1. Student Quality and Reported Student Quality: Higher Education Admissions Decisions Michael Conlin Michigan State University Stacy Dickert-Conlin Michigan State University Jeffrey Wooldridge Michigan State University Gabrielle Chapman Syracuse University University of Wisconsin – May 1, 2007

2. Overview Introduction to policy and goals Data Reduced form Model Future Work

3. 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)

4. 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 Report’s college rankings.” Colin Driver, President of Reed College, New York Times, 2006

5. 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

6. 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)

7. 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?

8. 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.

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

10. 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

11. 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 ScoreProbability 13000.2 12000.4 11000.3 10000.1

12. 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.

13. Table 1 College X N=7,023 College Y N=3,504 ConsiderNot ConsiderSSConsiderNot Consi der 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) *** N588310722659845

14. Table 1 College X N=7,023 College Y N=3,504 ConsidrNot ConsiderSSConsiderNot Consi der 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) *** N588310722659845

15. Table 2 College XCollege Y Consider SAT I Do Not Consider SAT I SSConsider 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]

16. Reduced Form Student’s Decisions: Submit SAT I and Apply Early Enroll College’s Decisions: Admit Financial Aid Grant Followup – Freshman GPA

17. Table 3 Linear Probability - SUR (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consider ed EarlyNot 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) _Constant1.628*** (0.059) 0.212*** (0.044) 1.145*** (0.097) 0.471*** (0.071) N6951 3504 R2R2 0.160.0140.040.08

18. Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consid ered EarlyNot consid ered 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) N6951 3504 R2R2 0.160.0140.040.08

19. Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consid ered EarlyNot conside red Early Female Student0.033*** (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 American0.051 (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 Race0.001 (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 HS0.021** (0.009) -0.011 (0.007) 0.042*** (0.016) -0.012 (0.012) N6951 3504 R2R2 0.160.0140.040.08

20. Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consid ered EarlyNot 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 sdq0.003 (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) _Constant1.628*** (0.059) 0.212*** (0.044) 1.145*** (0.097) 0.471*** (0.071) N6951 3504 R2R2 0.160.0140.040.08

21. Table 3 Linear Probability - SUR (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consider ed EarlyNot 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) _Constant1.628*** (0.059) 0.212*** (0.044) 1.145*** (0.097) 0.471*** (0.071) N6951 3504 R2R2 0.160.0140.040.08

22. Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consid ered EarlyNot consid ered 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) N6951 3504 R2R2 0.160.0140.040.08

23. Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College XCollege Y Not Consid ered EarlyNot conside red Early Female Student0.033*** (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 American0.051 (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 Race0.001 (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 HS0.021** (0.009) -0.011 (0.007) 0.042*** (0.016) -0.012 (0.012) N6951 3504 R2R2 0.160.0140.040.08

24. TABLE 4 Linear Probability (Dependent variable Accepted = 1) College XCollege Y Applied Early Admission0.508*** (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/1000.079*** (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) SAT2 Score(s) available (1=yes)-0.779*** (0.068) -0.345*** (0.127) -0.803*** (0.091) -0.795*** (0.093) Average SAT2/100*SAT2 Score(s) available (1=yes) 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) Requested school use SAT2 Score* SAT2 Score/100 0.088*** (0.022) 0.026 (0.018) N6951 3504 R2R2 0.28 0.34

25. TABLE 4 Linear Probability (Dependent variable Accepted = 1) College XCollege 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) N6951 3504 R2R2 0.28 0.34

26. TABLE 4 Linear Probability (Dependent variable Accepted = 1) College XCollege Y Female Student-0.163*** (0.011) -0.163*** (0.011) 0.087*** (0.014) 0.086*** (0.014) African American0.387*** (0.032) 0.387*** (0.032) 0.504*** (0.040) 0.499*** (0.040) Native American0.092 (0.084) 0.085 (0.084) 0.251 (0.155) 0.252 (0.155) Asian American0.154*** (0.025) 0.154*** (0.025) 0.289*** (0.032) 0.287*** (0.032) Hispanic0.141*** (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 HS0.031*** (0.011) 0.031*** (0.011) 0.049*** (0.016) 0.050*** (0.016)

27. TABLE 4 Linear Probability (Dependent variable Accepted = 1) College XCollege Y From State where College resides 0.017 (0.015) 0.017 (0.015) 0.016 (0.017) 0.017 (0.017) From Midwest0.106*** (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 Survey0.034* (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) # of HS offices/awards (sr)*Filled in sdq 0.008** (0.004) 0.009** (0.004) 0.003 (0.006) 0.003 (0.006) # of HS honors classes (sr)*Filled in sdq 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) N6951 3504 R2R2 0.28 0.34

