Student Quality and Reported Student Quality: Higher Education Admissions Decisions Michael Conlin Michigan State University Stacy Dickert-Conlin Michigan

Student Quality and Reported Student Quality: Higher Education Admissions Decisions

Michael Conlin Michigan State UniversityStacy Dickert-Conlin Michigan State UniversityJeffrey Wooldridge Michigan State UniversityGabrielle Chapman Syracuse University

University of Wisconsin – May 1, 2007

Overview

Introduction to policy and goals Data Reduced form Model Future Work

Optional SAT Policies

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


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

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. (Bruno, 2006)

Research Questions

How much does a school attempt to maximize the quality of their student body compared to the reported quality of their student body?

How would the composition of the student body change if the schools did not consider rankings when making admission decisions?

Key: Use optional SAT Policy as means to identify

How does this policy inform the voluntary disclosure literature?

Data

Application data for 2 liberal arts schools in the 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.

College Board Data

SAT scores for those who elected not to submit them to the college.

Student Descriptive Questionnaire (SDQ) SAT II ScoresSelf Reported incomeHigh school GPAHigh school activities

Optional SAT I policies

College X required applicants to choose between submitting the ACT scores or three SAT II: Subject Tests must submit one of the above if do submit SATI

scores 15.3 percent of the 7023 applicants choose option

At College Y, must submit SAT II ACT three Advanced Placement (AP) exams or a combination of the above testing requirements. 24.1 percent of the 3054 applicants choose option

Voluntary Disclosure Models with Zero Disclosure Costs Example: Student i with given

characteristics has the following probability distribution in term of SAT I scores:

School knows distribution of SAT I scores and applies Bayes Rule when inferring an SAT score for a student who doesn’t report.

Bayesian Nash Equilibrium results in every type except the worst revealing and the worst being indifferent between revealing and not revealing.

SAT I Score Probability

1300 0.2

1200 0.4

1100 0.3

1000 0.1

Voluntary Disclosure Models with Zero Disclosure Costs

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 lowest SAT I scores do not disclose.

Eyster and Rabin (Econometrica, 2005) propose a new equilibrium concept which they call cursed equilibrium.

Table 1College XN=7,023

College YN=3,504

Consider Not Consider SS Consider Not Consider

SS

Income Missing (sr) 0.453(0.498)

0.462(0.499)

0.559(0.497)

0.559(0.497)

Income <50K (sr) 0.092(0.289)

0.114(0.318)

**0.076

(0.264)0.097

(0.296)**

50K <Income <100K (sr)

0.186(0.390)

0.191(0.393)

0.159(0.366)

0.129(0.335)

**

SAT1 Score 1272(124)

1137(113)

***1267(144)

1229(120)

***

Female Student 0.657(0.475)

0.777(0.416)

***0.487

(0.500)0.548

(0.498)***

White 0.836(0.370)

0.832(0.374)

0.877(0.328)

0.859(0.348)

Attended Private HS 0.475(0.499)

0.507(0.500)

*0.353

(0.478)0.431

(0.495)***

From State where College resides

0.132(0.339)

0.122(0.328)

0.335(0.472)

0.254(0.436)

***

From Northeast 0.638(0.481)

0.600(0.491)

**0.498

(0.500)0.568

(0.496)***

N 5883 1072 2659 845

Table 1College XN=7,023

College YN=3,504

Considr Not Consider SS Consider Not Consider

SS


0.462(0.499)

0.559(0.497)

0.559(0.497)

Income <50K (sr) 0.092(0.289)

0.114(0.318)

**0.076

(0.264)0.097

(0.296)**

50K <Income <100K (sr)

0.186(0.390)

0.191(0.393)

0.159(0.366)

0.129(0.335)

**

SAT1 Score 1272(124)

1137(113)

***1267(144)

1229(120)

***


0.777(0.416)

***0.487

(0.500)0.548

(0.498)***

White 0.836(0.370)

0.832(0.374)

0.877(0.328)

0.859(0.348)

Attended Private HS 0.475(0.499)

0.507(0.500)

*0.353

(0.478)0.431

(0.495)***


0.132(0.339)

0.122(0.328)

0.335(0.472)

0.254(0.436)

***

From Northeast 0.638(0.481)

0.600(0.491)

**0.498

(0.500)0.568

(0.496)***

N 5883 1072 2659 845

Table 2College X College Y

Consider SAT I

Do Not Consider SAT I

SS Consider SAT I

Do Not Consider

SAT I

SS

SAT I Score (1600) – all applicants

1272(124)[5883]

