A Revealed Preference Ranking of US Colleges and Universities

I. Why a Revealed Preference Ranking?

The study’s output is a ranking of colleges based on their popularity. When a pupil does matriculation decisions among colleges he/she is accepted to, he determines which college “wins” in a direct competition. The paper shows how to consider for the likely compounding impacts of tuition markdowns, financial supports, and other factors that can potentially get a college to “win” when it would lose in terms of its inherent attractiveness.

The constructed rankings are based on a survey of 3,240 greatly commendable pupils specifically conducted for the study. Although the ranking is more of an example and not definitive; it is, however less manipulable than the rudimentary measures of revealed preferences, like admissions rate and matriculation rate. Furthermore such crude measures are often used inadequately. The revealed preference ranking effectively combines the information from each student’s decisions. Various colleges feel pressured to participate in strategic admittance activities in order to maximize their published college ratings, and often forced to manipulate such rates. The rankings in this paper would mitigate such pressure.

The rankings grounded on pupils’ revealed preference assess a college’s quality in the eyes of the students which vary from person to person. The demand by pupils and their parents for such measures is due to several reasons. First, it is because of the fact that pupils think and act as if their counterparts are important because per quality influences the teaching level that is offered. If peer effect is vital, then student might prefer to be surrounded by peers having high college aptitude.

Second, pupils are aware of college quality through different information gathered from different sources such as publications, friends and family, advisers, and others. A revealed preference ranking effectively combines observations on quality from different students.

Third, according to Spencer (1974) the specific colleges’ degrees act as indications of a student’s ability, which is often difficult for future employers to determine.

II. The Manipulability of Various Measures of Revealed Preference

The first common proxy for revealed preferences is matriculation rate which deals with the number of students who enroll at a college over the number of pupils who are actually admitted. This rate can be manipulated in various ways, and the methods are often successful due to fact that the rate is just a general statistics and does not consider the composition of the pool of attendees or of which within the pool are matriculating.

Such manipulation can be done through early decision program, since having more students included in it would mean higher matriculation rate. However, as a college increasingly takes in students in its early decision program, the actual admission standards drop, thereby leaving pupils with less meritorious peers. 

Another method would be intentionally not admitting pupils who are potentially admitted by other colleges that are more preferred. This strategy would cause the college to lose some of the desirable pupils; however it is a sensible sacrifice in order to seem more attractive on a flawed indicator. On the other hand, pursuing this may lead to the decline of peer quality. In terms of matriculation rate the college’s estimated appeal would increase, while its actual desirability decreases.

Furthermore, the college will reject pupils in the range in which it may potentially lose in a matriculation competition.  However, a strategic college will likely accept the student regardless of stiff completion given that a student’s merit is sufficiently high, since the potential gains from admitting a top student will more than compensate for the probable losses due to higher admissions rate and lower matriculation rate.

The second measure for revealed preference is the admission rate which is the number of admitted students to number of students who apply. This rate does not consider which applicants a college takes in. A college can opt to take in fewer pupils if its matriculation rate is greater. Thus the means for manipulating the matriculation rate are also applicable to admission rate.

In addition, admission rate can be manipulated by encouraging more applications regardless of the chance of providing admittance. This increases the number of applications which then decreases (improves) the admission rate and thus increases apparent appeal, even if the actual desirability remains the same.

Although the two general measures can be manipulated, it comes with a price. A college must choose between admitting the optimal class (actual desirability) and manipulating the admission and matriculations rates (apparent desirability). Colleges refraining from manipulations would end up losing if other colleges choose not to refrain.

III. A Model of College

A. A Desirability of Colleges

Ranking is predicated on the concept that there are underlying variables that specify the desirability of each college. The measures of attractiveness include all school attributes, perceived educational quality, campus location, and tuition.

The principal desirability is assumed to be well defined on a national basis for the majority of academically best colleges as well as specialized colleges in the United States.  Since the data used in the study is comprised of high-performing pupils and are unlikely to apply outside academically elite colleges, the ranking will deal first with such universities. Note however that this paper does not force the existence of latent desirability.

