Margins and averages: college edition

By Eric Crampton 17/04/2014 1


College grads earn more than those who don’t go to college. Does it follow that governments should encourage more kids into university? Not necessarily. 

Bryan Caplan here points to work by Eberly and Athreya showing that while the college premium increased substantially, college enrolment did not. Why? Because mediocre students are likely to fail out, and the returns to dropping out of college aren’t that high. Caplan summarises:

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.

 Bryan then looks to other “no-brainers”:

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 mirrors what Wolfers and Stephenson have been saying about the returns to marriage: the decline in marriage among the poor comes down to its lower expected value for poor people.

I will leave as an exercise for the student the following problem. New Zealand recently changed the university funding model. Previously, universities were funded based on student numbers and research output. Now, they’re also rewarded for their degree-completion rates: they’re punished for drop-outs. What happens to:

  • equilibrium standards for passing grades
  • the average college premium
  • the absolute college premium for better students
  • the expected college premium for better students
  • the absolute college premium for worse students
  • the expected college premium for worse students


One Response to “Margins and averages: college edition”

  • “College grads earn more than those who don’t go to college. Does it follow that governments should encourage more kids into university? Not necessarily.”

    A really good point although I would suggest that it might be better stated that “On average college grads earn more as there will be some who don’t go to college that earn more than those that do.

    In Christchurch at the moment it is possible to move straight into the workforce and earn decent money by getting involved in the rebuild.
    Also for students with solid rather than stellar high NCEA marks there are many career paths through polytechnics which long term could provide them with higher incomes than universities, e.g. trades, engineering and ICT.