1137(112)[1072]

*** 1267(144)[2659]

1229(120)[845]

***

Predicted SAT I Score* (based on those that

submitted)

1272 (88)

[5879]

1224#

(79)[1072]

*** 1262 (77)

[2659]

1258#

(79) [845]

Probability of Acceptance .417(0.493)[5883]

.392(0.488)[1072]

.445(0.497)[2659]

.488(0.500)[845]

**

SAT I Score conditional on Acceptance

1323(110)[2456]

1171(98)[421]

*** 1344(115)[1182]

1260(103)[412]

***

Probability of Enrolling if Accepted

.294(0.455)[2456]

.451(0.498)[421]

*** .297(0.457)[1182]

.328(0.470)[412]

SAT I Score conditional on Enrollment

1281 (107)[725]

1155(99)[190]

*** 1299 (114)[351]

1227 (97)[135]

***

Freshman GPA(4.0 Scale for College X;

100 Scale for College Y)

3.29(0.428)[721]

3.26(0.392)[190]

84.9(5.4)[334]

84.7(5.2)[132]

Reduced Form

Student’s Decisions:Submit SAT I and Apply EarlyEnroll

College’s Decisions:AdmitFinancial Aid Grant

Followup – Freshman GPA

Table 3Linear Probability - SUR(Dependent variable Submit SAT = 1)(Dependent variable Apply Early = 1)

College X College Y

Not Consider

ed

Early Not conside

red

Early

Income Missing (sr) 0.025**(0.012)

-0.0003(0.009)

0.007(0.022)

0.002(0.018)

Income <50K (sr) -0.013(0.016)

-0.007(0.012)

0.070**(0.031)

0.005(0.023)

50K <Income <100K (sr) 0.014(0.013)

-0.002(0.010)

-0.002(0.025)

0.009(0.018)

Intend to Apply for Financial Aid -0.012(0.009)

-0.021***(0.007)

-0.062***(0.016)

-0.047***(0.012)

SAT1 Score/100 -0.128***(0.004)

-0.010***(0.003)

-0.081***(0.007)

-0.023***(0.005)

SAT2 Score(s) available (1=yes) -0.301***(0.053)

0.032(0.040)

-0.520***(0.091)

0.178***(0.067)

Average SAT2/100*SAT2 Score(s) available (1=yes)

0.052***(0.009)

-0.007(0.006)

0.106***(0.015)

-0.028***(0.011)

_Constant 1.628***(0.059)

0.212***(0.044)

1.145***(0.097)

0.471***(0.071)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08

Table 3Linear Probability (Dependent variable Submit SAT = 1)(Dependent variable Apply Early = 1)

College X College Y

Not Considered

Early Not considered

Early

No High School GPA reported (sr) 0.018(0.019)

0.009(0.014)

0.025(0.033)

-0.020(0.024)

HS GPA A+ (SR) 0.062***(0.024)

-0.023(0.018)

0.007(0.041)

-0.067**(0.030)

HS GPA A (sr) 0.069***(0.017)

-0.011(0.013)

0.027(0.032)

-0.010(0.023)

HS GPA A- (sr) 0.041***(0.015)

-0.014(0.011)

0.060**(0.030)

-0.036(0.022)

HS GPA B+ (SR) -0.004(0.016)

0.014(0.012)

0.067**(0.030)

-0.014(0.022)

HS GPA B- (SR) -0.029(0.029)

0.014(0.022)

-0.102*(0.056)

-0.007(0.041)

HS GPA C or below (sr) -0.109**(0.054)

0.015(0.040)

-0.161*(0.093)

-0.063(0.068)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08


College X College Y

Not Consid

ered

Early Not conside

red

Early

Female Student 0.033***(0.009)

-0.009(0.007)

0.033**(0.014)

-0.022**(0.011)

African American -0.113***(0.025)

-0.042**(0.019)

0.036(0.041)

-0.094***(0.030)

Native American 0.051(0.067)

0.078(0.050)

-0.002(0.157)

0.026(0.114)

Asian American -0.011(0.020)

-0.035**(0.015)

-0.041(0.032)

-0.052**(0.024)

Hispanic -0.066(0.021)

0.000(0.016)

-0.001(0.038)

-0.067**(0.028)

Unknown Race 0.001(0.019)

-0.030**(0.014)

Legacy (1=yes) 0.012(0.026)

