Economics Strategy Policy Dec 1, 2010

Matric­u­la­tion Matters

Refin­ing the col­lege admis­sions guess­ing game

Based on the research of

Peter Nurnberg

Morton Schapiro

David Zimmerman

The col­lege appli­ca­tion and deci­sion process is fraught with uncer­tain­ty, and not just for hope­ful high school seniors

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Col­leges have their own form of admis­sions anx­i­ety — they need to guess how many offers will be accept­ed. If too few appli­cants decide to attend, a col­lege must call on its wait list. If too many accept, prob­lems abound — dorm rooms must be recon­fig­ured, finan­cial aid bud­gets must be bol­stered, and class sizes need to be reconsidered.

All admis­sions depart­ments have for­mu­las to esti­mate how many prospec­tive stu­dents will matric­u­late each fall, and they often do quite well. Yet for all their accu­ra­cy in guess­ing accep­tance rates, these mod­els are not well suit­ed to flesh­ing out the details of the incom­ing class. The sim­ple yes-or-no num­ber is the vital sta­tis­tic, but the par­tic­u­lars are almost as impor­tant, includ­ing num­bers relat­ing to stu­dents who need finan­cial aid, lega­cy stu­dents, and minor­i­ty students.

With that in mind, three econ­o­mists set out to build a bet­ter mouse­trap. Using sophis­ti­cat­ed econo­met­ric tech­niques, they con­struct­ed a mod­el that eval­u­ates the char­ac­ter­is­tics of dif­fer­ent stu­dents and pre­dicts the prob­a­bil­i­ty of each student’s accept­ing an offer of admission.

Mor­ton Schapiro, pres­i­dent of North­west­ern Uni­ver­si­ty, devel­oped the mod­el with Peter Nurn­berg and David Zim­mer­man, pro­fes­sors at Williams Col­lege. Their results were high­ly accu­rate when test­ed against Williams’ class of 2013, although Schapiro admits the Williams admis­sions department’s sim­pler for­mu­las arrived at near­ly the same answer as their mod­el. There’s an old expres­sion that goes, You don’t use a tank to squash a grape,’ ” Schapiro says. This is obvi­ous­ly a more sophis­ti­cat­ed mod­el to fore­cast yield than any­body uses, I think. But I’m not sure if it’s a tank.”

Indi­vid­ual Assess­ments
While the new mod­el may be overkill for esti­mat­ing straight­for­ward yield — what admis­sions depart­ments call the per­cent­age of admit­ted stu­dents who accept an offer — it is well suit­ed to deter­min­ing the like­li­hood of any one individual’s matric­u­lat­ing. In the case of Williams Col­lege, stu­dents who were class vale­dic­to­ri­ans or salu­ta­to­ri­ans were 20 per­cent less like­ly to matric­u­late than stu­dents in the top 5 per­cent of their high school class.

The rea­son? High school seniors with top aca­d­e­m­ic records tend to be admit­ted to more col­leges, increas­ing their choic­es and decreas­ing the prob­a­bil­i­ty that they will attend any one insti­tu­tion. Those with slight­ly less glow­ing aca­d­e­m­ic records prob­a­bly have few­er choic­es and thus are more like­ly to accept an offer (Fig­ure 1).

Fig­ure 1. Dif­fer­ence in prob­a­bil­i­ty of accept­ing admis­sion for stu­dents of dif­fer­ent aca­d­e­m­ic rat­ings. For exam­ple, stu­dents with an aca­d­e­m­ic rat­ing of 2 are 22 per­cent less like­ly to accept an offer than stu­dents with an aca­d­e­m­ic rat­ing of 1.

But to size up appli­cants, Schapiro and his col­leagues’ mod­el looks at far more than aca­d­e­m­ic records and SAT scores. It also exam­ines extracur­ric­u­lar activ­i­ties, the dis­tance from home to cam­pus, the amount of con­tact between the stu­dent and the school, and the total finan­cial cost to be borne by the stu­dent and their family.

There’s an old expres­sion that goes, You don’t use a tank to squash a grape,’ ” Schapiro says. This is obvi­ous­ly a more sophis­ti­cat­ed mod­el to fore­cast yield than any­body uses, I think. But I’m not sure if it’s a tank.”

Accord­ing to the mod­el, the most like­ly appli­cant to matric­u­late at Williams is a white male liv­ing with­in 10 km of cam­pus who attends a pub­lic school. He is in the top 10 per­cent of his high school class and is a var­si­ty ath­lete. He has a fam­i­ly mem­ber who attend­ed Williams, is reli­gious and polit­i­cal­ly active and has vis­it­ed the school’s admis­sions office. He also has no clue what his major will be.

Some of these qual­i­ties may be a reac­tion to the way the school sells itself. The most like­ly applicant’s lack of a major is a good exam­ple. At Williams, you can’t even declare your major until the end of your sopho­more year,” Schapiro says. It’s the way Williams por­trays itself. It’s a place to go to stretch.”

Where the mod­el says Williams Col­lege falls short is among minor­i­ty appli­cants, those who live more than 10,000 km from cam­pus, and those who come from a big city. Prospec­tive stu­dents inter­est­ed in art and the­ater are also less like­ly to attend Williams.

For schools that find them­selves less attrac­tive to a par­tic­u­lar type of appli­cant, the mod­el rais­es a few ques­tions. In the case of art and the­ater stu­dents at Williams, Schapiro won­ders, Does it mean that your pro­grams are bad, or does it mean that your pro­grams are good and no one rec­og­nizes it?” The mod­el could help a col­lege deter­mine if it needs to bol­ster its aca­d­e­m­ic pro­grams or sim­ply redou­ble its pro­mo­tion­al efforts in that area.

Behind the Deci­sion
Deter­min­ing why stu­dents accept an offer of admis­sion is Schapiro’s next tar­get. His cur­rent research focus­es on what he calls edu­ca­tion­al good­will.” In a sense, it tries to answer the ques­tion, why would some­one attend Har­vard or Yale or UC Berke­ley over anoth­er col­lege, all else being equal?

We look at every­thing you could pos­si­bly imag­ine could explain the attrac­tion of a school,” Schapiro says. Some schools do bet­ter than you would ever be able to explain and some schools do worse, despite the fact that they have a lot of great things going on.”

Relat­ed read­ing on Kel­logg Insight

On the Ori­gin of Schools: The diver­si­ty of Arizona’s char­ter schools

Prin­ci­pal Per­for­mance: What if school prin­ci­pals’ pay was tied to job per­for­mance? Turns out, it already is

Featured Faculty

Morton Schapiro

President, Northwestern University, and Professor of Strategy, Kellogg School of Management

About the Writer

Tim De Chant was science writer and editor of Kellogg Insight between 2009 and 2012.

About the Research

Nurnberg, Peter, Morton Schapiro, and David Zimmerman. 2012. Students Choosing Colleges: Understanding the Matriculation Decision at a Highly Selective Private Institution. Economics of Education Review, February, 31(1): 1-8.

Read the original

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