This analogy can't be original. But I don't remember hearing it before (though that doesn't mean much).
I was reading Morgan Kelly (H/T Tyler Cowen) on Irish banks. And I was also thinking about my next lecture in ECON1000, on common resources. Then it struck me. They are the same. Banks are a common pool of funds. They pool risks. And if banks go bad you get the same externalities and under- or over-investment in the common pool as in any common resource.
But there's an empirical problem. If bad banks are a common resource, then it could be socially optimal for them to borrow at 8% and lend at 5%. But it could never be an equilibrium for them to have negative spreads like that. Yet in Ireland they do. What the hell is going on?
Suppose safe loans normally yield 5%. But the banks are bad, and can only borrow at 8%, because lending to a bank is risky. Suppose a bad (risky) bank finds a good (safe) borrower. Will the bank be willing to lend at 5% (plus markup); or at 8% (plus markup)?
The marginal loan to a safe borrower does not add to the total risk of lending to the bank. In fact, it will make a small reduction in the average risk of all loans to the bank. So efficency requires the bank to offer the new loan to a safe borrower at 5%. But if the bank can only borrow extra funds at 8%, because the bank is risky, the bank will only be willing to lend at 8%, even to a safe borrower.
If the ultimate lenders could circumvent the bank, and lend directly to the ultimate (safe) borrower, they would be willing to lend at 5%. But ultimate lenders don't like lending directly to ultimate borrowers; that's why banks exist. Banks pool risks.
The problem is the externality. The ultimate lender who provides the funds for the extra loan to the ultimate safe borrower creates a positive externality for the existing lenders to the bank. Because he reduces the average risk of the bank's total assets. Whenever there's a positive externality to some activity, the equilibrium level of that activity will be less than is socially optimal.
The peasant who spreads fertiliser on the commons raises its output. But if he is only one of a hundred commoners, he himself will only see 1% of those benefits. So there's under-investment in fertisilising the commons. 99% of the benefits are reaped as positive externalities by the other peasants. The peasant who spreads fertiliser cannot exclude the 99 other peasants from reaping the benefits of his investment.
The ultimate lender who extends an additional $100 loan to the bank so it can lend to the safe borrower is like the peasant who fertilises the commons. He cannot exclude the other ultimate lenders from benefiting. If the bank goes bust, his safe $100 is not separated. It's part of the common pool of resources from which all ultimate lenders can try to recover their loans. We get rid of the externality if new lenders take precedence over old lenders if the bank goes bust. But the whole point of a bank is to pool risks, so that all share in the gains and losses.
If the bank is good, there's no externality, since the equity holders bear all the risks. But if the bank is bad, a new lender shares the existing risks of the old lenders. So if banks are bad, even safe borrowers will face higher interest rates. Which has undesirable macroeconomic consequences.
If new loans are safer than old loans, new loans create a positive externality, and bad banks do too little lending. Coversely, if new loans are riskier than old loans, new loans create a negative externality, and bad banks do too much lending.
But there's something very wrong with this theory, at least empirically, right now, In Ireland. Here's Morgan:
"The other crumbling dam against mass mortgage default is house prices. House prices are driven by the size of mortgages that banks give out. That is why, even though Irish banks face long-run funding costs of at least 8 per cent (if they could find anyone to lend to them), they are still giving out mortgages at 5 per cent, to maintain an artificial floor on house prices. Without this trickle of new mortgages, prices would collapse and mass defaults ensue."
Why are banks willing to lend at 5% when they can only borrow at 8%? Morgan says it's because all the banks are colluding to try to support house prices. Might it instead be that they are all trying to internalise the externality of the common resource problem? And they are aided in this by the fact that there is only one, large, ultimate lender, the ECB? And the Irish government is holding the bag (sort of, maybe) for the existing loans?
I can't work it out.
[Addendum 1. I Googled, and found some hits making the analogy between banks and the Tragedy of the Commons. But it was either about robbing banks, or banks having an incentive to make too many risky loans, rather than too few safe loans.]
[Addendum 2. As the son of a commoner, I know that the Tragedy of the Commons is at least partly myth. If the lord didn't act as central planner (with consultation) us commoners worked out an informal system ourselves over whose cattle grazed which land. It only broke down when townies moved in and didn't understand the informal set of property rights, and started cutting the grass with lawnmowers, and riding their horses on it.]