Schools, Jobs, Relationships … It’s Hard to Find a Good “Fit”

There are many ways to interpret these figures, but one is that most people are not great at selecting the school or spouse or job that suits them. It’s hard to find “the one.”

How to improve this process of matching has been a long-standing puzzle for economists, with implications that stretch across a wide range of markets, from labor and education to ride-sharing and real estate.

“There is a big literature on this,” says Benjamin Friedrich, an associate professor of strategy at Kellogg, “that mostly assumes participants in a market know how best to rank their options.”

In most real-life situations, however, Friedrich explains that we usually don’t have all the information we need. For example, colleges or employers might want to know what their competitors know about a given applicant, along with what the applicant thinks about the schools or jobs to which she’s applying. Likewise, applicants would like to know how colleges or companies view them compared with other applicants. Finding the best match is often contingent on information other parties choose to withhold.

New research by Friedrich illuminates the importance of this hidden information in finding good matches—and finds that greater transparency has the potential to improve the process, though this transparency can be difficult to implement in practice.

With Martin Hackmann of UCLA, Adam Kapor and Sofia Moroni of Princeton, and Anne Brink Nandrup of VIVE, Friedrich studied the dynamics of the matching process in the context of Danish medical schools.

Danish medical schools have some of the highest dropout rates of any reporting country. For instance, at Aarhus University in northeastern Denmark, the figure is 20 percent. For comparison, dropout rates in the U.S. and U.K. range between 2 and 4 percent. Improving matches between Danish medical schools and their applicants, then, would mean fewer students who don’t graduate, fewer wasted resources for schools, and more and better doctors in a market that is facing shortages.

“Doctors are scarce, and the shortage is growing, especially in rural areas,” Friedrich says. “This is an important problem from a policy perspective.”

The Danish medical-school market

In Denmark, high-school students who want to attend college submit a ranked list of their top eight preferred universities, along with the area of study (or major), to the Central Admission Secretariat. For example, a student may list a major in medicine at the University of Copenhagen as their first choice; medicine at Aarhus University second; biology at the University of Copenhagen third; and so on. (Denmark combines its undergraduate and medical education into a six-year program, unlike the U.S., which has separate programs for college and medical school.)

On the other side of the equation, universities offer admissions in two ways. First, a percentage of every class is filled with students purely based on their GPA. A second pool of applicants is then admitted based on other admissions criteria designed by the university, like personal essays or interviews. Applicants can choose whether they want to be considered in this second pool by, say, submitting an essay or agreeing to an interview. At this stage, applicants do not know the GPA threshold for admission (and thus whether submitting supplementary materials will be beneficial). Applicants are then matched with the school that accepts them and is highest on their top-eight list.

Importantly, the schools do not know where they rank in each applicant’s list, and students do not know how they scored on the program assessments such as interviews or quantitative tests.

But the researchers wanted to know: Could the matching process be improved if they did have this information?

To find out, researchers analyzed data that included applicants’ rankings of medical schools, as well as information showing how three Danish medical schools ranked applicants whom they did not automatically accept based on GPA. The team also had data on where applicants ultimately matriculated, along with their outcomes: whether they dropped out and what their job prospects were after graduation.

The value of private information

The researchers found that the success of matches in the college–medical school market is heavily dependent on information that parties sometimes withhold from one another, such as an applicant’s true commitment level. When medical schools get access to this information, they are better at identifying the applicants most likely to stick with their program.

This becomes apparent when comparing applicants who were admitted based on GPA alone (which was mandatory to provide) with those admitted based on supplemental information (which was voluntary to provide). For colleges, an applicant’s willingness to submit additional information to the school signals a degree of commitment on the part of the applicant that would otherwise be hidden. “It communicates that the student is serious about trying to get into the school,” says Friedrich.

Indeed, applicants accepted through supplemental information had significantly lower dropout rates than those accepted through GPA alone. Even among applicants admitted based on GPA alone, those who submitted supplemental information in case they did not make the initial GPA cut had lower dropout rates than those who didn’t—emphasizing the value of a screening process that reveals applicants’ level of commitment. And when the researchers compared applicants who were just above the threshold for admittance by GPA alone with those who were just below but still admitted based on secondary information, they found that this second group was far more successful in terms of graduation rate.

In other words, when schools had additional information about an applicant’s interest and commitment to a program, as well as screening tools to assess their fit, it resulted in a better match than when this information remained hidden.

The impact of information transparency was demonstrated in a real-world experiment at one of the medical schools, Odense. In 2002, the school instituted a more-demanding screening process for applicants who were not initially accepted based on GPA alone. The process required them to take a knowledge test, submit an essay explaining their motivation to pursue medicine, and complete a personal interview. The researchers found that after the school launched this initiative—which required applicants to provide personal insight that used to be unavailable with the prior screening process—there was a substantial decrease in its overall dropout rate.

This change also had a spillover effect on other schools. As Odense revamped its screening process and decreased dropout rates, its closest rival school, Aarhus, saw the opposite occur—an increase in its dropout rates.

“This is another place where interdependency shows up,” Friedrich says. “We have a list of students who ranked Odense above Aarhus who got rejected by Odense through this new screening. Those are among the worst students who enrolled at Aarhus, and they pulled down the overall graduation rate.”

The challenge of improving matches

Though Odense was able to improve its graduation rates through more-informative screening, the researchers find that sweeping improvements to a matching market like this one are difficult to design.

To explore the possibilities, they constructed a model to simulate the dynamics of the Danish medical-school market. With this model, they created a world in which everyone knows everything about everybody; there is no privately held information among schools or applicants. In this scenario, they found that dropout rates decline precipitously. In short: there is a lot of room for improvement in the real world through information transparency.

Using this result as a benchmark, the researchers then simulated several different interventions that policymakers could implement to improve outcomes. For instance, they explored what it would look like if all schools were able to learn each applicant’s first choice. In theory, this could offer another signal for schools to determine which students are most serious about attending their program.

According to the model, this intervention makes almost no difference in student dropout rates, as applicants start to use their first choice strategically to game the system.

“It’s a disappointing outcome, and it demonstrates how hard it is to design mechanisms or interventions in these information structures that actually improve match quality,” Friedrich says. “Though we know there is lots of room for improvement, we have, unfortunately, not found any low-hanging fruit.”

That’s not to say improvement is a lost cause. Though the reforms at one school (Odense) negatively affected another (Aarhus), they did demonstrate that improvements are possible. What’s essential to keep in mind when considering new policy interventions is that the information held by each actor—in this case, students and schools—plays a joint role in how well everyone fares, Friedrich says.

“Here we have the first evidence of these interdependent strategic agents,” he says. “If we’re designing a change to a market like this one, then we need to think really carefully through the potential strategic responses of everyone involved.”