The main problem faced in ranking colleges is the collection of multiple comparisons having different preferences.

B. Matriculation Tournaments as a Multiple Comparison Problem

Provided a group of students has been admitted to a set of colleges wherein each school’s appeal is patterned as an underlying distribution of values and each pupil efficiently holds a competition among the set of schools that have admitted him in which the winning school is the college he matriculates at, it can be assumed given no other confounding variables that the chosen school is preferred over the other schools. By merging the information from each of the pupils’ tournaments, implication with regards to college desirability can be derived.

The study based on the models of Bradley-Terry (1952) and of Luce (1959) wherein the desirability spread is an extreme value distribution. Models based on extreme value distribution are inclined to be more tractable and computationally adequate.

Note however that the extreme-value or normal distribution of possible desirableness is a probabilistic assumption on the individual school’s merit and not an assumption on the spread of the average desirableness among schools. The approach used by the paper allows for the likelihood that a small number of schools are measured to have average desirableness considerably higher than the other schools.

C. The Matriculation Model

A school’s desirability can be considered as a blend of the attributes that its mean admittee faces. It is rationally impossible to determine all of the desirability parameters of a college’s traits that do not differ within college separately from the attribute impacts what are consistent within the school.

D. College Characteristics that Vary Across Admittees

Some school traits differ across admitted pupils, such as tuition fees, grants or scholarships, loans, distance between school and student’s home, and so forth. Such individually-varying attributes are encompassed within the model since they could improve the model’s explanatory strength.

IV. Model Fitting

In summarizing the estimated college desirability and computing for the rankings, maximum likelihood – particularly, that of Newton-Rapshon algorithm for multinomial logit models as applied in Stata is used. Difficulty however with such method is that it does not offer distinction in desirability between the colleges having different rankings.

To remedy this, Markov chain Monte Carlo (MCMC) simulation is utilized, which produces the same rankings but is able to provide the desired distinction.

V. Data

The data is from the College Admissions Project survey which includes high school seniors belonging to the college graduation class of 2004. The survey is designed in such a way that the data obtained would be on pupils having a high college aptitude who can potentially gain admission to the schools having a national or broad regional appeal.

The summary statistics does show that the total of 1357 participants were high achieving. 45 percent of the pupils went to private school with their parents having an averaged income of $119,929 in 1999. On the other side, 76 percent of the sample belongs to an income bracket below the cut-off wherein the family is candidate for aid by certain private colleges. In addition 59 percent of the pupils applied for need-based financial aid. Among the survey participants, 73, 16, 3.8 and 3.5 percent were white, Asian, black and Hispanic, respectively.

The statistics suggests that pupils aimed little high in their applications but considered some schools as “safety nets”. Schools acting as such are infrequently matriculated into by students.

 

VI. A National Ranking

In spite of the fact that the draw were national in nature, the small sample may have failed include a small college in the national ranking.

A. National Ranking

Harvard University topped the ranking based on matriculation. All of the top twenty colleges are private institutions with the exception of the University of Virginia.[1] Meanwhile the next twenty institutions are a combination of public and private, small and big, colleges and universities.

 Generally, the lower the ranking in the revealed preference, the less distinct is a college’s appeal in comparison to its direct neighbors in the ranking. For those ranking ten and above there is roughly 75 percent that a college is ranked greater higher than the college placed one or two below it. However this confidence fall to approximately 65 percent for those ranking eleven to twenty, and falls further down for those ranked below twenty. This is expected given that in ordinal rankings, cardinal appeal is more clustered as one goes lower down the ranking.

B. Comparing Measures of Revealed Preference

The findings indicate that the top twenty colleges in terms of revealed preference would not belong in the top twenty if based on admission rates (ten of the colleges are out of the top twenty) and even more so on matriculation rate (all are outside of the top 100).

It is apparent that there are many colleges having low admission rates and high matriculation rates that are not perceived to be attractive.

