Voluntary Disclosure and the Strategic Behavior of Colleges
Michael Conlin
Michigan State University
Stacy Dickert-Conlin
Michigan State University
Gabrielle Chapman
Syracuse University
June 2008
Abstract: This paper investigates how outside ranking organizations such
as U.S. News and World Report affect colleges’ admission decisions. To do
so, we focus on a policy that has received criticism for being motivated by
ranking concerns: optional reporting of SAT I scores. This policy allows
colleges to report an average SAT I score based on those applicants who
chose to submit their scores which may not be reflective of actual student
body quality. We use proprietary data from two liberal arts colleges to
address how the optional reporting policy affects the colleges’ admission
decisions as well as how applicants’ SAT I scores influences their decision to
submit these scores to the colleges. The data suggest that college admission
departments are behaving strategically by rewarding applicants who do
submit their SAT I scores when their scores will raise the college’s average
SAT I score reported to U.S. News and World Report and rewarding
applicants who do not submit when their SAT I scores will lower the
college’s reported score. The data also suggest that applicants are behaving
strategically by choosing not to reveal their SAT I scores if they are below a
value one might predict based on their other observable characteristics.
(JEL Classifications: I20, I21, C70)
Acknowledgments: We thank Jeff Wooldridge for valuable advice. We also thank
seminar participants at Michigan State University, the Michigan/Michigan State/Western
Ontario Labor Day Conference, the University of Notre Dame, the University of
Wisconsin-Madison and the University of Quebec at Montreal.
1
Whether they get 1300 or 1250 doesn’t really tell you anything about them as a
person or a student” says Ken Himmelman, Bennington dean of admissions. All the
attention to numbers “becomes so crazy it’s almost a distraction.”
- Bruno in USA Today (2006)
“I SOMETIMES think I should write a handbook for college admission officials
titled “How to Play the U.S. News & World Report Ranking Game, and Win!” I would
devote the first chapter to a tactic called “SAT optional.”
The idea is simple: tell applicants that they can choose whether or not to submit
their SAT or ACT scores. Predictably, those applicants with low scores or those who
know that they score poorly on standardized aptitude tests will not submit. Those with
high scores will submit. When the college computes the mean SAT or ACT score of its
enrolled students, voilà! its average will have risen. And so too, it can fondly hope, will
its status in the annual U.S. News & World Report’s college rankings.”
Colin Driver, President of Reed College, New York Times, 2006
There's almost a schizophrenia in college admissions," says Dan Lundquist, vice
president and dean of admissions at New York's Union College.
"There's this mercenary instinct to put your colleges at the best possible
advantage. At the same time, most of us are educators who are against that kind of crude
positioning."
Nowhere is that clash of values more evident than in how administrators view
their favorite whipping boys, the U.S. News & World Report college guide and the SAT.
If one could find a way to use the test they love to hate to improve their standing in the
rankings they love to hate, the result might prove irresistible.
Brownstein in The Chronicle of Higher Education (2001)
I. Introduction
As the above quotes suggest, the adoption of optional SAT policies is extremely
controversial and the trend is toward more colleges1 making the reporting of standardized test
scores, such as the SAT I (the two-part standardized verbal and math test)2, voluntary. The
adopting schools often argue that the test score differentials in the SAT are not a result of
aptitude differences but rather biases in the test that favor particular groups. For example,
when University of California President Richard C. Atkinson announced his recommendation
that the university no longer include the SAT I test as a requirement he stated, “[T]hat a
perception among ethnic minority groups that the SAT I is unfair cannot be easily
dismissed[.]” (University of California 2001). The implication is, as stated by Martha
Allman, Wake Forest’s director of admission in a recent New York Times article: “[B]y
making the SAT and ACT optional, we hope to broaden the applicant pool and increase
1
As of Spring 2007, more than 700 colleges have such policies in place
(http://www.fairtest.org/optinit.htm), although many are religious or technical schools.
2
The SAT I is now a three part exam that includes a writing portion. However, the years in our data
included only the two parts.
2
access at Wake Forest for groups of students who are currently underrepresented at selective
universities” (Lewin, 2008).
Critics of these policies suggest that the policies are an attempt to increase the
school’s ranking. For those schools that implement an optional SAT policy, the mean SAT
score the school reports to the ranking organizations is computed based not on the entire
student body but only on the scores from those students who chose to submit. If students
with higher SAT scores are more likely to submit, an optional SAT policy will increase the
average SAT score the school reports to the ranking organizations.3 Brownstein (2001) in
The Chronicle of Higher Education describes it this way:
The thesis, first stated last year by The New Republic, is that colleges are being
less than honest about why they abolish requirements that applicants submit their SAT
scores. Behind the rhetoric about "enhancing diversity" and creating a more "holistic
approach" to admissions, the theory goes, many colleges "go optional" on the SAT to
improve their rankings. The logic is rather simple: At an SAT-optional college, students
with higher scores are far more likely to submit them, raising the institution's mean SAT
score and hence the heavily test-influenced rankings.
Levin (2002) suggests that “[I]n an effort to boost their selectivity rankings some schools
have dropped the SAT requirement for admission; other schools may be tempted to admit
more students with high SATs [page 8].” Perhaps this criticism explains the following
excerpt from a May 27, 2008 press release issued by Wake Forest University (2008)
announcing their adoption of an optional policy:
Like other universities, Wake Forest is asked to provide standardized test score
data to outside agencies. For this data to be accurate, Wake Forest will ask students who
chose not to submit scores during the admissions process to provide them after they are
accepted and before they enroll at Wake Forest.
Skeptics will note that disclosure of SAT I scores is still voluntary and, therefore, may be
incomplete. A more accurate measure of enrolled student’s SAT I scores can come from
requesting those scores for free from the College Board.
3
An optional SAT policy may also affect the pool of applicants which is likely to influence schools’
rankings by changing their acceptance and yield rates.
3
There are many such ranking organization, but the rankings provided by U.S. News and
World Report, a publication that has circulation of more than 2 million every year (Selingo,
2007, http://chronicle.com/free/v53/i38/38a01501.htm), receives considerable attention.
Mechanically, SAT I scores make up 40 percent of the student selectivity ranking category of
the U.S. News and World Report rankings, thereby providing incentives to maximize the
revealed quality of students.4 A survey of 241 schools conducted by the Association of
Governing Boards found that 51 percent of schools reported attempting to increase their
rankings in the U.S. News and World Report (Levin, 2002) and there are many anecdotal
reports of efforts to boost rankings (see Ehrenberg, 2002 and Farrell and Van Der Werf,
2007). About one quarter of the top 100 liberal arts colleges ranked by U.S. News & World
Report have optional SAT I policies. In addition to being widely read and considered
influential among higher income students (Levin, 2002), there is evidence that spending per
pupil and objective measures of college quality are positively correlated with improvements
in rankings (Jin and Whalley, 2007 and Monks and Ehrenberg, 1999).
This optional SAT policy gives us an ideal setting for testing not only whether schools’
incentives to increase their rankings in publications such as U.S. News and World Report
influence admissions decisions, but also the theoretical implications of the voluntary
disclosure literature. This paper is the first to empirically test whether colleges’ incentives to
increase their ranking influenced their admissions processes. Using the admissions data from
two colleges with an optional SAT I policy, we find evidence that these colleges behave
strategically in their admission decisions in an effort to improve their school’s ranking. The
data suggest that, ceteris paribus, the college is more likely to accept applicants who do not
submit their SAT I scores if submitting their scores would decrease the average SAT I score
4
During the time period of our data, US News and World Report used the following criteria and weights for
ranking colleges: Student Selectivity 15%, Academic reputation (survey of other colleges) 25%, Faculty
resources 20%, Graduation and retention rate 20%, Financial resources (expenditure per student) 10%,
Alumni giving (rate) 5%, and Graduation rate 5%. Under the Student Selectivity criterion, the weights
associated with the different selectivity rankings are SAT/Act scores 40%, Acceptance Rate 15%, Yield
10% and High school class standing in top ten percent 35%.
4
the colleges report to the ranking organizations. Likewise, the college is more likely to accept
applicants who do submit their SAT I scores if submitting their scores would increase their
reported average SAT I score. As for the applicants’ decisions, we find a large share who
choose not to submit their SAT I scores. In addition, we show that applicants behave
strategically by choosing not to submit their SAT I scores if their actual scores are below a
value one might predict based on their other observable characteristics.
Section II describes the data and specific optional SAT policies from two liberal arts
colleges while Section III summarizes the relevant literature. Section IV presents evidence
that colleges are acting strategically to increase a student quality measure (average SAT I
scores) reported to the ranking organizations and applicants are acting strategically when
deciding whether to submit their SAT I score. Section V concludes.
