P

Ja

b

a

ARRA

KAC

JIJK

1

sBttta

asdim

c

(

S(o(

0d

International Review of Law and Economics 31 (2011) 1–15

Contents lists available at ScienceDirect

International Review of Law and Economics

eer effects in affirmative action: Evidence from law student performance

ohn R. Lott Jr. ∗, J. Mark Ramseyera, Jeffrey Standenb

Harvard Law School, Cambridge, MA 02138, United StatesWillamette Law School, Salem, OR, United States

r t i c l e i n f o

rticle history:eceived 28 May 2009eceived in revised form 4 August 2010ccepted 6 January 2011

a b s t r a c t

In the Grutter case, Justice O’Connor suggested that universities could justifiably try to enroll a “criticalmass” of minority students. Enroll fewer than that “critical mass,” reason some observers, and minoritystudents will feel too marginalized to perform at their highest levels. In this article, we test whetherminority students perform better with other students from their ethnic group in a class or school. To doso, we assemble data on the ethnicity and performance of each student in all classes at two law schools

eywords:ffirmative actionritical mass

EL classification:27

– for three years at one, and for 16 years at the other. Although these schools enrolled a smaller fractionof African-Americans than most law schools, they are located in states with a much smaller fractionof African-Americans than in the United States as a whole. There is also a large amount of variationin the percent African-American across classes. At these schools, we find no consistent evidence thathaving additional students from one’s ethnic group raises a student’s performance. Instead, we find someevidence that having additional ethnic peers lowers performance – albeit by a very small amount.

19

. Introduction

The patterns of affirmative action in modern professionalchools raise questions about peer effects on student performance.y the very definition of affirmative action, minority students tendo enter the schools less prepared than their peers. They may alsoend to self-segregate.1 Given these two phenomena, how mighthe number of minority students in a school (or classroom) affectcademic performance?

Plausibly, the peer effects could cut either way. By someccounts, minority students in schools (or classrooms) with fewertudents from their ethnic group feel marginalized in ways that

iscourage them from succeeding. The fewer the minority students

n a school (or classroom), the lower the minority student perfor-ance.Yet, at least hypothetically, minority students in schools (or

lassrooms) with fewer other minority students might perform bet-

∗ Corresponding author.E-mail addresses: johnrlott@aol.com (J.R. Lott Jr.), ramseyer@law.harvard.edu

J.M. Ramseyer), jstanden@willamette.edu (J. Standen).1 This may occur by the actions of the students (Art McFarland, Self

egregation in School Cafeterias?” WABC-New York, March 27, 2006http://abclocal.go.com/wabc/story?section=our schools&id=4029353&ft=print))r by parents when they decide where to send their children to schoolGajendragadkar, 2006). For a related discussion, see Hanushek (1972).

144-8188/$ – see front matter © 2011 Elsevier Inc. All rights reserved.oi:10.1016/j.irle.2011.01.001

© 2011 Elsevier Inc. All rights reserved.

ter. If a school (or classroom) includes a large number of minoritystudents, those students might choose to study primarily with eachother. By inducing them to study with their (by definition) better-prepared non-affirmative action peers, a school (or classroom) withfewer minority students might cause minority students to performat higher levels.

We use data from student performance at two law schools(1 for 3 years, 1 for 16) to test these cross-cutting potentialeffects. From these schools, we received student grades brokendown by ethnicity and by course. We then ask whether thelevel of minority student performance changes with the num-ber of other minority students in the school (or classroom). Oneschool had 3% African Americans among its students while theother had 2%. Obviously, this is lower than at many schools, andpotentially limits the generality of our results. At least at theseschools, however, we find no consistent evidence that havingadditional students from one’s ethnic group raises a student’sperformance. Instead, we find some evidence that having addi-tional ethnic peers lowers performance – albeit by a very smallamount.

2. Peer effects in affirmative action

Over the past four decades, university faculty and admin-istrators have justified affirmative action in a variety of ways.Initially, some appealed to what they saw as the need to rec-tify that legacy of slavery. When courts rejected the approach,universities instead turned to Lewis Powell’s approving reference

2 w of L

imGlas

amliobpcs

dcilgt

sitmjstchtt

ssAypBtmpt

naasfcrbi(

J.R. Lott Jr. et al. / International Revie

n Bakke to “diversity.”2 With Sandra Day O’Connor’s endorse-ent in Grutter, the phrase acquired totemic status.3 William. Bowen and Derek Bok claim, “virtually every selective col-

ege and professional school has affirmed the value of race asn important aspect of diversity in broadening the education oftudents.”4

Speaking for a generation of university administrators, Bowennd Bok suggest that the benefits to diversity accrue to white andinority students alike. “Race almost always affects an individual’s

ife experiences and perspectives, and thus the person’s capac-ty to contribute to the kinds of learning through diversity thatccur on campuses,” explain the two. “This form of learning wille even more important going forward than it has been in theast.”5 All students learn best, they write, when they learn in alassroom that reflects the diverse racial composition of Americanociety.6

Proponents of race-sensitive admission policies add that stu-ents earn a significant market premium from attending a selectiveollege.7 Critics, however, argue that the policy sets up minor-ty students for failure: enrolled at schools for which they haveess preparation than their non-minority peers, they less oftenraduate.8 Within the legal community, they then less often passhe bar.9

Generally, African-American students perform at levels sub-tantially below those of their white peers. Disproportionately,n U.S. law schools they perform at levels that place them nearhe bottom of the class. As Ian Ayres and Richard Brooks sum-

arized the situation, “the average black law student’s grades areaw-droppingly low. With the exception of traditionally black lawchools (where blacks still make up 43.8% of the student body),he median black law school grade point average is at the 6.7 per-entile of white law students. This means that only 6.7% of whitesave lower grades than 50% of blacks. One finds similar results athe other end of the distribution – only 7.5% of blacks have gradeshat are higher than the white median.”10

Justice O’Connor endorsed the need to ensure for minoritytudents a “critical mass.”11 Given the often-repeated claim thattudents learn best when not marginalized, might the currentfrican-American performance levels suggest that law schools haveet to reach that critical mass? Some studies do claim, for exam-le, that African-American students learn better at the historicallylack universities than elsewhere.12 If minority students learn bet-

er when in a school (or classroom) with a large number of other

inority students, might African-American students today performoorly because they still number too few? Without other peers ofheir same race, might those minority students who do attend law

2 Bakke (1978) and Levinson (1999–2000). See generally Schuck (2002).3 Bollinger (2003).4 Bowen and Bok (1998).5 Bowen and Bok (1998), supra note, at 279.6 Carneiro, James, and Dimitriy (2005) find that the basic deficit in minority cog-itive skills arises early in life and that affirmative action through schooling will notddress that. They find evidence that this cognitive skill test gap between whitesnd minorities widens over time for blacks but not Hispanics, implying that unequalchooling might be a relevant factor for blacks but not Hispanics. As they note, “theailure of the Hispanic-white gap to widen with schooling or age casts doubt on thelaim that poor schools and bad neighborhoods are the reasons for the slow growthate in black test scores.” In any case, their work suggests that there might very welle differential effects across different minority groups. They also provide interest-

ng discussions of changes in noncognitive skills. See also Carneiro and Heckman2003).

7 E.g., Hoxby (2001), Brewer and Ehrenberg (1996) and Light and Strayer (2000).8 Thernstrom and Thernstrom (1999a, 1999b).9 Sander (2006).

10 Ayres and Richard (2004). See generally Sander (2006).11 Grutter, 539 U.S. at 316.12 E.g., Allen (1992) and Flowers and Ernest (1999).

aw and Economics 31 (2011) 1–15

school find themselves isolated – unable to learn because they haveno support system?13

Neither the University of Michigan admissions office nor Jus-tice O’Connor ever explicitly defined what fraction (or number)of students might constitute a “critical mass.” The admissionsoffice explained it as “a number that encourages underrepre-sented minority students to participate in a classroom and not feelisolated.”14 In turn, Justice O’Connor wrote that minority studentswere underrepresented when the fraction of “minority studentswho ultimately enroll[ed] in the Law School differ[ed] substan-tially from their representation in the applicant pool.” Recognizingthe ambiguity involved, we use Justice O’Connor’s formulation toanchor the concept of critical mass in this article: students from agiven ethnic group constitute a critical mass when their proportionof the student body equals their proportion in the applicant pool.15

Yet, as mentioned, the peer effects just as plausibly cut in theother direction. As anyone who has visited a university cafeteriaknows, American students segregate voluntarily.

