I. INTRODUCTION

Social scientists agree that peers affect one's learning although debate continues on the nature of classroom peer effects. (1) Identification of peer effects is complicated by the reflection problem: just as one student is affected by his classmates, so does that student affect his classmates (Manski 1993). Recent evidence relies on experimental and quasi-experimental assignment of peers to avoid this reflection problem. Sacerdote (2014) concludes from his review of the literature that the evidence on peer effects remains too inconclusive to inform policy choices.

Part of the peer effects literature explores the role of the racial composition of one's peers in elementary and secondary schools. I expand this discussion of racial peer effects to higher education, at a time when many colleges and universities are striving to increase the diversity of their student bodies. The analysis employs data from a selective, private, Catholic liberal arts college. Students at this college take a team-taught four-semester course series on the development of western civilization (DWC). Upon matriculation, students are preregistered into their course section without regard to their race, ethnicity, sex, or ability. Unique features of the course allow for the inclusion of team fixed effects. Within a faculty team, some sections end up with a higher proportion of students of color than other sections. Using this variation in student characteristics, I estimate the effects of having more classmates of color on academic outcomes, allowing the effects to differ for white students and students of color.

The results provide evidence of racial peer effects that differ for white students and students of color. Students of color earn lower grades when enrolled in sections with a greater proportion of students of color; these effects occur exclusively for students of color with lower SAT scores. Allowing for nonlinear effects displays important nonlinearities for white students. At above average fractions of classmates of color, white students earn higher grades in sections with more students of color.

This paper contributes to two strands of the education literature. First, it expands the racial peer effects discussion to higher education. Second, it broadens the analyses of higher education galvanized by affirmative action. Much of this evidence relies on cross-institutional variation in racial composition. By identifying racial peer effects within an institution, this paper directly considers a policy lever available to colleges and universities: class assignments. The results suggest that white students are more successful in sections with more students of color. Lower test score students of color may be less successful in more racially diverse classrooms, although these effects are not always statistically significant.

II. RACIAL PEER EFFECTS

Racial peer effects may stem from a variety of sources. First, students may be more heavily influenced by peers of their own race. For example, some results in Hoxby (2000) imply stronger ability peer effects intrarace; Fruehwirth (2013) also finds that the strength of ability peer effects differs by race. Second, teachers may modify their expectations as their students' racial and ethnic composition changes. Third, black students may feel pressured to avoid "acting white" and underachieve to conform to their peers (Austen-Smith and Fryer 2005; Fordham and Ogbu 1986; Ogbu 2003). Fourth, in psychology, the concept of "stereotype threat" (e.g., Steele and Aronson 1995) implies a protective role arising from students sharing a classroom with peers of their own race. With stereotype threat, individuals worry that their actions may confirm negative stereotypes held about one's social identity; this worry inhibits performance, substantiating the negative stereotype. (2) The stereotype threat literature suggests that a critical mass of peers who look like you may reduce the threat of being stereotyped, improving performance (Kanter 1977). (3)

The K-12 peer effects literature indicates that an increased proportion of black peers may lower academic performance, although the magnitude of this effect differs between black students and nonblack students (Billings, Deming, and Rockoff 2014; Hanushek, Kain, and Rivkin 2009). (4) The magnitude of racial peer effects in K-12 also appears to differ for high-achieving and low-achieving black students (Hanushek and Rivkin 2009) with larger effects for higher achievers. In contrast, Fryer and Torelli (2010) find that attending a school with a high proportion of black students protects against the acting white phenomenon, reducing the negative relationship between popularity and achievement among black students.

The relevant literature in higher education tends to focus on the potential benefits of attending a more diverse college. The results are mixed. Papers comparing the outcomes of students attending more diverse colleges find higher earnings for white men (Daniel, Black, and Smith 2001), possibly lower earnings for whites and Asians once one controls for student's major (Arcidiacono and Vigdor 2010), and no effect once accounting for selection on unobservables (Hinrichs 2011). At all levels of schooling, racial peer effects may affect outcomes through learning, grades, or both.

My paper improves upon the existing evidence in two ways. First, unlike higher education studies that rely on differences across institutions, my paper relies on variation across classes at the same institution. It is most similar to Hoxby (2000) which uses natural population variation in K-12 or the ability peer-effect research at the military academies that relies on random assignment (e.g., Carrell, Fullerton, and West 2009). Second, I add to the peer effects literature by estimating the role of the racial and ethnic composition of one's classmates in college, in a more typical, although still selective, higher educational setting. The students reside in a policy environment relevant to a large variety of educational institutions where the class composition could be manipulated.

III. BACKGROUND AND DATA

All students at this selective, Catholic, and liberal arts college are required to take a four-semester sequence studying the DWC. (5) Upon matriculation to the college, Enrollment Services registers students for the first semester of DWC, DWC 101, as well as the suggested courses for their declared major or the major in which they indicated an interest. Enrollment in DWC 101 is made without regard to the student's background, race, ethnicity, or gender. There are, however, some sections that would conflict with the freshman biology sequence or other courses required for one's major. To the extent that majors correlate with demographic characteristics, this may produce some of the variation in the racial, ethnic, and gender composition of sections. (6) The identification strategy, however, mitigates most of this concern by relying on variation between two sections that share a lecture time and faculty team but differ in their seminar time.

Students have two potential opportunities to change their first semester schedule. First, students attend an advising day prior to starting classes, typically in the summer. At that time, students can adjust their schedule as needed as long as seats are available. Second, students can adjust their schedule during the first several days of class. Changing DWC sections tends to be difficult as the scheduled times overlap many other course time slots and the program does not overenroll students into the classes. Students and advisors are encouraged to build the remainder of a student's schedule around DWC 101. I assume students are assigned to their first semester section without regard to their race or ethnicity and show evidence below that assignments appear random.