II. Data and Institutional Details
Our primary data come from two schools in the northeast, each with approximately
1800 students enrolled.5 Both report a typical SAT I score in the upper 1200s (out of 1600
and relative to a mean score for all persons taking the SAT I of approximately 1020 (College
Board, 2002)). For College X, we have two recent years of data, about five years into the
school’s optional SAT policy. For College Y, we have one recent year of data, the first year
that the school instituted the optional SAT policy.
For each applicant, our primary source is the details from the applications that were
entered into the admissions’ databases. Of course, we know whether or not applicants chose
to submit their SAT I scores. The admissions’ databases contain SAT I scores for those who
submit them as well as SAT II6 and ACT scores, more curriculum based exams, for those
who submit. More generally, the data contain characteristics of the applicants that include
5
We signed agreements with the colleges and College Board to allow us to use the data. This agreement
stipulates that we cannot reveal the names of the colleges.
6
There are 20 different SAT II: Subject Tests and not all students take these exams.
5
race, gender, legacy status, and high school grade point average (GPA). The data include
characteristics of the high school such as type (private or public), high school name, and
state. In addition, the data identify whether the applicant applied early decision and intended
to apply for financial aid. The dataset also contains the admissions decision made on the
applicant, accept or not, and enrollment decision. These data are similar across the colleges.
The data also contain numerous college performance measures for those who enroll in
College X and a few of these measures for College Y.
One crucial variable that is often missing from the college admissions data is the
SATI scores for the applicants who chose not to submit their SAT I scores. Although the
college obtains these data for a minority of applicants, particularly those who ultimately
enroll, we purchased a data match of SAT scores from the College Board to identify SAT I
scores for the remainder. We drop the international applicants from our analysis primarily
because the probability of obtaining a match with the College Board data is very low due to
the lack of social security numbers.7 Finally, we exclude applicants who withdrew from
consideration before admission decisions were made, which is about 13 percent from College
X and 5 percent from College Y.8 The College Board data also include SAT II scores, AP
test scores, and responses to the student descriptive questionnaire (SDQ) that is filled out at
the time the applicants take their SATs. The SDQ includes self-reported data on family
income as well as high school activities, awards, grades9, and class rank.
While both Colleges X and Y allow applicants to choose whether to submit their
SATI scores, they differ in terms of other required test scores. Whether or not they submit
their SAT I scores, College X requires applicants to submit either their ACT scores or three
7
We also drop fewer than two percent of domestic students for whom we cannot identify an SAT I score.
The reduced form results are similar with and without these observations.
9
As an alternative measure of academic preparedness, high school GPA has the potential to be crucial in
analyzing student and college behavior. Unfortunately, GPA scales as reported on applications are not
even remotely standardized across high schools and therefore comparisons are extremely difficult (see
Chaker, 2003). College Y did not even record high school GPA for many of their applicants in their
admissions data. We contacted as many high schools as possible and asked them for their GPA scales but
the resulting data were extremely complicated, giving us little confidence in their usefulness.
8
6
SAT II scores. Along with their SAT I scores, applicants at College Y can elect to submit
scores from their SAT II exams, ACT exam, and/or Advanced Placement (AP) exams.10
College Y requires applicants to submit at least one of these scores if they choose not to
submit their SAT I scores.11
For College X, 16 percent of the 6,560 applicants chose not to submit their SAT I
scores, while 24 percent of the 3,602 applicants from College Y chose not to submit their
SAT I scores. Overall, Table 1 describes the colleges’ admissions pools and the differences
in those that chose to submit their SAT I scores and those who did not. Perhaps not
surprisingly, the average SAT I score is less for applicants who do not submit their score, by
an average of 133 points for College X and 38 points for College Y. Figure 1 depicts the
distributions of SAT I scores at Colleges X and Y for those who submit and do not submit
their scores. Not only is the average SAT I score greater for those who submit but the
variance of SAT I scores is also greater compared to those who do not submit.
Table 1 also indicates that for those with SAT II scores, the average SAT II score is
higher at College X for applicants that submit their SAT I scores but not at College Y.12 At
both colleges, the average ACT scores are similar for those who submit and do not submit
their SAT I scores. As another measure of academic preparedness, more students who
submit their SAT I score have the highest self reported high school grade point average (A+)
relative to those who do not submit. Between one-third and one-half of applicants attended
private high schools. More than 65 percent of applicants are female at College X, while
around 50 percent are female at College Y. Private high school attendees and women are
more likely not to submit their SAT I scores.
10
There are 35 AP exams available, administered through the College Board. While it is not required, most
students take a year long AP course in high school before taking the exam (see
http://www.collegeboard.com/prod_downloads/student/testing/ap/AP-bulletin.pdf accessed 4/16/07).
11
Based on the data, a few applicants appear not to have satisfied these requirements.
12
As a “uniform” measure for those who take at least one SAT II exam, we create an “average SAT II
score”, which is the average of up to three SAT II scores from either the college data base or the College
Board match. Each test is out of 800 points.
7
Overall, applicants at both schools are from the high end of the income distribution.
Conditional on reporting a family income, and many do not, income greater than $100,000 is
the most common response. While small fractions of applicants at both schools are legacies
and apply early decision, slightly more than half indicate that they intend to apply for
financial aid. More than 83 percent of all applicants are white and more than three-quarters
are from the northeast United States, which includes the states where the colleges reside.
III.
Literature Review
Because schools are imposing a voluntary disclosure policy, we consider both the
theoretical and empirical literature on voluntary disclosure. Our hypothesis is that these
policy choices are motivated by incentives to improve college rankings; therefore, we also
discuss the literature on college rankings.
IV.
Theoretical Literature
The theory of voluntary disclosure suggests that, if disclosure is costless, mandatory
disclosure is not necessary to solve the problem of asymmetric information between two
parties. This theory implies that even with voluntary disclosure, all individuals (or firms) will
have an incentive to reveal their private information to avoid the other party assuming that
their decision to withhold information implies something worse than their actual private
information. Grossman and Hart (1980) formalize this “unraveling” equilibrium.13 Grossman
(1981) generalizes the results in Grossman and Hart (1980) and considers voluntary
disclosure of a product’s quality. Milgrom (1981) also generalizes the results by considering
voluntary disclosure along multiple dimensions instead of a single dimension. Similar to
Grossman and Hart, Milgrom proves that, in every sequential equilibrium, the informed party
fully discloses all private information when disclosure is costless. With costly disclosure,
13
They present this “unraveling” equilibrium in the context of the Security and Exchange Commission
requiring parties to a takeover bid to disclose particular information instead of allowing voluntary
disclosure while outlawing false statements.
8
Jovanovic (1982) identifies an equilibrium where unraveling occurs but the unraveling is not
complete. Specifically, the equilibrium is such that an individual will voluntary disclose if
this private information is above some “quality” threshold and will not reveal if it is below
this threshold.14, 15
These theoretical papers model environments as standard Bayesian games and make
strong assumptions about the informational structure. Specifically, they all assume common
knowledge and that the beliefs of the uninformed party are based on Bayesian updating.
Eyster and Rabin (2005) present an equilibrium concept where each player correctly predicts
the distribution of the other players’ actions, but underestimates the degree to which these
actions are correlated with their private information. They term this equilibrium concept a
“cursed equilibrium” and provide anecdotal evidence that this concept explains many
empirically observed phenomena, including the winner’s curse. Eyster and Rabin apply this
concept to voluntary disclosure games to explain why everyone might not disclose their
information even when disclosure is costless.
Under the assumptions of common knowledge, Bayesian updating, and low costs of
submitting SAT I scores, the basic voluntary disclosure theory predicts that only those with
the lowest SAT I scores should withhold them. In the context of college admissions the
common knowledge and Bayesian updating assumptions may be inappropriate for a number
of reasons. First, common knowledge may not exist because applicants generally have
limited experience applying to colleges. In addition, particularly in early years of the policy,
as we have in our data for College Y, the college may have imperfect information about an
applicants’ decisions not to submit and how the policy affects their applicant pool.
Furthermore, colleges may be motivated in their enactment of the optional SAT I policy by
measures of reported quality to ranking institutions, which may not be fully understood by
14
Jovanovic applies the model to an environment where a business chooses whether or not to disclose its
product’s quality and proves that it may not be socially-optimal to mandate disclosure.
15
Shavell (1994) contributes to the voluntary disclosure literature by endogenizing a party’s decision to
acquire the private information.
9
applicants. Finally, colleges may not fully understand the mapping between an applicant’s
SAT I scores and his/her decision to submit, perhaps resulting in a “cursed equilibrium”.
V.
Empirical Literature
There are several empirical papers testing voluntary disclosure. The ideal
information to test this theory includes whether the private information is revealed and, if it is
not, what that private information is. In practice, these data are rarely available and,
therefore, most researchers attempt to infer this information from related outcome measures.
