They are all the same.
Do bank runs cause recessions, or do recessions cause bank runs? Both. Neither. They are the same thing.
(This post isn't as clear as I want it to be, because my mind isn't as clear as I want it to be, so read at your own risk.)
I was making a second attenpt to read (as opposed to skim) John Cochrane's excellent paper "Toward a run-free financial system" (pdf). I got distracted at the top of page 8, where John says:
"A run requires that if one investor pulls out, the firm is closer to bankruptcy, giving a second investor greater incentive to pull out.
This is the core externality of run-prone debt. My action to pull out alters your incentives. Externalities do suggest a need for regulation, even once all the unintended disincentives and subsidies have been fixed."
We need to be a little careful here. Let your utility U be a function of my action M and your action Y. U=U(M,Y). (Similarly, let my utility V be a function of your action and my action V=V(Y,M)).
At the equilibrium point, where Uy=0 and Vm=0:
1. If Um =/= 0, we have a (positive or negative) externality, because my action affects your utility.
2. If Umy =/= 0, we have (positive or negative) feedback (our actions are strategic complements or substitutes), because my action affects your incentives.
In bank runs we have both: my pulling out lowers your utility and increases your incentive to pull out too. My pulling out creates a negative externality and positive feedback.
The same is true of the Old Keynesian multiplier. My cutting my spending lowers your utility, and gives you an incentive to cut your spending too.
(And it is not written in stone, despite what Maynard said, that the marginal propensity to spend is less than one. If people expect everyone else to cut their spending by 1%, they might respond by cutting their own spending by more than 1%. If so, the Keynesian multiplier, like a bank run, might spiral out of control.)
The same is true of the Old Monetarist cold potato story (the hot potato in reverse). If I decide to hold more money, by cutting my spending of money below my receipts of money, that means you sell less, and hold less money, which lowers your utility. And it gives you an incentive to cut your spending to try to restore your stock of money.
But is there more than just a formal similarity between a bank run and the Keynesian multipler and the monetarist cold potato? I think there is. To see this, consider a hypothetical counterexample, where these processes would be formally similar but unrelated in practice:
Car banks. Suppose the Jalopnik devil waved a wand and made cars a fungible asset. All cars are suddenly identical, and will always be identical. Car banks spring up. You give your car to the car bank. In return, the car bank pays you rent/interest, and promises to pay you one car on demand. Since most of the time most people don't need a car, car banks become fractional reserve car banks. There's no profit in having cars sit idle. Owning the bank's promise to pay you one car on demand is as good as owning a car, provided the bank can always deliver on that promise.
Fractional reserve car banks would be vulnerable to Diamond Dybvig runs. If you expect that everyone else will withdraw a car from the bank, you will withdraw one too, in case you suddenly need a car and find they have none left in reserve.
But there would be no obvious relation between runs on car banks and recessions. Would a run on car banks cause a recession? Probably not (unless people can't get to work if they don't have a car, but that would be a drop in labour supply and not a drop in labour demand). Would recessions cause a run on car banks? Probably not (if anything, since people drive less in recessions, runs on car banks would be less likely).
And would we want the government to act as car-lender of last resort? Not unless the government has a 3-D printing press, and can print cars for free. And if the government could print cars for free, we wouldn't need car banks anyway. The government would just print everyone a car.
But if cars were the medium of exchange, and unit of account -- if cars, and promises to pay cars, were used as money -- things would be very different. You wouldn't be able to buy things, without a car.
Start with a very simple monetarist model. A fixed stock of money M circulates around the Wicksellian roundabout in exchange for an annual flow of newly-produced final goods and services Y going in the opposite direction. MV=PY.
V might not be stable. If one person postpones his spending, even if just temporarily, the person he buys from might postpone his spending too. We would observe a wave of postponed spending circling around the roundabout. Would the wave die out over time, or get bigger? That depends.
If people think it's just a one-time delay in payment, and a one-time reduction in income, their reactions to the shock will be smaller than the shock that caused that reaction. The wave will die out. The whole point of leaving a flexible buffer zone between you and the car in front is so you don't have to adjust your speed exactly to the speed of the car in front. The whole point of holding a flexible buffer stock of money is so you don't have to adjust your spending exactly to the spending of the people who buy from you.
But if people think this is the start of something new, the wave will get bigger. If you think the car in front has an erratic driver, who is liable to slow down or speed up at random, you leave a larger average buffer zone. You hold a larger average buffer stock of money if you become less certain of the spending of people who buy from you. There is a fall in the velocity of circulation of cars on the Wicksellian roundabout. There is a recession.
You could tell a very similar story in Keynesian language, if you throw in a little bit of Friedman. Suppose a temporary shock causes a drop in spending and income. If people think their drop in income is only temporary, their response to a drop in income will be a drop in spending that is smaller than the drop in income that caused it. The wave gets smaller and dies out. But if people think their drop in income is permanent, they may cut their spending by as much or by even more (consumer durables and other investment accelerators) than the drop in income. The wave gets bigger.
In the simplest version of the Wicksellian roundabout, money circulates in one direction, and newly-produced goods and services circulate in the other direction. But if we add other assets to the mix, especially short-duration IOUs for money that need to be rolled over, it wouldn't change the basic story. I won't buy your (newly-produced) goods because I expect to have difficulty selling my own newly-produced goods. I won't buy your IOUs because I expect to have difficulty selling my IOUs, or re-selling your IOUs. We call one a recession; we call the other a bank run, or shadow bank run. They are all just positive feedback slowdowns on the Wicksellian roundabout.