Selectivity and Selection Bias: Are Selective Colleges Better?

If you have ever been through the process of applying to colleges, you have almost certainly heard the term “selective colleges.” If you haven’t the basic idea is that some colleges are harder to get into, for example as measured by what percentage of applicants are accepted to the school. The assumption of both applicants and schools is that a more selective college is “better” in some sense than a less selective college. But is it?

In a new working paper, Mountjoy and Hickman explore this question in great detail. The short version of their answer: selective colleges don’t seem to matter much, as measured by either completion rates or earnings in the labor market. That’s an interesting result in itself, but understanding how they get to this result is also interesting and an excellent example of how to do social science correctly.

Here’s the problem: when you just look at outcomes such as graduation rates or earnings, selective colleges seem to do better. But most college freshmen could immediately identify the problem with this result: that’s correlation, not causation (and importantly, they probably knew this before stepping onto a college campus). Students that go to more selective colleges have higher abilities, whether as measured by SAT scores or by other traits such as perseverance. It’s a classic selection bias problem. How much value is the college really adding?

Here’s how this paper addresses the problem: by only looking at students that apply to and are accepted to colleges with different selectivity levels, but some choose to go to the less selective colleges. What if we only compare this students (and of course, control for measurable differences in ability)?

Now this approach is not a perfect experiment. Students are not randomly assigned to different colleges. There is still some choice going on. But are the students who choose to attend a less selective college different in some way? The authors try to convince us in a number of ways that they are not really that different. Here’s one thing they point out: “nearly half of the students in our identifying sample choose a less selective college than their most selective option, suggesting this identifying variation is not merely an odd choice confined to a small faction of quirky students.”

Perhaps that alone doesn’t convince you, but let’s proceed for now to the results. This chart on post-college earnings nicely summarizes the results (see Figure 3 in the paper, which also has a very similar chart for completion rates)

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It’s a Trap!

When I was 22 I applied to the MFA programs in creative writing at the Iowa Writers Workshop and Columbia. They summarily rejected me with a minimum of fuss. They were right to do so, but it is also without question one of the greatest pieces of good fortune to ever befall me.

Let’s talk about “trap” degrees – expensive, often multi-year endeavors that rarely lead to salaries commensurate with the investment and arguably carry negative signal value in the labor market. We could all dunk on the aspiring filmmakers and puppeteers who look as though they were sent from central casting to play exactly the sort of dude who forks over >$100K for the shortest path to becoming the next Spielberg without doing all the messy fundraising, friend-haranguing, lighting improvising, actor recruiting, writing, and film festival peddling that looks an awful lot like high-risk hard work. We could dunk on them, but…but I can’t think of a way to finish that sentence that isn’t arrogant and condescending.

Anyway, we really should put aside the “they did this to themselves” schadenfreude, at least for a second, because regardless of blame, a lot of high opportunity cost human life years are being scammed with the siren song of “look at this great investment in yourself that will feel just like consumption while you are doing it!” There’s nothing new here, mind you. “Eat yourself thin” diets cycle through the zeitgeist with regularity, conveniently next to the book/video/3-week courses that will help you get rich in real estate with no money down. But we should be concerned when an entire sub-industry appears to be selling a human capital investment with negative real value. They may not be the modal or flagship product of higher education, but neither was the Pinto.

There’s similarly no shortage of people eager to point out that a lot of undergraduate education looks like a 4 year cruise, a pretirement if you’ll excuse a shameless attempt at coining unnecessarily cute terminology. We shouldn’t be shocked that purveyors are bundling consumption within an investment where, by design, the check-writers face high monitoring costs — part of the point of college is leaving the nest, right? Think about it from the other side of the equation– higher education is a scammer’s dream. The money folks are out of sight and desperately credulous to believe their child is on the path to status and financial independence. The customer is naïve and unworldly, eager to follow any external entity (other than their parents) that will do their decision-making for them. But the best part is the con’s mark won’t know for sure they’ve been scammed until well after the check is cleared (but not before they’ll receive their first solicitation for alumni donations).

