The value of education is not the same as the value of a degree

A few commenters have

said that they like the recondite stuff, so I did quite enjoy, earlier today,

throwing out a blog post talking about the CFTC and the CDS market and hazard

rates without bothering to spell everything out. Maybe I went too far –

but it just so happens that Arnold

Kling Bryan Caplan has a blog entry today which allows me to spell out some of the assumptions

I was making. Here he is on bankers:

Borrowers rarely default on their loans. Nevertheless, differences in default

rates have huge effect on rates of return. Suppose, for example, that two

lenders charge 3% interest, but one has a default rate of 1% and the other

has a default rate of 2%. The first lender has twice the rate of return of

the second. After all, when the first guy lends out $100, he gets back .99*$103=$101.97,

while the second only gets back .98*$103=$100.94.

Caplan’s rhetorical point is right, but his mathematics is wrong, unless the

recovery rate on the loans is zero. When a borrower defaults, the bank

doesn’t get back nothing. Usually the borrower has already repaid some principal

and interest, and nearly always the bank can sell the loan to a collections

agency for more cash still. Let’s say the lender with a 2% default rate has

a 50% recovery rate – then his total return is .98*103+.02*50=101.94.

See, I’ve doubled his return at a stroke!

Caplan goes on to talk about education in similar terms:

People often enroll for

a year of school, attend for a while, and then give up. And sometimes they

attend for a full year, but get failing grades. Either way, they spend most

or all of the cost of a year of education (including foregone earnings), with

little or no benefit. It’s analogous to defaulting on a loan – you spend the

resources, but don’t get the return.

The omission matters. If there is a 7% return to successfully completed education,

but a 3.5% default rate, the expected rate of return is 3.5% – half as big

as the naive estimate.

Once again, Caplan is assuming a recovery rate – the value of a non-completed

transaction – of zero, which is ridiculous. Obviously an extra year’s

education has some value. Let’s say that the 7% return to a successfully-completed

four-year degree is comprised of 1% for each year completed, plus an extra 3%

for the piece of paper you get at the end. Then if 3.5% of students "default"

– drop out after one year, say – then the expected rate of return

is 0.965*1.07+0.035*1.01=1.0679, for a 6.8% return.

It’s important not to write off anything completely – either loans or

students.