Voluntary Disclosure, Inference and the Strategic Behavior of Colleges

1
Voluntary Disclosure, Inference and the
Strategic Behavior of Colleges

• Michael Conlin Michigan State University
• Stacy Dickert-Conlin Michigan State University
• Gabrielle Chapman Syracuse University
• Oregon State University May 2009

2
Optional SAT Policies

• 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 Reports
  college rankings.
• Colin Driver, President of Reed College, New York
  Times, 2006

3
Optional SAT Policies

• 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.
• Brownstein (2001) in The Chronicle of Higher
  Education

4
U.S. News World Report (Criteria and weights
for rankings colleges)
5
Prevalence of Optional Policy

• As of Spring 2007, more than 700 colleges have
  SAT- or ACT- optional policies.
• 24 of the top 100 liberal arts colleges ranked by
  U.S. News World are SAT- or ACT- optional.

6
Overview

• Research Questions
• Data
• Voluntary Disclosure Literature
• Reduced Form Results
• - Colleges Decisions to Accept
• - Applicants Decisions to Submit SAT I
• Structural Framework
• Future Work

7
Research Questions

• Are Colleges Admission Decisions influenced by
  their incentive to increase their ranking in
  publications like U.S. News World Report?
• Do Applicants behave strategically when deciding
  whether to submit their SAT I scores and how does
  this inform the voluntary disclosure literature?
• What is the colleges inference for applicants
  who choose not to submit their SAT I scores?

8
College Data

• Application data for 2 liberal arts schools in
  north east
• Each with approximately 1800 students
  enrolled.
• Both report a typical SAT I score in the
  upper 1200s/1600.
• College X 2 years 5 years after the
  optional policy
• was instituted.
• College Y the year after the optional policy
  was instituted.
• Numerical Score from Admission Department
• Acceptance and Enrollment Decisions.
• Performance Measures for those who Enroll.

9
College Board Data

• SAT scores for those who elected not to submit
  them to the college.
• Student Descriptive Questionnaire (SDQ)
• SAT II Scores
• Self Reported income
• High school GPA
• High school activities

SATII are Subject Exams 20 of them
Also have High School GPA from colleges but not
standardized
10
Optional SAT I policies

• College X
• Whether or not applicant submits SAT I scores,
  require applicants to choose between submitting
  the ACT scores or three SAT II Subject Tests.
• College Y
• Along with their SAT I scores, applicants can
  submit scores from their SAT II exams, ACT exam,
  and/or Advanced Placement exams. College Y
  applicants are required to submit at least one of
  these scores if they choose not to submit their
  SAT I scores.

11
Summary Statistics

• 15.3 percent of the 7,023 applicants to College X
  choose not to submit SAT I scores.
• 24.1 percent of the 3,054 applicants to College X
  choose not to submit SAT I scores.

12
Table 1 Summary Statistics
13
Table 1 Summary Stats (cont)
14
Table 1 Summary Stats (cont)
15
Voluntary Disclosure Theory

• Grossman Hart (1980) when disclosure is
  costless, complete unraveling occurs.
• Grossman (1981) and Milgrom (1981) -generalizes
  Grossman Hart (1980)
• Jovanovic (1982) when disclosure is costly,
  unraveling is not complete and it may not be
  socially optimal to mandate disclosure

16
Voluntary Disclosure Example

• Student i has the following probability
  distribution in term of SAT I scores.
• When disclosure is costless, Bayesian Nash
  Equilibrium results in every type except the
  worst disclosing and the worst being indifferent
  between disclosing and not disclosing.

Expected SAT I Score 1300(.2)1200(.4)1100(.3)10
00(.1)1170
17
Voluntary Disclosure Models

• Comments
• Distribution depends on student characteristics
  that are observable to the school such as high
  school GPA.
• With positive disclosure costs, the unraveling
  is not complete and only the types with the lower
  SAT I scores do not disclose.
• Assumptions
• Common Knowledge.
• Colleges use Bayesian Updating to Infer SAT I
  Score of those who do not Submit/Disclose
• Colleges incentives to admit an applicant is
  only a function of his/her actual SAT I score
  (not whether the applicant submits the score)

18
Voluntary Disclosure Theory

• Eyster and Rabin (Econometrica, 2005) propose a
  new equilibrium concept which they call a Cursed
  Equilibrium. College correctly predicts the
  distribution of the other players actions but
  underestimates the degree these actions are
  correlated with the other players private
  information.

