A Dive into College Admissions
In the increasingly competitive atmosphere of college admissions, students increasingly turn to rankings to determine whether to apply or enroll at certain colleges. Perhaps the unspoken leader in the field, now notoriously synonymous with college admissions itself, is the annual US News ranking. How much of a role do universities’ “prestige” influence students’ tastes?
In this blog, I use US News ranking as a proxy for College prestige. Moreover, I use students’ propensity to attend given admission by yield rates (the #/applicants who enroll at a college ÷ the #/applicants who are accepted).
Above is the scatterplot of college rankings and corresponding yield rates; it is immediately clear that there is a strong correlation between the two. Institutions with higher US News rankings also had higher yield rates and vice versa. From here, the extent to which students base their college preferences on rankings is clear. Although many confounding variables are at play, it is safe to say that students do make college decisions based on rankings. So, given a US News Ranking, one can roughly predict the yield rate. Therefore, colleges have very little direct control over the yield rates and try hard to move up the US News Ranking leaderboard.
Looking more in-depth at the top 5 schools and the top 20–25 schools can give us further evidence of rankings’ effects on yield. (In particular, I was trying to compare Stanford and UC Berkeley and understand their yield and acceptance rates).
The top 3 schools— Princeton, Harvard, and Yale— all have extremely similar statistics for all figures. That is, they all have relatively high yield rates and low acceptance rates.
The top 20–25 schools have drastically lower yield rates than the top 3. However, all these schools are in approximately the same range of yield rates. Roughly the same percentage of Cal and UMich admits eventually enroll, which corresponds to their similar positions on the US News list. Moreover, the enrolled class varies quite a bit across these colleges and does not seem to influence the yield rates. That is, yield rates are strongly correlated to their ranking.
Using this information, it is possible to answer some relevant questions related to the admissions process.
Are universities’ acceptance rates driven by their rankings?
There is a common misconception that more people choose to enroll in schools with lower acceptance rates. The truth is, determinants of the acceptance rate include the size of the applicant pool in comparison to the desired class size, the yield rates, and the graduation rates. That is:
the acceptance rates = graduating class / (application pool size * yield rate * graduation rate) or
the acceptance rates = enrolled / (application pool size * yield rate)
So, colleges can predict the yield rate from historical information (which is strongly dependent on their ranking), know the exact application pool size and the number they want to enroll and can calculate the necessary acceptance rates.
Say two colleges receive the same number of applicants and need the same incoming class size, but have different yield rates. The college with the higher yield rate needs to accept fewer applicants since they have a higher chance of enrolling if admitted. Whereas, the college with a lower yield rate would have to accept a larger percentage of applicants. As demonstrated above, as schools’ US News ranking increases, a larger proportion of admits choose to enroll. So, acceptance rates would be correlated with a school’s US News ranking, but it is incorrect to say that higher US News rankings directly result in lower acceptance rates.
Knowing this, we can answer some more pressing questions.
Why does Berkeley have such a high acceptance rate compared to Stanford?
Straight off the bat, Berkeley’s yield rate is drastically lower. This tells us that to admit the same number of students from equivalent-sized applicant pools, Berkeley would need to admit nearly 2 students for every student Stanford accepts. If Cal had the same yield as Stanford, it would only need to accept 9% of applicants to maintain the same class size.
One reason for Cal’s much lower yield rate is simply its lack of a binding early decision admissions program. Stanford institutes early decisions, forcing students to commit if admitted, artificially increasing the yield.
Berkeley is magnitudes larger than Stanford, and can thus manage to accept more students, explaining the larger incoming class sizes.
Everything else equal, do larger acceptance rates lead to larger graduating classes?
Yes.
Let’s say School A has 10,000 applicants, a 10% acceptance rate, a 100% yield rate, and a 100% graduation rate. School B has 10,000 applicants, a 50% acceptance rate, a 100% yield rate, and a 100% graduation rate.
That would give school A a graduating class of 10,000(.1) = 1,000 and school B a graduating class of 10,000(.5) = 5,000. Therefore, everything else equal, larger acceptance rates would result in a larger graduating class.
That’s it for this post. If you enjoyed this post, you should check out my previous piece on the college admissions funnel and the underlying economics of the whole process.
If you have any thoughts/questions, feel free to leave a comment. Thank you.
