TODO: Finish the "Chetty Et Al" and "Net Present Value" sections after finishing up the college rankings.
Mobility: College Selectivity
[ Part of a sequence of posts on income mobility ]
A note: Bryan Caplan suggests thinking of the correlation between college quality as being divided into ability bias, signaling, and human capital increases The case against education. On this page, I consider the sum of signaling and human capital increases, because that is the expected causal effect on an individual attending a college. The net society-wide effect of attending college should exclude signaling, and such an analysis would presumably find much smaller returns to college quality.
Rankings
A number of college rankings claim to measure the value of a degree from different colleges. I find them all very unsatisfying.
The Case Against Education
Probably the first place to start in checking how much it matters where you go to school is Bryan Caplan's The Case Against Education The case against education (summary), because it is recent (2018), a literature review, and conducted by a man who, I feel, is sufficiently aware that correlation ≠ causation.
Basically, he considers studies that examine the correlation between measures of college quality and alumni earnings after controlling for various alumni variables such as average SAT score. Ignoring some studies we'll touch on in the next section, Caplan considers Do measures of college quality matter? The effect of college quality on graduates' earnings Monks Brewer Brand Long, M. C., and gives particular weight to College quality and wages in the United States Estimating the returns to college quality with multiple proxies for quality How robust is the evidence on the effects of college quality? Evidence from matching.
He ends up concluding
The most impressive research carefully merges diverse measures into an overall index of college quality. Punch line: moving from the bottom to the top quartile raises male earnings by about 12% and female earnings by about 8%.
There is some ambiguity in Caplan's prose regarding whether he means the 25th and 75th percentile or the average of each quartile (i.e. ~12.5th and ~87.5th percentiles). However, diving into the three studies he deems the best makes it clear the answer is the latter. From this we can conclude that Caplan believes a 1 SD increase in college quality causes a ~4% increase in earnings.
Finally, Caplan notes that these estimates might be affected if going to a better school increases or decreases the probability of graduating. He ends up concluding that it probably doesn't matter much:
Intuitively, you would expect better schools to be harder, and harder schools to have lower completion probabilities. Could you even survive at Caltech? A glance at graduation rates shows that students at better schools have unusually high completion probabilities, but there’s an obvious explanation: students at top schools are awesome enough to surmount the toughest coursework with ease.
Strangely, most experts on this topic ultimately reject this commonsense story. The consensus, instead, is that top schools are a free lunch. Hand Princeton a random student, and it boosts their graduation probability along with their salary after graduation. How? Maybe studying and slacking are contagious; if you’re surrounded by diligent students, you’re slacking alone. Personally, I suspect students at top schools have extra advantages that researchers overlook. Still, in light of the evidence, my rates of return treat college quality and completion probability as unrelated.
Dale & Krueger
Dale & Krueger have published a number of studies Estimating the payoff to attending a more selective college: An application of selection on observables and unobservables Estimating the return to college selectivity over the career using administrative earnings data (No. w17159) Estimating the effects of college characteristics over the career using administrative earnings data, where they find that previous researchers just hadn't added enough human capital controls. In particular, they suggest adding controls related to the application process such as the number of schools a student applies to or the average SAT score of the school a student applies to - the story is that these variables help control for ambition, which isn't well captured by SAT or GPA.
They ended up finding that including such variables as controls caused the (presumed) effect of college selectivity/quality to drop to essentially zero (except for some sub-groups, see also Isaac).
Naively, the Dale & Krueger studies seem fairly definitive: they found a control variable that removes the observed effect and they have a reasonable story regarding why the effect shrinks. Nevertheless, Caplan doesn't take them literally:
If Dale and Krueger’s results feel implausible, picture all the faculty attention and support the University of Delaware would shower on a student good enough for Harvard.
Intriguing as Dale and Krueger’s studies are, they remain outliers. Virtually all other specialists detect some payoff for college pedigree. Indeed, whenever Dale and Krueger discard what they know about college applications, they detect payoffs for college pedigree, too.
If only someone would reproduce their analysis with a much larger dataset!
Chetty Et Al
Chetty et al use millions of tax returns over multiple decades to construct a dataset which includes child income percentile (age 32-34), race, ACT/SAT score, parental income percentile, and college attended.
There are two things to note here. First, the slope between parent- and child-income is much shallower after including measures of college quality. This has interesting implications that are beyond the scope of this post. Second, there are large gaps between colleges and between college tiers. This suggests that either where you go to college can have large effects or that large additional confounders remain beyond parental income.
Chetty et all then add race and ACT/SAT score controls.
Finally, they take that model and start throwing in even more controls in (Table VII). In particular, they find adding high school FEs shrink the college FEs by about ~10% and that adding the average SAT score of applied-to colleges shrinks it by another ~5%. The latter step represents a failure to reproduce the results of Dale & Krueger, since large college FEs still remain.