Fully Cursed Equilibrium (?1) College infers
if applicant doesnt disclose that his/her
expected SAT I score is 1300(.2)1200(.4)1100(.3
)1000(.1)1170
Partially Cursed Equilibrium (?.4 for
example) College infers if applicant doesnt
disclose that his/her expected SAT I score is
(1-.4) (1100(.3)1000(.1))/.4 (.4)1170 1113
19
Voluntary Disclosure Empirical

• Mathios (2000) fat content in salad dressings.
• Jin and Leslie (2003) hygiene quality grade
  cards for restaurants in Los Angeles.
• Jin (2004) HMO accreditation and summary
  statistics.
• Robinson and Monk (2005) applicants submitting
  SAT scores to Mount Holyoke College.

20
Colleges Incentive to Institute Optional SAT
Policy Table 2
21
Colleges Acceptance Decision Table 3 Columns I
and III Probit Regression(Dependent Variable 1
if accept)
ME .11
ME .24
ME -.16
ME -.07
ME .14
ME .17
ME .01
ME -.03
22
Possible Explanations for Negative Coefficient
Estimate Associated with Submit SATI

• For those who dont submit, school might be
  overestimating their score
• Not submitting may be correlated with error term
  applicants who do not submit are more mature
  or are athletes.
• School is behaving strategically when deciding
  who to accept.

23
Colleges Acceptance Decision Table 3 Columns I
and III (cont.)
ME .08
ME .05
ME -.21
ME .12
Note High School GPA B is omitted category
24
Colleges Acceptance Decision Table 3 Columns I
and III (cont.)
ME .29
ME .12
ME .58
ME .44
ME -.10
ME -.03
ME .48
ME .55
Note White is omitted category
25
Is the college more likely to accept Applicant A
or Applicant B if influenced by Ranking
Organizations?

• Applicant A
• White, Female, HS GPA is A-, Class Rank in top
  10, Private High School, Legacy, Submitted SATII
  of 600, Submitted SAT I of 1400.
• Applicant B
• White, Female, HS GPA is A-, Class Rank in top
  10, Private High School, Legacy, Submitted SATII
  of 600, Did not Submitted SAT I but college
  infers an SAT I score of 1400 (based on
  observables to college).

26
Is the college more likely to accept Applicant C
or Applicant D if influenced by Ranking
Organizations?

• Applicant C
• White, Female, HS GPA is B, Class Rank in top
  quintile, Private High School, Legacy, Submitted
  SATII of 550, Submitted SAT I of 1100.
• Applicant D
• White, Female, HS GPA is B, Class Rank is top
  quintile, Private High School, Legacy, Submitted
  SATII of 550, Did not Submitted SAT I but college
  infers an SAT I score of 1100 (based on
  observables to college).

27
Colleges Acceptance Decision Table 3 Columns
II and IV Probit Regression
ME .09
ME .03
28
Colleges Acceptance Decision Table 4
Predicted rather than Actual SAT I Score
In the spirit of Eyster Rabins fully cursed
equilibrium.
29
Interpretation of Point Estimates

• College X
• An applicant who scores a 1,000 on the SAT I
  score decreases her probability of being accepted
  by 9.7 percentage points if she submits her score
  while an applicant who scores a 1,500 increases
  her probability of being accepted by 3.8
  percentage points if she submits.
• College Y
• An applicant who scores a 1,000 on the SAT I
  score decreases her probability of being accepted
  by 16.8 percentage points if she submits her
  score while an applicant who scores a 1,500
  increases her probability of being accepted by
  12.6 percentage points if she submits.

30
Interpretation of Point Estimates

• College X
• Applicants who submit their SAT I score are
  less likely to be accepted by College X if their
  SAT I score is less than 1,392 and are more
  likely to be accepted if their score is greater
  than 1,392.
• College Y
• Applicants who submit their SAT I score are less
  likely to be accepted if their SAT I score is
  less than 1,272 and are more likely to be
  accepted if their score is greater than 1,272.

