In recent years, college admissions have become a hot topic in the national news, and for good reason. Competition intensifies each year as increasingly qualified and ambitious high school seniors vie for a limited number of spots.  Those familiar with the process know the anxiety involved. Furthermore, since many applicants receive several offers of admission, colleges themselves are uncertain about the percentage of students who will eventually matriculate. In their 2009 paper, “A Supply and Demand Model of the  College Admissions Problem”, Professors Hector Chade of Arizona State University, Gregory Lewis of Harvard, and Lones Smith of the University of Michigan at Ann Arbor, have rephrased the complicated relationship between applicants and colleges in terms of an economic allocation problem. They recognized the uncertainty between both involved parties and sought to explain it systematically.

     The researchers identified two important qualities of college admissions: applications are costly to the applicant and these admissions are noisily evaluated (noise being uncertainty, misinformation, or even hype in a marketplace). From these initial observations, the researchers developed a supply and demand model where the classical “price” variable is replaced by “admissions standards.” These standards are tacitly recognized in college admissions as grades, test scores, and extracurricular activities. When this metric was compared against college vacancies open to incoming freshmen, the researchers encountered some surprising conclusions.

     The researchers applied the model to a simplified case involving only two hypothetical colleges. In equilibrium, optimized sorting suggests that better students will enroll in the better college, lesser students will enroll in the lesser college, and that the worst students will not enroll in either college. The model showed that this was not necessarily the case. Because the college assignment problem is a supply and demand situation, a college’s standards of admission, the “price” in the usual sense, depend on that college’s capacity.

     Stochastic assignment of students to appropriate colleges occurs when schools differ greatly in quality and the lesser college is not too small. This is because the better college must represent discernible improvement over the lesser college to warrant an additional (costly) application. If the lesser college is very small, then it may raise its admissions standards to beyond what its actual quality might suggest. It can do this because it will require less of the total applicant pool to fill its incoming class. Hence, the lesser college must not be too small or else its admissions standards might be distorted in relation to that of the better college.

     The researchers concluded that, between two schools, higher admissions standards might not correspond to the better college, as long as the worse college is either comparatively good enough or small enough, or if the application process is noisy enough. This means that the quality of a particular school cannot be inferred by its admissions standards; worse schools may set higher standards, just as long as they’re small enough.

     While the researchers’ work is theoretical in nature, it is certainly of practical interest. It suggests that there is misinformation in both parties involved with college admissions, and that applicants should recognize erroneous perceptions before making important choices. A more selective school does not strictly mean a better education. In today’s cutthroat world of college admissions, prospective students should welcome these findings with open arms. •

Adapted from “A Supply and Demand Model of  the College Admissions Problem” by Hector Chade, Gregory Lewis, and Lones Smith. Chade, Lewis, and Smith are professors at Arizona State University, Harvard University, and the University of  Michigan at Ann Arbor, respectively. Their paper may be found at http://ssrn.com/abstract=1358343.