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.

Posted by Felix at 21:13 EST

Comments

FYI: this was a Bryan Caplan entry.

Posted by: Isaac at 21:17 EST, February 06, 2007

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.

Posted by: just the messenger at 17:32 EST, February 08, 2007