DWC has two unique features that combine to help identify plausibly exogenous variation in the racial composition of classes. First, students are assigned to a team of two to five faculty members. Second, the course each semester consists of two parts: a large lecture and a smaller seminar section. All students assigned to a faculty team attend their team's lectures. Each faculty member then leads two separate seminar sections of a fixed, smaller group of students. Administratively, this shows up as though students in the large lecture are split into two sections: one half assigned to one seminar time and the other half assigned to a different seminar time. Students with the same faculty team operate under the same syllabus and share assessment methods and grading weights but potentially differ in instructors' grading of participation.

As an example, in Fall 2011, the same team of faculty members taught sections 5 and 6 of DWC 101. The lecture for both sections occurred Tuesdays, Wednesdays, and Fridays from 10:30 to 11:20 a.m. in the same room. The seminar for section 5 occurred on Mondays from 8:30 to 10:20 a.m.; the seminar for section 6 occurred on Fridays from 12:30 to 2:20 p.m. In the data, students appear as either enrolled in section 5 or section 6 even though these sections share a lecture and a team of faculty members. This is the variation on which I rely. The estimation method compares students' performances between sections 5 and 6 based on the differences in the racial and ethnic composition between sections 5 and 6. Effectively, the racial composition of that half of the class is a proxy for the racial composition of the student's seminar. The same faculty team assigns grades for both sections 5 and 6. The rules charge each team to determine grades together. In practice, some teams have faculty members determine their seminar students' grades alone. The empirical approach assumes that a faculty member uses similar metrics to grade both sections of his or her seminar students. Continuing the example, I assume that each member of the faculty team of, say, Professors A, B, and C, grade each of their two seminars using the same standards. In other words, Professor A grades her section 5 seminar using the same standard as her section 6 seminar.

One thousand freshmen matriculate each fall. Of these, roughly 10% are honors students. Because honors students take a separate honors version of DWC, I omit them from the analysis. The sample used below consists of 4,435 nonhonors students over five entering cohorts, from Fall 2009 to Fall 2013. Summary statistics for these students appear in Table 1 by race and ethnicity.

The student body is predominantly white: 85% of nonhonors students are white. I characterize students as white or nonwhite. (7) Students who report their race but do not report their race as white are defined as nonwhite. This includes students who are American Indian/Alaskan Native (0.3%), Asian (1.5%), black/African American (4.5%), Hispanic/Latino (6.9%), Native Hawaiian or other Pacific Islander (0.2%), or two or more races (1.8%). I separately consider those students identifying as black/African American and those identifying as Hispanic. Almost 9% of students do not identify their race. I count these students as white students. (8) During the five observed years, the fraction of students who are nonwhite increases from 12% to 19%.

White students earn higher grades in DWC 101 than do nonwhite students. The average grade point average (GPA) for white students is 2.88, slightly below B; nonwhite students earn lower grades. White students also enter the college with higher high school GPAs and SAT test scores. Twenty percent of students are first generation college students; 44% are males; 11 % are National Collegiate Athletic Association Division I athletes; 1% are international students; and 16% received Pell grants their first semester, an indicator of family income. Nonwhite students are more likely to be first generation, female, athletes, international students, and Pell grant recipients. Nonwhite students are more likely to have switched roommates at least once in their first year.

The college is an SAT-optional school. Although students who have taken the SAT are required to submit their scores for advising, about 14% of students in the sample are not linked to SAT scores. I generate two indicators for missing SAT verbal and math scores to retain these students in the sample. (9)

The sample contains 54 sections of DWC 101 over five cohorts. Although the average student experiences a DWC 101 section that is 15% nonwhite, this percentage varies from 0% to 30%. One student is the sole nonwhite member of her 45-person section; four sections contain three or fewer nonwhite students (with class sizes of 34, 37, 45, and 68). Ninety-five percent of students are in a section with 5 or more students of color; half are in a section with 14 or more students. The average section size is 67 students.

I provide three empirical tests of whether the percent of nonwhite students in each section is credibly distributed randomly. First, I use the population of matriculating students in each cohort to assign students randomly to sections. For each cohort, I use the number of observed sections so that the simulated sections are similar in size to the observed sections. (10) The section is randomly assigned 10,000 times. I then calculate the fraction of simulated sections with values below each observed section's values. Under randomization, these calculated p values are distributed uniformly. 1 use a one-sample Kolmogorov-Smirnov test to test whether the distribution of calculated p values differs significantly from a uniform distribution. The one-sample Kolmogorov-Smirnov tests fail to reject the null hypothesis of no difference in the distributions for the proportion of students in each group: nonwhite, black, and Hispanic. (11) In addition, I test the section's average SAT verbal score for nonwhites, blacks, and Hispanics. I fail to reject equality of distribution for each of these variables.

Second, I consider whether DWC 101 section characteristics differ by race and ethnicity. I regress each section characteristic, such as the average SAT math score of the section, on indicators for whether a student is white, black, or Hispanic; the omitted category is "other." Because the racial composition and characteristics of each cohort differ, I include cohort fixed effects and a set of ten variables capturing the days and times that the section meets. Table 2 presents these results. Average SAT scores, the racial and ethnic composition of the section, as well as the percent of the section who are males, international students, first generation students, or Pell grant recipients does not differ for white, black, and Hispanic students. These estimates are consistent with a credibly exogenous allocation of students across sections. (12) Table 2 presents 30 statistical tests; at the 10% level, we would expect three of these tests to be statistically significant even if the null hypothesis of no correlation is true. There are two statistically significant estimates in Table 2: black students appear in sections with fewer classmates who are black and in sections with more athletes. (13)

The third empirical test examines how white students' characteristics correlate with the percent minority in their section. (14) If students are assigned to sections without regard to their race and ethnicity, then white students' SAT scores and high school GPAs should be uncorrelated with the fraction minority. I regress SAT scores on the percent minority for the sample of white students. During the observed 5 years, matriculating students' SAT scores and high school GPAs are falling and the percent minority is increasing. To account for these trends, the regressions also include indicators for each matriculating cohort.

