Wednesday, April 16, 2008

The Market for Students

Our college search started me thinking about the economics of the process, in particular about the problem colleges face in using scholarship money to buy students. One question that occurred to me is why colleges care about need.

I've written and webbed a first draft of an article on the subject. What I like about it is that the observed pattern—more money offered to students with poorer parents—comes out of the model without having to be put in. I don't assume that colleges have ideological or public relation reasons to admit poor students, although it's certainly possible—in part because they also have reasons to admit rich students, on the theory that they are more likely to end up as rich alumni. Yet I conclude that, in equilibrium, poorer students will be offered more money, ceteris paribus.

Comments welcome.


Steamboat Lion said...

A possible hypothesis - there is some chance that a student admitted on a scholarship may turn out to be a future Nobel winner, or at least bring fame and credit to the university.

This could be be tested by comparing academic acheievement of past scholarship students, general admissions and alumni admissions.

Anonymous said...

I couldn't follow the argument, but the result is plausible. (It's interesting. I may look at it again.)

It's plausible that the general equilibrium would not be equal scholarship money to all comers (of equal ability). Consider the son of Croesus vs. a student barely hanging onto life in a shantytown. Suppose they both have IQs of 140. The son of Croesus is indifferent to the scholarship money. Whether he comes to your college or not has nothing to do with scholarships. For the student in the shantytown, it could be a matter of life and death. You, the college official, have $1000 to split between Croesus' son and the shantytown kid. You offer all $1000 to the shantytown kid. This is the allocation of the $1000 that is most likely to maximize the quality of your college.

If all the colleges have the same quality, it's plausible that, in equilibrium, they all make the same offer. If college A has a more efficient scholarship offering than college B, then college B will change its offering to copy college A's method.

I think general equilibrium arguments are more interesting than the micro-economic arguments, where we assume a bunch of stuff doesn't change. I'm not sure that it's going to stay constant! But if you argue general equilibrium, then you've taken everything into account.

Steve_Roberts said...

Assuming that a set amount of money is less likely to sway the decision of a rich student than a poor one, then the total amount of money I need to offer to persuade a specific number of students to change their decision and come to my college will be least if I offer the money to poor students rather than rich ones.

Look no math

David Friedman said...

Anonymous and Steve both see the intuition. What I was trying to do in the paper was to formalize it—to set up a model of the process and see if the intuitive result came out of it.

Anonymous said...

(By the way) are you aware of works like this?



This paper develops a model in which colleges seek to maximize the quality of the educational experience provided to their students. We deduce predictions about the hierarchy of schools that emerges in equilibrium, the allocation of students by income and ability among schools, and about the pricing policies that schools adopt. The empirical findings of this paper suggest that there is a hierarchy of school qualities which is characterized by substantial stratification by income and ability. The evidence on pricing by ability is supportive of positive peer effects in educational achievement from high ability at the college level.