Mathios (2000) shows that before mandatory disclosure laws, salad dressings with
the highest fat content, as measured ex-post to mandatory disclosure, were more likely not to
report their ingredients. Using pre- and post- sales data, he also provides evidence that
consumers incorrectly inferred the fat content for those salad dressings that did not disclose.
Jin and Leslie (2003) test the implications of the voluntary disclosure models using
information on city council votes to adopt a Los Angeles County ordinance requiring
restaurants to publicly display hygiene grade cards. While unable to observe which
restaurants voluntarily disclosed their hygiene rating, the paper provides evidence consistent
with the notion that unraveling occurred in the jurisdictions that did not adopt the
ordinance.16 Jin (2005) considers individual HMOs’ decisions to reveal accreditation and
specific performance measures. She finds evidence that the level of competition in the
market affects disclosure decisions, namely that HMOs in highly competitive markets have
stronger incentives to differentiate via disclosure.
Although they do not focus on the unraveling hypothesis, Robinson and Monks
(2005) look at the voluntary disclosure of SAT I scores in the first year of the policy at
Mount Holyoke College. Using a select sample of non-submitters for whom they have
SAT I scores (48 percent of non-submitters, most of whom enrolled), they show that non16
Jin and Leslie (2003) also find evidence that overall hygiene went up following the mandatory disclosure
laws, suggesting that mandatory disclosure may have a beneficial effect on consumers.
10
submitters have average SAT I scores that are lower (by 141 points) than submitters and
that those who do not submit perform relatively poorly on the test relative to their other
qualities. They also conclude that students who do not submit their scores have an
advantage in the admissions process. Unlike Robinson and Monks, we have the private
information for almost all applicants in our data and we use this information to consider
whether ranking organizations influence the school’s admission decisions. To properly
address this question, we also document which types of applicants choose not to disclose
and find results qualitatively similar to those of Robinson and Monks.
We turn now to the sparse empirical evidence on the effect U.S. News and World
Report and other ranking organizations on school policies and outcomes. Jin and Whalley
(2007) are the only researchers, to our knowledge, that look for behavioral responses to
rankings. They find that colleges newly exposed to the U.S. News and World Report
rankings experienced increased expenditure per student, a factor that receives approximately
20 percent weight in the ranking formula. They show that this increase is driven by increases
in state appropriations. In other words, states directly increase the expenditures per students
in their budgets. They hypothesize that states’ responses reflect increased attention to college
quality due to inclusion in the U.S. News and World Report rankings.
There is a relatively small literature on the reverse question: how do rankings affect
college outcomes? An early paper by Monks and Ehrenberg (1999) uses a set of national
universities and liberal arts colleges that are highly ranked by U.S. News and World Report
between 1989 and 1999. They show that improvements in rankings are correlated with
higher selectivity, as measured by the admissions rates (students admitted/applicants), and
lower uncertainty in the admission process through higher yield rates (matriculants/admitted
students). Improved rankings are also associated with attracting different students, in
particular, those with higher SAT scores and less financial aid need. Using individual data
for a sample of students admitted to Colgate University between 1994 and 2004, Griffith and
11
Rask (2007) find that schools with higher U.S. News and World Report rankings have an
advantage in attracting students and the advantage is greater among students who are not
receiving financial aid. Both of these papers suggest that improved rankings are positively
correlated with improvements in measurable college outcomes.
VI.
Colleges’ and Applicants’ Strategic Behavior
A. Colleges’ Admission Decisions
Ehrenberg (2005) and others argue that the intense competition for students among
colleges is magnified by the U.S. News and World Report’s ranking of schools and this
ranking encourages colleges to implement policies designed to manipulate the rankings. The
survey conducted by the Association of Governing Boards found that many schools admit
taking actions specifically designed to increase their rankings in the U.S. News and World
Report (Levin, 2002). The potential benefit in terms of the rankings associated with
implementing an optional SAT I policy is evident from Table 2. For both colleges, the table
shows that for applicants who do not submit, not only is the average SAT I score lower but
the average is also lower conditional on being accepted and conditional on enrolling. With
the potentially strong assumption that the optional SAT I policy does not affect the applicant
pool, the college’s acceptance decisions or the applicants’ enrollment decisions, this policy
would increase the average SAT I score reported to U.S. News and World Report from 1,254
to 1,281 for College X and from 1,280 to 1,301 for College Y. While our data set does not
allow us to test whether the applicant pool or the enrollment decisions change as the result of
the optional SAT I policy, it does allow us to test whether ranking concerns influence the
colleges’ acceptance decisions.
To do so, we regress the college’s acceptance decision on a set of observables that
include the student’s decision to submit his/her SAT I score. In addition, we control for
his/her actual SAT I score in hundreds (whether the applicant submitted the score or not), a
12
dummy for whether the applicant submitted his/her SAT I score, a dummy for whether the
applicant submitted his/her SAT II (ACT) score, the actual SAT II (ACT) score if the
candidate submitted it, a dummy for whether the applicant applied early decision, and a set of
ability and demographic measures from the candidate’s application. The first and third
columns of Table 3 present the coefficient estimates of a probit regression. The actual SAT I
score is positively and statistically significantly related to the probability of acceptance. The
coefficients on whether the applicant submitted his/her score are negative and statistically
significant for both Colleges X and Y. These coefficient estimates suggest that submitting
SAT I scores decreases the probability of acceptance by 0.16 for Colleges X and Y. In other
words, colleges reward students who take advantage of the optional SAT I policy, all else
equal.
Our hypothesis is that this reward may vary, depending on how the student’s SAT I
score might affect the average reported score. For example, there may be higher probability
of admissions conditional on not submitting scores if an applicant has a lower SAT I score,
relative to an applicant with a higher SAT I score, because that applicant’s score will
decrease the average reported SAT I score if he/she enrolls. Likewise, schools have incentive
to differentially reward an applicant with a higher score if he/she submits the score, because
the applicant’s score will increase the reported SAT I score if he/she enrolls. To account for
this, we add an interaction term between whether an applicant submits his/her SAT I score
and his/her actual SAT I Score/100. The second and fourth columns of Table 3 present the
coefficient estimates of this specification. For both colleges, the coefficient estimate
associated with submitting an SAT I score remains negative while the estimate associated
with the interaction term is positive and statistically significant. These coefficient estimates
indicate that the negative effect of reporting your SAT I score on the probability of being
accepted decreases with the SAT I score. This is consistent with the premise that the
admission departments behave strategically to favor applicants with low SAT I scores who
13
do not submit (relative to those that do submit) and this favoritism decreases as the scores
increase.
Recalling that the school does not view the actual SAT I score for those who do not
submit, we now suppose that the colleges naively infer that the SAT I scores of those who do
not submit are the “predicted” scores based on the applicants’ other observables.17 We
estimate this “predicted” score by regressing the SAT I scores for applicants who submitted
their scores on the set of applicant characteristics observable to the college (the regression
results are in Table A1). We then use the coefficient estimates from this regression and the
applicants’ observables to “predict” SAT I scores for those who did not submit their SAT I
scores. The predicted test scores, where the averages are shown in Table 2, for those who did
NOT submit are substantially above their actual SAT I scores. For College X, the average
predicted SAT I scores is 1219 versus an actual average of 1139, while for College Y the
average predicted SAT I score is 36 points higher than the actual average (1264 versus 1228)
and these means are statistically different than one another at standard levels.
In Table 4, we show the coefficient estimates and bootstrapped standard errors for a
specification identical to that in Table 3 except we use the predicted SAT I scores, rather than
the actual scores, for those applicants that do not submit. By comparing the SAT I related
coefficient estimates in Table 3 with those in Table 4, it is evident that the main conclusions
drawn from these estimates change little if we assume the colleges naively infer instead of
perfectly infer the non-submitters’ SAT I scores.
The magnitudes of the point estimates in Table 4 (associated with whether the
applicants submit their SAT I score and the SAT I interaction term) are particularly
supportive of our hypothesis that rankings motivate the colleges’ behaviors. They suggest
that, ceteris paribus, applicants who submit their SAT I score are less likely to be accepted by
17
This is in the spirit of Eyster and Rabin’s “cursed” equilibrium where the school believes that an
applicant’s action, whether to submit his/her SAT I scores, is uncorrelated with the applicant’s private
information, his/her actual SAT score.
14
College X if their SAT I score is below 1388 and are more likely to be accepted if their score
is above 1388. For College Y, applicants who do submit their SAT I score are less likely to
be accepted if their SAT I score is below 1335 and are more likely to be accepted if their
score is greater than 1335. Taking into account that the average SAT I score for those who
submit and enroll is 1281 for College X and 1301 for College Y, these results suggest that the
colleges’ admission departments behave strategically by raising the probability of acceptance
to applicants who do not submit their SAT I scores if submitting their scores would decrease
the average SAT I score the colleges report to the ranking organizations and to applicants
who do submit their scores if submitting their scores would increase the average SAT I score
the colleges report.