At the university level, surveys locate substantial levels of thisself-segregation.16 And at the secondary school level, as one litera-ture review put it, black students form “peer groups that disengagefrom academic competition.”17 Conclude Seymour Martin Lipsetand his colleagues, as “the proportion of black students enrolled atthe institution rose, student satisfaction with their university expe-rience dropped, as did assessments of the quality of their education,and the work efforts of their peers.”18

Consider the implications that this self-segregation poses forstudy patterns. Suppose (it follows from the definition of affir-mative action) that minority students are disproportionately lesswell-prepared than their peers. If a law school (or classroom)enrolls few affirmative-action students, then those students may(by sheer lack of choice) study with non-affirmative action students– and those students on average are academically better preparedthan the minority students. By contrast, if a school (or classroom)enrolls more affirmative-action students, they may choose to studywith other affirmative-action students. To the extent that studentslearn from each other, the minority students in the school (or class-room) with more minority students thus lose the benefit that wouldcome from studying with better-prepared peers. The fewer theaffirmative-action students in a school (or classroom), in short, themore effectively those students may learn.19

Hence the puzzle: Do minority law students do better in schools(or classrooms) with larger numbers of other minority students? Dothey learn better in schools (or classrooms) with fewer minoritystudents? Or are peer effects really not important?

3. Data and regression structure

3.1. Data

To examine potential peer effects, we take student performancerecords from two law schools. Under the terms of the confidential-ity agreements imposed by the deans involved, we cannot disclose

13 The impact of these cases is now being felt in K-12 schools. In a case currentlybefore the Supreme Court from Jefferson County, Washington, the district court inMeredith v. Jefferson Co. Bd. of Educ. accepted the school’s argument that maintainingintegration was a compelling state interest in K-12 public education. See Jones andRamsey (2007).

14 Grutter, 539 U.S. at 329–330.15 Grutter, 539 U.S. at 347.16 E.g., Schofield (2001).17 Ferguson (1998).18 Rothman, Lipset, and Nevitte (2003).19 For a study investigating this possibility in the context of elementary school

busing but finding limited evidence for it in one program, see Angrist and Kevin(2004).

J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15 3

Table 1Attrition rates by race and sex who entered School A during 1998–2000.

Total students Semester that student left law school

First year Second year Third year

First Second Third Fourth Fifth Sixth Seventh

(A) Number of studentsWhite 621 1 0 0 14 32 573 1Asian 97 0 0 0 1 5 91 0African-American 28 0 0 0 1 1 26 0Hispanic 73 0 0 0 0 2 70 1Other 21 0 0 0 0 3 17 1

No race information 33 0 0 0 3 1 29 0Male 405 1 0 0 8 23 372 1Total students 873 1 0 0 19 44 806 3

Percent of total Percent of students who left law school by race by semester Percent who advance to second year

(B) Percent of studentsWhite 71.1% 100% 0% 0% 73.68% 72.73% 71.1% 33.33% 99.84%Asian 11.1% 0% 0% 0% 5.26% 11.36% 11.3% 0.00% 100.00%African-American 3.2% 0% 0% 0% 5.26% 2.27% 3.23% 0.00% 100.00%Hispanic 8.4% 0% 0% 0% 0.00% 4.55% 8.68% 33.33% 100.00%Other 2.4% 0% 0% 0% 0.00% 6.82% 2.11% 33.33% 100.00%No Race information 3.8% 0% 0% 0% 15.79% 2.27% 3.60% 0.00% 100.00%Male 46.4% 100% 0% 0% 36.36% 52.27% 46.2% 33.33% 99.75%Grade 87.67 0 0 82.27 81.83 81.67 82.60

Table 2Grade distribution for first year students by race and sex who entered School A during 1998–2000.

Asian African-American Hispanic White Other No race information Male Overall

A+ 0.6% 0.4% 1.5% 1.9% 1.6% 0.0% 2.3% 1.7%A 4.7% 2.4% 3.5% 9.3% 13.1% 0.0% 9.1% 8.3%A− 10.9% 6.3% 7.7% 16.0% 15.8% 12.5% 15.3% 14.4%B+ 26.5% 25.1% 24.3% 29.9% 27.3% 25.0% 28.9% 28.7%B 27.3% 27.5% 27.5% 22.0% 17.5% 50.0% 22.0% 23.3%B− 11.7% 17.3% 15.6% 6.7% 8.2% 0.0% 7.8% 8.4%C+ 5.2% 5.9% 4.9% 2.2% 2.2% 0.0% 2.5% 2.9%

0.5%0.3%0.1%1.0%

tcegwrdse

pnpAs(tfue

aLb

C 1.5% 2.0% 2.0%C− 0.5% 1.2% 1.2%D 0.2% 0.4% 0.5%Pass 11.0% 11.8% 11.4% 1

he identities of the two schools. However, in exchange for thatonfidentiality, we were provided not only with a complete set ofach student’s grades and the classes in which he earned thoserades, but also information about his race and sex and the teacherho taught the class. To maintain student anonymity, each school

eplaced student names with random numbers. Because each stu-ent’s number remained the same through his entire time in lawchool, however, we are able to follow him over his law schoolducation.

With this data, we examine the effect on minority studenterformance of having other peers from the student’s own eth-ic group. More specifically, we examine the effect on the examerformance of (i) African-American, (ii) Hispanic, and (iii) Asian-merican law students, of having different numbers of othertudents from the same ethnic group in either (a) a given classroom;b) a course, allowing for multiple sections of the same class; or (c)he entire law school. Although we know each student’s sex and,or one school, some LSAT scores, the regressions that we presentse individual fixed effects that already account for all these differ-nces.

School A is an urban law school with approximately 300 annu-lly entering J.D. (Juris Doctor) students. School A also maintains anL.M. (Masters of Law) program. In law school rankings, it placesetween the 10th and 50th place.20 It graduates over 97% of each

20 http://www.usnews.com/usnews/edu/grad/rankings/law/brief/lawrank brief.php.

2.2% 0.0% 0.6% 0.7%0.5% 0.0% 0.4% 0.4%0.0% 0.0% 0.1% 0.2%

11.5% 12.5% 11.0% 11.0%

entering J.D. class (Table 1). During the years in our data, only onestudent left during the first year, and it was not because the studentwas doing poorly (the student was earning an “A” average). Duringthis time, the school enrolled about 3% African-American and 8%Hispanic J.D. students. We were provided with all the grades of theJ.D. candidates who started the program from 1998 to 2000.

Class size at School A ranged from 2 students to 118. The classwith the most African-American students had 8 (8.4% of the class),while there were multiple classes with either zero or one African-American. The number of Hispanic students ranged from 1 inmultiple classes to 17 (14.4%). The median grade African-Americanand Hispanic grade was a “B” during a student’s first year of school,while the median for whites and “other” was a “B+” (Table 2).

In contrast, School B is a smaller school, and maintains no sub-stantial LL.M. program. For the first year classes between 1985 and2000, it enrolled on average about 140 J.D. students each year – 2%African-American and 2% Hispanic, Mexican American, or PuertoRican. In the U.S. News law school rankings, it typically places muchlower than School A.21 During the years we studied, only 83% ofthe students made it to the second year. The dropout rate varied

by race: 90.4% of whites and 93% of Native Americans advanced tothe second-year class, but only about 76% of the African-Americanstudents and 82% of the Hispanic students advanced (Table 3B).

21 http://www.usnews.com/usnews/edu/grad/rankings/law/brief/lawrank brief.php.

4 J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15

Table 3Attrition rates by race and sex who entered School B during 1985–2000.

Total students Semester that student left law school by race and by semester

First year Second year Third year

First Second Third Fourth Fifth Sixth Seventh Eighth Ninth

(A) Number of studentsAsian 112 0 13 1 1 1 88 2 4 2Pacific Islander 24 0 4 1 0 0 18 0 0 1African-American 45 1 10 0 2 1 27 3 1 0Native American 21 0 2 0 2 0 16 0 2 0Hispanic 43 0 9 0 0 0 33 0 1 0Mexican American 12 0 0 1 0 0 8 1 1 1Puerto Rican 1 0 1 0 0 0 0 0 0 0White 1801 27 146 16 70 65 1372 35 60 11Foreign student 24 1 3 1 0 0 15 1 2 1Resident Alien 2 0 0 0 0 1 1 0 0 0Other race 3 0 0 0 1 0 2 0 0 0No race information 285 9 19 1 9 12 222 4 6 3Male 1452 22 131 12 51 48 1090 29 57 12Total students 2373 38 207 21 85 80 1802 46 77 19

Percent of total Percent of students who left law school by race and by semester Percent advancing to 2nd year

First Second Third Fourth Fifth Sixth Seventh Eighth Ninth

(B) Percent of studentsAsian 4.7% 0.0% 6.3% 4.8% 1.2% 1.3% 4.9% 4.3% 5.2% 10.5% 88.39%Pacific Islander 1.0% 0.0% 1.9% 4.8% 0.0% 0.0% 1.0% 0.0% 0.0% 5.3% 83.33%African-American 1.9% 2.6% 4.9% 0.0% 2.4% 1.3% 1.5% 6.5% 1.3% 0.0% 75.56%Native American 0.9% 0.0% 0.7% 0.0% 2.4% 0.0% 0.9% 0.0% 2.6% 0.0% 93.02%Hispanic 1.8% 0.0% 4.4% 0.0% 0.0% 0.0% 1.8% 0.0% 1.3% 0.0% 79.07%Mexican American 0.5% 0.0% 0.0% 4.8% 0.0% 0.0% 0.4% 2.2% 1.3% 5.3% 100.00%Puerto Rican 0.0% 0.0% 0.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.00%White 75.9% 71.1% 70.6% 76.2% 82.4% 81.3% 76.1% 76.1% 77.9% 57.9% 90.42%Foreign student 1.0% 2.6% 1.5% 4.8% 0.0% 0.0% 0.8% 2.2% 2.6% 5.3% 83.33%Resident Alien 0.1% 0.0% 0.0% 0.0% 0.0% 1.3% 0.1% 0.0% 0.0% 0.0% 100.00%