Results from this third empirical test appear in Table 3. Most estimates on percent minority are positive and statistically insignificant, supporting the claim that variation in racial diversity is uncorrelated with a variety of student characteristics. One exception is that white students' high school GPAs are significantly lower in sections with a greater percentage of black classmates. (15) More caution in interpreting results for the percent black in the analysis that follows may be warranted. Note, however, that given the number of estimates considered, this one significant estimate may have occurred by chance. (16)

Statistical tests support Enrollment Services' claim of assigning students into sections without regard to their race, ethnicity, or SAT scores.

IV. EMPIRICAL METHOD

This paper considers students enrolled in the first semester of a required, four-semester sequence, assuming that students are assigned to their first semester section without regard to their race or ethnicity. The focus of the analysis is how the fraction of classmates who are students of color affects one's outcomes. Two primary outcomes are analyzed: grades in the first semester course and the likelihood of not persisting to the second semester. The specification allows the magnitude of the effect to differ for white and nonwhite students. The basic specification is an estimate of the following for student i in cohort c enrolled in section s with team t:

[outcome.sub.icts] - [[beta].sub.1][pctminority.sub.icts] + [[beta].sub.2][minority.sub.i] x ([pct.sub.minorityicts]) + [[beta].sub.3][minority.sub.i] + X'[delta] + [[rho].sub.ct] + [[tau].sub.c] + [[epsilon].sub.icts].

The coefficients of interest are [[beta].sub.1] and [[beta].sub.2]. The coefficient on the interaction term allows this effect to differ for minority students. If having peers of one's own race is protective for minority students, as with stereotype threat, we would expect [[beta].sub.2] to be positive. If having more peers of one's own race negatively impacts academic outcomes, as with existing evidence in K-12, we would expect [[beta].sub.2] to be negative. I measure percent minority in three ways: the percent nonwhite, the percent black/African American, and the percent Hispanic. For specifications considering the effect of the percent black/African American and the percent Hispanic, I omit other students of color from the sample; the comparison group becomes, only white students and students of unknown race. The specification includes indicators for the student's racial and ethnic identification.

The vector X controls for a variety of student characteristics including indicators for whether the student is a first generation college student, male, a student athlete, an international student, or received a Pell grant. In addition, the specification controls for the student's high school GPA, SAT math, and verbal scores, whether they commute or live on campus, and if they changed roommates their first year. (17) A set of variables capturing the days and meeting times of the section capture potential differences in academic outcomes based on time of day. (18)

Fixed effects control for the cohort-faculty team, [[rho].sub.ct]. DWC is a team-taught course; teams range in size from two to five professors. Many teams appear as teaching two sections of DWC 101 with a shared large lecture and two separate seminar times, one for each section. The team fixed effects compare outcomes for students between these two sections based on the diversity of their classmates. With these fixed effects, the source of identification on the percent minority is the variation in the proportion of students of color in the half of the lecture who share the same seminar time compared to the other half of the lecture with a different seminar time. The syllabus is common to the lecture and each member of the faculty-team teaches one seminar in each section (i.e., one at each of the two seminar times). The cohort-team fixed effects thus capture many potential sources of bias such as professor quality, grading standards, and the like. Any remaining bias requires differential sorting within lecture and faculty team into seminar times by achievement level and the racial composition of one's classmates. For example, if higher grade-earning students enroll in a seminar time with more racially diverse classmates, this biases the results upward; if lower grade-earning students enroll in a seminar time with more racially diverse classmates, this biases the results downward. Tests of distribution of students into sections by SAT verbal scores, however, indicate that SAT scores are distributed randomly across sections, even by race and ethnicity. As another example, consider a faculty team whose two seminars meet at Monday 8:30 a.m. and Friday 12:30 p.m. where the Monday 8:30 seminar half has fewer students of color. Bias could arise if the students of color in the Monday seminar sort into the easier grading professor while the students of color in the Friday seminar (with more students of color) sort into the harder grading professor. This would appear as though having more students of color led to lower grades. However, this requires a complicated, differential sorting of students within a lecture and faculty team.

Year dummies control for the possibility of grade inflation over time. Because percent minority is measured at the section level, standard errors are clustered by the student's section of DWC 101.

The empirical method tests how changing the racial and ethnic composition of a class affects academic outcomes. Note that the specification does not include controls for other section average characteristics; this method of analysis asks how adding more students of color, along with their academic characteristics, affects students.