28. TABLE 5 – Tobit – College Y only (Financial Aid Award|Accepted) Applied Early Admission2248* (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 Aid23914*** (1062) SAT1 Score/100792 (1495) 544 (1802) Requested school use SAT1 Score2474 (18073) 1077 (22004) Requested school use SAT1 Score* SAT1 Score/100 -49 (1503) 45 (1816) SAT2 Score(s) available (1=yes)737 (945) -922 (1130) Requested school use SAT2 Score6468 (17456) 11439 (21168) Requested school use SAT2 Score* SAT2 Score/100 -427 (938) -788 (1127) N1594 R2R2 0.070.03

29. 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) N1594 R2R2 0.070.03

30. TABLE 5 – Tobit – College Y only (Financial Aid Award|Accepted) Female Student142 (758) -20 (902) African American3728** (1876) 11866*** (2373) Native American-285 (6417) 2350 (7842) Asian American4507*** (1375) 7090*** (1686) Hispanic6644*** (1685) 12556*** (2066) Legacy (1=yes)1469 (1528) -1280 (1814) Attended Private HS-2591*** (865) -5665*** (1023) From State where College resides684 (860) -26 (1033) From Midwest321 (1888) -891 (2227) From West-1094 (1568) -3284* (1829) From South-498 (1671) -3210 (1988) _Constant-31521* (18315) -16807 (22150)

31. TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College XCollege Y Applied Early Admission0.679*** (0.022) 0.659*** (0.029) Income Missing (sr)0.010 (0.020) 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 Aid0.022 (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) Average SAT2/100*SAT2 Score(s) available (1=yes) -0.040** (0.017) 0.236 (0.147) Wanted SAT II considered-0.017 (0.025) -0.034 (0.022) N28761594 R2R2 0.350.36

32. TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College XCollege 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) N28761594 R2R2 0.350.36

33. TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College XCollege Y Female Student0.011 (0.015) 0.009 (0.019) African American-0.186*** (0.040) -0.118** (0.057) Native American0.213* (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 West0.008 (0.026) -0.034 (0.036) From South-0.032 (0.025) -0.016 (0.040)

34. TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College XCollege Y Filled in College Board Survey-0.010 (0.030) -0.012 (0.034) # of HS Extracurricular Activities (sr)*Filled in College Board Survey 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) _Constant1.060*** (0.128) 0.808*** (0.182) N28761594 R2R2 0.350.36

35. 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 Aid0.080*** (0.030) 0.392 (0.692) Financial Aid Grant0.00002 (0.00004) SAT1 Score/1000.038** (0.016) 0.362 (0.313) Did not want SAT1 considered0.046 (0.035) 0.775 (0.673) Requested school use SAT2 Score0.050 (0.042) -0.106 (0.894) SAT2 Score(s) available (1=yes)-0.529*** (0.1812) -9.150** (3.584) Average SAT2/100*SAT2 Score(s) available (1=yes) 0.088*** (0.029) 1.571*** (0.564)

36. TABLE 7 – OLS Freshman GPA College X (4.0 Scale) College Y (100 point scale) No High School GPA reported (sr)0.074 (0.060) 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) Female Student0.160*** (0.027) 1.282*** (0.472) African American-0.275*** (0.078) 0.450 (1.622) Native American-0.289* (0.154) -7.792*** (2.897) Asian American-0.109 (0.068) -0.573 (1.173) Hispanic-0.407*** (0.077) -2.745** (1.360) Unknown Race-0.089 (0.067)

37. 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) # of HS Extracurricular Activities (sr)*Filled in College Board Survey 0.003 (0.006) 0.158 (0.118) # of HS sports (sr)*Filled in sdq -0.009 (0.008) -0.343** (0.161) # of HS offices/awards (sr)*Filled in sdq -0.002 (0.010) -0.028 (0.208) # of HS honors classes (sr)*Filled in sdq -0.005 (0.003) 0.038 (0.072) _Constant2.567*** (0.212) 77.555*** (4.319) N908466 R2R2 0.2810.263

38. 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

39. 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 (fa i ) in order to maximize the objective function

40. Ψ i is probability student i is admitted and attends P, sticker price of college fa i, financial aid offered to student i Λ P is the perceived average ability of the incoming students, Λ R 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.

42. Student’s maximization problem Whether or not to apply early decision Whether or not to submit SAT I score

43. Ψ i is probability student i is admitted and attends WTP i is student i’s willingness to pay to attend the school C sub,I is i’s cost of submitting her SAT I score

44. Ψ i (early decision, submit SAT I)

45. 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

46. 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?)