The regressions in Tables 3 and 4 also show that other measures of academic ability,
such as SAT II scores, ACT scores and high school GPAs are positively correlated with the
probability of acceptance. Those that attended private high schools, legacies, and apply early
decision are also more likely to be accepted, all else equal. Some of the other coefficients
reflect diversity goals. For example, women are less likely to be accepted at College X
where more than 65 percent of applicants are women and less likely at College Y. College X
is also more likely to accept applicants with lower income. In both schools, racial minorities
are more likely to be accepted. Applicants from the Midwest are more likely to be accepted
by College X and applicants from the South are more likely to be accepted by College Y, all
else equal.
An alternative explanation for the positive correlation between not submitting one’s
SAT I scores and acceptance is an omitted variable bias. Specifically, perhaps there are
characteristics of the applicant observable to the admissions offices, but not to us, which
make the applicant a good “match” for the college. These characteristics might include
15
interview or essay quality or expected participation on the college’s varsity athletic teams.18
This alternative explanation may seem reasonable in explaining the positive correlation
between not submitting and acceptance, but is less plausible when the interaction term is
included as a covariate. For the “match” quality argument to explain these results, applicants
with lower scores who do not submit must have higher match quality, which manifests itself
in higher probabilities of acceptance. Likewise, those with higher scores who chose not to
submit must have lower match quality, manifested in lower acceptance probabilities.
While we do not find it particularly plausible that the match quality is correlated with
scores and submission decisions in this way, we further consider the possibility that the
admission decision reflects information about the quality of the applicant-college match. To
do this, we consider whether subsequent measures of college performance are correlated with
scores and submission decisions in a similar manner as the admission decisions. If so, this
would suggest that the results in Tables 3 and 4 are attributable to our inability to control for
characteristics of the applicant that are observed by the admission departments and correlated
with the decision to submit.
We have numerous college performance measures to proxy for the match quality.
Some are academic, such as GPAs and academic honors. Other measures that are not
necessarily academic, such a retention and involvement in the social life of the college
through student government, sports and study abroad, may better reflect how the
unobservable characteristics manifest themselves in positive college outcomes.
In Tables 5A and 5B, each column represents a regression where the dependent
variable is a different college outcome measure. The covariates are the same as in Tables 3,
but we report only the coefficients of interest. Table 5A shows the results when the decision
to submit and the SAT I score are entered separately, but not interacted, and Table 5B
18
The admission departments at both colleges construct numerical academic and personal scores for each
applicant. The personal scores reflect the college’s interactions with the applicant. Including the scores as a
covariate in Tables 3 and 4 changes the results very little.
16
presents the results when we include the interaction term.19 Without the interaction term in
Table 5A, submitting his/her SAT I scores is often negatively correlated with the college
outcome, but among the negative coefficients we can only reject that the coefficient is
significantly different than zero when the dependent variable is number of sports at College
X or freshman year GPA at College Y. More importantly, when we include the interaction
term as a covariate in Table 5B, only three of the 15 performance measures have a negative
coefficient estimate associated with submitting an SAT I score and a positive estimate
associated with the interaction term. In all three cases, the coefficient estimates are not
statistically significant. There is no evidence from these measures of subsequent college
performance, that match quality is correlated with the decision to submit one’s SAT I scores
or that applicants with lower SAT I scores who submit have higher match quality. In
summary, our empirical findings that suggest ranking concerns influence admissions
decisions do not seem to be due to applicants’ characteristics unobservable to us but
observable to the colleges.
Tables 5A and 5B find predictive power in the SAT I score, primarily with respect to
academic achievements such as GPAs and academic honors such a Phi Beta Kappa. Work by
Rothstein (2004) suggests that there is predictive value in knowing a student’s SAT I score,
even controlling for the selection through matriculation. SAT I score is also positively
correlated with freshman retention, but only for College Y. Note that the SAT I score is not
correlated with any of our retention measures for College X. This is likely due to a
combination of poor performing students being asked to leave the college and strong
performing students transferring to better colleges.
B. Applicants’ Voluntary Disclosure Decisions
The previous subsection suggests that schools behave strategically in their admissions
decisions. Given that we have the private information, SAT I scores, of the applicants who
19
The results are similar when we replace actual SAT I scores with predicted SAT I scores for those
applicants who choose not to submit these scores. These results are available from the authors.
17
choose not to submit them, we further investigate the strategic behavior of applicants. The
results in Table 2 that average predicted SAT I scores (see Table A1) are greater than average
actual SAT I scores for those who do not submit their scores provides evidence that at least a
set of applicants behave strategically. The scatterplots in Figure 2 show the entire
distribution of the difference in the predicted SAT I score and the actual SAT I score for
those who do not submit their SAT I scores. These scatterplots indicate a positive
relationship between actual and predicted SAT I scores with the predicted score being greater
than actual score for the majority of applicants who choose not to submit. Eighty-three
percent of the College X applicants and 66 percent of College Y applicants that do not submit
the SAT I score have a predicted score greater than their actual score.
Table 6 provides additional evidence that some applicants behave strategically when
deciding whether to submit their SAT I scores based on a probit regression of whether an
applicant chooses to not submit his/her SAT I scores on the same set of ability and
demographic measures as in Table 3.20 The coefficient estimates suggest that, ceteris
paribus, applicants with higher SAT I scores are less likely to choose not to submit their
score. Specifically, an increase of 100 points in an applicant’s SAT I score decreases the
probability of not submitting by 0.11 for College X and 0.09 for College Y. However,
applicants with higher alternative measures of academic ability, like SAT II scores and high
school GPAs are more likely to choose not to submit their score, all else equal. Some of the
correlates suggest that students who are better informed may be more likely to not submit
their SAT I scores. For example, students from private high schools are more likely to not
submit their SAT I scores and African Americans applicants to College X are less likely to
not submit their SAT scores. Conditional on the applicant pool, these correlations are not
consistent with the stated goals of the schools adopting these policies in an effort to increase
diversity. Women applicants are more likely to not submit their SAT scores, conditional on
20
Note that the dependent variable equals one when the applicant does not submit.
18
those scores. One possible explanation for the gender difference is that the psychological
costs of reporting one’s score varies with gender. Specifically there are numerous claims that
the standardized SAT exams are biased against certain demographic groups including
women, which might impose higher psychological costs of submitting their SAT scores. 21 22
While these results suggest that some applicants are behaving strategically when
choosing whether to submit their SAT I scores, they do not provide much insight into why so
many applicants do not submit. The theoretical models of voluntary disclosure predict that
almost all applicants will submit if the cost of disclosure is nominal – as we expect it is for
the majority of applicants. One explanation for why 16 percent of applicants to College X
and 24 percent to College Y do not submit is that some applicants are poorly informed in
terms of how the colleges make admission decisions. Specifically, our earlier results suggest
that the colleges act strategically to improve their reported quality so that the combination of
actual SAT I scores and whether the applicant submits them is what the colleges care about.
Another possible explanation is that applicants believe the colleges will incorrectly infer their
actual SAT I scores if they do not submit them, consistent with the cursed equilibrium.
VII.
Conclusions
Colleges increase the uncertainty associated with their applicants’ quality through
voluntary SAT I policies. The applicant characteristics correlated with not submitting their
SAT I scores are not consistent with the colleges’ stated goal of increasing economic and
social diversity. Specifically, applicants from private high schools who are non-minorities
are more likely to take advantage of the policy, all else equal. More generally, college
admission data matched with confidential data from the College Board allows us to show that
21
FairTest, the National Center for Fair & Open Testing, cites admissions staff members who indicate that
some college applicants do not report their test scores for “philosophical reasons” (page 19) or as a “show
of support” (page 23) for the school’s policy (Rooney and Schaeffer 1998). For evidence that women and
men compete differently, see Niederle and Vesterlund (2007).
22
For research that considers whether the SAT exams are biased, see Bridgeman and Lewis (1996), Steele
(1999), and Wainer and Steinberg (1992).
19
applicants who under-perform on the standardized test relative to their other observables are
most likely to take advantage of the policy.
Critics suggest this policy that introduces uncertainty about the standardized tests
scores of applicants is an attempt to improve their college’s ranking in places like U.S. News
and World Report. Indeed, we find evidence that colleges are rewarding applicants in the
admission process who submit their SAT I scores when their SAT I scores will raise the
college’s average and rewarding applicants who do not submit when their SAT I scores will
lower the college’s average.
