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# Three Graphs About Trying and Failing

 Gary S. Becker, RIP... Robert P. Murphy on Capital...
The true return to college heavily depends on the probability of successful completion.  That probability in turn heavily depends on pre-college academic performance.  How heavily?  Check out these three graphs from Bound, Lovenheim, and Turner's "Why Have College Completion Rates Declined?" (American Economic Journal 2010).  BLT compare results for the NLS72 (high school graduation cohort of 1972) and NELS:88 (high school graduation cohort of 1992), using a standardized high school math test to measure pre-college performance.

First, check out your probability of trying college if you finish high school.

Notice: By 1992, college is the default choice for most of the achievement distribution.  Almost half of high school grads in the lowest quartile of math performance - and two-thirds in the second-lowest quartile - try college.

Next, look at the probability of finishing college if you try college.  To get credit for finishing college, you have to graduate within eight years of your cohort high school graduation.  For the class of 1972, that's 1980; for the class of 1992, that's 2000.

Probability of success for the bottom half of the distribution started low in absolute terms: about one-quarter for the bottom quartile, and one-third for the second quartile.  Over time, though, the bottom's success rates have gone from worse to awful: Barely 10% of those who try college manage to get over the finish line.

Last, let's multiply the preceding probabilities together to get the the probability of finishing college if you finish high school.

Notice: Although kids in the bottom quartile became much more likely to try college, they became no more likely to finish.  The fruits of effort for the second quartile are also underwhelming.  How can this be?  Because the probability of finishing college if you try college actually fell for the bottom three-quarters of the distribution!  This is the fruit of America's college-for-all mania.

Will I tell my kids to go to college?  Sure.  Does this make me a big hypocrite?  Not at all.  I shall follow the same principle I commend to others: Encourage high academic achievers to go to college, and urge the rest to do something else.  More specifically: Push college for the top quartile, tolerate it for the third, discourage if for the second, and decry it for the first.

To be clear, this is prudential advice aimed at individual students, not a public policy recommendation.  From a social point of view, I'd only push college on the top 5%.  Unless, of course, the student loves learning enough to attend classes unofficially.  The more of these rare unicorns on campus, the merrier.

Jared writes:

Can't help but notice that the paper also decomposes the difference in completion rates into both student and school characteristics, and finds that it is the decline in the latter (particular resources per student) rather than the change in the former (the addition of more marginal students) that drives the overall difference in completion rates.

Jeff writes:

Great analysis. I can’t argue too much with your conclusions.

But it does hit home for me a bit. I’m part of the 5.0% to 5.6% (bottom quartile that finished college) in your last graph.

It amazes me how much the odds were against me at the time, I had no idea, and if someone had explained it to me at the time I would not have understood it.

But I did barely squeak in with respect to your definition finishing college, it took me 7 years straight to get my BS in engineering. I was so far behind in math, physics, and chemistry that I spent almost 3 years just catching up.

I have no idea what drove me, my parents didn’t push college on me (they both just have high school diplomas). It was discussed a bit in high school. I just remember nearing graduation and freaking out a bit about my future and then I just went on automatic pilot.

I went to junior college, wanted to be an architect (Brady Bunch influence), then discovered it was more art than technical and I was certainly was not an artist. I decided architectural engineering was close enough, so I started taking courses in math, physics, and chemistry, and I struggled at first, but then connected with some motivated older students and I really started to excel.

I took one class on “The Ecology of Man” and learned about the environment and the concept of entropy and was sold on Environmental Engineering and transferred to a 4 year university once I had all the prerequisites complete. After my BS I even went on to earn a Masters degree in Chemical Engineering, although I must admit I started out as a PhD student and decided to take my masters and run.

I’ve come to realize I had all of this potential inside of me with respect to math, physics, science, and engineering. But it was never discovered in high school. What a waste of time, I could be so much further ahead today.