0.043**(0.020)

-0.034(0.029)

0.068***(0.022)

Attended Private HS 0.021**(0.009)

-0.011(0.007)

0.042***(0.016)

-0.012(0.012)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08


College X College Y

Not Consid

ered

Early Not conside

red

Early

Filled in College Board Survey (sdq) 0.046***(0.016)

0.010(0.012)

-0.009(0.034)

-0.035*(0.021)

# of HS Extracurricular Activities (sr)*Filled in sdq

-0.001(0.002)

0.001(0.001)

-0.003(0.004)

0.003(0.003)

# of HS sports (sr)*Filled in sdq 0.003(0.003)

0.001(0.002)

0.004(0.005)

0.007**(0.004)

# of HS offices/awards (sr)*Filled in sdq

0.002(0.003)

0.001(0.002)

-0.010*(0.006)

0.005(0.005)

# of HS honors classes (sr)*Filled in sdq

0.000(0.001)

0.000(0.001)

0.005**(0.002)

-0.002(0.002)

_Constant 1.628***(0.059)

0.212***(0.044)

1.145***(0.097)

0.471***(0.071)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08

Table 3Linear Probability - SUR(Dependent variable Submit SAT = 1)(Dependent variable Apply Early = 1)

College X College Y

Not Consider

ed

Early Not conside

red

Early

Income Missing (sr) 0.025**(0.012)

-0.0003(0.009)

0.007(0.022)

0.002(0.018)

Income <50K (sr) -0.013(0.016)

-0.007(0.012)

0.070**(0.031)

0.005(0.023)

50K <Income <100K (sr) 0.014(0.013)

-0.002(0.010)

-0.002(0.025)

0.009(0.018)

Intend to Apply for Financial Aid -0.012(0.009)

-0.021***(0.007)

-0.062***(0.016)

-0.047***(0.012)

SAT1 Score/100 -0.128***(0.004)

-0.010***(0.003)

-0.081***(0.007)

-0.023***(0.005)


0.032(0.040)

-0.520***(0.091)

0.178***(0.067)


0.052***(0.009)

-0.007(0.006)

0.106***(0.015)

-0.028***(0.011)

_Constant 1.628***(0.059)

0.212***(0.044)

1.145***(0.097)

0.471***(0.071)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08


College X College Y

Not Considered

Early Not considered

Early


0.009(0.014)

0.025(0.033)

-0.020(0.024)

HS GPA A+ (SR) 0.062***(0.024)

-0.023(0.018)

0.007(0.041)

-0.067**(0.030)

HS GPA A (sr) 0.069***(0.017)

-0.011(0.013)

0.027(0.032)

-0.010(0.023)

HS GPA A- (sr) 0.041***(0.015)

-0.014(0.011)

0.060**(0.030)

-0.036(0.022)

HS GPA B+ (SR) -0.004(0.016)

0.014(0.012)

0.067**(0.030)

-0.014(0.022)

HS GPA B- (SR) -0.029(0.029)

0.014(0.022)

-0.102*(0.056)

-0.007(0.041)

HS GPA C or below (sr) -0.109**(0.054)

0.015(0.040)

-0.161*(0.093)

-0.063(0.068)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08


College X College Y

Not Consid

ered

Early Not conside

red

Early


-0.009(0.007)

0.033**(0.014)

-0.022**(0.011)


-0.042**(0.019)

0.036(0.041)

-0.094***(0.030)


0.078(0.050)

-0.002(0.157)

0.026(0.114)


-0.035**(0.015)

-0.041(0.032)

-0.052**(0.024)

Hispanic -0.066(0.021)

0.000(0.016)

-0.001(0.038)

-0.067**(0.028)

Unknown Race 0.001(0.019)

-0.030**(0.014)

Legacy (1=yes) 0.012(0.026)

0.043**(0.020)

-0.034(0.029)

0.068***(0.022)

Attended Private HS 0.021**(0.009)

-0.011(0.007)

0.042***(0.016)

-0.012(0.012)

N 6951 6951 3504 3504

R2 0.16 0.014 0.04 0.08

TABLE 4Linear Probability (Dependent variable Accepted = 1)

College X College Y

Applied Early Admission 0.508***(0.020)

0.510***(0.020)

0.345***(0.023)

0.346***(0.023)

Income <50K (sr) 0.092***(0.021)

0.093***(0.021)

-0.037(0.031)

-0.039(0.031)

50K <Income <100K (sr) 0.037**(0.016)