The decisions to make SAT I scores optional appear particularly paradoxical in light
of increased reliance on standardized testing. This reliance contributes to the estimated $500
million per year test preparation industry (Eduventures, 2004) and is central to the No Child
Left Behind Act of 2001 (http://www.nochildleftbehind.gov/), which required states to
develop a grade by grade standardized testing system as measures of accountability.23 The
empirical results in this paper and others suggests that SAT I scores do provide additional
information on how the applicant will perform in college. By choosing to implement an
optional SAT policy, these colleges must perceive the benefit of this policy on the college’s
ranking and other goals to be greater than the cost associated with forgoing the additional
information on the applicants contained in their SAT I scores.
23
The intention of the Act is to equalize education for all students, as measured by eliminating the
achievement gap among socioeconomic groups. Test score differences are one measure of achievement
gaps.
20
References:
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2008.
21
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Compete Too Much?” Quarterly Journal of Economics, 122(3): 1067-1101.
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22
Table 1
Summary Statistics: Means and Standard Deviations
College X
N=6,560
Chose to
Submit
SAT I
Chose Not
to Submit
SAT I
***
1266
(144)
1228
(120)
***
570
(67)
***
632
(84)
611
(68)
***
632
(70)
569
(67)
***
634
(78)
618
(72)
***
0.856
(0.351)
0.815
(0.388)
***
0.677
(0.468)
0.804
(0.397)
***
633
(68)
590
(68)
***
632
(76)
633
(61)
0.015
(0.122)
0.013
(0.112)
0.199
(0.400)
0.139
(0.347)
24.6
(3.7)
23.7
(2.4)
26.6
(3.8)
26.1
(3.3)
0.477
(0.500)
0.503
(0.500)
0.364
(0.481)
0.440
(0.497)
***
0.657
(0.475)
0.778
(0.416)
0.487
(0.500)
0.553
(0.497)
***
No High School GPA reported (sr)
0.259
(0.438)
0.237
(0.425)
0.345
(0.475)
0.332
(0.471)
HS GPA A+ (sr)
0.042
(0.201)
0.029
(0.169)
*
0.064
(0.245)
0.040
(0.197)
***
0.156
(0.362)
0.180
(0.384)
*
0.174
(0.380)
0.144
(0.351)
**
0.227
(0.419)
0.228
(0.420)
0.166
(0.372)
0.190
(0.395)
*
0.186
(0.389)
0.174
(0.379)
0.138
(0.345)
0.189
(0.392)
***
0.103
(0.304)
0.121
(0.326)
0.084
(0.278)
0.088
(0.283)
0.022
(0.147)
0.025
(0.155)
0.022
(0.145)
0.012
(0.107)
0.006
(0.075)
0.006
(0.077)
0.007
(0.081)
0.006
(0.076)
5543
1017
2734
868
SAT I Combined (math+verbal) Score
SAT I Verbal Score
SAT I Math Score
SAT II Score(s) available (1=yes)
Average SAT II Score (when available)
ACT Score(s) available (1=yes)
Average ACT Score (when available)
Attended Private HS
Female Student
HS GPA A (sr)
HS GPA A- (sr)
HS GPA B+ (sr)
HS GPA B (sr)
HS GPA B- (sr)
HS GPA C or below (sr)
N
Chose to
Submit
SAT I
Chose Not
to Submit
SAT I
1272
(124)
1139
(116)
641
(74)
College Y
N=3,602
SS
***
*
SS
***
*
SS, statistical significance ; *** statistically different at 1% level, ** statistically different at 5% level, * statistically different at
10% level. (sr) indicates self reported and # of HS extracurricular activities, sports, offices/awards and honors classes are based
on responses of those who filled in College Board Survey.
23
Table 1 (continued)
Summary Statistics: Means and Standard Deviations
College X (N=6,560)
Chose to
Submit
SAT I
0.304
(0.460)
Chose Not
to Submit
SAT I
0.332
(0.471)
0.225
(0.417)
0.195
(0.396)
Class rank 2nd 10th
0.193
(0.395)
Class rank 2nd 5th
College Y (N=3,602)
*
Chose to
Submit
SAT I
0.346
(0.476)
Chose Not
to Submit
SAT I
0.379
(0.485)
**
0.212
(0.409)
0.182
(0.386)
0.200
(0.400)
0.135
(0.342)
0.135
(0.342)
0.112
(0.316)
0.121
(0.326)
0.071
(0.257)
0.090
(0.286)
Class rank middle or bottom
0.166
(0.372)
0.152
(0.360)
0.236
(0.425)
0.214
(0.411)
Income Missing (sr)
0.456
(0.498)
0.464
(0.499)
0.563
(0.496)
0.560
(0.497)
Income <50K (sr)
0.090
(0.287)
0.109
(0.312)
0.076
(0.265)
0.097
(0.296)
*
0.182
(0.386)
0.189
(0.392)
0.157
(0.364)
0.131
(0.338)
*
0.271
(0.445)
0.238
(0.426)
0.204
(0.403)
0.212
(0.409)
Legacy (1=yes)
0.024
(0.153)
0.022
(0.146)
0.062
(0.242)
0.052
(0.222)
Apply Early
0.058
(0.235)
0.120
(0.325)
0.108
(0.310)
0.096
(0.294)
0.500
(0.500)
0.515
(0.500)
0.592
(0.492)
0.508
(0.500)
White
0.835
(0.371)
0.834
(0.372)
0.874
(0.332)
0.853
(0.355)
African American
0.029
(0.168)
0.031
(0.175)
0.033
(0.178)
0.051
(0.219)
0.003
(0.052)
0.007
(0.083)
0.002
(0.043)
0.003
(0.059)
Asian American
0.043
(0.202)
0.041
(0.199)
0.056
(0.230)
0.044
(0.205)
Hispanic
0.038
(0.190)
0.046
(0.210)
0.035
(0.185)
0.048
(0.215)
0.053
(0.224)
0.040
(0.197)
5543
1017
2734
868
Class rank missing
Class rank 1st 10th
50K <Income <100K (sr)
Income >100K (sr)
Intend to Apply for Financial Aid
Native American
Unknown Race
N
SS
*
**
***
**
SS
*
*
*
***
**
*
*
SS, statistical significance ; *** statistically different at 1% level, ** statistically different at 5% level, * statistically different at
10% level. (sr) indicates self reported and # of HS extracurricular activities, sports, offices/awards and honors classes are based
on responses of those who filled in College Board Survey.
24
Table 1 (continued)
Summary Statistics: Means and Standard Deviations
College X
College Y
N=6,560
N=3,602
Chose to
Submit
SAT I
0.134
(0.340)
Chose Not
to Submit
SAT I
0.122
(0.327)
Chose to
Submit
SAT I
0.328
(0.469)
Chose Not
to Submit
SAT I
0.253
(0.435)
***
0.626
(0.484)
0.589
(0.492)
**
0.495
(0.500)
0.559
(0.497)
***
0.051
(0.220)
0.084
(0.277)
***
0.045
(0.208)
0.043
(0.202)
From West
0.088
(0.284)
0.094
(0.293)
0.072
(0.258)
0.060
(0.237)
From South
0.100
(0.301)
0.111
(0.314)
0.047
(0.212)
0.070
(0.256)
0.877
(0.329)
0.898
(0.303)
0.798
(0.401)
0.821
(0.383)
# of HS Extracurricular Activities (sr)
5.418
(3.060)
5.410
(3.024)
4.692
(3.230)
4.525
(3.275)
# of HS sports (sr)
2.428
(1.964)
2.543
(1.989)
2.314
(1.981)
2.325
(2.013)
# of HS offices/awards (sr)
1.062
(1.475)
1.090
(1.510)
0.992
(1.513)
0.842
(1.355)
4.130
(4.523)
3.323
(4.127)
3.677
(4.582)
3.546
(4.437)
5543
1017
2734
868
From State where College resides
From Northeast
From Midwest
Filled in College Board Survey
# of HS honors classes (sr)
N
SS
*
***
SS
***
**
SS, statistical significance ; *** statistically different at 1% level, ** statistically different at 5% level, * statistically different at
10% level. (sr) indicates self reported and # of HS extracurricular activities, sports, offices/awards and honors classes are based
on responses of those who filled in College Board Survey.
25
TABLE 2 : Additional Descriptive Statistics
Means
(standard deviations)
[number of observations]
SAT I Score (1600) –
all applicants
College X
Chose Not
Chose to
to Submit
Submit
SAT I
SAT I
1139
1272
(116)
(124)
[1017]
[5543]
SS
***
College Y
Chose Not
Chose to
to Submit
Submit
SAT I
SAT I
1228
1266
(120)
(144)
[868]
[2734]
SS
***
.446
(0.497)
[2734]
.492
(0.500)
[868]
**
***
1343
(114)
[1218]
1260
(103)
[427]
***
1156
(101)
[190]
***
1301
(113)
[361]
1225
(98)
[138]
***
1219#
(82)
[1017]
***
1266
(99)
[2734]
1264#
(96)
[868]
Probability of
Acceptance
.419
(0.493)
[5543]
.396
(0.489)
[1017]
SAT I Score
conditional on
Acceptance
1323
(107)
[2321]
1172
(99)
[403]
SAT I Score
conditional on
Enrollment
1281
(107)
[692]
Predicted SAT I Score*
(based on those that
want SAT I considered)
1272
(89)
[5540]
SS, statistical significance ; *** statistically different at 1% level, ** statistically different at 5% level, *
# Statistically different than the actual SATI score at the 1% level.
*Regression Results are in Table A1 of the Appendix.