V. RESULTS

Table 4 presents estimates of the baseline specification. (19) Column 1 displays estimates using the percent of students who are students of color. The point estimates imply that the fraction of nonwhite students in one's section has statistically insignificant effects on the grades of white and nonwhite students. Column 2 considers the percent of students who are black. Here, the results suggest that grades are lower in sections with more black students. This effect is stronger for black students themselves, although the interaction term is not statistically significant. Column 3 uses the variation in the percent of students who are Hispanic. For white students, the fraction of the class who is Hispanic results in higher grades; a 10 percentage point increase in Hispanic classmates raises grades by 0.045 grade points. This effect reverses for Hispanic students: grades are lower for Hispanic students enrolled in sections with a higher proportion of Hispanic students. A 10 percentage point increase in Hispanic classmates lowers grades by 0.16 grade points. These results do not support the idea of a protective critical mass, although the fraction of students of color in a section tops out at 30%. (20)

Previous evidence in elementary and secondary schools suggests that the effect of the percent of classmates who are minority students may differ for lower and higher ability students. In Table 5, I allow the effects to differ by including interaction terms of the percent minority with an indicator for whether a student has an above median verbal SAT score. (21) Column 1 displays the results for percent nonwhite. For white students, having more nonwhite classmates slightly raises grades, with an even smaller effect on higher SAT students. The effects for nonwhite students differ significantly from those for white students. Nonwhite students with below median SAT scores earn lower grades when enrolled in sections with more students of color, although this effect is small and statistically insignificant. Below median nonwhite students receive grades 0.08 grade points lower when in a section with 10 percentage points more students of color (p value = .177). For nonwhite students with above median SAT scores, the sign switches: a 10 percentage point increase in the percent nonwhite raises grades by 0.06 grade points (p value = .331).

Much of the existing literature focuses on black students. In column 2, the pattern of results differs somewhat, although the limited number of African American students on campus leads to less precise estimates. Specifically, we observe lower grades in sections with more black students for all but high SAT black students. Above median SAT black students in a section with 10 percentage points more black classmates earn grades that are half a letter higher. None of these effects are statistically different from zero.

The results in column 3 for the percent Hispanic correspond with the results for the percent nonwhite in column 1. A higher percent of classmates who are Hispanic raises grades for white students and for above median SAT score Hispanic students. However, for below median SAT Hispanic students, having more Hispanic classmates leads to lower grades: a 10 percentage point increase lowers grades by about 0.23 grade points (p value = .058).

Having more classmates of color results in higher grades for students of color with high SAT scores but lower grades for students of color with low SAT scores. Grades are higher for white students with more classmates of color. Racial peer effects differ for white and nonwhite students.

Joecks, Pull, and Vetter (2013), on the critical mass of women on corporate boards, find that the direction of the effect of the proportion female changes above 30%. In my sample, the proportion of students in a section who are not white tops out at 30%; it may be that higher proportions of students of color would lead to different results on students' grades and retention. Table 6 examines the possibility of nonlinear effects.

The effect of the percent of classmates of color on grades appears strongly nonlinear. Column 1 presents estimates using all nonwhite students. Allowing for the quadratic term in percent minority, the estimates show no statistical difference in effects for whites and for nonwhites. At low levels of diversity, the effect of increasing the percent minority is negative; the sign of this effect turns positive with about 18% of classmates being students of color. For a class with 25% students of color, the effect of a 10 percentage point increase is a positive and statistically significant increase of about 0.1 grade points (p value = .003). The pattern of estimates using the percent of students who are black, in column 2, is similar although less precisely estimated. The estimates using the percent of students who are Hispanic, in column 3, are again similar to those in column 1. At low levels of diversity, the effect of increasing the percent Hispanic is negative; the sign of this effect turns positive with about 8% of classmates being Hispanic. For a class with 10% Hispanic students, the effect of a 10 percentage point increase is a positive and statistically significant increase of about 0.1 grade points (p value = .007). The effect for Hispanic students is not statistically different than that for white students.

Table 7 presents results for a second academic outcome: whether students drop out of the college after the first semester. I find no statistically significant effects of the percent nonwhite, percent black, or percent Hispanic on the probability of dropping out, controlling for one's grade in DWC 101. Point estimates are small and statistically insignificant. For example, 10 percentage points more classmates of color reduces the likelihood of dropping out by 0.0008 percentage points (column 1) for students of color. In columns 4 through 6, I allow the effects to differ for students with above and below median SAT scores. These estimates show no statistical differences between these groups; effects are small and statistically insignificant.

I observe one additional, potentially relevant outcome: whether students switched teams for their second semester. Enrollment Services automatically rolls students over to the same team for the second semester in the sequence, DWC 102. (22) However, students can and do switch sections: about 33% of students switch teams. During the first semester, students become more savvy about how the institution works and learn how their team compares to other students' teams.

To conduct the analysis, I create two variables: a dummy variable indicating whether the student switched DWC teams and a measure of team grading easiness. To generate the grading easiness measure, I regress students' DWC 101 grades on the cohort-team fixed effects. The estimated fixed effects measure the average student grade for that team. I standardize the estimated fixed effects to a mean zero, standard deviation one, variable.

Table 8 presents the estimated effects of racial composition on whether a student switched teams. Students in sections with more classmates of color are more likely to switch sections. In the more basic specification, this effect is only statistically significant for Hispanic students (column 3). When I allow the effects to differ by above and below median verbal SAT score, the effect of more Hispanic classmates is statistically significant for both lower and higher SAT score white students. A 10 percentage point increase in Hispanic classmates increases the probability of switching teams by 0.3. This stands somewhat in contrast to the findings in Carrell, Hoekstra, and West (2016). They find that freshmen at the U.S. Air Force Academy who are assigned to more and higher performing black squadron mates are more likely to pair with a black roommate as sophomores.

VI. CONCLUSIONS

Racial peer effects continue to be an important topic in education research and policy. A primary difficulty in identifying peer effects stems from the nonrandom assignment of peers. Much of the economics literature for higher education relies on peers as defined by freshman year roommates in institutions where roommates are randomly assigned. Using data from a selective, private, Catholic liberal arts college, I use the assignment of students to a first semester core course as a source of credibly exogenous variation in classmates' characteristics. The questions are whether students perform better in a classroom with a larger number of students of color and whether this effect differs for students of color.