High school to me was nothing but a popularity contest, in which I did not compete very well. My sole purpose was to fit in and not get beat up. I barely remember studying or doing work. High school in America is broken, but I do not know how to fix it. I can see how success breeds success and why strong correlations exist between parents education/success/achievements and a child’s. Without a parent constantly pushing, encouraging, and challenging a child, they will easily be lost, as it is rare to receive the required magnitude and duration of encouragement from high school staff.

I will just say be careful about ignoring the first quartile, but you have already alluded to this. Perhaps that 5% to 5.6% is just the natural amount of students who will eventually find their way without active and ongoing encouragement.

Eric writes:

Charles Murray said education is about finding what you are good at and becoming excellent at it. For many, that means something outside of intellectual pursuits, and there's no shame in that.

Bostonian writes:

If you want to increase political support for the idea that many people just aren't smart enough to study at the college level, you should not encourage the immigration of people who are likely to have children who are not college material. Open borders enthusiasts should consider this. The existence of large racial differences in academic achievement in the U.S. already makes it difficult to talk sensibly about education.

Philo writes:

{From your 2012 post:} "Take Marxism. As far as I'm concerned, it's no more a merit good than creation science. Grasping the thoughts of economically illiterate 19th-century hate-mongers is not a crucial ingredient of a life well-lived."

This is too dismissive. A knowledge of intellectual history is valuable to the would-be intellectual: it shows him or her some of the blind alleys that have shown their broad appeal to the human mind (no doubt partly from deep emotional sources rather than for good reasons). History gives the intellectual valuable perspective on his/her own activity. (Also, there have been some very bright and knowledgeable Marxists, who have said valuable things that are detachable from their Marxism.)

Admittedly, there are diminishing returns; for most of us a little history suffices.

Maniel writes:

@Jeff,
Nice comment. Celebrate your success; you mastered the most fundamental skill, learning. I believe that it is no accident that high math achievers are successful. That is because each math discipline – algebra, geometry, trigonometry, calculus, probability, real and complex analysis, statistics, etc. – demands that we acquire a new world view, a new vocabulary, a new tool set, and new approaches to problem-solving. You mention that high school was a waste of time – but, college is also a waste of time for many. IMO, learning to learn demands acceptance of two fundamental truths: that learning something new is hard, because it demands a new way of thinking; and that, because it is hard, learning demands time (like hours and hours) and focus.
As for the PhD, why bother? Why not get paid for all your hard work?

AS writes:

The third graph is a bit of a statistical lie. You can't just multiply those numbers. You don't have the counterfactuals. The third graph is a pooled statistic that doesn't really show how the probability changed for the original group of students since it pools it with the additional students who tried.

Mike W writes:

"Encourage high academic achievers to go to college, and urge the rest to do something else."

The discussion that needs to be had in the US is...what else?

If the university Anthropology and Communications grads are taking the semi-skilled jobs that don't really require a degree how do the capable but un-degreed compete?

Jonathan L writes:

"Encourage high academic achievers to go to college, and urge the rest to do something else. More specifically: Push college for the top quartile, tolerate it for the third, discourage if for the second, and decry it for the first."

But this fails to account for the expected payoff. For instance, if I only have a one in three chance of winning the lottery, should I buy a ticket? The answer depends on the price of the ticket relative to the payoff. In the above quote, Caplan concludes that if one has a less than fifty percent chance of a payoff, one should not play the game. But the expected value depends not only on the probability of success, but also on the amount of the payoff.

David L writes:

The timing of your post is impeccable. The SF Fed just did a PSID study which completely ignored the issue of college dropouts. I would be interested in your take on that.
http://www.frbsf.org/economic-research/publications/economic-letter/2014/may/is-college-worth-it-education-tuition-wages/?utm_source=mailchimp&utm_medium=email&utm_campaign=economic-letter-2014-05-05

MingoV writes:

The college completion rate has improved slightly in recent years because colleges continue to water down their curricula and make their exams easier. One of my daughters graduated college in 2012, the other is in her sophomore year. Both told me that a number of their college courses were easier than non-honors high school courses. Not only was the difficulty less, but the amount of material covered was less due to classes meeting only three times per week with semesters of fifteen weeks minus holidays.