31
Possible Explanations for Negative Coefficient
Estimate Associated with Submit SATI

• For those who dont submit, school might be
  overestimating their score
• Not submitting may be correlated with error term
  applicants who do not submit are more mature
  or are athletes.
• School is behaving strategically when deciding
  who to accept.

32
Submission on College X PerformanceTable 5B
33
Applicants Disclosure Decisions Table 2
34
Figure 2 Predicted versus Actual SAT I Score
for those who Chose not to Submit
35
Figure 2 Predicted versus Actual SAT I Score
for those who Chose not to Submit
36
Conclusions from Reduced Form

• College admission departments are behaving
  strategically by more (less) likely accepting
  applicants who do not submit their SAT I scores
  if submitting their scores would decrease
  (increase) the average SAT I score the colleges
  report to the ranking organizations.
• 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.
• Note that the reduced form estimates do not
  address directly the colleges inference for
  those applicants who do not submit.

37
Model and Structural Estimation
38
Summary Statistics for College X
N895
N122
N5216
N324
39
Summary Statistics for College Y
N294
N83
N2440
N785
40
Notation

• µ(Xi)eap een ,expected utility from attending
  the college for applicant i
• µ(Xi) is portion of the applicant specific
  preferences for attending College X that depends
  on the observables variable.
• eap is unobservable applicant specific
  preferences for attending College X that is known
  to the applicant at the time she submits her
  application.
• een is unobservable applicant specific
  preferences for attending College X that is known
  to the applicant at the time she makes enrollment
  decision but not at time she submits her
  application

41
Notation (cont)

• UR ,expected utility if applicant does not attend
  College X and does not apply early decision at
  College X.
• UR-C , expected utility if applicant does not
  attend College X and does apply early decision at
  College X.
• K , fixed cost of applying
• een , unobserved cost of submitting SAT I

42
Applicants Decision to apply early decision
and/or submit SAT I

• Expected Utility if applicant applies early and
  submits
• Pa(X,ed,s) Pe(X,ed,s) µ(X)eapeen
• 1-Pa(X,ed,s) Pe(X,ed,s)UR-C-K- es
• Expected Utility if applicant doesnt apply early
  or submit
• Pa(X,ned,ns) Pe(X,ned,ns) µ(X)eapeen
• 1-Pa(X,ned,ns) Pe(X,ned,ns)UR-K
• Apply early, dont submit and Dont apply early,
  submit are analogous

43
Applicant applies early decision and submits
assuming E(een)0 if

• es ?1eap gt ?1-µ(X)C ,
• ?2eap gt ?2-µ(X)1- Pa(X,ed,ns)Pe(X,ed,ns)
  C
• and
• es?3eap gt ?3-µ(X)1Pa(X,ed,ns)Pe(X,ed,ns)
  C
• ?1Pa(X,ed,ns)Pe(X,ed,ns)-Pa(X,ed,s)Pe(X,ed,s),
• ?2Pa(X,ed,ns)Pe(X,ed,ns)-Pa(X,ned,ns)Pe(X,
  ned,ns)
• ?3Pa(X,ed,ns)Pe(X,ed,ns)-Pa(X,ned,s)Pe(X,ned,s)

44
Whether to Apply Early Decision and/or Submit
SATI Score
45
Literature on College Objective Function

• Ehrenberg (1999) single well-defined objective
  function may explain fairly well the behavior of
  small liberal arts colleges (page 101).
• Epple, Romano, and Seig (2006) GE model
• assume a school maximizes quality (average
  quality of the student body, school expenditure
  per student, and the mean income of the student
  body)
• s.t. balanced budget constraint and a fixed
  student body size.
• Our Model
• To account for the colleges concern for the
  quality of its current and future students and
  the understanding that future student quality
  depends on the colleges ranking, we allow the
  colleges objective function to depend on the
  perceived ability of the incoming students, the
  reported ability of these students, and the
  demographic characteristics of the student body.

46
Colleges Decision to Accept Applicant

• College accepts applicant i if
• Pe(Xi,k,l) ?P(XiP)eqi ?R(XiR) ?D(XiD)
• (1- Pe(Xi,k,l)) ?P(X-iP) ?R(X-iR) ?D(X-iD)
• gt ?P(XriP) ?R(XriR) ?D(XriD)

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