Controlling for faculty team fixed effects and a wide variety of student characteristics, I find evidence of racial peer effects that differ significantly for white students and students of color. Students of color enrolled in classes with greater fractions of students of color earn lower grades. These effects occur exclusively for those with lower SAT verbal scores; grades of nonwhite students with above median SAT scores increase, although the effect is statistically insignificant. Effects on white students are nonlinear: white students with sufficiently large fractions of classmates of color earn higher grades. There are no observed effects on retention for the second semester.

These estimates suggest that increasing classroom diversity may improve many students' grades. White students and higher test score nonwhite students perform better when classroom diversity increases. Students of color with lower SAT scores may experience lower grades when enrolled in sections with more students of color. Policymakers, however, would be wise to heed the warning of Carrell, Sacerdote, and West (2013), who found that military students reassigned to "optimal" squadrons formed different kinds of peer groups with unintended consequences.

ABBREVIATIONS

DWC: Development of Western Civilization

GPA: Grade Point Average

APPENDIX

TABLE A1
Are Other-Race Students' Characteristics Correlated
with Their Section's Percent Minority?

               (1)        (2)        (3)
                        SAT Math

                       Mean = 490

% minority    267.30
             (320.79)
% black                  59.21
                        (406.97)
% Hispanic                          613.06
                                   (509.75)
[R.sup.2]      0.03       0.02       0.04

               (4)        (5)        (6)
                        SAT Verbal

                       Mean = 486

% minority    187.37
             (282.99)
% black                  18.90
                        (420.98)
% Hispanic                          474.08
                                   (429.71)
[R.sup.2]      0.04       0.04       0.05

              (7)      (8)      (9)
                 High School GPA

                    Mean = 3.3

% minority    0.01
             (0.48)
% black               -0.86
                      (0.77)
% Hispanic                     -0.16
                               (0.91)
[R.sup.2]     0.03     0.03     0.03

Notes: The sample comprises 168 other-race students.
Regressions also include indicators for each entering
cohort. Robust standard errors clustered by section
in parentheses.

*** p < .01, ** p < .05, * p < .1.

TABLE A2
Are Black and Hispanic Students' Characteristics
Correlated with Their Section's Percent Hispanic and Black?

                  (1)         (2)             (3)
                       Sample of Hispanic
                       Students (N = 305)

               SAT Math    SAT Verbal   High School GPA

% black          550.1       588.0           -0.1
                (400.4)     (392.1)          (0.8)
% Hispanic

[R.sup.2]        0.029       0.035           0.013
Outcome mean      441         440             3.3

                  (4)         (5)             (6)
                 Sample of Black Students (N = 203)

               SAT Math    SAT Verbal   High School GPA

% black

% Hispanic      -296.0       -328.4           0.8
                (464.7)     (461.6)          (0.8)
[R.sup.2]        0.068       0.070           0.094
Outcome mean      374         376             3.1

Notes: Regressions also include indicators for each
entering cohort. Robust standard errors clustered
by section in parentheses.

*** p < .01, ** p < .05, * p < .1.

TABLE A3
Effect of Racial Composition of DWC
101 on Grades in DWC 101

                               (1)          (2)          (3)
                             Nonwhite      Black       Hispanic

% minority for whites         0.144       -1.366 *      0.450
                             (0.481)      (0.771)      (0.644)
% minority * minority         -0.763       -0.881      -2.042 *
                             (0.575)      (1.926)      (1.043)
Monday                        -0.477       -0.606       -0.594
                             (0.330)      (0.467)      (0.405)
Tuesday                     -0.210 **    -0.196 **    -0.237 ***
                             (0.088)      (0.084)      (0.084)
Wednesday                   -1.549 ***     -0.735       -0.737
                             (0.266)      (0.540)      (0.491)
Thursday                    -0.535 ***   -0.626 ***   -0.458 **
                             (0.194)      (0.223)      (0.176)
Friday                        -0.531     -0.784 **    -0.640 **
                             (0.320)      (0.299)      (0.256)
Monday time                   0.000        0.001        0.001
                             (0.000)      (0.000)      (0.000)
Tuesday time                 0.000 **      0.000      0.000 ***
                             (0.000)      (0.000)      (0.000)
Wednesday time              0.002 ***     0.001 **    0.001 ***
                             (0.000)      (0.000)      (0.000)
Thursday time               0.000 ***     0.000 **    0.000 ***
                             (0.000)      (0.000)      (0.000)
Friday time                 0.001 ***    0.001 ***    0.001 ***
                             (0.000)      (0.000)      (0.000)
First generation            -0.074 **     -0.063 *    -0.064 **
                             (0.030)      (0.033)      (0.030)
High school GPA             0.693 ***    0.697 ***    0.714 ***
                             (0.036)      (0.038)      (0.036)
Male                        -0.039 **    -0.037 **      -0.031
                             (0.019)      (0.018)      (0.020)
Asian                         -0.322
                             (0.244)
Black/African American        -0.241
                             (0.261)
Hispanic                      -0.206                    0.005
                             (0.251)                   (0.076)
Native Hawaii/Other           -0.273
Pacific Islander             (0.358)
Race/ethnicity unknown        -0.172      0.190 *
                             (0.263)      (0.104)
Two or more races             0.135
                             (0.245)
White                         -0.171      0.193 *       0.004
                             (0.260)      (0.110)      (0.035)
Athlete?                    -0.217 ***   -0.209 ***   -0.220 ***
                             (0.033)      (0.030)      (0.034)
SAT verbal score            0.002 ***    0.002 ***    0.002 ***
                             (0.000)      (0.000)      (0.000)
Sat math score                -0.000       0.000        -0.000
                             (0.000)      (0.000)      (0.000)
SAT verbal missing          1.273 ***    1.161 ***    1.246 ***
                             (0.122)      (0.119)      (0.124)
SAT math missing              0.039        0.154        0.056
                             (0.131)      (0.133)      (0.146)
International?               0.132 *       0.042       0.185 **
                             (0.071)      (0.086)      (0.079)
Pell Grant recipient?         -0.007       0.015        -0.023
                             (0.032)      (0.037)      (0.038)
Assigned on campus          -0.171 ***    -0.112 *    -0.138 **
room                         (0.055)      (0.062)      (0.059)
Switched to a different     -0.216 ***     -0.126     -0.154 **
room                         (0.078)      (0.077)      (0.074)