167

ssodtBgoA“i

TG

Other race 0.1% 0.0% 0.0% 0.0% 1.2%No race information 12.0% 23.7% 9.2% 4.8% 10.6%Male 61.2% 57.9% 63.8% 57.1% 60.0%Grade point average 76.25 71.00 73.45 72.73 75.17

The class sizes at School B ranged from 2 students to 151. Yet,imilarly to School A, the class with the most African-Americantudents had 7 (6.1% of the class). There were multiple classes withnly one African-American student. The number of Hispanic stu-ents ranged from 1 to 5 (6%) (this adds together those who classifyhemselves as Hispanic, Mexican American, or Puerto Rican). Schoolawards far fewer “A’s” than School A. Only 8.9% of the first year

rades are some type of “A” as compared to School A where 24.4%

f the grades were “A’s” (Table 4). The median first-year grade forfrican-Americans, Asians, and Hispanics is a “C+,” lower than theB−” for whites, those who identify themselves as Mexican Amer-cans, foreign students, or “other.”

able 4rade distribution for first year students by race and sex who entered School B during 19

Asian PacificIslander

African-American

NativeAmer.

His-panic

MexicanAmerican

A+ 0.0% 0.0% 0.1% 0.0% 0.0% 0.0%A 0.8% 0.5% 1.2% 1.6% 1.0% 1.1%A− 4.7% 3.9% 3.1% 4.9% 3.9% 4.2%B+ 6.2% 5.9% 6.4% 10.8% 7.0% 10.5%B 11.9% 10.3% 12.9% 15.7% 10.9% 16.8%B− 15.0% 16.7% 14.0% 14.1% 14.7% 18.9%C+ 16.8% 19.1% 14.5% 20.5% 13.4% 17.9%C 20.0% 15.2% 18.3% 12.4% 20.9% 20.0%C− 10.3% 14.2% 12.7% 8.6% 10.9% 5.3%D+ 5.6% 8.3% 5.5% 2.2% 5.2% 3.2%D 2.7% 2.9% 3.6% 1.6% 2.8% 2.1%D− 0.1% 0.0% 0.8% 1.6% 0.8% 0.0%Pass 5.8% 2.9% 6.8% 5.9% 8.5% 0.0%

0.0% 0.1% 0.0% 0.0% 0.0% 100.00%5.0% 12.3% 8.7% 7.8% 15.8% 90.18%0.0% 60.5% 63.0% 74.0% 63.2% 89.43%6.17 76.77 75.96 76.83 75.21

While we will generally focus on whether more students of aparticular race in a class help other students of that race do well, wealso test whether there is a “critical mass” (as apparently envisionedby O’Connor) – whether the effect of having additional studentsfrom one’s race is discontinuous. The effect envisioned under thisalternative non-linear hypothesis is that student X’s performancedoes not merely depend on the number of other students of X’srace. Instead, it depends on the number of other students of X’s

race only if the share of such students exceeds a critical cut-off.Quite where that cut-off might lie is itself ambiguous, but we inter-pret it to refer to the share of applicants of that race in the school’sapplicant pool. In other words, the number of students of X’s race

85–2000a.

White Foreignstudent

No raceinfor

Otherrace

Male Overallgradedistrib.

0.2% 0.0% 0.1% 0.0% 0.1% 0.1%2.3% 5.0% 2.1% 0.0% 1.9% 2.2%7.0% 9.0% 6.5% 0.0% 6.4% 6.6%

11.0% 10.1% 11.2% 0.0% 10.3% 10.5%17.0% 14.1% 15.3% 0.0% 16.2% 16.2%16.1% 13.6% 15.7% 8.0% 15.8% 15.9%15.7% 10.1% 14.7% 24.0% 15.6% 15.6%13.5% 11.6% 14.1% 32.0% 14.4% 14.1%

6.8% 12.1% 7.2% 12.0% 7.3% 7.4%2.7% 5.5% 2.3% 8.0% 3.1% 3.0%1.1% 1.5% 0.7% 16.0% 1.4% 1.3%0.2% 2.0% 0.2% 0.0% 0.3% 0.3%6.5% 5.5% 9.8% 0.0% 7.2% 6.8%

J.R.Lott

Jr.etal./InternationalR

eviewofLaw

andEconom

ics31 (2011) 1–15

5

Table 5Application rates by race for students who entered School B.

Year Total Black % Black Asian/PacificIslander

% Asian Hispanic/Mexican-American

%Hispanic/Mexican-American

White %White

Other % Other No info % noinfo

(A) Actual shares of students enrolled by race during 1985–2000Total 2373 45 1.9% 136 5.7% 55 2.4% 1801 75.9% 51 2.1% 285 12.0%

(B) Application rates by race from 2001 to 2005 for students who applied to School B2001 743 25 3.4% 53 7.1% 31 4.2% 510 68.6% 57 7.7% 67 9.0%2002 750 19 2.5% 55 7.3% 23 3.1% 532 70.9% 44 5.9% 77 10.3%2003 957 21 2.2% 65 6.8% 48 5.0% 656 68.5% 55 5.7% 112 11.7%2004 1268 35 2.8% 79 6.2% 56 4.4% 821 64.7% 69 5.4% 208 16.4%2005 1555 46 3.0% 112 7.2% 40 2.6% 1039 66.8% 78 5.0% 240 15.4%Total 5273 146 2.8% 364 6.9% 198 3.8% 3558 67.5% 303 5.7% 704 13.4%

% of Classes with >20 students during1985 to 2000 that had a higher percentof students by group than shown intotals for each group

18.9% 25.5% 15.9%

Year Total Black % Black Asian/PacificIslander

% Asian Hispanic/Mexican-American

%Hispanic/Mexican-American

White Other No info % noinfo

(C) Application rates by race from 2001 to 2005 for students who applied to all law schools2001 73,658 8503 11.5% 5278 7.2% 4262 5.8% 47,238 64.1% 6931 9.4% 1446 2.0%2002 76,329 8648 11.3% 5527 7.2% 4330 5.7% 50,462 66.1% 6644 8.7% 718 0.9%2003 98,329 10,604 10.8% 8059 8.2% 5951 6.1% 61,730 62.8% 9609 9.8% 2376 2.4%2004 99,763 10,673 10.7% 8568 8.6% 6131 6.1% 62,625 62.8% 9525 9.5% 2241 2.2%2005 95,013 10,006 10.5% 7943 8.4% 6114 6.4% 61,317 64.5% 8391 8.8% 1242 1.3%Total 44,3092 48,434 10.9% 35,375 8.0% 26,788 6.0% 28,3372 64.0% 41,100 9.3% 8023 1.8%

% of Classes with >20 students during1985 to 2000 that had a higher percentof students by group than shown intotals for each group

0.24% 17.2% 3.8%

(D) Assuming a minority student is in a class with at least two other studentsof the same race—Classes with at least 50 students and at least 5% of studentsare African-American or Hispanic/Mexican-American or at least 10% areAsian/Pacific Islander

Num-ber ofobser-vations

713 3480 1866

6 w of L

rrrdest1

IsBtcpst

muBaftoicpp

AoAttAsw

ccotAHdofog

wiLsTT1s

wsP

share of the students in the bottom portion of the class grading

J.R. Lott Jr. et al. / International Revie

aises X’s performance if but only if the percentage of students of X’sace in the student body exceeds the percentage of students of X’sace in the applicant pool. Unfortunately, schools do not generallyisclose the racial composition of their applicant pools. After muchffort, however, we were able to obtain the applicant racial compo-ition for School B for years 2001–2005 (Table 5). We were assuredhat the 2001–2005 figures should be roughly representative of the985–2000 period.

These numbers indicate that African-American, Asian/Pacificslander, and Hispanic and Mexican-American students comprise amaller fraction of the School B student body than they do of School’s applicant pool. They students also comprise a smaller fraction ofhe student body than they do of the Law School Admission Coun-il (LSAC) law schools’ national applicant pool. The contrast is lessronounced with School B’s applicant pool, however, given thattudents from these groups are less likely to apply to School B thanhey are to apply to law school more generally.

However, two points need to be made. While African-Americansade up 12.8 of the population in from 2001 to 2005, they made

p just 10.9% of law school applicants and 5.4% of those enrolled.y contrast, School B might only have about 2% of the studentsnd 2.8% of applicants being African-American, but the five statesrom which 81% of the applicants come from had just 2.45% ofheir population being African-American.22 For a regional school,nce one accounts for the small percentage of African-Americansn their area, School B does quite well in obtaining a “critical mass”ompared to the average law school – whether it is defined as aercentage of African-Americans in the applicant pool or in theopulation from which applicants could be drawn.

