## Variability in returns to education

10/05/2013 § 1 Comment

The headline in the *LA Times* was ‘College is a bad financial bet for some, study says’. The story focused on the cases in which students had a negative return on investing in higher education:

A surprising 14% of high-school graduates earn at least as much as people with bachelor’s degrees, and 17% of those with bachelor’s degrees outearn compatriots with professional degrees, the authors found.

The study in question is here, a Brookings Institutions report about the variability of returns to education.

The main thing I wanted to point out was the framing of these numbers. Research has shown that the way that percentages are presented changes how people react to them. Is it a 20% chance of failure or 80% chance of success? Is it a 1% probability of damage or a 1-in-a-hundred chance? It matters.

So let’s flip it around. Are you surprised that 86% of high school graduates earn less than people with bachelor’s degrees? How about that 83% of people with bachelor’s degrees earn less than graduates with professional degrees? If you were playing the percentages, would those results encourage you to get a degree?

What the authors are telling us is that earnings by degree have a distribution around some mean. There is some distance between the means, and the overlap of the distributions isn’t all that large (15%-ish). I haven’t gone through the report, but the results would be affected by whether they are doing a sort of t-test of the two distributions, or doing something like analysing joint distributions of two random variables.

Does this mean we are sending too many people to university? I’d suggest we don’t have enough information. If we think of it as a comparison of two distributions, what would we be trying to do? Are we trying to:

- create enough distance between the means so that the overlap is small? But why should we encourage a larger premium for education when on average the benefit-cost ratio of education is already around 5?
- shrink the left-hand tail of the distribution for the more-highly educated? But how do we reliably identify these students, and should we give up on majors or degrees that don’t have a high enough return on investment?
- do something with the right-hand tail of the high school graduate distribution? But what do we do with them? They have done well as high school graduates — it doesn’t then logically follow that they should have more education.

I don’t see that there’s necessarily a problem. The fact that a small-ish percentage of people don’t get much from a university education means that we are casting the net wide enough to bring in most of the people who potentially would. The fact that some high-school graduates can still make a good living shows that there are still opportunities for all kinds of people, not just top STEM graduates from top schools.

Bets don’t always pay off; investments sometimes fail. But if I were playing blackjack and winning 86% of the time, I’d be at the table all night.

Or at least not enough information from those few numbers. The data may be out there.