Switched more than once       0.283       0.330 *       0.287
                             (0.190)      (0.194)      (0.258)
Observations                  4,435        3,969        4,066
[R.sup.2]                     0.353        0.346        0.346

Notes: Regressions also include fixed effects for each

DWC 101 team-cohort. The omitted room category is whether
the student commutes. Robust standard errors clustered by
DWC 101 section in parentheses.

*** p < .01, ** p < .05, * p < .1.

REFERENCES

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Joecks, J., K. Pull, and K. Vetter. "Gender Diversity in the Boardroom and Firm Performance: What Exactly Constitutes a 'Critical Mass'?" Journal of Business Ethics, 118, 2013, 61-72.

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Manski, C. F. "Identification of Endogenous Social Effects: The Reflection Problem." Review of Economic Studies, 60, 1993, 531-42.

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Sacerdote, B. "Peer Effects in Education: How Might They Work, How Big Are They and How Much Do We Know Thus Far?," in Handbook of the Economics of Education, Vol. 3, edited by E. A. Hanushek, S. Machin, and L. Woessmann. Amsterdam: North Holland, 2011, 249-77.

--. "Experimental and Quasi-Experimental Analysis of Peer Effects: Two Steps Forward?" Annual Review of Economics, 6, 2014, 253-72.

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(1.) See Sacerdote (2011, 2014) for reviews.

(2.) Dee (2014) provides an example in economics. Student athletes, particularly males, may be stereotyped as "dumb jocks." Dee paired student athletes and nonathletes with similar math SAT scores. He then randomly assigned the pairs to treatment groups. Treated groups were asked a series of questions about their student-athlete status, priming these participants to think about their social identity as a student athlete or a nonathlete. All students then took a difficult academic assessment. Nonathletes performed similarly in both groups. Athletes in the treated group, however, answered fewer questions correctly than athletes in the control group, consistent with stereotype threat.

(3.) For example, Joecks, Pull, and Vetter (2013) find that the fraction of women sitting on a corporate board affects firms' performance. Initially, having more women on a board reduces performance. As the board reaches a critical mass of 30% females, firm performance increases with the fraction of women. The argument is that, when the share of the underrepresented group is large enough, diversity within that group dispels stereotypes.

(4.) In contrast, Angrist and Lang (2004) analyze Metco, the Boston-area program busing black students to predominantly white schools, and find no impact of the program on white students.

(5.) Professors are primarily faculty members in English, History, Philosophy, or Theology.

(6.) Majors differ in their racial composition. A chi squared test shows statistically significant differences. For example. 23% of the 13 physics majors are Hispanic and 10% of the 156 political science majors are black. Art History and Music, both small majors, have no nonwhite majors. However, I do not observe students' majors or the other classes in which they are enrolled.

(7.) Although "nonwhite" may not be the term of art, it more clearly illustrates how I separate students into categories based on their self-reported race and ethnicity.

(8.) Treating these students as nonwhite students makes the results for the effect of the percent nonwhite appear more like the results for the percent Hispanic.

(9.) All students who are missing their SAT verbal scores are also missing their SAT math scores; 23 students report their math but not their verbal score.

(10.) In order, there are 10, 14, 12, 9, and 9 sections in entering cohorts for 2009 to 2013.

(11.) The Kolmogorov-Smirnov statistics and exact p values for the percent nonwhite, percent black, and percent Hispanic are 0.0854 (p value = .863), 0.1143 (p value = .529), and 0.1053 (p value = .637). The Kolmogorov-Smirnov statistics and exact p values for the average SAT verbal scores for all students, for nonwhites, for blacks, and for Hispanics are 0.101 (p value = .688), 0.0726 (p value = .592), 0.1089 (p value = .592), and 0.0968 (p value = .738).

(12.) Results are similar when students' own characteristics are included in the regression.

(13.) The estimates of racial peer effects are qualitatively similar when the controls for percent athlete, percent male, percent international, percent first generation, and percent Pell grant recipients are included.

(14.) I thank the editor for this useful suggestion.

(15.) In specifications controlling for students' own characteristics, none of the coefficients on the percent minority are statistically significant.

(16.) I estimate similar specifications for students reporting a race other than white, black, or Hispanic. These estimates are in Appendix Table Al. The percent of their section who are minority students is uncorrected with SAT math scores, SAT verbal scores, and high school GPAs. I repeat the exercise for the sample of black students using the percent Hispanic and for the sample of Hispanic students using percent black. Appendix Table A2 presents these results. His panic students' characteristics are uncorrelated with the percent black; black students' characteristics are uncorrelated with the percent Hispanic. Controlling for students' own characteristics generates similar results for Appendix Tables Al and A2.

(17.) The specifications also include indicators for whether the SAT scores are missing to retain observations. I do not observe the student's major or other coursework.

(18.) Dills and Hernandez-Julian (2008) demonstrate effects of time of day and frequency of meeting on college students' grades.

(19.) The full set of results appears in Appendix Table A3.

