Thursday 17 April 2014

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. 

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


  1. Caplan was on EconTalk recently talking about this.

  2. Quick partial equilibrium intuition gives me the following answers:

    equilibrium standards for passing grades fall (i.e. less work required to pass)
    average college premium falls
    absolute college premium falls for both groups
    expected college premium falls for better students
    expected college premium rises for worse students

    As a bonus answer, welfare implications depend on your social welfare function.

  3. comes down to design? that is, how much funding is at risk and the balance of funding triggers between inputs (enrollments), outputs (completions rates) and even if outcomes (employment, rates of return, time on benefits... post graduation) were taken into account in funding decisions.

  4. Cheers. I have always harboured a view that management (along with Tourism and a few other things) are not really worthy topics to be studied in a university. Her comments do not change my mind.

  5. yes that right, I rang up the tradesman, I said can you fix my heat pump,
    or alternatively can you fix my laptop, or my shower.
    The NZ tradesman said you poofter we don't even come near to you unless yo give us $200 upfront.
    I said OK, I will do it myself.
    I rang this fancy lawyer and said can you transfer our family home, he said yes, don't you know I am graduated it will cost you $1200 here and $US 1000 over there for your daughter who is overseas.
    I said thanks college idiot, what you boys do down there in Canterbury weakling university,
    I will do it myself
    and i did

  6. A quick guess

    1. Equilibrium standards for passing grades fall
    2. The average college premium is indeterminate but will probably fall (you have worse students graduating on average if the university lowers passing standards, but students may be better trained if they put more effort into teaching, or may be excluded from university in the first place if more restrictive entry criteria are adopted. I would expect the lowering of standards to dominate so the premium would likely fall).
    3. The absolute premium for better students is unchanged as employers should still be able to identify them on the basis of transcripts and work performance (standards for high grades probably wouldn't change with the policy, only low grades).
    4. The expected college premium for better students essentially unchanged (as above, and they always had a high chance of passing)
    5. The absolute college premium for worse students indeterminate, but probably falls (as in (1), more attention from uni + more restrictive entry criteria vs lower standards)
    6. The expected college premium for worse students indeterminate as in (5) but I'd guess would rise with a significantly higher probability of passing.

    Maybe I'm not quite as fatalistic as you regarding bad students. Surely unis would respond to the new policy with a mixture of lowering standards and greater effort in teaching (or excluding bad students).
    Ideally you'd fund unis based on graduate pay as measured by tax returns, then you'd get real market incentives for them :-)