Student Quality and Reported Student Quality Higher Education

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 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) ¢

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

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, 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 1200 s/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 Scores l Self Reported income l High school GPA l High school activities l

Optional SAT I policies ¢ ¢ College X required applicants to choose between submitting l the ACT scores l or three SAT II: Subject Tests l must submit one of the above if do submit SATI scores l 15. 3 percent of the 7023 applicants choose option At College Y, must submit l SAT II l ACT l three Advanced Placement (AP) exams or l a combination of the above testing requirements. l 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 1 College X N=7, 023 Consider Not Consider College Y N=3, 504 SS Consider Not SS Consi der Income Missing (sr) 0. 453 (0. 498) 0. 462 (0. 499) Income <50 K (sr) 0. 092 (0. 289) 0. 114 (0. 318) 50 K <Income <100 K (sr) 0. 186 (0. 390) 0. 191 (0. 393) 1272 (124) 1137 (113) Female Student 0. 657 (0. 475) 0. 777 (0. 416) White 0. 836 (0. 370) 0. 832 (0. 374) Attended Private HS 0. 475 (0. 499) 0. 507 (0. 500) From State where College resides 0. 132 (0. 339) 0. 122 (0. 328) From Northeast 0. 638 (0. 481) 0. 600 (0. 491) 5883 1072 SAT 1 Score N 0. 559 (0. 497) 0. 076 (0. 264) 0. 097 (0. 296) ** 0. 159 (0. 366) 0. 129 (0. 335) ** *** 1267 (144) 1229 (120) *** 0. 487 (0. 500) 0. 548 (0. 498) *** 0. 877 (0. 328) 0. 859 (0. 348) 0. 353 (0. 478) 0. 431 (0. 495) *** 0. 335 (0. 472) 0. 254 (0. 436) *** 0. 498 (0. 500) 0. 568 (0. 496) *** 2659 845 ** * **

Table 1 College X N=7, 023 Considr Not Consider College Y N=3, 504 SS Consider Not SS Consi der Income Missing (sr) 0. 453 (0. 498) 0. 462 (0. 499) Income <50 K (sr) 0. 092 (0. 289) 0. 114 (0. 318) 50 K <Income <100 K (sr) 0. 186 (0. 390) 0. 191 (0. 393) 1272 (124) 1137 (113) Female Student 0. 657 (0. 475) 0. 777 (0. 416) White 0. 836 (0. 370) 0. 832 (0. 374) Attended Private HS 0. 475 (0. 499) 0. 507 (0. 500) From State where College resides 0. 132 (0. 339) 0. 122 (0. 328) From Northeast 0. 638 (0. 481) 0. 600 (0. 491) 5883 1072 SAT 1 Score N 0. 559 (0. 497) 0. 076 (0. 264) 0. 097 (0. 296) ** 0. 159 (0. 366) 0. 129 (0. 335) ** *** 1267 (144) 1229 (120) *** 0. 487 (0. 500) 0. 548 (0. 498) *** 0. 877 (0. 328) 0. 859 (0. 348) 0. 353 (0. 478) 0. 431 (0. 495) *** 0. 335 (0. 472) 0. 254 (0. 436) *** 0. 498 (0. 500) 0. 568 (0. 496) *** 2659 845 ** * **

College X Table 2 College Y Consider SAT I Do Not Consider SAT I SS Consider 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] 3. 29 (0. 428) [721] 3. 26 (0. 392) [190] 84. 9 (5. 4) [334] 84. 7 (5. 2) [132] Freshman GPA (4. 0 Scale for College X; 100 Scale for College Do Not Consider SAT I SS ***

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

Table 3 Linear Probability - SUR (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consider ed College Y 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 <50 K (sr) -0. 013 (0. 016) -0. 007 (0. 012) 0. 070** (0. 031) 0. 005 (0. 023) 50 K <Income <100 K (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) SAT 1 Score/100 -0. 128*** (0. 004) -0. 010*** (0. 003) -0. 081*** (0. 007) -0. 023*** (0. 005) SAT 2 Score(s) available (1=yes) -0. 301*** (0. 053) 0. 032 (0. 040) -0. 520*** (0. 091) 0. 178*** (0. 067) Average SAT 2/100*SAT 2 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 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consid ered Early College Y Not 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) N 6951 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consid ered College Y 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 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consid ered College Y 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. 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 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability - SUR (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consider ed College Y 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 <50 K (sr) -0. 013 (0. 016) -0. 007 (0. 012) 0. 070** (0. 031) 0. 005 (0. 023) 50 K <Income <100 K (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) SAT 1 Score/100 -0. 128*** (0. 004) -0. 010*** (0. 003) -0. 081*** (0. 007) -0. 023*** (0. 005) SAT 2 Score(s) available (1=yes) -0. 301*** (0. 053) 0. 032 (0. 040) -0. 520*** (0. 091) 0. 178*** (0. 067) Average SAT 2/100*SAT 2 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 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consid ered Early College Y Not 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) N 6951 3504 R 2 0. 16 0. 014 0. 08

Table 3 Linear Probability (Dependent variable Submit SAT = 1) (Dependent variable Apply Early = 1) College X Not Consid ered College Y 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 3504 R 2 0. 16 0. 014 0. 08