VII. Extending the Model to Handle Early Decision

At a certain point, the early decision program can be viewed as an extreme version of an individually-varying attribute. Recall that the program offers less stringent admission standards to the applicant, thus the college expects the students to commit to matriculate once admitted. Early decision program also prohibits applicants to apply early to more than one college, and if admitted, must not submit any regular application elsewhere. The paper considered the constraint to be the problem of the program.

There are two reasons as to why preference ordering rather than matriculation tournament is expected to generate ranking more favorable to early decision schools. First, pupils having a strong idiosyncratic preference for a college are probably more inclined to apply for early decision. Second reason would be that preference ordering could be influenced by the strategy connected in early decision.

The preference ordering is used first as a pseudo matriculation tournament wherein the top ranked college is assumed to be where the pupil would have matriculated and all other colleges act as “tournament losers”.

Second, all of the information in the students’ preference orderings is used through estimation of a rank-ordered logistics model. The results suggest that rankings derived from the preference orderings are very similar to those derived from actual matriculation tournaments.

Nonetheless, preference orderings are no broad alternate for actual matriculation tournaments. This is because matriculation tournaments contain the choices of student who actually gets into the college while the preference ordering-based ranking also relies on pupils for whom the colleges are only a dream.  Another reason would be matriculation tournaments occur when a student already has an extensive knowledge and information regarding his options and the colleges’ attributes, while rankings based on preference ordering transpire before any information is revealed. Lastly, matriculation tournaments are based on actual decisions and not desires.

The result shows that colleges practicing early decisions are to some extent higher in rankings based on preference orderings.

VIII. Self-Selection and Rankings for Subgroups of Students

The desirability parameter of college attributes can be estimated from the matriculation decisions of admitted applicants. Intuitively before a student is admitted, he or she must first apply, and a pupil self-sort into applying to different colleges. Self-selection can cause problem when some schools are more taste-intensive than others, for instance, specialty schools particularly engineering colleges, strongly religious schools, and gender exclusive school. The resulting bias from this problem can be mitigated by considering ranking for sub-groups of pupils who may have an interest to specific specialties.

The results showed that the basic ranking and the rankings for pupils from each groups of target major have a reasonable degree of similarity. This implies that most colleges have fairly equal strength across the different fields of study.

Further observation indicates that there is a great consistency among the region with regards to the ranking of the top ten institutions. Regionalism is more apparent in colleges ranked 31 to 60.

Overall, in terms of sub-group rankings, given enough data, it would be logical to compute a range of sub-rankings for sets of students having well-defined tastes.

IX. Conclusion

The paper demonstrates that revealed preference rankings of American colleges and universities can be derived from a students’ college selection behavior. The procedure used in this study produces a ranking that would be difficult for a college to manipulate via strategic admission activities.

The strong demand for measures of revealed preferences among parents and pupils forces colleges and universities to supply such related information. However, the lack of availability of revealed preference like that produced in this paper, leaves colleges and college guides to use two unsound proxies: admission and matriculations rates, wherein both can be easily manipulated. These proxies provoke college to increase “apparent” desirability at the expense of the “actual” desirability.

Various colleges believe they are in a bad equilibrium, however, as long as they find it beneficial to have early decision programs and other pricey admission strategies, such unstable equilibrium is likely to continue.

Ultimately, the measures of revealed preference are just measures of desirability derived from students and families making college choices and do not essentially represent to education quality.

Source:

Christopher Avery, Mark Glickman, Caroline Hoxby, and Andrew Metrick, “A Revealed Preference Ranking of US Colleges and Universities”, Harvard University, December 2005.

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[1] Top twenty-one: Harvard University, California Institute of Tech, Yale University, MIT, Stanford University, Princeton University, Brown University, Columbia University, Amherst College, Dartmouth,  Wellesley College, University of Pennsylvania, University of Notre Dame, Swarthmore College, Cornell University, Georgetown University, Rice University, Williams College, Duke University, University of Virginia and Brigham Young University.