We lack the information on what states the students from Schoolapply from, but School A also comes from a state and a region

f the country that has a noticeably smaller share of African-mericans. Indeed, the state that School A is in has about half

he percentage of African-Americans as is observed nationally andhe rate in other states in that region tend to be well below that.lthough School A does fit in many ways within the “national lawchool” category, at least measured by the environment withinhich it is located it appears to meet the “critical mass” criteria.

Secondly, the students do not distribute themselves amonglasses randomly. As a result, even in School B minority studentsonstitute a larger fraction than O’Connor’s “critical mass” thresh-ld in many classrooms. More specifically, even if we limit ourselveso classes with at least 50 students, we have 713 observations forfrican-Americans, 3480 for Asian/Pacific Islanders, and 1866 forispanic/Mexican-Americans where the fraction of same-race stu-ents exceeded that threshold. Obviously, this raises the possibilityf sample bias: minority students may be selecting “minority-riendly” instructors. Note, however, that any such bias would biasur study in favor of finding that minority students obtain higherrades in classes with larger fractions of minority students.

LSAT scores were only obtained for School B, and even then theyere only available for part of the sample period for students start-

ng from 1990 to 2000. Nationally from 1993 to 1999 the averageSAT score was 142 for African-Americans and 152 for whites.23 Fortudents starting at School B, the difference was about 43% as large.

he LSATs were 132.6 for African-Americans and 138.9 for whites.he average was only 125 for Hispanics and Mexican-Americans,31.4 for Asian-Americans, and 126 for Native Americans. For thistudy, these numbers indicate that the African-American-White

22 This information is again obtained from School B. The number 2.45 is theeighted average based on their relative shares of applicants coming from those two

tates. To calculate that rate, we used “Race and Hispanic Origin in 2005,” Populationrofile of the United States: Dynamic Version, U.S. Census Bureau.23 Shepherd (2001).

aw and Economics 31 (2011) 1–15

gap at School B was substantially smaller than at many other lawschools.

3.2. Regression structure

The simplest way to explore peer effects would be to try to cal-culate how a student’s grade in a particular class varies with thenumber of other students of the same race. Obviously, though, wewant to ensure that the results do not simply reflect the quality ofthe student, the types of classes that he chose to take, the pro-fessors who taught him, or any general change in grading overtime. For example, certain professors may have a reputation forawarding a large number of high grades; when a large number ofstudents of a particular type enrolled, they may have tended to beunusually strong or weak; and grades may be inflated or deflatedover time.24

Fortunately, there is an easy method to deal with these con-cerns: separate fixed-effects for students, classes, professors, andsemesters. By following a student as he goes through the school,the fixed effect will account for his ability to do well in law school.This measure is much better than any measure that we could obtainfrom either the student’s LSAT scores or undergraduate GPA. Thisoccurs because the fixed effect is pulling out the student’s averagegrade in law school and the race variable is picking up deviationsfrom the average grade for the other students of the same race(indeed, since neither the LSAT nor the fixed effect changes overthe time that the student is in school, one cannot simultaneouslycontrol for both). As we follow a student through his classes, wethus can see how well he does as the number of students of thesame race (or other races) varies – holding constant differences inclass, professor, and year.

While checking individual classes might be the most obviousway to examine the impact of race, it is not the only way that therace of fellow students might affect a student’s grade. Even if twostudents of the same race attend different sections of a course, forexample, they may study together or help each other with ques-tions and thus perform better on tests. And if the “critical mass”proponents are right, simply having other students of the samerace in the school at the same time might help a student perform.Because of these possibilities, we examine the possible impact ofrace at the classroom, course, and school levels.

School B, which provided us sixteen years of data, went throughseveral different grading scales. Nonetheless its administratorsgave us a detailed conversion scale they use to compare transcriptsover time. Rather than the letter grades, we used this scale in regres-sions for both schools (see Table 6). School A did not change itsgrading policies over the time examined. Note that School B doesnot give grades of “D+” and “D−.”

One potential bias should be mentioned with this estimationmethod. Suppose that a group of students were overrepresented atthe bottom of the class in terms of grades. To the extent that gradesare determined on a curve, raising the percentage of students inthese low scoring groups in a class would thus raise their averagegrade in the class simply because they would represent a greater

curve. For both schools, while no group overwhelmingly domi-nates the bottom of the grade distribution, African-Americans andother minority groups tend to be over represented among students

24 Additionally, one reader suggested that a professor might “grade in such a wayas to ensure that the highest black grade in the class is not too low.” Please note,however, that if a professor were to do so the African-American student will obtainthe higher grade no matter how many other African-Americans there were in theclass. As a result, the practice should not affect the relationship between the num-ber of African-Americans and African-American grades in general—the focus of thispaper.

J.R. Lott Jr. et al. / International Review of L

Table 6Relationship between letter grades and numerical scores.

Letter grades Numerical scores

A+ 90A 88.5A− 84.5B+ 81B 78B− 75.5C+ 73.5C 71C− 68

gtmiafotbh

4

4

Altdfcit

abrAabw

oSsaam

4

SmscAat

D+ 65D 61.5D− 57.5

etting lower grades. To the extent that this bias exists, it workso raise these minority student grades as more members of these

inority groups are enrolled in the classes. A similar bias worksn the other direction for whites, who tend to be overrepresentedmong students making the highest grades. There is thus some biasrom enrolling more whites towards lowering the average gradebtained by whites. While we do not know for sure the extento which grading is done on a curve, to the extent to which theiases exist, both these biases work in favor of the affirmative actionypothesis.

. Results

.1. A first look at the data

We begin with some simple graphs showing how grades vary forfrican-Americans and whites at both the classroom and course

evel as the number of African-Americans increases. The bottomwo lines show the average grades for the African-American stu-ents (gaps in the lines appear when there are no observationsor that number of African-American students in the classroom orourse). In neither Fig. 1 nor Fig. 2 do African-American gradesncrease with the number of African-Americans. Instead, if any-hing, they fall.

Of course, these figures do not control for other factors. Asresult, the apparently negative relationship between the num-

er of African-American students and their grades could simplyeflect the fact that the classes with the largest number of African-merican students are first year classes – and grades in these classesre lower. Nevertheless, it is hard to see any positive relationshipetween the number of students and their grades, even in classesith one to three or four African-Americans.

Figs. 3 and 4 show a similar relationship between the numberf Hispanic students in a classroom or course and their grades. Forchool B, Fig. 4 aggregates as Hispanic all those who identify them-elves as either Hispanic, Mexican American, or Puerto Rican. Ifnything, the relationship here is even more clearly negative forll eight lines, especially when going from one Hispanic student toore than one.

.2. Regressions

We present three sets of regressions using Ordinary Leastquares. The first is the simplest: the effect on grades of havingore students of only one’s own race in a classroom, course, or

chool (Table 7). For example, a white student’s grade in a particularlass is regressed on the number of white students, an African-merican’s grade on the number of African-American students,nd so on. Note that we account for the number of students inhe classroom, and use fixed effects for professors, students, class-

aw and Economics 31 (2011) 1–15 7

room, and semester. We account for the number of students ina classroom to see if the proportion of the class that is of differ-ent races matters (dropping the variable tends to make the impactof more minority students on the grades of those minority stu-dents even more negative). Because we only have the enteringclass characteristics for 1998, 1999, and 2000 at School A, we haveschool level racial characteristics for all students only for 2000.We do not have that problem at School B since we have data for16 years.

Aggregating African-Americans, Hispanics, Mexican Americans,Asians, Native Americans, and Pacific Islanders together producedsimilar results.

In Table 8, we combine all the variables from the separateTable 7 regressions into one regression for each school. For SchoolA, that means we have a regression that simultaneously controls forthe classroom and course racial characteristics. For School B, thatmeans simultaneously controlling for classroom, course and schooleffects. Finally, we examine the cross effect of race (Table 9): theimpact that more students of a particular group has on the gradesof other groups.

Begin with Table 7. While 14 of the 35 race based coeffi-cients are statistically significant, it is hard to see any consistentpattern across the schools. School B provides evidence at boththe classroom and the course level that more African-Americans,Asians, and Hispanics reduce, not increase, the grades for stu-dents within their own group. Nevertheless, both effects (whilesometimes statistically significant) are relatively small. An addi-tional seven African-Americans in a classroom lowers the averageAfrican-American’s grade from a solid B− to a solid C+. It takes 9more Hispanics (at the course level) and over 21 more Asians in aclassroom or a course to produce the same reduction in their grades.Any of these changes in the number of students only explains a tinyfraction of the variation in grades. Indeed, a one standard devia-tion in these variables explains less than one percent of a standarddeviation of the grades.

These results cannot be explained by minority students drop-ping out of school after the more difficult first year classes. At SchoolA, students do not drop out. More importantly, the fixed classroomeffects will account for whether the class is for first year or secondand third year students – the class fixed effects will account for howdifficult the different classes are.

The only minority students who seem to benefit from havingmore students from that group in a course or school are those whoidentify themselves as Mexican American. Again, however, with amaximum of three such self-identified students in a course, the sizeof the impact is miniscule. Changes in the number of Mexican Amer-icans in a classroom explain just a tiny fraction of one percentagepoint of the change in Mexican American grades.

