid loans into the cash to honor its promise; and once depositors see that the cash is there, they stop running, for the reason to run is gone. The second device is deposit insurance: the state guarantees that depositors will be repaid even if the bank fails, so that no depositor has any reason to run — the promise is now the state's, not merely the bank's, and the state cannot run out of its own money. Both cures work the same way: not by holding enough cash to pay everyone, which no bank can, but by removing the fear that there will not be enough, and so preventing the run that the fear would cause. They cure a crisis of confidence with a restoration of confidence.4

4. Since the run is a confidence failure, the cure is restored confidence, not more cash. Two devices: (1) the lender of last resort — Walter Bagehot's rule (1873) that the central bank lend freely to a sound but illiquid bank, against good collateral, at a penalty rate, supplying the cash to honor the promise so the run subsides (the central bank can create cash without limit); (2) deposit insurance — the state guarantees deposits, so none need run (the promise becomes the state's, which cannot run out of its own money). Both remove the fear that causes the run.

The bank run might seem a local thing, a danger of one institution, cured by a backstop. But the same fragility runs all the way up the tower of money, to the money the backstop is made of. For the value of state money itself — the cash the central bank creates without limit — rests on exactly the same self-fulfilling confidence: it is accepted because each expects others to accept it, and holds its value because each trusts that it will. And that confidence too can collapse. When a state, to pay its debts, creates its money without limit, and holders come to fear that the money is losing its value, they rush to spend it before it falls further — and the rush to spend is itself what drives the value down, in a flight from the currency that is a run on the money itself. Hyperinflation is the bank run of state money: the same self-fulfilling collapse of confidence, the same rush to convert the doubted promise into something real before it becomes worthless, the same destruction of value by the very fear of it. So the lender of last resort, which cures the bank run by promising the cash of the state, cannot cure a run on that state's cash; there is no lender of last resort for the currency itself, save the discipline that keeps its quantity from outrunning the confidence that sustains it. The fragility is not a flaw of banks but of money as such, which rests, at every level, on a confidence that can dissolve.5

5. The same fragility runs up to state money itself: cash holds value only by the same self-fulfilling confidence (accepted because expected to be accepted). When a state over-issues its money and holders fear its value falling, they rush to spend before it falls further — and the rush drives the value down: a flight from the currency, a run on the money itself. Hyperinflation is the bank run of state money (The Debasement). There is no lender of last resort for the currency — only the discipline keeping its quantity within the confidence that sustains it. The fragility is money's, not merely banks'.

The run, then, is the moment money's deepest secret is laid bare: that the bank's deposit, like all money, is a promise that holds only on confidence, and that confidence is a belief about others' beliefs, which can collapse in a rush. The bank borrows short and lends long, and so cannot pay every depositor at once; its promise works only while not all test it together; and Diamond and Dybvig showed that whether the test comes depends on nothing but belief — the run a self-fulfilling prophecy, the doubt made true by being held. The cures restore confidence rather than supply cash: the lender of last resort, the deposit guarantee, both removing the fear that would cause the run. But the same fragility runs up to state money itself, where the flight from a currency is a run on money as such, and no last resort can save it. What the run reveals, the flagship will make the heart of the matter: that money is trust made transferable, and that trust, at every level, can evaporate. A promise believed is money; a promise doubted is paper. The next plate is the deepest turn of the volume: the ledger.