Wednesday, September 13, 2006

An End to "Early Decision"

Harvard University announced Tuesday that it would cease its early admission program. Early news reports, including an editorial in The New York Times, lauded the University for leading the way in dismantling an aspect of the college admissions process that favors the rich and the well-connected. Greg Mankiw, himself a Harvard professor, celebrates this move and declares on his blog that it's "Time for Princeton and Yale to Sneeze."

Economists typically evaluate any policy change in terms of how it affects efficiency and equity. Normally, economic efficiency means that all profitable trades have taken place. For example, if I value a certain item at $30 and you value it at $50, it is inefficient for me to own the item because you could pay me between $30 and $50 for the item and we would both be better off.

However, one class of economic models, called two-sided matching models (a good introductory read is Al Roth's page at Harvard), defines efficiency somewhat differently. In a two-sided matching model, economic agents don't trade things; they match with one another. Economists use two-sided matching models to analyze college admissions, job search, and even marriage. As proposed by Gale and Shapley in a 1962 paper entitled "College Admissions and the Stability of Marriage," two-sided matching models achieve efficiency when everyone cannot be made better off by rearranging who was matched with whom.

Consider a college admissions scenario with two students, Bart and Lisa, and two colleges, Yale and Harvard. Suppose Bart prefers Yale to Harvard, and Lisa prefers Harvard to Yale. Suppose further that Harvard and Yale are indifferent between the two. Then it would be inefficient for Bart to go to Harvard and Lisa to go to Yale: everyone would be at least as well off, and some would be better off, if they matched up the other way. (This is called a "Pareto improvement.")

In such a scenario, early admission programs improve efficiency. Such a program would allow Bart to signal to Harvard that it was his top choice, and allow Lisa to do the same for Yale. The universities would be better off, too, because they could raise tuition. After all, by definition, universities would be accepting students with the highest willingness to pay.

However, early admission programs increase efficiency at the expense of equity. With many early admissions programs (though not the one that Harvard just ended), a student commits to attending the school if they are accepted. Consequently, students who were admitted early could not compare financial aid offers from multiple schools. Students from low-income families are therefore at a distinct disadvantage, since they are more likely to be sensitive to price relative to other factors in making their college choices. In the words of Harvard's interim president, Derek Bok, "the existing process has been shown to advantage those who are already advantaged."

So, we might think that Harvard's move will decrease economic efficiency but increase equity. But there's one more catch: Harvard is one of the very top schools in the country. As a consequence, it may be very certain that all students would rank it as #1. In this case, it doesn't need an early admissions program to extract the preferences of applicants -- it can just go ahead and choose the students it likes the best, knowing that they too will generally accept its offer. Indeed, according to one study by Christopher Avery, Mark Glickman, Caroline Hoxby, and Andrew Metrick, Harvard does not need to engage in "strategic admissions practices," while even Yale and Princeton do. (See the graph on page 7, and the discussion on page 6. UPDATE: A New York Times article over the weekend elaborates on this point.) So while Harvard certainly deserves credit for shifting to a more equitable policy, it remains to be seen how contagious its sneeze will be.

1. Does Harvard's move make the admission process completely equitable? Why might low-income students still be at a disadvantage in college admissions?

2. Suppose all colleges were to abandon their early decision programs. Would students be better off? Would colleges? Why?

3. Suppose all students were to submit a ranking of all the colleges they applied to along with each of their college applications. If you were a college admissions officer, how would you use that information in deciding whom to admit, and what kind of financial aid package to give them?

4. A similar problem to the college admissions problem is the assignment of medical students to residency programs. Unlike college admissions, this is arranged through a centralized process called the National Residents Matching Program. It works like this: students submit a list ranking their prospective programs, and residency programs submit a list ranking students. A computer algorithm then matches students to programs. Do you think a similar program would work well for college admissions? Why or why not?

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