But, you might be saying, graduate and professional schools are meant to be different. This is focused preparation for a narrow field of endeavor. These programs are decidedly not pretirement cruises. This is training. Why would anyone pay for training in something that has no payoff? I’ll offer a couple possibilities:

  1. This isn’t training, it’s consumption, and the buyers are fully aware of it.

I’m sure this accounts for a fair amount of fine arts training, particularly for retirees and hobbyists attending local community colleges, as well on the children of wealthy parents who have no intention of ever pursuing a vocation. More on them in a second.

2. This is training for aspiring men and women of leisure.

Remember gentlemen and ladies of leisure? They used to have their own Census occupation code! This might seem redundant with the previous point, but if your intention is to hob-nob with the rich and more-rich, there is something very much to be said for being able to discuss certain artistic fields at more esoteric levels. There’s also a modern middle-class version of this as well, what in an earlier, more coldly misogynistic, male-dominated time would have been referred to as an “MRS” degree. I imagine there are plenty of men and women who view school as a way of biding their time until a partner emerges who will be the primary earner. Match.com profiles and fix-ups are likely to be more economically fruitful for students mid-pursuit of a graduate degree than those working unimpressive jobs.

We also shouldn’t dismiss those opting for a graceful slide down the economic ladder. Generous families, perhaps a universal basic income, a rich artistic education, and comfortably living in a bohemian southern university town are for many the formula for a quiet, comfortable life unencumbered by the toils of a career. I’ve always enjoyed the company of such folks, at least until they try to tell me how the economy really works. Never follow these people to a second location.

3. This is a scam, and one with potentially far reaching costs.

Like so many scams, you could write a pithy story about well-dressed con-artists who open a “college” in an abandoned strip mall, throw on a coat of paint, and scam the spoiled children of upper-middle class social climbers by offering fake degrees that promise a shortcut to white collar riches and bohemian prestige. It’d be a two-act romp followed by a third where everyone ends up ok and kids learn the value of hard work.

In reality, though, no small number of the victims will be kids from higher education information deserts, who emerge from their undergraduate years with a relatively weak career they were guided towards after they struggled their first semester. Facing grim job prospects, they’re hoping two more years will thin the competition in the rarefied air of the applicants with “graduate education”. It is for these students that I fear the most.

It gives me pause when I see overly narrow masters’ programs that target a specific job rather than training in a set of tools. In service to my own cowardice, I won’t name specific programs, but suggest caution when considering a degree where the only job you’ll be qualified for is in the name of the degree.

I similarly worry about third- and fourth-tier MBA programs (especially if your employer isn’t paying for it). So much of the value of an MBA is the social network it will wire you into. If your parents haven’t heard of the school, it’s probably not much of a network.

Aspiring masters degree students, my advice is this: look up the individual courses you’ll be taking and then explain to the mirror what you’ll learn in each one and the market in which those skills are in demand. If you can’t do that, I advise reconsideration.


That’s all great, but what should we do?

I have no policy solutions, but I do have a piece of pedagogical advice. We need to update the standard operating procedure of guidance counselors in schools everywhere. We’ve been working so hard to convince kids they should go to college, we forgot to teach them how to be discerning customers of higher education. I’m all about caveat emptor as life advice, but if we want to hit people with it as an ex post I-told-you-so, we have to teach it to them ex ante, especially when we’re talking about 17-year-old and (ahem, perhaps mildly infantilized) 21-year-old kids. Just because you’ll walk away with a degree doesn’t mean that degree will be worth the time and tuition.

My guess is that we should up the status of community college, technical certificates, and not going to college at all. At the same time, we should probably lower the status of arts degrees for for artistic fields that are better suited to learning by doing and autodidacts.

Or maybe we just need guidance counselors to bring college seniors on field trips to carnivals across the country. Nothing will teach you the cold truth of scams faster than losing your last 20 bucks pursuing a fluffy bit of googly-eyed asbestos shooting on a bent basketball hoop in front of someone you planned on asking to prom but could never see value in you again after missing 10 shots in a row.

Trust me, that’ll stick with them.

Should student debt be dischargeable in bankruptcy?

I’m not an economist who studies education or bankruptcy, and I’m not 100% confident I spelled dischargeable correctly. I am, however, above average at highlighting the difficulty of a question when dissuading a grad student from attempting an impossible thesis question, so let’s dig into this one, which sounds pretty hard to me.