26
TABLE 3
Probit: Dependent Variable (Accepted = 1)
College X
College Y
I
II
III
IV
SATI Score/100 (16 max)
0.2953***
(0.0221)
0.2279***
(0.0438)
0.6249***
(0.0365)
0.4462***
(0.0510)
Submitted SATI Score
-0.4018***
(0.0546)
-1.3144**
(0.5391)
-0.4077***
(0.0607)
-3.1273***
(0.6875)
0.0781*
(0.0458)
Submitted SATI Score* SATI Score/100
0.2180***
(0.0545)
Submitted SATII Score
-2.6687***
(0.2706)
-2.6485***
(0.2707)
-2.0652***
(0.4928)
-2.1755***
(0.4944)
Submitted SATII Score* SATII Score/100
0.4514***
(0.0426)
0.4481***
(0.0426)
0.3215***
(0.0766)
0.3374***
(0.0770)
-0.2173*
(0.1128)
-0.2250**
(0.1129)
-0.6183
(0.5458)
-0.6619
(0.5456)
Submitted ACT Score*ACT Score
0.0129***
(0.0043)
0.0134***
(0.0043)
0.0304
(0.0198)
0.0317
(0.0198)
Attended Private High School
0.1274***
(0.0402)
0.1277***
(0.0402)
0.1888***
(0.0565)
0.1935***
(0.0569)
Female
-0.5387***
(0.0401)
-0.5375***
(0.0401)
0.3128***
(0.0512)
0.3112***
(0.0514)
No High School GPA reported
0.4598***
(0.0912)
0.4616***
(0.0913)
0.4985***
(0.1270)
0.5044***
(0.1275)
High School GPA A+
0.9201***
(0.1212)
0.9216***
(0.1212)
0.9382***
(0.1628)
0.9334***
(0.1627)
High School GPA A
0.8489***
(0.0862)
0.8516***
(0.0863)
0.8689***
(0.1300)
0.8738***
(0.1306)
High School GPA A-
0.6529***
(0.0768)
0.6545***
(0.0769)
0.6956***
(0.1230)
0.6933***
(0.1235)
High School GPA B+
0.4115***
(0.0764)
0.4125***
(0.0765)
0.5051***
(0.1203)
0.5044***
(0.1206)
High School GPA B-
-0.2839*
(0.1668)
-0.2834*
(0.1664)
-0.1829
(0.2535)
-0.1944
(0.2532)
High School GPA C
-0.5795
(0.4302)
-0.5813
(0.4357)
0.1878
(0.6140)
0.0153
(0.5489)
Class rank missing
0.1376*
(0.0708)
0.1406**
(0.0708)
-0.0492
(0.1134)
-0.0361
(0.1128)
Class rank 1st 10th
0.3936***
(0.0748)
0.3947***
(0.0748)
0.4333***
(0.1209)
0.4431***
(0.1206)
Class rank 2nd 10th
0.2087***
(0.0690)
0.2111***
(0.0690)
-0.0108
(0.1170)
0.0016
(0.1166)
-0.1538
(0.1215)
-0.1506
(0.1216)
-0.0562
(0.1982)
-0.0436
(0.1974)
Submitted ACT Score
Class rank middle or bottom
27
TABLE 3 (continued)
College X
College Y
I
II
III
IV
Missing Income
0.1912***
(0.0534)
0.1922***
(0.0535)
0.0965
(0.0768)
0.0928
(0.0771)
Income <50K
0.3308***
(0.0750)
0.3289***
(0.0750)
-0.1686
(0.1136)
-0.1979*
(0.1138)
50K <Income <100K
0.1125**
(0.0566)
0.1147**
(0.0566)
-0.2010**
(0.0869)
-0.2088**
(0.0872)
Legacy (1=yes)
0.7487***
(0.1236)
0.7470***
(0.1239)
0.3053***
(0.1057)
0.3063***
(0.1063)
Applied Early Decision
1.8276***
(0.0872)
1.8258***
(0.0868)
1.2040***
(0.0914)
1.2206***
(0.0925)
Intend to Apply for Financial Aid
-0.0848**
(0.0407)
-0.0847**
(0.0407)
-0.2308***
(0.0565)
-0.2251***
(0.0566)
African American
1.3612***
(0.1268)
1.3616***
(0.1268)
1.8630***
(0.1723)
1.8260***
(0.1720)
Native American
0.1538
(0.3361)
0.1503
(0.3347)
1.2115**
(0.5357)
1.1687**
(0.5504)
Asian
0.5052***
(0.0948)
0.5034***
(0.0947)
1.1601***
(0.1315)
1.1672***
(0.1333)
Hispanic
0.5219***
(0.1024)
0.5184***
(0.1024)
1.5441***
(0.1827)
1.4995***
(0.1810)
Unknown Race
-0.2117***
(0.0805)
-0.2127***
(0.0806)
0.0509
(0.0546)
0.0502
(0.0545)
0.0518
(0.0599)
0.0591
(0.0600)
0.3398***
(0.0823)
0.3423***
(0.0822)
-0.1191
(0.1242)
-0.1208
(0.1246)
From West
-0.0039
(0.0666)
-0.0012
(0.0667)
0.0602
(0.0995)
0.0647
(0.0995)
From South
-0.1205*
(0.0624)
-0.1192*
(0.0624)
0.4084***
(0.1304)
0.3977***
(0.1297)
Filled in College Board Survey (SDQ)
-0.1802
(0.1376)
-0.1778
(0.1378)
-0.0685
(0.1975)
-0.0715
(0.1978)
# of HS Extracurricular Activities (sr)*Filled in SDQ
0.0166*
(0.0087)
0.0163*
(0.0087)
-0.0189
(0.0131)
-0.0176
(0.0132)
-0.0243**
(0.0113)
-0.0241**
(0.0113)
0.0247
(0.0184)
0.0239
(0.0186)
# High School offices/awards (sr) *Filled in SDQ
0.0279*
(0.0158)
0.0281*
(0.0158)
0.0039
(0.0219)
0.0027
(0.0218)
# High School honors Classes (sr) *Filled in SDQ
0.0052
(0.0050)
6557 / 0.2487
0.0052
(0.0050)
6557 / 0.2490
0.0077
(0.0073)
3602 / 0.3049
0.0084
(0.0074)
3602 / 0.3083
From State where College resides
From Midwest
# High School Sports (sr) *Filled in SDQ
Observations / R-Squared
Notes: sr is “self reported” on SDQ. Omitted Categories: Income >$100K (sr); Race = white; HS GPA B, From Northeast.
Standard errors in parentheses: *** significant at 1%; ** significant at 5%; * significant at 10%
28
TABLE 4
Probit: Dependent Variable (Accepted = 1)
Selected Coefficients
With Predicted SAT I Score as Independent Variable
College X
College Y
I
II
III
IV
Predicted SATI Score/100 (16 max)
0.3087***
(0.0244)
0.2023***
(0.0667)
0.6453***
(0.0429)
0.3368***
(0.0798)
Submitted SATI Score
-0.1645***
(0.0510)
-1.4892*
(0.7769)
-0.2112***
(0.0620)
-4.2773***
(0.9095)
0.1073*
(0.0627)
Submitted SATI Score* SATI Score/100
0.3204***
(0.0712)
Submitted SATII Score
-2.4855***
(0.2818)
-2.5815***
(0.2893)
-1.6991***
(0.5181)
-2.2294***
(0.5367)
Submitted SATII Score* SATII Score/100
0.4240***
(0.0443)
0.4389***
(0.0456)
0.2567***
(0.0808)
0.3425***
(0.0840)
-0.1895
(0.1170)
-0.2181*
(0.1147)
-0.3431
(0.5741)
-0.7225
(0.5647)
0.0130***
(0.0044)
0.0139***
(0.0044)
0.0199
(0.0208)
0.0332*
(0.0205)
6557
0.2468
6557
0.2471
3602
0.2903
3602
0.2959
Submitted ACT Score
Submitted ACT Score*ACT Score
Observations
R-Squared
Notes: Includes same set of covariates as in Table 3. Bootstrapped standard errors in parentheses: *** significant at
1%; ** significant at 5%; * significant at 10%
29
Table 5A
Probit and Ordinary Least Squares: Dependent Variables (College Performance Measures)
No interaction term between SATI and Submitted Score
SATI
Score/100
Submitted
SATI Score
N
R-Squared
Mean (SD)
of Y
Freshman
Year GPA
GPA at
Grad.