(20.) Instead of the faculty team fixed effects, I could control for the sex and race of the professor. Of the 71 professors who teach DWC 101 during this time, 8 are nonwhite and 13 are females. Including these indicators instead of the faculty team fixed effects suggests little to no effect of professors' characteristics on the students, even allowing the effects to vary by sex or whether the student is nonwhite.

(21.) Results are qualitatively similar using math scores. Given the intensive reading and writing in the course, verbal scores seems a more appropriate choice.

(22.) The teams themselves are also not fully stable. In many cases, one professor replaces another because of sabbaticals, parental leaves, or differences in the area of expertise.

ANGELA K. DILLS, I thank Melanie Sullivan for her hard work extracting, merging, and compiling the anonymized student records and Gina DeBarnardo for explaining the enrollment process. I thank Laurie Grupp, Rey Hernandez-Julian, Kurt Rotthoff, and participants at Western Carolina University and the 2016 Eastern Economic Association meetings for their helpful comments.

Dills: Gimelstob-Landry Distinguished Professor, Department of Economics, Management, and Project Management, Western Carolina University, Cullowhee, NC 28723. Phone 828-227-3309, Fax 828-227-7075, E-mail [email protected]; [email protected]

doi: 10.1111/ecin.12481

TABLE 1
Variable Means for Nonhonors Students
by Race and Ethnicity

                               White        Nonwhite
                            (N = 3,766)    (N = 669)

Grade in DWC 101               2.88         2.52 ***
High school GPA                3.32         3.24 ***
SAT verbal                      585         523 ***
SAT math                        578         522 ***
Did not persist                0.033         0.034
Missing SAT verbal             0.141        0.169 **
Missing SAT math               0.135        0.166 **
First generation               0.146       0.517 ***
Male                           0.446        0.400 **
Athlete                        0.113        0.130 *
International                  0.008       0.033 ***
Pell recipient                 0.099       0.507 ***
No roommate switching          0.953        .930 ***

                             Black       Hispanic
                           (N = 203)    (N = 300)

Grade in DWC 101            2.29 ***     2.56 ***
High school GPA             3.11 ***      3.29 *
SAT verbal                  480 ***      534 ***
SAT math                    478 ***      533 ***
Did not persist             0.059 **      0.020
Missing SAT verbal         0.217 ***      0.167
Missing SAT math           0.217 ***     0.163 *
First generation           0.640 ***    0.537 ***
Male                        0.384 **      0.413
Athlete                    0.217 ***     0.087 *
International              0.030 ***    0.027 ***
Pell recipient             0.635 ***    0.533 ***
No roommate switching        0.961       .907 ***

Notes: Means of SAT scores do not include zeros
for missing observations. The number of observations
is smaller for these variables. Asterisks indicate the
significance of a t test of means between minority
group and white students.

*** p <.01, ** p <.05, * p <.1.

TABLE 2
Do Classmates' Characteristics Differ by Race and Ethnicity?

             (1) Avg    (2) Avg     (3) %
            Math SAT     Verbal    Minority
                          SAT

White         0.399      0.288      0.002
             (0.752)    (0.754)    (0.004)
Black         0.211      -0.363     0.003
             (0.992)    (0.994)    (0.005)
Hispanic      0.810      1.344      -0.000
             (0.917)    (0.920)    (0.004)
[R.sup.2]     0.121      0.132      0.376

              (4) %      (5) %      (6) %
              Black     Hispanic   Athlete

White        -0.003      -0.000     0.004
             (0.002)    (0.003)    (0.007)
Black       -0.005 **    -0.000    0.018 **
             (0.003)    (0.003)    (0.009)
Hispanic     -0.003      -0.003     -0.003
             (0.002)    (0.003)    (0.008)
[R.sup.2]     0.143      0.420      0.101

             (7) %        (8) %         (9) %        (10) %
             Male     International     First         Pell
                                      Generation   Recipients

White       -0.004        0.002         -0.000       0.001
            (0.005)      (0.001)       (0.003)      (0.003)
Black        0.006        0.002         -0.006       -0.005
            (0.006)      (0.002)       (0.004)      (0.004)
Hispanic    -0.003        0.001         -0.002       -0.001
            (0.006)      (0.002)       (0.004)      (0.004)
[R.sup.2]    0.135        0.187         0.196        0.188

Notes: There are 4,435 observations. Regressions
include indicators for each cohort and ten variables
capturing the section meeting times.

*** p< .01, ** p < .05, * p <.l.

TABLE 3
Are White Students' Characteristics Correlated
with Their Section's Percent Minority?

             (1)      (2)       (3)
                    SAT Math

                   Mean = 500

% minority   44.5
             (72.0)
% black               61.6
                      (117.9)
% Hispanic                      29.4
                                (89.6)
[R.sup.2]    0.017    0.017     0.017

             (4)      (5)       (6)
                   SAT Verbal

                   Mean = 502

% minority   28.7
             (68.5)
% black               -77.2
                      (121.6)
% Hispanic                      83.1
                                (87.9)
[R.sup.2]    0.023    0.023     0.023

             (7)     (8)        (9)
                High School GPA

                   Mean = 3.3

% minority   -0.2
             (0.1)
% black              -0.6 ***
                     (0.2)
% Hispanic                      0.1
                                (0.2)
[R.sup.2]    0.004   0.006      0.004

Notes: The sample comprises 3,769 observations of
white students. Regressions also include indicators
for each entering cohort. Robust standard errors
clustered by section in parentheses.

