What Bad Students Know that Good Economists Don't
The college premium skyrocketed over the last three decades. B.A.s now out-earn high school grads by 70-80%.* College graduation, in contrast, barely rose. In econospeak, the supply of college graduates looks bizarrely price-inelastic.
Over the last two months, I’ve read virtually everything ever written on this puzzle. All of the compelling stories converge on a single factor I’ve emphasized for years: The return to trying to get a degree is far lower than the return to successfully getting a degree. Why? Because marginal students routinely fail to graduate. The single best paper on this theme: “The Education Risk Premium” by Janice Eberly and Kartik Athreya.
Eberly and Athreya begin by spelling out the puzzle:
When measured by the ratio of hourly wages of skilled to unskilled workers, the college premium increased by nearly 20% between 1980 and 1996 (see Autor, Katz, and Krueger (1998)). However, enrollment did not respond substantially. Over the period 1979-2005, even though the fraction of young adults (29 years and younger) with a college degree rose by 9 percentage points (23% to 32%), the increase in male enrollment accounted only for one percentage point (Bailey and Dynarski (2009)).
Quick version of their solution: Expected returns heavily depend on graduation rates – and graduation rates heavily depend on students’ pre-existing academic ability.
The presence of failure risk generates asymmetric changes in the net return to college investment: those with low failure risk see a large increase in expected returns, but are inframarginal because they will enroll under most circumstances. Those with high failure risk see a much smaller increase in expected returns, and hence remain largely inframarginal.
Let me illustrate. Suppose you’re at the 90th-percentile of high school graduates, so your probability of graduating college if you enroll is around 90%. When the college premium ascends from 50% to 70%, your expected premium goes from 45% to 63%. In plain English, the payoff goes from very good to excellent. Either way, enrollment is a no-brainer.
If instead you’re at the 25th-percentile of high school graduates, your probability of graduating college if you enroll is around 20%. When the college premium ascends from 50% to 70%, your expected premium goes from 10% to 14%. In plain English, the payoff goes from really crummy to crummy. Either way, non-enrollment is a no-brainer… especially when you dwell on the fact that colleges don’t refund drop-outs’ tuition, much less the earnings and work experience they forfeited to attend.
Eberly and Athreya simulate college enrollment under a range of assumptions about the college premium and the completion probability. The right-most column shows the overall fraction of each cohort of kids
that enrolls in college as a function of the college premium. Here is wisdom:
[W]ell-prepared enrollees face low failure risk and so already receive a high rate of return from college under any skill premium in the approximate vicinity of the current one. Similarly, the ability of the skill premium to meaningfully alter mean returns for the ill-prepared is minimal. The only remaining question is then: how large is the set of marginal households? The answer provided by the model is: not very big.
My favorite feature of Eberly-Athreya: Their story readily generalizes to other weighty life choices widely seen as “no-brainers.” Conventional wisdom condemns dropping out of high school. After all, standard estimates say that finishing high school raises your income by 50%. For good students, it’s easy money. For stereotypical “bad students,” though, it’s hard money – or a waste of money. Why? Because when bad students attend high school, their probability of graduation – and their expected return – remains fairly low.
The same holds for marriage. The economic benefits of stable marriage are massive. But as Charles Murray explains, the probability of stable marriage varies widely by social class. Divorce rates for the working class are about four times as high as for professionals. Marginal brides and grooms therefore face a high probability of marital failure – and can reasonably fear that marriage will make them worse off despite its palpable benefits.
To be fair, Eberly and Athreya are not the first or only education researchers to highlight the chasm between ex ante and ex post returns to education. But as far as I can tell, no one makes the logic clearer. If anyone taunts, “So your kids should go to college, but other people’s kids shouldn’t,” the honest answer is “Don’t shoot the messenger – or his kids.” The numbers don’t lie: College is a great investment for great students, a mediocre investment for mediocre students, and a bad investment for bad students.
* This is seriously inflated by ability bias, but over half of the effect looks causal.