0.0440***
(0.0153)
-0.0467
(0.0346)
860
0.2752
3.288
(0.420)
0.0266**
(0.0122)
-0.0287
(0.0257)
687
0.3035
3.449
(0.289)
Academic Achievements
Dual
Recv’d
Phi Beta
Major
Honor,
Kappa
(=1 if
Distnctn or
(=1 if
Dual
Award in
Phi Beta
Major)
Major
Kappa)
(=1 if
recv’d)
-0.0008
(0.0193)
-0.0332
(0.0455)
687
0.0731
0.236
(0.425)
0.1570**
(0.0636)
-0.2206
(0.1437)
684
0.1335
0.617
(0.486)
0.2184**
(0.0856)
-0.3010
(0.2238)
654
0.2301
0.106
(0.308)
Summa
/Magna
Cum Laude
(=1 if
Summa/
Magna)
Completed
Freshman
Year
(=1 if
completed)
0.2174***
(0.0771)
-0.2557
(0.1706)
654
0.1854
0.245 (0.430)
-0.1336
(0.0989)
0.1913
(0.2755)
800
0.1977
0.975
(0.156)
Retention
Grad.
within 4
years of
enrolling
(=1 if
graduated
in 4 yrs)
-0.0178
(0.0591)
-0.0966
(0.1421)
881
0.0660
0.790
(0.407)
Grad,
(=1 if
grad.)
-0.0137
(0.0614)
-0.1135
(0.1466)
881
0.0599
0.823
(0.382)
Community Involvement
Number of
Student
Study
Sports
Gov’t
Abroad
Program
Position
(=1 if
(=1 if
have
studied
position)
abroad)
0.0309
(0.0273)
-0.1585**
(0.0688)
687
0.1299
0.406
(0.634)
-0.1268
(0.0795)
0.4665**
(0.2232)
684
0.0941
0.098
(0.297)
-0.0784
(0.0641)
-0.1674
(0.1478)
684
0.1104
0.610
(0.488)
College Y Performance Measures
SATI
Score/100
Submitted
SATI Score
N
R-Squared
Mean (SD)
of Y
0.5571*
(0.3036)
-1.3477**
(0.5469)
479
0.2671
84.89
(5.40)
0.3321**
(0.1427)
-0.2903
(0.3459)
426
0.3333
0.960
(0.196)
-0.1288***
(0.0367)
0.0697
(0.0725)
479
0.1183
0.357
(0.589)
Notes: All specifications include same set of covariates as in Table 3. For College Y number of sports is over college career and for College Y number of sports is freshman
year. The probit coefficients are not marginal effects. Standard errors in parentheses: *** significant at 1%; ** significant at 5%; * significant at 10%.
30
Table 5B
Probit and Ordinary Least Squares: Dependent Variables (College Performance Measures)
Interaction term between SATI and Submitted Score
Freshman
Year GPA
GPA at
Grad.
Academic Achievements
Dual
Recv’d
Phi Beta
Major
Honor,
Kappa
(=1 if
Distnctn
(=1 if Phi
Dual
or
Beta
Major)
Award in
Kappa)
Major
(=1 if
recv’d)
Summa
/Magna
Cum
Laude
(=1 if
Summa/
Magna)
Completed
Freshman
Year
(=1 if
completed)
Retention
Grad.
within 4
years of
enrolling
(=1 if
graduate
d in 4
yrs)
Grad,
(=1 if
grad.)
Community Involvement
Number of
Student
Study
Sports
Gov’t
Abroad
Position
Program
(=1 if
(=1 if
have
studied
position)
abroad)
College X Performance Measures
SATI
Score/100
Submitted
SATI Score
Submitted
SATI Score*
SATI
Score/100
N
R-Squared
Mean (SD)
of Y
0.0529*
(0.0278)
0.0838
(0.3248)
-0.0111
(0.0276)
0.0513**
(0.0238)
0.3239
(0.2915)
-0.0299
(0.0246)
0.0067
(0.0368)
0.0739
(0.4609)
-0.0091
(0.0392)
0.2450*
(0.1381)
1.0471
(1.7249)
-0.1082
(0.1461)
0.4835***
(0.1798)
3.4713
(2.2770)
-0.3107
(0.1906)
0.2283
(0.1565)
-0.0947
(2.0266)
-0.0134
(0.1689)
-0.1325
(0.1415)
0.2075
(1.7435)
-0.0014
(0.1442)
0.0600
(0.1218)
1.0244
(1.4770)
-0.0953
(0.1257)
0.0605
(0.1294)
0.9641
(1.5674)
-0.0915
(0.1335)
0.0150
(0.0591)
-0.3866
(0.6764)
0.0194
(0.0580)
0.1299
(0.1655)
3.9033*
(2.0303)
-0.2910*
(0.1706)
0.0883
(0.1280)
2.2091
(1.5437)
-0.2017
(0.1313)
860
0.2753
3.288
(0.420)
687
0.3052
3.449
(0.289)
687
0.0732
0.236
(0.425)
684
0.1342
0.617
(0.486)
654
0.2330
0.106
(0.308)
654
0.1855
0.245
(0.430)
800
0.1977
0.975
(0.156)
881
0.0667
0.790
(0.407)
881
0.0605
0.823
(0.382)
687
0.1301
0.406
(0.634)
684
0.0986
0.098
(0.297)
684
0.1130
0.610
(0.488)
College Y Performance Measures
SATI
0.4014
Score/100
(0.5888)
Submitted
-3.6942
SATI Score
(7.3398)
Submitted
0.1887
SATI Score* (0.5864)
SATI
Score/100
N
479
R-Squared
0.2673
Mean (SD)
84.89
of Y
(5.40)
0.3002
(0.2633)
-0.7387
(3.241)
0.0368
(0.2533)
-0.0160
(0.0567)
1.7685***
(0.6605)
-0.1366
(0.0526)
426
0.3333
0.960
(0.196)
479
0.1275
0.357
(0.589)
Notes: All specifications include same set of covariates as in Table 3. For College Y number of sports is over college career and for College Y number of sports is freshman
year. The probit coefficients are not marginal effects. Standard errors in parentheses: *** significant at 1%; ** significant at 5%; * significant at 10%.