TABLE 4 Linear 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 <50 K (sr) 0. 092*** (0. 021) 0. 093*** (0. 021) -0. 037 (0. 031) -0. 039 (0. 031) 50 K <Income <100 K (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. 053*** (0. 016) -0. 052*** (0. 016) SAT 1 Score/100 0. 079*** (0. 006) 0. 055*** (0. 012) 0. 135*** (0. 007) 0. 056** (0. 028) Requested school use SAT 1 Score -0. 114*** (0. 015) -0. 424*** (0. 143) -0. 141*** (0. 052) -1. 102*** (0. 326) Requested school use SAT 1 Score* SAT 1 Score/100 0. 027** (0. 012) 0. 083*** (0. 028) SAT 2 Score(s) available (1=yes) -0. 779*** (0. 068) -0. 345*** (0. 127) -0. 803*** (0. 091) -0. 795*** (0. 093) Average SAT 2/100*SAT 2 Score(s) available (1=yes) 0. 133*** (0. 011) 0. 059*** (0. 021) 0. 137*** (0. 015) 0. 135*** (0. 015) Requested school use SAT 2 Score -0. 003 (0. 017) -0. 526*** (0. 132) -0. 119** (0. 056) -0. 543* (0. 324) Requested school use SAT 2 Score* SAT 2 Score/100 0. 088*** (0. 022) 0. 026 (0. 018) N 6951 3504 R 2 0. 28 0. 34

TABLE 4 Linear Probability (Dependent variable Accepted = 1) College X College Y No High School GPA reported (sr) 0. 132*** (0. 024) 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. 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 3504 R 2 0. 28 0. 34

TABLE 4 Linear Probability (Dependent variable Accepted = 1) College X College Y Female Student -0. 163*** (0. 011) 0. 087*** (0. 014) 0. 086*** (0. 014) African American 0. 387*** (0. 032) 0. 504*** (0. 040) 0. 499*** (0. 040) Native American 0. 092 (0. 084) 0. 085 (0. 084) 0. 251 (0. 155) 0. 252 (0. 155) Asian American 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. 049*** (0. 016) 0. 050*** (0. 016)

TABLE 4 Linear Probability (Dependent variable Accepted = 1) College X College Y From State where College resides 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. 121*** (0. 032) 0. 119*** (0. 032) Filled in College Board Survey 0. 034* (0. 021) 0. 034 (0. 021) -0. 040 (0. 025) # of HS Extracurricular Activities (sr)*Filled in College Board Survey 0. 004* (0. 002) -0. 006 (0. 004) -0. 005 (0. 004) # of HS sports (sr)*Filled in sdq -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) # of HS honors classes (sr)*Filled in sdq 0. 003** (0. 001) 0. 004** (0. 002) 0. 004* (0. 002) -0. 732*** (0. 076) -0. 463*** (0. 141) -1. 409*** (0. 106) -0. 490 (0. 326) 6951 3504 _Constant N

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 <50 K (sr) 15652*** (1615) 23783*** (1997) 50 K <Income <100 K (sr) 9737*** (1278) 16903*** (1536) Intend to Apply for Financial Aid 23914*** (1062) SAT 1 Score/100 792 (1495) 544 (1802) Requested school use SAT 1 Score 2474 (18073) 1077 (22004) Requested school use SAT 1 Score* SAT 1 Score/100 -49 (1503) 45 (1816) SAT 2 Score(s) available (1=yes) 737 (945) -922 (1130) 6468 (17456) 11439 (21168) Requested school use SAT 2 Score* SAT 2 Score/100 -427 (938) -788 (1127) N 1594 Requested school use SAT 2 Score

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 R 2 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) -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) -31521* -16807 Attended Private HS _Constant

TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College X College Y Applied Early Admission 0. 679*** (0. 022) 0. 659*** (0. 029) Income Missing (sr) 0. 010 (0. 020) 0. 051* (0. 028) Income <50 K (sr) 0. 078*** (0. 029) 0. 007 (0. 046) 50 K <Income <100 K (sr) 0. 020 (0. 023) -0. 026 (0. 034) Intend to Apply for Financial Aid 0. 022 (0. 017) 0. 004 (0. 021) -0. 058*** (0. 009) -0. 049* (0. 027) Did not want SAT 1 considered -0. 029 (0. 023) -0. 038*** (0. 012) SAT 2 Score(s) available (1=yes) 0. 280** (0. 109) 0. 130*** (0. 040) Average SAT 2/100*SAT 2 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) SAT 1 Score/100

TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College X College Y -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 R 2 0. 35 0. 36 No High School GPA reported (sr)

TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College X College Y Female Student 0. 011 (0. 015) 0. 009 (0. 019) African American -0. 186*** (0. 040) -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) -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) Attended Private HS

TABLE 6 - Linear Probability (Dependent variable Enrolled = 1|Accepted) College X College 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) _Constant 1. 060*** (0. 128) 0. 808*** (0. 182) N 2876 1594 R 2 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 <50 K (sr) -0. 078 (0. 049) -2. 631** (1. 224) 50 K <Income <100 K (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) SAT 1 Score/100 0. 038** (0. 016) 0. 362 (0. 313) Did not want SAT 1 considered 0. 046 (0. 035) 0. 775 (0. 673) Requested school use SAT 2 Score 0. 050 (0. 042) -0. 106 (0. 894) SAT 2 Score(s) available (1=yes) -0. 529*** (0. 1812) -9. 150** (3. 584) Average SAT 2/100*SAT 2 Score(s) available (1=yes) 0. 088*** (0. 029) 1. 571*** (0. 564)

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 Student 0. 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) -0. 407*** (0. 077) -2. 745** (1. 360) Hispanic Unknown Race -0. 089

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) _Constant 2. 567*** (0. 212) 77. 555*** (4. 319) N 908 466 R 2 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) l 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. l l ¢ 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 l l 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.

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 ¢

¢ Ψi (early decision, submit SAT I)

Conclusions ¢ Students are strategic: Lower actual SAT I scores more likely to choose option l ¢ Colleges are strategic: Colleges are less likely to admit students who submit their SAT I scores, unless their SAT I scores are particularly high l ¢ Same students have higher predicted scores 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? )