First of all, it is very difficult to discharge student debt during Chapter 7 or 13 bankruptcy, but I think you still can do it if you convince a judge that continued attempts at repayment would create undue hardship i.e. put you in a state of poverty in the wake of previous good faith efforts.

That said, maybe you shouldn’t have to face literal starvation to discharge student loans. That’s a reasonable idea, but what would the broader consequences be? This is tricky question to untangle because there are both welfare consequences and knock-on effects where we are put down different forking paths of politics and policy.

If debt is dischargable, then lenders will expect lower rates of repayment. This increase in lender risk and decrease in return on capital would likely have immediate consequences in the form of:

  1. Higher interest rates
  2. Lower rates of loan approval
  3. Greater dependence on loan collateral
  4. Greater lender interest in what the loaned funds will be applied towards.

Before we tackle those, we also have to consider the different policy environment paths lenders may have to anticipate:

  1. The government stops subsidizing loans. This would lower tuition, but also lower access for low income students.
  2. A loan forgiveness program. Great for people with outstanding debt, but changes how expectations are formed forever going forward.
  3. The government launches a massive “free college” program that covers tuition at state colleges and universities. This would have all kinds of consequences potentially.

But where this really leaves us is with a billion dollar question: will dischargeable students loans lead to lower costs of higher education? I am confident that the answer is a definitive, unassailable maybe.

Higher interest rates is a pretty straightforward prediction, but the consequences are less clear. Higher interest rates could lead to less college matriculation, greater barriers for lower income individuals, and higher expected rates of bankruptcy, in part because decisions are being made by young people who don’t know the future, their future, or, really, anything. Related to this, lenders will become more discerning regarding who they lend to, giving more money on more favorable terms to matriculants from wealthier backgrounds, in no small part because wealthy parents are filled to the brim with collateral, making for excellent co-signers and providers of high school graduation gifts nicer than any car I ever hope to drive.

That is all boring and moderately obvious. It’s 4) that I’m most curious about. If you get into medical school, there is no shortage of institutions eager to dump several hundred thousand dollars in the foyer of your home. Part of the reason for this is the expected future income of physicians and their high graduation rates from medical school thanks to rigorous admission screening. But what is underappreciated is the 100% rate at which medical school students study medicine.

Not so with undergraduate education. You might study electrical engineering with a minor in computer science. You also might study something a senior tells you is the easiest major at your school. You might major in something that sounds fun or interesting. You might study Miscelleneous Studies, where Miscelleneous is a subject that is likely interesting and possibly extremely important, but within which you can choose classes that facilitate your avoiding learning anything useful or applicable in the labor market.

Herein lies the problem. Lenders treat loans for consumption very differently than loans for investment. Nursing and statistics degrees are investments. Art History classes (for most people) are consumption. What’s going to happen to higher education when the lender tells you you can have $200K at 3% to study any STEM field or $75K at 6% to study anything in the humanities? Will the demand for humanities degrees drop? Will the supply of humanities education recede? Are humanities and STEM education complements or substitutes?1

Let me phrase it a different way? Are wealthy fine arts majors cross-subsidizing STEM majors pursuing the first college degrees in their family? Or are they driving up the price of tuition because heavily subsidized credit is facilitating pre-career retirement lifestyles for 4 years?

All of this leaves me with the suspicion that dischargeable student loans will lower tuition for some while raising it for others. This heterogeneity would likely shift the electoral popularity of free tuition programs while also shifting the nature of those program. Maybe “free college” turns into a means-tested program. Maybe “free college” becomes “free STEM college”. Maybe both.