31
TABLE 6
Probit Regression: Dependent Variables (Chose Not to Submit SAT I = 1)
College X
College Y
I
SATI Score/100 (16 max)
II
-0.6261***
(0.0302)
III
IV
-0.3094***
(0.0279)
Verbal SATI Score/100 (8 max)
-0.7131***
(0.0420)
-0.3914***
(0.0426)
Math SATI Score/100 (8 max)
-0.5479***
(0.0437)
-0.2270***
(0.0431)
SATII Score(s) available (1=yes)
-1.1078***
(0.3022)
-1.2023***
(0.3015)
-1.9544***
(0.3000)
-2.0130***
(0.3020)
Average SATII/100*SATII Score(s) available
0.2045***
(0.0508)
0.2208***
(0.0506)
0.4013***
(0.0502)
0.4113***
(0.0506)
ACT Score(s) available (1=yes)
-2.6582**
(1.0691)
-2.6626**
(1.0678)
-0.8522**
(0.4149)
-0.8861**
(0.4140)
Average ACT/100*ACT Score(s) available
0.0854**
(0.0428)
0.0855**
(0.0428)
0.0212
(0.0154)
0.0226
(0.0154)
Attended Private High School
0.1019**
(0.0472)
0.1103**
(0.0473)
0.1279**
(0.0549)
0.1277**
(0.0549)
Female
0.2247***
(0.0497)
0.2419***
(0.0505)
0.1160**
(0.0494)
0.1397***
(0.0503)
No High School GPA reported
0.0888
(0.0998)
0.0910
(0.1000)
0.0732
(0.1136)
0.0724
(0.1138)
High School GPA A+
0.2608*
(0.1443)
0.2622*
(0.1445)
0.0172
(0.1580)
0.0205
(0.1583)
High School GPA A
0.3263***
(0.0970)
0.3231***
(0.0970)
0.1039
(0.1186)
0.1042
(0.1187)
High School GPA A-
0.1835**
(0.0849)
0.1860**
(0.0849)
0.1952*
(0.1054)
0.1972*
(0.1056)
High School GPA B+
-0.0001
(0.0832)
0.0000
(0.0832)
0.2025**
(0.1031)
0.2019*
(0.1034)
High School GPA B-
-0.0870
(0.1575)
-0.0918
(0.1576)
-0.4555**
(0.2027)
-0.4492**
(0.2037)
High School GPA C
-0.5389*
(0.2919)
-0.5418*
(0.2986)
-0.4325
(0.3311)
-0.4305
(0.3299)
Class rank missing
0.0852
(0.0799)
0.0777
(0.0802)
-0.0971
(0.0989)
-0.0985
(0.0989)
Class rank 1st 10th
0.0542
(0.0892)
0.0460
(0.0894)
-0.0856
(0.1135)
-0.0956
(0.1134)
Class rank 2nd 10th
0.0248
(0.0810)
0.0211
(0.0810)
-0.0906
(0.1073)
-0.0890
(0.1073)
Class rank middle or bottom
-0.1429
(0.1196)
-0.1450
(0.1197)
-0.0738
(0.1575)
-0.0775
(0.1580)
32
TABLE 6 (continued)
College X
College Y
I
II
III
IV
Missing Income
0.1004
(0.0615)
0.1066*
(0.0617)
0.0052
(0.0723)
0.0055
(0.0725)
Income <50K
-0.0953
(0.0873)
-0.0880
(0.0878)
0.2071**
(0.1047)
0.2096**
(0.1052)
50K <Income <100K
0.0757
(0.0676)
0.0888
(0.0678)
0.0021
(0.0845)
0.0045
(0.0847)
Legacy (1=yes)
0.0722
(0.1363)
0.0620
(0.1367)
-0.1263
(0.1050)
-0.1277
(0.1049)
Intend to Apply for Financial Aid
-0.0498
(0.0491)
-0.0424
(0.0493)
-0.1996***
(0.0555)
-0.1955***
(0.0556)
African American
-0.5953***
(0.1386)
-0.5984***
(0.1397)
0.0721
(0.1333)
0.0846
(0.1340)
Native American
-0.1163
(0.3490)
-0.0951
(0.3424)
0.2776
(0.6056)
0.2876
(0.6083)
Asian
-0.1015
(0.1107)
-0.1279
(0.1116)
-0.1923*
(0.1130)
-0.2295**
(0.1146)
-0.4294***
(0.1251)
-0.4389***
(0.1259)
-0.0362
(0.1280)
-0.0418
(0.1286)
Unknown Race
0.0101
(0.1030)
0.0148
(0.1032)
From State where College resides
-0.1191*
(0.0668)
-0.1188*
(0.0670)
-0.1817***
(0.0593)
-0.1827***
(0.0594)
0.3075***
(0.0885)
0.3034***
(0.0886)
0.1110
(0.1226)
0.1039
(0.1226)
From West
0.1280
(0.0780)
0.1373*
(0.0780)
-0.1256
(0.1014)
-0.1189
(0.1016)
From South
0.0856
(0.0706)
0.0774
(0.0708)
0.1869*
(0.1060)
0.1915*
(0.1058)
Filled in College Board Survey (SDQ)
0.0685
(0.1467)
0.0766
(0.1467)
-0.0207
(0.1671)
-0.0310
(0.1674)
# of HS Extracurricular Activities *Filled in SDQ
-0.0039
(0.0099)
-0.0011
(0.0099)
-0.0100
(0.0123)
-0.0074
(0.0123)
# High School Sports*Filled in SDQ
0.0155
(0.0133)
0.0110
(0.0135)
0.0101
(0.0171)
0.0068
(0.0173)
# High School offices/awards *Filled in SDQ
0.0153
(0.0167)
0.0152
(0.0168)
-0.0415*
(0.0215)
-0.0411*
(0.0215)
# High School honors Classes *Filled in SDQ
0.0003
(0.0060)
-0.0010
(0.0061)
0.0133*
(0.0073)
0.0124*
(0.0073)
Hispanic
From Midwest
Observations
6557
6557
3602
3602
R-Squared
0.2017
0.2042
0.0781
0.0799
Notes: sr is “self reported” on SDQ. Omitted Categories: Income >$100K (sr); Race = white; HS GPA B, From
Northeast. Standard errors in parentheses: *** significant at 1%; ** significant at 5%; * significant at 10%.
33
Figure 1: Distribution of SAT 1 Scores
College X
Chose not to submit SATI
0
.05
Fraction
.1
.15
Chose to submit SATI
400
600
800
1000
1200
1400
1600 400
600
800
1000
1200
1400
1600
SATI Score
Graphs by SAT I Option
College Y
Chose not to submit SATI
0
.05
Fraction
.1
.15
Chose to submit SATI
400
600
800
1000
1200
1400
1600 400
600
800
1000
1200
1400
1600
SATI Score
Graphs by SAT I Option
34
Figure 2: Predicted versus Actual SAT 1 Score for those who Chose not to Submit SAT1
College X
45°
1550
1500
1450
1400
Predicted SATI Score
1350
1300
1250
1200
1150
1100
1050
1000
950
900
850
800
800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550
Actual SATI Score
College Y
1550
45°
1500
1450
1400
Predicted SATI Score
1350
1300
1250
1200
1150
1100
1050
1000
950
900
850
800
800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550
Actual SATI Score
35
Appendix
TABLE A1
Ordinary Least Squares: Dependent Variable (SAT I Score)
Obtain “Predicted” SAT Scores for those who Don’t Submit
College X
College Y
Submitted SATII Score
-7.1498***
(0.1277)
-6.2366***
(0.2773)
Submitted SATII Score* SATII Score/100
1.1880***
(0.0187)
1.0322***
(0.0421)
Submitted ACT Score
-0.9247***
(0.0931)
-5.5478***
(0.3056)
Submitted ACT Score*ACT Score
0.0255***
(0.0035)
0.1984***
(0.0113)
0.0316
(0.0265)
0.0867*
(0.0487)
-0.2197***
(0.0252)
-0.3117***
(0.0429)
No High School GPA reported
0.1510**
(0.0592)
0.5034***
(0.1010)
High School GPA A+
0.3703***
(0.0748)
0.6675***
(0.1248)
High School GPA A
0.1849***
(0.0565)
0.4722***
(0.1009)
High School GPA A-
0.1933***
(0.0491)
0.3448***
(0.0944)
High School GPA B+
0.0719
(0.0471)
0.1880**
(0.0945)
High School GPA B-
-0.0763
(0.0991)
-0.1361
(0.1698)
High School GPA C
-0.8005***
(0.2214)
-1.0003***
(0.3271)
Class rank missing
0.0597
(0.0465)
0.2125**
(0.0857)
Class rank 1st 10th
0.1644***
(0.0503)
0.4595***
(0.0940)
Class rank 2nd 10th
0.0184
(0.0450)
0.1554*
(0.0901)
-0.1572**
(0.0722)
0.0293
(0.1525)
-0.0431
(0.0316)
0.0431
(0.0567)
-0.2724***
(0.0515)
-0.4386***
(0.1004)
Attended Private High School
Female
Class rank middle or bottom
Missing Income
Income <50K
36
TABLE A1 (cont.)
College X
College Y
50K <Income <100K
-0.0151
(0.0362)
-0.0688
(0.0645)
Legacy (1=yes)
0.0827
(0.0622)
-0.0789
(0.0870)
Applied Early Decision
-0.0837
(0.0546)
-0.3557***
(0.0600)
Intend to Apply for Financial Aid
-0.0598**
(0.0268)
-0.2529***
(0.0451)
African American
-0.8145***
(0.1034)
-1.2221***
(0.1678)
Native American
-0.7610**
(0.3858)
-0.5939
(0.8702)
-0.0243
(0.0552)
-0.0994
(0.1062)
Hispanic
-0.7021***
(0.0924)
-0.8816***
(0.1643)
Unknown Race
0.1696***
(0.0560)
From State where College resides
-0.1248***
(0.0362)
-0.1544***
(0.0507)
From Midwest
0.0887
(0.0644)
0.0753
(0.0863)
From West
0.0869*
(0.0470)
0.2013***
(0.0734)
From South
-0.0025
(0.0397)
-0.1403
(0.0926)
Filled in College Board Survey (SDQ)
-0.1335
(0.0849)
0.0015
(0.1601)
# of HS Extracurricular Activities (sr) *Filled in SDQ
0.0131**
(0.0056)
0.0234**
(0.0110)
# High School Sports (sr) *Filled in SDQ
-0.0194***
(0.0071)
-0.0388**
(0.0156)
# High School offices/awards (sr) *Filled in SDQ
-0.0195**
(0.0092)
-0.0218
(0.0160)
# High School honors Classes (sr) *Filled in SDQ
0.0245***
(0.0032)
0.0537***
(0.0057)
Constant
12.5719***
(0.1127)
12.3123***
(0.2066)
5540
0.5222
0.4706
Asian
Observations
R-squared
2734
Notes: sr is “self reported” on SDQ. Omitted Categories: Income >$100K (sr); Race = white; HS GPA B, From Northeast.
Standard errors in parentheses: *** significant at 1%; ** significant at 5%; * significant at 10%
37