Suppose that a bank calculates that the net value of the mortgage to the bank as a fraction of its principal is equal to four years' interest minus the chance of default:
π = 4r - d
And suppose that the homeowners and homebuyers who come to the bank have a chance of default which is:
d = 15% + 20r2
Then bank profits expected from a typical homeowner and home buyer are:
π = 4r - 20r2 - 15%
Which means that a bank can make profits as long as:
5% ≤ r ≤ 15%
And if there are a bunch of competitive banks, and if homeowners can comparison shop, competition will push the interest rate down to 5% and a bit more. And the observed default probability will be 20%.
Now suppose that there is bad economic news: the default probability rises by 5% to:
d = 20% + 20r2
Then, the way I have rigged this scenario, interest rates rise to 10%: no bank can make money charging less than 10%, given the new, higher default probability--and the observed default probability will rise not by 5% but by 20%, to 40%. The big increase in default, you see, comes not from the bad economic news but from the fact that a lot of people who could still make their mortgage payments at the old interest rate cannot make them at the new one.
And if the default probability rises even more, to:
d = 21% + 20r2
then the market collapses. There is no interest rate at which any bank--even a monopoly bank--wishes to be in this business. No loans are made at all.
Suppose that at this stage the government steps in. "We," the government says, "are going to cap your default losses at 20%." Then banks look at the situation and once again discover that it is profitable to make loans at any interest rate above 5%. Competition chases the market interest rate back down to 5% again. There is a problem--at a 5% interest rate default losses are not 20% but rather 26%--and so the government has to kick in money. But maybe a 26% default rate with the government having to kick in some money is better than a 40% default rate from a cultural, sociological, political, and in the presence of aggregate demand externalities economic point of view. And surely it is better than a complete collapse of the mortgage market.
That is the logic behind Frank, Dodd-Obama, the Barr-Tyson plan being pushed by Hillary Rodham Clinton, and the other variants: that when the major cause of large-scale defaults is not the fecklessness of the borrowers but rather the fact that the market equilibrium has high interest rates that are themselves both the consequence and cause of high default rates, that the government has a market-making role to play by providing guarantees. This seems to me to be a good logic.
Here is Alan Blinder on this issue:
How to Cast a Mortgage Lifeline?: THE financial markets are downright scary. And it seems unlikely that we can extricate ourselves from the current series of rolling financial crises without improving the situation in three related markets: those for houses, mortgages and securities based on mortgages. In a previous column for Sunday Business, I advocated one possible approach: creating a modern version of the Home Owners' Loan Corporation.... How would it work in practice? Let's concentrate on six major design issues:
STRUCTURE The original HOLC bought mortgages outright. But Representative Barney Frank, the Massachusetts Democrat, and Senator Christopher J. Dodd, Democrat of Connecticut, the chairmen of the two banking committees of Congress... would use a beefed-up Federal Housing Administration to guarantee new mortgages -- issued, say, by banks -- instead of buying up old ones. The effects would be much the same: old, unaffordable mortgages would be replaced by new, affordable ones; and the government would then assume the risk of default. But in the Frank-Dodd proposal, the federal government would be a big insurer rather than a big bank. Because the approach actually has a chance of becoming law, let's adopt its structure.
BAILOUTS The Frank-Dodd plan for a Super F.H.A. is intended to make a bad situation better. But it must not be too generous in shielding people and businesses from the consequences of their own bad decisions -- both for economic reasons (to minimize moral hazard) and for political reasons (to gain voter support)... existing mortgages would be bought below face value, forcing investors to, as they say in the trade, "take a haircut"... [and] the proposal would make homeowners relinquish part of any price appreciation on their houses for as long as their Super F.H.A. mortgages remain in effect....
LEGAL SAFE HARBOR The Super F.H.A. would have to deal with legal complexities.... Servicers are petrified of lawsuits if they sell individual mortgages... at a loss.... Congress must pass legislation shielding servicers from legal liability when (as now) market conditions depress prices....
SETTING PRICES The HOLC bought pre-existing mortgages at a discount. The Super F.H.A. would use government guarantees to induce private businesses to do so. In either case, we need prices for the old mortgages.... My suggestion is that the Super F.H.A. categorize the mortgages it might refinance into, say, "high," "medium," and "low" qualities... adjust those prices according to whether mortgage owners rush in to sell (meaning that the prices were set too high) or stay away (meaning that the prices were set too low)....
SUNSET Emergency measures must not outlast emergencies....
ELIGIBILITY AND SCALE How large should the mop-up operation be? Mr. Frank and Mr. Dodd are thinking about one million to two million mortgages, but they understand that a larger number might be necessary to stem the downward spiral....
The urgency of creating something like the HOLC or a Super F.H.A. has grown, not shrunk, since I wrote my previous column.... [T]he Frank-Dodd proposal... offers a smart approach to a knotty set of problems.... Their design is not flawless. But do you know of any perfect solutions? It deserves our support.