0.040**(0.016)

-0.039(0.025)

-0.038(0.025)

Intend to Apply for Financial Aid -0.020*(0.012)

-0.020*(0.012)

-0.053***(0.016)

-0.052***(0.016)

SAT1 Score/100 0.079***(0.006)

0.055***(0.012)

0.135***(0.007)

0.056**(0.028)

Requested school use SAT1 Score -0.114***(0.015)

-0.424***(0.143)

-0.141***(0.052)

-1.102***(0.326)

Requested school use SAT1 Score* SAT1 Score/100

0.027**(0.012)

0.083***(0.028)


-0.345***(0.127)

-0.803***(0.091)

-0.795***(0.093)


0.133***(0.011)

0.059***(0.021)

0.137***(0.015)

0.135***(0.015)

Requested school use SAT2 Score -0.003(0.017)

-0.526***(0.132)

-0.119**(0.056)

-0.543*(0.324)


0.088***(0.022)

0.026(0.018)

N 6951 6951 3504 3504

R2 0.28 0.28 0.34 0.34


College X College Y

No High School GPA reported (sr)

0.132***(0.024)

0.132***(0.024)

0.115***(0.032)

0.115***(0.032)

HS GPA A+ (SR) 0.346***(0.031)

0.345***(0.031)

0.308***(0.040)

0.302***(0.040)

HS GPA A (sr) 0.292***(0.021)

0.295***(0.021)

0.267***(0.031)

0.265***(0.031)

HS GPA A- (sr) 0.203***(0.019)

0.205***(0.019)

0.186***(0.030)

0.184***(0.030)

HS GPA B+ (SR) 0.106***(0.020)

0.107***(0.020)

0.113***(0.030)

0.112***(0.030)

HS GPA B- (SR) -0.089**(0.037)

-0.089**(0.037)

-0.020(0.056)

-0.029(0.056)

HS GPA C or below (sr) -0.112(0.069)

-0.108(0.069)

0.082(0.092)

0.086(0.092)

N 6951 6951 3504 3504

R2 0.28 0.28 0.34 0.34


College X College Y

Female Student -0.163***(0.011)

-0.163***(0.011)

0.087***(0.014)

0.086***(0.014)

African American 0.387***(0.032)

0.387***(0.032)

0.504***(0.040)

0.499***(0.040)


0.085(0.084)

0.251(0.155)

0.252(0.155)

Asian American 0.154***(0.025)

0.154***(0.025)

0.289***(0.032)

0.287***(0.032)

Hispanic 0.141***(0.027)

0.139***(0.027)

0.406***(0.038)

0.402***(0.038)

Unknown Race -0.081***(0.023)

-0.079***(0.023)

Legacy (1=yes) 0.204***(0.033)

0.202***(0.033)

0.074**(0.029)

0.075***(0.029)

Attended Private HS 0.031***(0.011)

0.031***(0.011)

0.049***(0.016)

0.050***(0.016)


College X College Y


0.017(0.015)

0.017(0.015)

0.016(0.017)

0.017(0.017)

From Midwest 0.106***(0.024)

0.112***(0.024)

-0.019(0.035)

-0.013(0.035)

From West -0.007(0.019)

-0.004(0.019)

0.008(0.028)

0.007(0.028)

From South -0.031*(0.018)

-0.031*(0.018)

0.121***(0.032)

0.119***(0.032)

Filled in College Board Survey 0.034*(0.021)

0.034(0.021)

-0.040(0.025)

-0.040(0.025)

# of HS Extracurricular Activities (sr)*Filled in College Board Survey

0.004*(0.002)

0.004*(0.002)

-0.006(0.004)

-0.005(0.004)

# of HS sports (sr)*Filled in sdq -0.007**(0.003)

-0.007**(0.003)

0.006(0.005)

0.005(0.005)


0.008**(0.004)

0.009**(0.004)

0.003(0.006)

0.003(0.006)


0.003**(0.001)

0.003**(0.001)

0.004**(0.002)

0.004*(0.002)

_Constant -0.732***(0.076)

-0.463***(0.141)

-1.409***(0.106)

-0.490(0.326)

N 6951 6951 3504 3504

R2 0.28 0.28 0.34 0.34

TABLE 5 – Tobit – College Y only(Financial Aid Award|Accepted)Applied Early Admission 2248*

(1151)1678

(1352)

Income Missing (sr) 7467***(1223)

10547***(1425)

Income <50K (sr) 15652***(1615)