Unfortunately, Chetty et al don't provide their estimated fixed effect coefficients for colleges. However, I reverse engineered their SAT-and-parent-income model in my college rankings sequence, so you can find the approximate FE values there. I found that moving up 1 SD in college quality (as measured by their FEs) is associated with a 5.9pp increase in earnings. After I threw in some other controls (mostly for majors and gender) and limited the schools to "normal" colleges, this shrank to about 4.3pp, depending on the model.
However, it's important to note that the rankings I ended up with are quite different than normal rankings like US News and Barron's tiers. For instance, schools of Ivy League calibre appear to cause just a ~2pp increase in alumni earnings. This all either means my analysis is garbage or that conventional wisdom regarding how good college X is for your career is not great. Maybe both.
Recall, Caplan estimates that a 1 SD increase in college quality appears to cause about a 4% increase in earnings - i.e. about 1.3pp increase in earnings. It looks like I'm generally finding numbers about half that size.
The tl;dr here is that the bulk of the evidence suggests that a 1 SD increase in college quality causes a ~13% increase in income, but that conventional measures of college quality (e.g. average SAT score, Barron ranking) don't correlate very well with this, and so moving up 1 SD on these measures only appears to cause about a quarter of that effect.
TODO Diversifying Society’s Leaders? The Causal Effects of Admission to Highly Selective Private Colleges
Other Studies
Chile is one of the most developed nations in Latin America, cinching the top spot in the HDMI rankings for the region and #42nd overall. Moreover, its inequality is roughly similar to the US's (Gini index of 0.426 v 0.486) List of countries by income equality. In Wikipedia. For these reasons, it seems plausible that the socioeconomic dynamics there are similar to those in the US - at least as similar as many European countries.
This preface is mostly just a rationalization for me to talk about this study Hastings, which takes advantage of the fact that Chile has a nearly comprehensive college admissions that is a special case of the mathematical "college admissions problem" Stable marriage problem whereby (a) each student is ranked by a single formula (b) each student ranks a number of colleges and (c) students are assigned via this algorithm. This is all made even more powerful (from a research perspective), because each student isn't just ranking colleges, they're ranking specific programs (fields of study) within each college.
This allows for a comprehensive regression discontinuity design Regression discontinuity design to tease apart the marginal effects of college and field of study. Here are the final estimates for the causal effect of college selectivity on earnings (with 0% being not attending college at all):
| Selectivity Quartile | Effect |
| 1st | 5% |
| 2nd | 8% |
| 3rd | 11% |
| 4th | 24% |
Another paper performs similar analysis on Chile college admissions and finds a significant increase in earnings from attending the two most selective universities (versus not) one year after graduation, but fails to find any effects after the first year Bordón. This suggests there aren't dramatically higher returns at the high tail in Chile's colleges.
Sadly, all this analysis is limited to Chile, and I couldn't find any other studies using quasi-experimental designs that weren't limited to one or a few colleges, which makes them poorly suited to answering the question of interest.
Family Studies
I found one twin study looking at the association between college quality and earnings that used identical twin fixed effects Behrman. The authors find that, within identical twin pairs, one who attends an Ivy League college typically earns ~30% more (relative to a large public university). There are some caveats. First, as is typical of twin studies, the sample is small (just 403 pairs), which leads to estimates that are just somewhat statistically significant. Second, the sample is comprised entirely of women, and it is fairly typical to find larger effect sizes among women, regarding educational quality and earnings. Finally, interpreting that 30% estimate as causal requires us to assume there are no remaining confounders within a pair of identical twins. This may seem benign, but recall that adding an IQ control when predicting income from educational attainment within twin pairs reduced the association by about 20%. In other words, this twin study is interesting, but hardly definitive.
More broadly, twin studies generally find that undergraduate institutional quality is largely caused by genes rather than common environment Smith-Woolley. If there were minimal causal effect of college quality on adulthood earning, this would suggest that the slope within siblings should be half of the slope within the general population This is roughly what we find, at least in Europe Lindahl Borgen. This suggests minimal effect by institutional selectivity, contradicting our lone twin study above.
Because these studies disagree, it is hard to see how we should integrate them into the other evidence we've examined. At this time, then, I'm inclined to ignore them.
TODO Ova and out
Net Present Value
If you assume that the real discount rate is 6%, that it takes you 4 years to graduate, and that you work for 40 years from that point forward, then you should be willing to pay $1 more in tuition to boost your income by $0.31.
The average college graduate makes about $70k, so they should be willing to pay about $23k to boost their later income by 10% - or about 3.2pp. This number scales upwards for students with higher earning potential (STEM, high SAT, rich parents). At the end of the day, it seems to me that if you're considering very selective colleges, its almost always a good idea to go to the best college that accepts you - the rub is (1) whether you can actually identify which college is "the best" and (2) whether there's even any trade-off as better colleges don't necessarily cost more.
Still, there are presumably non-financial benefits to attending a "good" college, and they plausibly make it worth it. Even from a purely financial perspective, the main actionable take-away is probably that there are some seriously undervalued colleges that you can probably take advantage of. As with many aspects of human life outside the stock market, lots of $20 bills are lying around.
Finally, given how incredibly cheap it is to apply to more colleges (in terms of time and money) it seems a no-brainer to apply to lots.