These results imply that if we are to find any impact on Hispan-ics, we will need to disaggregate the students as much as possible.One School B representative did tell us that students who clas-sify themselves as Mexican American are not obviously ethnicallydistinct from those who identify themselves as Hispanic. Specifi-cations 6 through 8 imply that if we aggregate all Hispanics thesignificant relationships between the number of Hispanics or Mex-ican Americans and grades disappear.

We also re-estimated specifications 1 and 3 in Table 7 usingOrdered Logits (see Appendix 1). While the coefficients indicatethat increasing the number of African-Americans in a class againreduces the grades of African-Americans for both schools thecoefficients are only statistically significant for School A. The dif-

ference between the impacts of more whites on white grades isnot statistically significantly different from the impact of eitherAfrican-Americans on African-Americans or Asians on Asian grades.Hispanics show different effects in the two schools, but in bothcases the relationship is statistically insignificant.

8 J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15

73

74

75

76

77

78

79

80

81

82

83

987654321

Number of Black Students in Class or Course

Average Score for Blacks in ClassAverage Score for Whites in ClassAverage Score for Blacks in CourseAverage Score for Whites in Course

Fig. 1. Comparing grades for Blacks and Whites as the number of blacks in their class or course increases (School A).

62

64

66

68

70

72

74

76

78

80

87654321Number of Black Students in Class or Course

Average Score for Blacks in ClassAverage Score for Whites in ClassAverage Score for Blacks in CourseAverage Score for Whites in Course

Fig. 2. Comparing grades for Blacks and Whites as the number of blacks in their class or course increases (School B).

72

74

76

78

80

82

84

86

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

ourse

Average Score for Hispanics in ClassAverage Score for Whites in ClassAverage Score for Hispanics in CourseAverage Score for Whites in Course

umbe

wDnda

Hwd

Number of Hispanics in Class or C

Fig. 3. Comparing grades for Hispanics and Whites as the n

We also tried a more complicated specification accounting forhether class size or class difficulty had different effects by race.25

ummy variables for each racial group were interacted with theumber of students in a class. As a proxy for the difficulty of theifferent courses, we used the average grade given in each course,nd then we interacted this new variable with a dummy variable

25 For the debate over the impact of class size on student performance seeanushek (1997). Hanushek, Hanushek, and Luque (2000) and Krueger (2003). Weould also thank an anonymous referee for suggesting that see whether there wereifferential impacts by race based on how hard the class is.

r of Hispanics in their class or course increases (School A).

for each racial group. Redoing the estimates shown in Table 7 withthese new variables further reduces the significance of the variableson the impact of minorities on other minorities’ grades, with thevariable coefficients for Asian and African-American grades beingno longer statistically significant (see Appendix 2 for the estimatesfor race and class size or course difficulty).

While the fixed effects employed should account for many dif-

ferences in classes, the estimates might vary in other systematicways so we also re-estimated the results for just first year stu-dents. For example, because law school tests are coded so thatstudent exams are anonymous, professors of large first year classesshould find it especially difficult to discriminate in favor or against

J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15 9

70

71

72

73

74

75

76

77

78

54321

Cou

Average Score for Hispanics in ClassAverage Score for Whites in ClassAverage Score for Hispanics in CourseAverage Score for Whites in Course

F o Rica(

piafis

TEp

Number of Hispanics in Class or

ig. 4. Comparing grades for Hispanics (Hispanics, Mexican Americans, and PuertSchool B).

articular students. First year students are also important to exam-

ne separately because most classes are mandatory, and studentsre assigned to the classes randomly. Thus examining these largerrst year classes possibly provides cleaner test of the impact thattudents have on each other.

able 7xamining the impact of fellow students’ race on the same race grades of other studentarentheses.).

School A

(1) (

Class C

African American grades based on # of African Americans in category 0.087 0(1.00) (

Hispanic grades based on # of Hispanics in category −0.009 −(0.28) (

Mexican American grades based on # of Mexican Americans in category

White grades based on # of Whites in category 0.009 0(2.73) (

Asian grades based on # of Asians in category 0.0287 −(1.07) (

Total number of students in category (class, course, or school) −0.008 −(2.31) (

F-Tests for difference between (Probability that these two coefficients are the same)African Americans and Hispanics 1.18 0

(0.28) (African Americans and Mexican Americans

African Americans and Whites 0.81 0(0.37) (

African Americans and Asians 0.34 0(0.56) (

Hispanic Americans and Mexican Americans

Hispanic Americans and Whites 0.67 0(0.25) (

Hispanic Americans and Asians 1.13 0(0.29) (

Mexican Americans and Whites

Mexican Americans and Asians

Asians and Whites 0.60 0(0.44) (

Number of observations 18,083 1F-Statistic 15.04 1Adj R-squared 0.4220 0Fixed student effects Yes YFixed professor effects Yes YFixed class effects Yes YFixed semester effects Yes Y

rse

ns) and Whites as the total number of Hispanics in their class or course increases

Examining only the first year students results in many fewer

results being statistically significant and some coefficient signs didchange. For example, the estimates that examined the racial com-position at the class level found that only the coefficients for whiteswere statistically significant at the 1% level for a two-tailed t-test

s separately by class, course and school (robust absolute t-statistics are shown in

School B School B (with Hispanic, MexicanAmerican, and Puerto Rican alladded together)

2) (3) (4) (5) (6) (7) (8)

ourse Class Course School Class Course School

.0157 −0.279 −0.229 0.0356 −0.276 −0.229 0.03360.35) (2.24) (2.43) (0.39) (2.22) (2.44) (0.37)0.011 −0.143 −0.229 −0.0397 −1.39 −0.097 .0501

0.73) (1.04) (2.05) (0.52) (1.00) (1.03) (0.76)0.138 0.8029 0.4276(0.35) (2.46) (2.78)

.0024 0.001 0.00037 −0.0026 0.0019 0.00037 −0.00261.63) (1.05) (0.36) (3.06) (0.122) (0.36) (3.04)0.0012 −0.094 −0.0934 −0.0292 −0.093 −0.0935 −0.029

0.10) (2.77) (3.78) (−1.51) (2.72) (3.79) (1.52)0.0007 −0.006 −0.0049 .002 −0.0066 −0.0048 .0019

0.49) (4.31) (3.43) (2.37) (4.47) (3.43) (2.28)

.40 .55 0.00 .41 4.93 1.03 0.020.528) (0.4603) (0.9967) (0.5208) (0.026) (0.3102) (0.236)

1.03 9.31 4.88(0.3099) (0.0023) (0.0271)

.09 5.11 5.94 .17 5.01 5.97 0.160.763) (0.0238) (0.0148) (0.6768) (0.025) (0.0145) (0.6929).16 2.09 2.01 0.49 2.06 2.02 0.460.686) (0.1479) (0.1566) (0.4843) (0.1507) (0.1553) (0.4965)

0.46 9.05 7.52(0.4979) (0.0026) (0.0061)

.90 1.1 4.23 0.24 1.50 1.08 0.640.34) (0.2933) (0.0398) (0.6249) (0.2214) (0.298) (0.4226).52 0.12 1.45 0.02 7.39 0.00 1.400.47) (0.7304) (0.2278) (0.8914) (0.0066) (0.9686) (0.2360)

0.12 6.05 7.85(0.7283) (0.0139) (0.0051).35 7.54 8.79(0.554) (0.0060) (0.0030)

.11 8.12 14.79 1.95 7.88 14.84 1.980.735) (0.0044) (0.0001) (0.1631) (0.005) (0.0001) (0.1592)8,083 68,178 68,178 68,178 68,178 68,178 68,1785.04 16.13 16.14 16.07 15.98 15.98 15.92.4219 0.3962 0.3962 0.3960 0.3961 0.3961 0.3944es Yes Yes Yes Yes Yes Yeses Yes Yes Yes Yes Yes Yeses Yes Yes Yes Yes Yes Yeses Yes Yes Yes Yes Yes Yes

1 w of L

fdrBs

sit“irgicts“s

rtasA

TEc

0 J.R. Lott Jr. et al. / International Revie

or both schools and they continued to imply that more white stu-ents in a class raised the scores of white students. The only otheresult that was statistically significant was for Asians for Schooland unlike previously they implied that more Asians raised the

cores of other Asians.While we have concentrated on disaggregated results to make

ure that a particular racial group does not drive the results andt is not always clear what racial groups are defined as being inrouble, minority students might study as a group. Assuming thatunderrepresented” minorities include African-Americans, Hispan-cs, Mexican Americans, Puerto Ricans, and American Indians, wee-estimated the regressions in Table 7 by combining these fiveroups together. The new minority variable is statistically signif-cant at the 10% level for a two-tailed t-test for only School B’slass and course level estimates and they show that more minori-ies reduce minority grades. However, the impact continues to bemall. If Asian Americans and Pacific Islanders are included in thisunderrepresented” group, none of the minority coefficients aretatistically significant.

