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


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2 Responses to The value of education is not the same as the value of a degree

  1. Isaac says:

    FYI: this was a Bryan Caplan entry.

  2. just the messenger says:

    It is easy to think of reasons why the return to a terminated education could be negative. If a degree is a signal of quality or ability to potential employers, dropping out or failing is a strong signal indeed. Of course, you might not list that on your resume, but any human resources dept is going to do their homework and see red flags.

    Negative psychological effects are also likely. Just having an application rejected can be unpleasant enough; in these cases, failing tends to outweigh the good feeling you get from knowing that you tried.

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