23783***(1997)

50K <Income <100K (sr) 9737***(1278)

16903***(1536)

Intend to Apply for Financial Aid 23914***(1062)

SAT1 Score/100 792(1495)

544(1802)

Requested school use SAT1 Score 2474(18073)

1077(22004)


-49(1503)

45(1816)

SAT2 Score(s) available (1=yes) 737(945)

-922(1130)

Requested school use SAT2 Score 6468(17456)

11439(21168)


-427(938)

-788(1127)

N 1594 1594

R2 0.07 0.03

TABLE 5 – Tobit – College Y only (Financial Aid Award|Accepted)

No High School GPA reported (sr) -3073(2372)

-2148(2744)

HS GPA A+ (SR) -292(2367)

8427***(2805)

HS GPA A (sr) 98(2180)

5466**(2557)

HS GPA A- (sr) -2679(2188)

911(2554)

HS GPA B+ (SR) -3831(2326)

-2890(2683)

HS GPA B- (SR) -3300(4908)

640(5781)

HS GPA C or below (sr) 11220(11801)

8594(15226)

N 1594 1594

R2 0.07 0.03

TABLE 5 – Tobit – College Y only (Financial Aid Award|Accepted)

Female Student 142(758)

-20(902)

African American 3728**(1876)

11866***(2373)

Native American -285(6417)

2350(7842)

Asian American 4507***(1375)

7090***(1686)

Hispanic 6644***(1685)

12556***(2066)

Legacy (1=yes) 1469(1528)

-1280(1814)

Attended Private HS -2591***(865)

-5665***(1023)

From State where College resides 684(860)

-26(1033)

From Midwest 321(1888)

-891(2227)

From West -1094(1568)

-3284*(1829)

From South -498(1671)

-3210(1988)

_Constant -31521*(18315)

-16807(22150)

TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted)

College X College Y

Applied Early Admission 0.679***(0.022)

0.659***(0.029)


0.051*(0.028)

Income <50K (sr) 0.078***(0.029)

0.007(0.046)

50K <Income <100K (sr) 0.020(0.023)

-0.026(0.034)

Intend to Apply for Financial Aid 0.022(0.017)

0.004(0.021)

SAT1 Score/100 -0.058***(0.009)

-0.049*(0.027)

Did not want SAT1 considered -0.029(0.023)

-0.038***(0.012)

SAT2 Score(s) available (1=yes) 0.280**(0.109)

0.130***(0.040)


-0.040**(0.017)

0.236(0.147)

Wanted SAT II considered -0.017(0.025)

-0.034(0.022)

N 2876 1594

R2 0.35 0.36


College X College Y

No High School GPA reported (sr) -0.058(0.039)

-0.111**(0.056)

HS GPA A+ (SR) -0.114***(0.043)

-0.126**(0.060)

HS GPA A (sr) -0.071**(0.036)

-0.151***(0.053)

HS GPA A- (sr) -0.076**(0.034)

-0.130**(0.052)

HS GPA B+ (SR) -0.010(0.035)

-0.062(0.054)

HS GPA B- (SR) 0.134(0.085)

0.052(0.128)

HS GPA C or below (sr) -0.165(0.193)

0.609(0.383)

N 2876 1594

R2 0.35 0.36


College X College Y


0.009(0.019)


-0.118**(0.057)

Native American 0.213*(0.127)

0.627***(0.189)

Asian American -0.115***(0.033)

-0.068*(0.038)

Hispanic -0.171***(0.038)

-0.095**(0.048)

Unknown Race -0.011(0.036)

Legacy (1=yes) 0.057(0.037)

0.034(0.038)

Attended Private HS -0.045***(0.016)

-0.074***(0.022)

From State where College resides -0.006(0.022)

0.025(0.023)

From Midwest -0.013(0.032)

0.042(0.045)

From West 0.008(0.026)

-0.034(0.036)

From South -0.032(0.025)

-0.016(0.040)


College X College Y

Filled in College Board Survey -0.010(0.030)

-0.012(0.034)


0.0004(0.003)

0.010**(0.005)

# of HS sports (sr)*Filled in sdq -0.003(0.004)

-0.0001(0.007)

# of HS offices/awards (sr)*Filled in sdq -0.008(0.005)

-0.010(0.008)

# of HS honors classes (sr)*Filled in sdq -0.001(0.002)

-0.003(0.003)

_Constant 1.060***(0.128)

0.808***(0.182)