Combining the effects for classroom, course and school into one

egression reduces what little support there had been for posi-ive peer effects among Mexican Americans (see Table 8). Whilen increase in the number of Mexican Americans at the course orchool level implies a significant increase in grades for Mexicanmericans, the reverse is true at the classroom level. We do not see

able 8xamining the impact of fellow students’ race on the same race grades of other studenolumns of estimates and the next three columns each represent one regression each) (ro

Regr(Spe

Class

African American grades based on # of African Americans in category 0.12(1.01

Hispanic grades based on # of Hispanics in category 0.01(0.30

Mexican American grades based on # of Mexican Americans in category

White grades based on # of Whites in category 0.00(1.55

Asian grades based on # of Asians in category 0.05(1.52

Grades based on size of category −0.0(2.05

F-Tests for difference betweenAfrican Americans and Hispanics 0.75

(0.38African Americans and Mexican Americans

African Americans and Whites 0.90(0.34

African Americans and Asians 0.30(0.58

Hispanic Americans and Mexican Americans

Hispanic Americans and Whites 0.02(0.89

Hispanic Americans and Asians 0.71(0.39

Mexican American’s and Whites

Mexican Americans and Asians

Asians and Whites 1.97(0.16

Number of observationsF-StatisticAdj R-squaredFixed student effectsFixed professor effectsFixed class effectsFixed semester effects

aw and Economics 31 (2011) 1–15

any reasonable explanation for why more Mexican Americans in aclassroom would lower Mexican American grades, but more Mexi-can Americans in a course or school would have the opposite effect.

None of the other estimates provide any evidence that moreminorities increase minority grades. Eleven coefficients imply anegative relationship for minorities (though only one is statisticallysignificant) and eight imply a positive relationship (though onlytwo for Hispanics are significant). Overall the pattern across groupsas well as the pattern within Hispanic groups seems random.

For School A, only the estimates for whites are statistically sig-nificant. The results imply that having more whites in a classroomor a course raises their grades. This effect too, however, is extremelysmall.

Finally, in Table 9 we break down all the possible interactionsbetween the races shown in Table 8. We examine, for example, notonly the impact of more African-Americans on African-Americans,but also on Hispanics, Asians, whites, and other. The table providestests for 99 combinations that do not include whites. Of those 99, 12are statistically significant at least at the 10% level for a two-tailedt-test, with 6 implying more minorities decrease minority grades

and 6 implying that they increase them.

Even where statistically significant, the results are not alwaysconsistent across schools: for example, in row 8 for School A havingmore Hispanics in a classroom increase an Asian student’s grades,but the reverse is implied for School B. Similarly, for the impact of

ts by simultaneously examining effects by class, course and school (the first twobust absolute t-statistics are shown in parentheses).

ession for School Acification 1)

Regression for School B(Specification 2)

Course Class Course School

38 −0.034 −0.1507 −0.175 0.074) (0.55) (0.99) (−1.51) (0.8)

37 −0.0175 0.04045 −0.234 −0.020) (0.86) (0.23) (−1.62) (0.26)

−1.0296 1.105 0.4086(1.95) (2.51) (2.56)

77 −0.00005 .0022 −0.0002 −0.0024) (0.02) (1.15) (−0.18) (2.77)

61 −0.0183 −0.026 −0.0782 −0.0193) (1.16) (0.61) (−2.52) (0.99)089 .0017 −0.006 −0.0008 .00205) (0.87) (−3.25) (−0.44) (2.42)

0.08 0.68 0.11 0.6460) (0.7762) (0.41) (0.74) (0.4243)

2.59 8.02 3.33(0.11) (0.0046) (0.068)

0.31 1.01 2.27 0.6917) (0.5753) (0.31) (0.1319) (0.4071)

0.07 0.64 0.68 147) (0.7843) (0.42) (0.4106) (0.3165)

3.72 8.48 5.91(0.05) (0.0036) (0.015)

0.84 0.05 2.63 0.0519) (0.3606) (0.83) (0.1046) (0.8154)

0.00 0.13 1.16 0.0088) (0.9652) (0.71) (0.2815) (0.9911)

3.83 6.32 6.62(0.05) (0.0120) (0.0101)3.62 7.25 7.13(0.06) (0.0071) (0.0076)

1.59 0.45 6.52 0.7803) (0.2068) (0.5) (0.0107) (0.3767)

18,083 68,17814.85 15.72

0.4220 0.3965Yes YesYes YesYes YesYes Yes

J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15 11

Table 9Examining the impact of fellow students’ race on grades across races: simultaneously examining effects by class, course and school (the first two columns of estimates andthe next three columns each represent one regression each) (the categories for Puerto Rican, multicultural, and “other” were left out categories. Robust absolute t-statisticsare shown in parentheses).

Regression for School A(Specification 1)

Regression for School B(Specification 2)

Class Course Class Course School

(1) African American gradesbased on # of AfricanAmericans in category

0.1443861 (0.85) 0.0006799 (0.00) −0.0538248 (0.36) 0.1171326 (0.82) 0.2860002 (1.7)

(2) Hispanic grades based on #of Hispanics in category

0.2231218 (3.43) −0.0464048 (−1.04) 0.0076291 (0.05) 0.1345178 (0.78) −0.0633107 (0.47)

(3) Mexican American gradesbased on # of MexicanAmericans in category

−0.0542492 (0.12) 0.2618631 (0.57) −0.0043529 (0.01)

(4) White grades based on # ofWhites in category

−0.010492 (0.97) −0.0020845 (0.33) −0.0072153 (3.58) −0.0060382 (3.62) −0.003051 (1.12)

(5) Asian grades based on # ofAsians in category

0.0074382 0.033347 (0.60) −0.0196552 (0.46) −0.0212082 (0.47) −0.0834859 (2.01)

(6) Asian grades based on # ofWhites in category

−0.0023492 (0.15) −0.0215206 (1.89) −0.0079277 −0.0092985 0.0034929

(3.74) (1.93) (0.75)(7) Asian grades based on # of

African-Americans incategory

−0.0571856 (0.69) .0447506 (0.70) −0.0096561 (0.11) −0.0572029 (0.75) −0.1379289 (1.8)

(8) Asian grades based on # ofHispanics in category

0.0965809 (1.65) 0.0413988 (1.04) −0.1082828 (1.19) −0.1745552 (1.87) −0.0249902 (0.29)

(9) Asian grades based on # ofMexican Americans incategory

0.0255559 (0.17) 0.1182428 (0.83) 0.2824154 (3.09)

(10) Asian grades based on # ofPacific Americans in category

−0.0701721 (0.65) 0.0765507 (0.68) −0.16107 (1.57)

(11) Asian grades based on # ofForeigners in category

.0541225 (0.46) 0.2623125 (2.26) 0.1388309 (0.94)

(12) White grades based on #of Asians in category

0.0622484 (1.86) −0.0424947 (−1.52) 0.0521045 (3.84) 0.0197536 (1.5) −0.0106075 (0.38)

(13) White grades based on #of African-Americans incategory

0.0099417 (0.24) 0.0075785 (0.23) 0.0831326 (3.36) 0.0761066 (3.32) 0.0897413 (1.9)

(14) White grades based on #of American Indians incategory

0.1101507 (3.59) 0.0740171 (2.51) −0.0805223 (0.99)

(15) White grades based on #of Hispanics in category

0.0652779 (2.11) 0.0143889 (0.65) −0.012289 (0.48) 0.0094079 (0.37) 0.0284375 (0.61)

(16) White grades based on #of Mexican Americans incategory

−0.0363034 (0.78) −0.1283996 (2.71) −0.0516275 (0.84)

(17) White grades based on #of Pacific Islanders incategory

0.0474503 (1.61) 0.0611793 (2.05) 0.1120737 (2.14)

(18) White grades based on #of Foreigners in category

0.1010509 (2.96) 0.0718945 (2.13) −0.0759756 (0.88)

(19) African-American gradesbased on # of Whites incategory

0.0125977 (0.42) −0.0345877 (−1.40) −0.0002071 (0.02) −0.0143869 (1.68) −0.0005104 (0.06)

(20) African-American gradesbased on # of Asians incategory

−0.2286666 (−1.64) 0.1277521 (1.04) −0.1067102 (1.21) 0.0019783 (0.02) −0.0352583 (0.41)

(21) African-American gradesbased on # of AmericanIndians in category

−0.0352577 (0.18) −0.0144318 (0.08) −0.3081405 (1.06)

(22) African-American gradesbased on # of Hispanics incategory

0.0932391 (0.81) 0.0944858 (0.122) −0.1178332 (0.75) −0.0012667 (0.01) −0.1193703 (0.78)

(23) African-American gradesbased on # of MexicanAmericans in category

−0.3237399 (1.27) −0.1732378 (0.73) −0.054749 (0.28)

(24) African-American gradesbased on # of PacificIslanders in category

−0.037048 (0.19) 0.1878951 (1.02) 0.1413932 (1)

(25) African-American gradesbased on # of Foreigners incategory

−0.1888844 (0.95) −0.1737145 (0.83) −0.2200559 (0.88)

(26) Hispanic grades based on# of Whites in category

−0.030077 (1.77) −0.0072623 (0.56) −0.0241723 (2.59) −0.0183872 (2.2) 0.0088366 (1.14)