We could speculate what this means for loan forgiveness or subsidies, but this post is too long already and, as should be already clear, we’re not going to solve anything today. My elegant and succinct point is this:

When you massively subsidize a [knowledge, signal] bundled good for so long that it transforms into a [knowledge, signal, 4-year luxury cruise with your peers] bundle, and to accommodate that subsidy you protect your poorly constructed macro-investment in human capital by exempting it from bankruptcy proceedings, and as a result of this weird landscape a bizarre higher education industry emerges that is both one of the greatest achievements in US history but also a trap that 19-year-olds fall into because, really, is there any trap we don’t fall into when we’re 19, and from which thousands of people never financially recover, but if you just fix one part of it no one knows what will happen, and if you try to fix all of it at once in the back of your mind you’re afraid it could turn into the US healthcare industry part deux, well then what you have is a real and important problem that I don’t know how we will solve but I remain confident that other people will be very confident that they know how to solve it and they will get extremely cross with me for not sharing their confidence.2

So maybe don’t try to solve that in your dissertation.3 Might be safer to just definitively estimate the natural rate of interest that underlines all monetary transactions. That’ll be easier.

1The answer is “Yes”.

2 This is, to be extremely clear, not me picking on Ms. Reisenwitz’s tweet which was good and interesting and left me thinking about student loans for two days when I should have been working on the research topics I have actual expertise in.

3 Of course, if you do find a natural experiment where huge chunks of student debt were accidentally made dischargeable in a state for 2 years because of a legislative SNAFU, you should write that dissertation and put me in the acknowledgements.

The Tall and Short of Student Experience

Every semester in my intro STAT course I have my students create a variety of survey questions. After I combine their questions into a single survey, they collect responses from the student body at Ave Maria University. Most of the questions are vanilla. Other are not. They typically get in excess of 100 responses from the ~1,100 person student body.

While exploring the data, I found a really beautiful example for the week that we spend on multiple regression and dummy variables.  The survey results illustrate a clear, linear association between student height (inches) and their student experience at AMU (scored 1-10).

So strange! Why might this be? Except for that solitary 7 ft+ student on the basketball team, how in the world might height matter for student experience?

As it turns out a separate relationship holds the key.

Confirmed with a simple unpaired t-test (unequal variances), women rank their student experience much more highly. For this, students have multiple explanations at the ready.

  • Our school is in a rural location and women are more socially satisfied.
  • Men are less happy generally.
  • Men are less studious or have lower grades.
  • Men get less sleep and stay up later

The list goes on and I don’t know what the reasoning is or which ones actually play a role. But what I do know, is how to make fun scatterplots in Stata. As it turns out, if you control for sex, height loses all of its effects on student experience. Men are taller on average and they aren’t happy students relative to women (apparently). We can see in the figure below that all of the action in the two fitted lines occurs in the intercept. The slopes are practically flat for both men and women. In other words, height neither adds nor subtracts from a student’s experience rating.

What’s going on is that neither men’s nor women’s experience is affected by being taller. But, what’s actually going on here – you know – statistically? The simple version is that the bar chart above dominates the scatter plot. If we subtract the mean male experience score from the male values and do the same for the females, then we’re left with what is practically white-noise. How do all those other students of a different height experience the world? Well, as students, not so differently from you.

The Matriculant Theory of Value

The Labor Theory of Value goes like this: the value of a good, and the price it should command in the market, will (should) reflect the amount of labor it takes to produce it. It’s a classic fallacy, but not one we should mock. Yes, Marxist thought still often cling to it as it chases its own Hegelian dragon, but Adam Smith and David Ricardo both struggled with understanding why something that yields so little predictive value could still feel so right.

Which brings me to the updated credentialist version of this fallacy:

Now, I apologize for picking on this person, and this tweet, in particular. Similar gripes appear appear regularly in social media and The Chronicle of Higher Education on a regular basis. The formula runs as such: I, and people such of myself, have spent many years in school, have successfully been credentialed with a BA/MA/MFA/PhD, but the labor market refuses to reward us appropriately.

To be clear, I understand the deeply intuitive appeal of the Labor Theory of Value– the more labor I put into making something, the more people should pay me for the product of my labor. The problem with this logic is the very core of the economic puzzle: goods are only worth what people are willing to exchange for them. If you spend a year molding rotting eggshells into a 25-foot statue of Mickey Mouse, it might earn you something at an art auction, but probably not as much as you would have earned working an equivalent number of hours at Taco Bell. At the same time, you could take an art class at a local community college, paint a soft focus acrylic of the local high school, and sell it to an alum for $100. Or you could find a dinosaur egg in your backyard the day after you bought the house and sell it for $2000. Which is the more compelling artistic statement or mantle centerpiece is debatable, but the price each commands in the market is entirely objective, and has nothing to do with the hours of labor that went into them.