N 2876 1594

R2 0.35 0.36

TABLE 7 – OLS Freshman GPA

College X(4.0 Scale)

College Y(100 point scale)

Applied Early Admission -0.011(0.026)

-0.600(0.506)

Income Missing (sr) -0.028(0.036)

-0.096(0.707)

Income <50K (sr) -0.078(0.049)

-2.631**(1.224)

50K <Income <100K (sr) -0.025(0.041)

-1.619*(0.894)

Intend to Apply for Financial Aid 0.080***(0.030)

0.392(0.692)

Financial Aid Grant 0.00002(0.00004)

SAT1 Score/100 0.038**(0.016)

0.362(0.313)

Did not want SAT1 considered 0.046(0.035)

0.775(0.673)

Requested school use SAT2 Score 0.050(0.042)

-0.106(0.894)


-9.150**(3.584)


0.088***(0.029)

1.571***(0.564)

TABLE 7 – OLS Freshman GPA College X

(4.0 Scale)College Y

(100 point scale)


1.340(1.169)

HS GPA A+ (SR) 0.327***(0.082)

5.102***(1.450)

HS GPA A (sr) 0.310***(0.056)

4.581***(1.099)

HS GPA A- (sr) 0.124**(0.053)

2.737**(1.081)

HS GPA B+ (SR) 0.101*(0.052)

2.006*(1.050)

HS GPA B- (SR) -0.280**(0.110)

3.073(2.366)

HS GPA C or below (sr) 0.262(0.267)

5.689(5.267)


1.282***(0.472)


0.450(1.622)

Native American -0.289*(0.154)

-7.792***(2.897)


-0.573(1.173)

Hispanic -0.407***(0.077)

-2.745**(1.360)

Unknown Race -0.089(0.067)

TABLE 7 – OLS Freshman GPA

College X(4.0 Scale)

College Y(100 point scale)

Filled in College Board Survey

0.004(0.053)

-0.897(0.851)


0.003(0.006)

0.158(0.118)

# of HS sports (sr)*Filled in sdq

-0.009(0.008)

-0.343**(0.161)


-0.002(0.010)

-0.028(0.208)


-0.005(0.003)

0.038(0.072)

_Constant 2.567***(0.212)

77.555***(4.319)

N 908 466

R2 0.281 0.263

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• students are matched with institutions of higher education, • how financial aid packages are selected for different students, and • how educational expenditures vary across schools.

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.

Ours allows uncertainty associated with student body size Our objective function

• reported average student body quality • gender and racial compositions of the student body

College’s Objective Function The Liberal Art Colleges make

decisions to maximize the mean quality of the student body in current and subsequent years

The school decides whether to admit each student i=1…N and how much financial aid to offer student i (fai) in order to maximize the objective function

Ψi is probability student i is admitted and attends P, sticker price of college fai, financial aid offered to student i ΛP is the perceived average ability of the incoming

students, ΛR is the reported average ability of the incoming

students γ is the weight the college places on perceived quality

relative to reported quality f(Ω) is a function of the demographic characteristics of

the student body.

N

i

RPii fCfaP

`1

1

N

iiipP

P z`1

N

i

RPii fCfaP

`1

1

RRR z

zf

Student’s maximization problem

Whether or not to apply early decision Whether or not to submit SAT I score

Ψi is probability student i is admitted and attends

WTPi is student i’s willingness to pay to attend the school

Csub,I is i’s cost of submitting her SAT I score

isubiiiii CfaPWTPfaPWTP ,

Ψi (early decision, submit SAT I)

isubiiiii CfaPWTPfaPWTP ,

iwtpiwtpiwtpwtpi vzWTP ,,,

iCiCCisub zC ,,,

Conclusions

Students are strategic: Lower actual SAT I scores more likely to choose option Same students have higher predicted scores

Colleges are strategic: Colleges are less likely to admit students who submit their SAT I scores, unless their SAT I scores are particularly high Suggestive of maximizing reported quality

College goals appear to include diversity

Future Work

Estimate Model to determine the weight the college places on perceived quality relative to reported quality (γ).

Simulate the Model to determine how admissions would change if γ = 1 and how the admissions changes affect quality of student body.

Estimate how school infers SAT score for a student who doesn’t report (Bayesian Nash Equilibrium or Cursed Equilibrium?)

Documents

Student Quality and Reported Student Quality: Higher Education Admissions Decisions Michael Conlin Michigan State University Stacy Dickert-Conlin Michigan