(27) Hispanic grades based on# of Asians in category

−0.0631407 (0.84) 0.0140278 (0.22) 0.1038276 (1.10) −0.0125281 (0.13) −0.1709601 (1.98)

12 J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15

Table 9 (Continued)

Regression for School A(Specification 1)

Regression for School B(Specification 2)

Class Course Class Course School

(28) Hispanic grades based on# of American Indians incategory

0.045034 (0.22) −0.0038042 (0.02) 0.1040934 (0.4)

(29) Hispanic grades based on# of Mexican Americans incategory

.199793 (0.51) 0.4346319 (1.17) 0.1157857 (0.56)

(30) Hispanic grades based on# of African-Americans incategory

−0.050565 (0.58) 0.1410313 (2.11) 0.174683 (1.05) 0.1051358 (0.7) 0.0855194 (0.66)

(31) Hispanic grades based on# of Pacific Islanders incategory

−0.1738718 (0.85) −0.0628625 (0.35) −0.096567 (0.74)

(32) Mexican American gradesbased on # of Whites incategory

−0.0095276 (0.57) 0.0029268 (0.19) 0.0645887 (1.86)

(33) Mexican American gradesbased on # of Asians incategory

0.058026 (0.43) −0.0094259 (0.08) −0.1720072 (0.87)

(34) Mexican American gradesbased on # of AmericanIndians in category

0.2868712 (0.90) 0.0153102 (0.05) −0.6028119 (0.57)

(35) Mexican American gradesbased on # ofAfrican-Americans incategory

0.5504439 (2.11) 0.4969786 (1.85) Dropped

(36) Mexican American gradesbased on # of PacificIslanders in category

0.1582121 (0.44) 0.3427652 (0.96) −0.6207345 (0.68)

(37) Hispanic grades based on# of Foreigners in category

0.0605457 (0.28) 0.0795408 (0.39) −0.0715026 (0.27)

(38) Mexican American gradesbased on # of Foreigners incategory

−0.4633029 (1.24) −0.2692576 (0.73) −0.8927606 (1.66)

(39) Mexican American gradesbased on # of Hispanics incategory

−0.3236924 (0.82) −0.4228513 (1.16) −0.7749381 (1.45)

(40) Grades based on size ofcategory

−0.0072626 (0.76) 0.0054347 (1.64) −0.0058652 (3.68) −0.0041759 (2.84) 0.0023814 (2.46)

F-Tests for difference betweenAfrican Americans andHispanics

0.19 (0.6634) 0.10 (0.7509) 0.08 (0.7835) 0.01 (0.9381) 2.68 (0.1013)

African Americans andMexican Americans

0.00 (0.9993) 0.09 (0.7631) 0.70 (0.4042)

African Americans andWhites

0.84 (0.3605) 0.00 (0.9845) 0.1 (0.7528) 0.74 (0.3905) 2.93 (0.0868)

African Americans andAsians

0.57 (0.4494) 0.05 (0.8299) 0.05 (0.8245) 0.85 (0.3573) 4.59 (0.0321)

Hispanic Americans andMexican Americans

0.02 (0.8961) 0.07 (0.7947) 0.03 (0.8577)

Hispanic Americans andWhites

12.93 (0.0003) 0.96 (0.3275) 0.01 (0.9294) 0.67 (0.4132) 0.20 (0.6553)

Hispanic Americans andAsians

5.40 (0.0201) 1.24 (0.2655) 0.02 (0.8747) 0.77 (0.3801) 0.02 (0.8836)

Mexican Americans andWhites

0.01 (0.9155) 0.34 (0.5590) 0.00 (0.9966)

Mexican Americans andAsians

0.01 (0.9381) 0.38 (0.5390) 0.07 (0.7950)

Asians and Whites 0.07 (0.7875) 0.40 (0.5293) 0.08 (0.7721) 0.11 (0.7357) 3.54 (0.0598)Number of observations 17,402F-Statistic 13.93Adj R-squared 0.4220 0.3965Fixed student effects Yes Yes

Attstg

Fixed professor effects YesFixed class effects YesFixed semester effects Yes

frican-Americans on whites, the estimates for School B indicated

hat more African-Americans raise the grades for whites, but nowhis time it does not show up for School A. The effects are also verymall: even when they are statistically significant they continueo explain only a fraction of a percent of the variation in studentrades. For School B, 12 African-Americans would have to be added

YesYesYes

to a class to increase white’s grades by 1 percentage point. Over-

all, the results reflect what one would expect if they were simplyrandom.

The bottom line is that the simplest estimates provide some sig-nificant evidence that adding more African-Americans to a class orcourse actually lowers the grades of other African-Americans. There

J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15 13

Table 10Testing the “critical mass” hypothesis using data from School B (fixed effects used for professor, class name, student and semester. Absolute t-statistics are shown inparentheses.).

(1) (2)

African-American’s grade when there is at least one otherAfrican-American in the class and at least 5% of the class areAfrican-Americans

0.003 (0.03) 0.022 (0.22)

Asian’s grade when there is at least one other Asian in the class and atleast 7% of the class are Asians

0.1066 (2.41) 0.1142 (2.58)

Hispanic or Mexican-American’s grade when there is at least one otherHispanic or Mexican-American in the class and at least 5% of the classare Hispanics or Mexican-Americans

−0.1066 (1.37) −0.1004 (1.34)

African American grades based on # of African Americans in class −0.3092 (2.52)Hispanic grades based on # of Hispanics in class −0.1603 (1.18)Mexican American grades based on # of Mexican Americans in class 0.0866 (0.22)White grades based on # of Whites in class −0.00064 (0.49)Asian grades based on # of Asians in class −0.1176 (3.54)Total number of students in class −0.0061 (5.89) −0.0054 (4.45)

ittogtdd

5

hstewnh

abtilmcpavitnti(p5bti

frs

Adjusted R2

Root MSE

s no evidence that the reverse is true. More sophisticated interac-ions were tried, but it is hard to see any consistent pattern fromhis data. Again, there is no evidence that more African-Americansr Hispanics in a class improve the grades of students in thoseroups. With about 68,000 observations for School B, it seems hardo attribute this lack of statistically significant results to a lack ofata. Whether this pattern occurs for other schools can only beetermined if data are eventually made available.

. Critical mass

The preceding results are inconsistent with the “critical mass”ypothesis. Nevertheless, even if having more classmates of theame race does not improve one’s school performance generally,he possibility remains that it might improve one’s performance if itxceeded a critical threshold. We do not understand why the effectould be discontinuous in this fashion, and O’Connor herself offerso explanation. Given that the hypothesis is there in the literature,owever, we offer this test.

Recall that we have information on the racial composition of thepplicant pool to School B for 2001–2005. Recall too that we haveeen assured that this composition roughly reflects the composi-ion of the applicant pool for 1985–2000. Using this information,n Table 10 we report two sets of estimates. The first specificationooks at different racial minorities when there is at least one other

ember of that minority in the class and the minority constitutes aertain “critical mass” percentage of the class. Fixed effects for therofessor teaching the class, the class name, student, and semesterre also accounted for. The second specification includes all thoseariables as well as the measures used earlier to look at a minor-ty’s grade as one increases the number of others of that minority inhe class. Both specifications imply similar relationships. The onlyew variable that is statistically significant concerns Asians, andhe effect is very small – having more than 7% of a class being Asianncreases an Asian student’s grade by just over a tenth of a pointabout 2% of one standard deviation). The point estimate for His-anics actually indicates that having Hispanics make up more than% of the class reduces their grade by a similar tenth of a point,ut it is only statistically significant at 15% level for a one-tailed-test. The point estimates for African-Americans are statistically

nsignificant, and smaller than those for the other two races.

Thus, we find evidence of the “critical mass” hypothesis onlyor Asian students, and the data suggest that there may even be aeverse “critical mass” effect for Hispanics. Even when statisticallyignificant, the magnitude of the coefficients is very small.

0.3947 0.39494.0071 4.0067

6. Conclusion

Would having additional students from one’s ethnic group inclass help a student perform? To explore the impact of such peereffects, we obtain student-level data at two law schools (3 yearsat one, 16 years at the other). We then follow a student’s gradesfrom class to class to see how they vary as the racial compositionof the class changes. At these schools, one had 3% African Ameri-can students and the other had 2%. Obviously, this may limit thegenerality of our results. Even after accounting for how difficultindividual classes or professors are and the quality of individualstudents, at least at these schools we find no consistent evidencethat having additional students from one’s ethnic group raises astudent’s performance.

It is hard to see any evidence that adding more African-Americans to a class increases the grades of African-Americans orany other group. If anything, in the simplest estimates for schoolB, the data show that adding more African-Americans to a class orcourse lowers the grades of other African-Americans. Those esti-mates indicate that replacing an African-American with a whitestudent appears to increase the grades of white students. Other-wise, it is hard to see any beneficial peer relationships.

Specifically testing for the “critical mass” hypothesis shows thatfor School B having Asians make up more than 7% of a class veryslightly increases other Asians’ grades, but while it is statisticallysignificant, the effect is very small.

