A Tale of Two Colleges

Students who attended a private four-year college in America paid an average of about $29,000 in tuition and fees in the 2012-2013 school year. Those who went to a public university in their home state paid less than $9,000. An elite private education might be better in many ways: the classes smaller, the athletic facilities newer, the faculty more distinguished, and the students smarter. But $20,000 per year of study is a big difference. It makes you wonder whether the difference is worth it.

The apples-to-apples question in this case asks how much a 40-year-old Massachusetts – born graduate of, say, Harvard, would have earned if he or she had gone to the University of Massachusetts (U-Mass) instead. Money isn’t everything, but, as Groucho Marx observed: “Money frees you from doing things you dislike. Since I dislike doing nearly everything, money is handy.” So when we ask whether the private school tuition premium is worth paying, we focus on the possible earnings gain enjoyed by those who attend elite private universities. Higher earnings aren’t the only reason you might prefer an elite private institution over your local state school. Many college students meet a future spouse and make lasting friendships while in college. Still, when families invest an additional $100,000 or more in human capital, a higher anticipated earnings payoff seems likely to be part of the story.

Comparisons of earnings between those who attend different sorts of schools invariably reveal large gaps in favor of elite-college alumni. Thinking this through, however, it’s easy to see why comparisons of the earnings of students who attended Harvard and U-Mass are unlikely to reveal the payoff to a Harvard degree. This comparison reflects the fact that Harvard grads typically have better high school grades and higher SAT scores, are more motivated, and perhaps have other skills and talents. No disrespect intended for the many good students who go to U-Mass, but it’s damn hard to get into Harvard, and those who do are a special and select group. In contrast, U-Mass accepts and even awards scholarship money to almost every Massachusetts applicant with decent tenth-grade test scores. We should therefore expect earnings comparisons across alma maters to be contaminated by selection bias, just like the comparisons of health by insurance status discussed in the previous chapter. We’ve also seen that this sort of selection bias is eliminated by random assignment. Regrettably, the Harvard admissions office is not yet prepared to turn their admissions decisions over to a random number generator.

The question of whether college selectivity matters must be answered using the data generated by the routine application, admission, and matriculation decisions made by students and universities of various types. Can we use these data to mimic the randomized trial we’d like to run in this context? Not to perfection, surely, but we may be able to come close. The key to this undertaking is the fact that many decisions and choices, including those related to college attendance, involve a certain amount of serendipitous variation generated by financial considerations, personal circumstances, and timing.

Serendipity can be exploited in a sample of applicants on the cusp, who could easily go one way or the other. Does anyone admitted to Harvard really go to their local state school instead? Our friend and former MIT PhD student, Nancy, did just that. Nancy grew up in Texas, so the University of Texas (UT) was her state school. UT’s flagship Austin campus is rated “Highly Competitive” in Barron’s rankings, but it’s not Harvard. UT is, however, much less expensive than Harvard (The Princeton Review recently named UT Austin a “Best Value College”). Admitted to both Harvard and UT, Nancy chose UT over Harvard because the UT admissions office, anxious to boost average SAT scores on campus, offered Nancy and a few other outstanding applicants an especially generous financial aid package, which Nancy gladly accepted.

What are the consequences of Nancy’s decision to accept UT’s offer and decline Harvard’s? Things worked out pretty well for Nancy in spite of her choice of UT over Harvard: today she’s an economics professor at another Ivy League school in New England. But that’s only one example. Well, actually, it’s two: Our friend Mandy got her bachelor’s from the University of Virginia, her home state school, declining offers from Duke, Harvard, Princeton, and Stanford. Today, Mandy teaches at Harvard.

A sample of two is still too small for reliable causal inference. We’d like to compare many people like Mandy and Nancy to many other similar people who chose private colleges and universities. From larger group comparisons, we can hope to draw general lessons. Access to a large sample is not enough, however. The first and most important step in our effort to isolate the serendipitous component of school choice is to hold constant the most obvious and important differences between students who go to private and state schools. In this manner, we hope (though cannot promise) to make other things equal.

Here’s a small-sample numerical example to illustrate the ceteris paribus idea (we’ll have more data when the time comes for real empirical work). Suppose the only things that matter in life, at least as far as your earnings go, are your SAT scores and where you go to school. Consider Uma and Harvey, both of whom have a combined reading and math score of 1,400 on the SAT.- Uma went to U-Mass, while Harvey went to Harvard. We start by comparing Uma’s and Harvey’s earnings. Because we’ve assumed that all that matters for earnings besides college choice is the combined SAT score, Uma vs. Harvey is a ceteris paribus comparison.

In practice, of course, life is more complicated. This simple example suggests one significant complication: Uma is a young woman, and Harvey is a young man. Women with similar educational qualifications often earn less than men, perhaps due to discrimination or time spent out of the labor market to have children. The fact that Harvey earns 20% more than Uma may be the effect of a superior Harvard education, but it might just as well reflect a male-female wage gap generated by other things.

We’d like to disentangle the pure Harvard effect from these other things. This is easy if the only other thing that matters is gender: replace Harvey with a female Harvard student, Hannah, who also has a combined SAT of 1,400, comparing Uma and Hannah. Finally, because we’re after general conclusions that go beyond individual stories, we look for many similar same-sex and same-SAT contrasts across the two schools. That is, we compute the average earnings difference among Harvard and U-Mass students with the same gender and SAT score. The average of all such group-specific Harvard versus U – Mass differences is our first shot at estimating the causal effect of a Harvard education. This is an econometric matching estimator that controls for—that is, holds fixed—sex and SAT scores. Assuming that, conditional on sex and SAT scores, the students who attend Harvard and U-Mass have similar earnings potential, this estimator captures the average causal effect of a Harvard degree on earnings.

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