Which me brings to me the Matriculant Theory of Value: the more labor and tuition money I put towards producing a more credentialed version of myself, the more people should pay for the product of my labor. I’m sorry to report that the market doesn’t care about your degrees, it cares about what you can produce and the value the market places on that product. If you didn’t acquire any skills valued by the labor market, then your degree is only worth however much the firm values any marginal prestige it might enjoy from your credentials or the interesting conversation you may offer in the break room. If I’m an academic drawing a salary from an institution of higher education (and I am), then I’m reading not as a sign that I should be angry we’re not getting paid enough, but as a sign that I should be terrified that employers don’t value educational product I am currently producing.

Now, unlike a lot of scolds, I am sympathetic to the academic misinformation that students often find themselves marinating in. Professors enjoy telling students who might be wary of joining the glut of PhDs applying for scarce academic jobs, “Don’t worry, you’ll get a job. You’re special and brilliant and you deserve a job.” Given that these professors need cheap labor, but often lack resources, they are all to happy to pay “in trade” i.e. with an advanced degree. For that deal to work though, you have to convince students that the degree has value. They are all too quick to valorize a “life of the mind” not unlike acolytes being invited to take a vow of poverty, and with more than a little implied denigration of more proletarian endeavors.

We also have a tendency to grossly overemphasize grades, academic status, and completion. Rarely do I see a student told that it might be better to get a C in a challenging technical class than dodge it for the sake of their GPA. Who is going to be better valued in the market: a 3.9 GPA student who glided on fluff for four years, or a student who took 5 challenging technical courses over 4 years, failing 2 of them, and collapses at the finish line with a 2.1 GPA and hard earned BS?

What I am less sympathetic to is the frequent failure to admit the other allures of degrees less valued by the market: they’re fun. For a certain type of person, there is pleasure bordering on euphoric to sitting in a comfortable chair and reading histories, grand theories, and poetics for 8 hours a day. If you love your job, you don’t have to work a day in your life. True, but that doesn’t mean anyone has to pay you for it. It should worry you if your anticipated vocation is what other people do on their vacation. Not that it doesn’t have social value (it may have significant social value), but you should be terrified of trying to make a career doing what someone else is willing to do for free. You’ll not be surprised to learn no one is paying me to write these rambling diatribes.

So, yes, $38k a year for 9 months of work giving 10 hours of lectures a week, plus prep, grading, and office hours maybe doesn’t seem like much in the way of wages to you. I was paid $34k (2003 dollars) for 10 months a year teaching 19 hours of lectures a week, plus prep, grading, and parent meetings when I was a high school teacher, so I guess I could make a snarky case that the professor in question is being overpaid, especially since I hold to the belief that public K-12 teachers are underpaid relative to the social value they produce, but that is another post. But I also have enough awareness to know not to complain too much about how an indoor job with no heavy lifting is underpaid, particularly if we are resorting to any version of the labor theory of value. I dare you to walk into any professional kitchen and tell them these exact contract details, the nature of your work, and then explain to them that you’re the one who deserves to be paid more.

One last gripe. If you are sufficiently talented, conscientious, and privileged to complete a PhD, but your field of study offers you no option better than $38k/year to teach, my guess is that you’ve been not just unlucky, but proactively diligent in dodging every bit of coursework that could lead to a higher wage in the market. And I don’t just mean all of that unpleasant math you hate. Or statistics. Or java/C++/Python/etc. I mean even the adjacent courses of study or research projects where the skill acquisition path is that much more taxing or unpleasant. You didn’t study computational anthropology or physical anthropology or field anthropology. You studied cultural anthropology, fine…but you were also careful to avoid data at every step, opting instead you to memorize soft theory jargon and write the kind of dissertation that tells everyone exactly how smart you are, but not much else. Make no mistake, if you spend 5-8 years getting a PhD you may have gotten bad advice, you may have suffered the fallacy of sunk costs, you may have been done a gratuitous disservice by the faculty guiding your education, and may have been deluded by the matriculant theory of value, but on the bright side you chose a safe and comfortable line of work.

And make no mistake, you did choose it.