Possibly the two laws schools that we are studying here aredifferent from other laws schools, but at the very least this studyshows that one cannot claim that there are universal peer benefitsto increasing minority enrollment. We spent several years tryingto obtain similar data from a wide variety of law schools. The onlyway one can test to see whether the law schools that we exam-ined are unique is for the remaining law schools to make their dataavailable.

Acknowledgements

Ph.D.; Mitsubishi Professor of Japanese Legal Studies, HarvardUniversity; Professor of Law, Willamette Law School. We gratefullyacknowledge the generous help of the deans and registrars whoprovided us with the data for this study. Ramseyer received gen-

erous financial assistance from the John M. Olin Center for Law,Economics & Business at the Harvard Law School. The usual dis-claimers apply. We would also like to thank the participants atthe George Mason Law School, the University of Miami, and theAmerican Law and Economics Association meetings.

1

A

TRr

TV

4 J.R. Lott Jr. et al. / International Review of L

ppendix A.

See Tables A1 and A2.

able A1e-examination Table 7: examining the impact of fellow students’ race on the same raceegressions (fixed effects are used in all specifications for students, classes, teachers, and

African American grades based on # of African Americans in category

Hispanic grades based on # of Hispanics in category

Mexican American grades based on # of Mexican Americans in category

White grades based on # of Whites in category

Asian grades based on # of Asians in category

Total number of students in category (class, course, or school)

F-Tests for difference between (Probability that these two coefficients are the same)African Americans and Hispanics

African Americans and Mexican Americans

African Americans and Whites

African Americans and Asians

Hispanic Americans and Mexican Americans

Hispanic Americans and Whites

Hispanic Americans and Asians

Mexican Americans and Whites

Mexican Americans and Asians

Asians and Whites

Number of observationsWald Chi-squared

Pseudo R-squaredFixed student effectsFixed professor effectsFixed class effectsFixed year effects

able A2alues of additional control variables when included in Specification 3 in Table 7.

Variables

African American grades based on # of African Americans in categoryHispanic grades based on # of Hispanics in categoryMexican American grades based on # of Mexican Americans in categoryWhite grades based on # of Whites in categoryAsian grades based on # of Asians in categoryTotal number of students in classInteracted with

Pacific IslanderAfrican-AmericanNative AmericanHispanicMexican AmericanPuerto RicanWhiteForeignMulticulturalOtherNo information

Average grade in courseInteracted with

Pacific IslanderAfrican-American

aw and Economics 31 (2011) 1–15

grades of other students separately by class, course and school using ordered logittime. Absolute z-statistics reported.).

School A School B(1) (2)Class Class

−0.043 −0.0093(1.82) (0.13)0.0099 −0.0064(1.47) (1.12)

0.0217(1.13)

−0.0054 0.00055(3.65) (0.62)−0.0172 0.0124(1.28) (0.64)0.0049 −0.000018(1.79) (0.03)

0.34 0.03(0.56) (0.8534)

0.01(0.9430)

0.67 0.01(0.25) (0.9050)0.00 0.00(0.9810) (0.9676)

0.02(0.8819)

3.52 0.02(0.06) (0.8992)0.35 0.09(0.58) (0.7654)

0.02(0.9002)0.00(0.9561)

0.69 0.38(0.27) (0.5384)18083 725981.76e+08 10.70.1760 0.072Yes YesYes YesYes YesYes Yes

Coefficient and absolute t-statistic

−0.1253 (0.87)0.0899 (0.54)−0.0053 (0.01)−0.0120 (2.34)−0.0109 (0.22)−0.0104 (2.68)

−0.00996 (1.41)0.0059 (0.94)−0.0035 (0.49)0.0006 (0.10)0.00287 (0.30)0.0424 (1.08)0.0138 (2.51)−0.00698 (1.00)−0.0224 (0.99)0.0239 (1.42)0.0077 (1.87)1.175 (2.94)

−0.0576 (0.42)0.3554 (3.30)

J.R. Lott Jr. et al. / International Review of Law and Economics 31 (2011) 1–15 15

Table A2 (Continued)

Variables Coefficient and absolute t-statistic

Native American −0.3006 (2.09)Hispanic 0.1301 (1.12)Mexican American −0.3944 (2.24)Puerto Rican 2.073 (1.83)White −0.1763 (2.99)Foreign −0.06229 (0.45)Multicultural −0.1591 (0.38)Other 0.3039 (0.75)

R

A

A

A

BBB

B

C

C

F

F

G

H

No Information −0.1760 (2.57)F-Statistic 13.22Adjusted R2 0.3970Root MSE 4.0592

eferences

llen, W. R. (1992). The Color of Success: African-American College Student Out-comes at Predominantly White and Historically Black Public Colleges andUniversities. Harvard Educational Review, 62, 45.

ngrist, J. D., & Kevin L. (2004). Does School Integration Generate PeerEffects? Evidence from Boston’s Metco Program (SSRN id 491482; January2004).

yres, I., & Richard, B. (2004). Does affirmative action reduce the number of blacklawyers? Stanford Law Review, 57

akke v. (1978). Regents of University of California, 438 U.S. 265, 311–313.ollinger, G. v. (2003). 539 U.S. 306.owen, W. G., & Bok, D. (1998). The shape of the river: Long-term consequences of con-

sidering race in college and university admissions Princeton: Princeton UniversityPress.

rewer, D. J., & Ehrenberg, R. G. (1996). Does it pay to attend an elite private col-lege? Evidence from senior class of 1980. In S. Polacheck (Ed.), Research in laboreconomics (pp. 239–271). Greenwich, CT: JAI Press.

arneiro, P., & Heckman, C. J. (2003). Human capital policy. In J. Heckman, & A.Krueger (Eds.), Inequality in America: What role for human capital policies? (pp.77–240). Cambridge, MA: MIT Press.

arneiro, P., Heckman, J. J., & Masterov, D. V. (2005). Labor market discriminationand racial differences in premarket factors. Journal of Law and Economics, (April),1–40.

erguson, R. F. (1998). Teachers’ perceptions and expectations and the Black-Whitetest score gap. In C. Jencks, & M. Phillips (Eds.), The Black-White test score gap300.

lowers, L., & Pascarella, E. T. (1999). Cognitive effects of college racial compositionon African American students after 3 years of college. Journal of College Student

Development, 40, 669.

ajendragadkar, S. S. (2006). The constitutionality of racial balancing in charterschools. Columbia Law Review, 144.

anushek, E. A. (1972). Will quality of peers doom those left in the public schools? InP. T. Hill (Ed.), Choice with equity (pp. 121–140). Stanford, CA: Hoover InstitutionPress.

Hanushek, E. A. (1997). Assessing the effects of school resources on student perfor-mance: An update. Educational Evaluation and Policy Analysis, 19(Summer (2)),141–164.

Hanushek, E. A., Hanushek, L. E. A., & Luque, J. (2000). Smaller classes, lower salaries?The effects of class size on teacher labor markets. In W. M. Sabrina, Laine, G.James, & Ward (Eds.), Using what we know: A review of the research on implement-ing class-size reduction initiatives for state and local policymakers (pp. 35–51). OakBrook, IL: North Central Regional Educational Laboratory.

Hoxby, C. (2001). The return to attending a more selective college: 1960 to thepresent. In M. Devlin, & J. Meyerson (Eds.), Forum futures: Exploring the futureof higher education, 2000 papers (pp. 13–42). New York: Jossey-Bass.

Jones, S. D., & Ramsey, E. N. (2007). Discrimination veiled as diversity: The use ofsocial science to undermine the law. Journal of Educational Controversy, 2.

Krueger, A. B. (2003). Economic considerations of class size. Economic Journal,113(January (1)), 34–63.

Levinson, S. (1999–2000). Diversity, 2 U. Pa. J. Const. L. 573, 578 (rhetorical switchto “diversity” rationale as a variation on “Simon Says”).

Light, A., & Strayer, W. (2000). Determinants of college completion: School qualityor student ability. Journal of Human Resources, 35(2), 299–332.

Rothman, S., Lipset, S. M., & Nevitte, N. (2003). Does enrollment diversity improveuniversity education. International Journal of Public Opinion Research, 8, 15.

Sander, R. H. (2006). A systematic analysis of affirmative action in American lawschools. Stanford Law Review, 57, 367.

Schofield, J. W. (2001). Maximizing the benefits of student diversity: Lessons fromschool desegregation research. In G. Orfield, & M. Kurlaender (Eds.), Diversitychallenged: Evidence of the impact of affirmative action. Cambridge: Harvard Uni-versity Civil Rights Project.

Schuck, P. H. (2002). Affirmative action: Past, present and future. 20 Yale L. & Pol’y Rev.1, 34 (diversity as a “rhetorical Hail Mary pass, an argument made in desperationwhen all other arguments for preferences have failed”).

Shepherd, G. B. (2001). No African-American lawyers allowed: The inefficient racism ofthe ABA’s accreditation of law schools. Emory University School of Law. March 5.

Thernstrom, S., & Thernstrom, A. (1999a). America in Black and White: One nationindivisible. New York: Simon & Schuster.

Thernstrom, S., & Thernstrom, A. (1999b). Book review: Reflections on the shape ofthe river. UCLA Law Review, 46, 1583–1631.