*** p< .01, ** p< .05, * p< .1.

TABLE 4
Effect of Racial Composition of DWC 101 on
Grades in DWC 101

                              (1)        (2)        (3)
                            Nonwhite    Black     Hispanic

% minority for whites        0.144     -1.366 *    0.450
                            (0.481)    (0.771)    (0.644)
% minority*minority          -0.763     -0.881    -2.042 *
                            (0.575)    (1.926)    (1.043)
Observations                 4,435      3,969      4,066
[R.sup.2]                    0.353      0.346      0.346
% minority for nonwhites     -0.619     -2.247     -1.592
                            (0.576)    (2.262)    (1.193)

Notes: Regressions also include fixed effects for each
DWC 101 team and indicators for whether the student is a
first generation student, male, an athlete. Pell grant
recipient, or international student. Additional control
variables are the student's SAT verbal score, SAT math
score, high school GPA, meeting days and times, and
indicators for whether the student lived on campus,
commuted, the number of times a student changed
roommates during the first year, and whether their
SAT math or SAT verbal scores are missing. Robust
standard errors clustered by DWC 101 section
in parentheses.

*** p < .01, ** p < .05, * p <. 1.

TABLE 5
Effects of the Diversity of DWC 101 on Grades
in DWC 101, Allowing Different Effects for
Students with Above Median SAT Scores

                               (1)        (2)         (3)
                            Nonwhite     Black      Hispanic

% minority                    0.336      -1.497      0.658
                             (0.465)    (0.902)     (0.656)
% minority * minority       -1.152 **    -0.756    -2.985 ***
                             (0.533)    (1.958)     (0.919)
% minority * above           -0.284      0.216       -0.192
median SAT                   (0.418)    (0.685)     (0.584)
% minority * above          1.719 ***    7.024     4.441 ***
  median SAT * minority      (0.355)    (5.259)     (0.831)
Above median SAT             -0.0235    -0.0544     -0.0302
                            (0.0680)    (0.0457)    (0.0496)
Observations                  4,435      3,969       4,066
[R.sup.2]                     0.356      0.347       0.350
% minority for               -0.816      -2.252     -2.327 *
nonwhites, low SAT           (0.594)    (2.325)     (1.194)
% minority for                0.619      4.987       1.922
nonwhites, high SAT          (0.629)    (6.326)     (1.293)
% minority for whites,        0.336      -1.497      0.658
  low SAT                    (0.465)    (0.902)     (0.656)
% minority for whites,       0.0520      -1.281      0.466
  high SAT                   (0.552)    (0.785)     (0.747)

Notes: Regressions also include team fixed effects and the
full set of control variables from Table 4. Robust standard
errors clustered by DWC 101 section in parentheses.

*** p < .01, ** p < .05, * p < .1.

TABLE 6
Effects of the Diversity of DWC 101 on Grades
in DWC 101, Allowing for Nonlinear Effects

                               (1)        (2)         (3)
                            Nonwhite     Black      Hispanic

% minority                  -2.658 **    -1.817    -3.755 ***
                             (1.073)    (1.275)     (1.388)
% [minority.sup.2]          7.265 ***    4.297     24.634 ***
                             (2.210)    (13.449)    (6.654)
% minority * minority        -0.292      -5.658      4.419
                             (2.892)    (5.499)     (3.949)
% [minority.sup.2] *         -0.938      46.282     -34.272
  minority                   (8.389)    (39.498)    (20.774)
Observations                  4,435      3,969       4,066
[R.sup.2]                     0.353      0.346       0.348
% minority for nonwhites     -2.950      -7.475      0.664
  (level)                    (3.021)    (5.613)     (4.124)
% minority for nonwhites      6.327      50.58       -9.638
  (squared)                  (8.359)    (41.010)    (21.310)

Notes: Regressions also include team fixed effects and the
full set of control variables from Table 4. Robust standard
errors clustered by DWC 101 section in parentheses.

*** p <.01, ** p <.05, * p <.1.

TABLE 7
Effects of the Diversity of DWC 101 on
Dropping Out after First Semester

                                              (1)          (2)
                                            Nonwhite      Black

% minority                                  -0.0427       0.1860
% minority * minority                       (0.093)      (0.297)
                                             0.0342      -0.0190
% minority * above median SAT               (0.131)      (0.558)
% minority * above median SAT * minority
Above median SAT
Grade in DWC 101
                                           -0.047 ***   -0.047 ***
Observations                                (0.007)      (0.008)
                                             4,435        3,969
[R.sup.2]                                    0.055        0.058
% minority for nonwhites                    -0.00849      0.167
                                            (0.130)      (0.589)
% minority for nonwhites, low SAT
% minority for nonwhites, high SAT
% minority for whites, low SAT
% minority for whites, high SAT

                                              (3)          (4)
                                            Hispanic     Nonwhite

% minority                                  -0.1392      -0.0066
% minority * minority                       (0.116)      (0.119)
                                             0.1993       0.0142
% minority * above median SAT               (0.208)      (0.151)
                                                         -0.0574
                                                         (0.0953)
% minority * above median SAT * minority                  0.0184
Above median SAT                                         (0.0963)
                                                          0.0150
Grade in DWC 101                                         (0.0163)
                                           -0.045 ***   -0.047 ***
Observations                                (0.008)      (0.007)
                                             4,066        4.435
[R.sup.2]                                    0.054        0.055
% minority for nonwhites                     0.0601
                                            (0.201)
% minority for nonwhites, low SAT                        0.00757
% minority for nonwhites, high SAT                       (0.125)
                                                         -0.0315
% minority for whites, low SAT                           (0.174)
                                                         -0.00661
% minority for whites, high SAT                          (0.119)
                                                         -0.0640
                                                         (0.093)

                                              (5)          (6)
                                             Black       Hispanic

% minority                                   0.243        -0.166
% minority * minority                       (0.301)      (0.173)
                                            -0.0610       0.213
% minority * above median SAT               (0.556)      (0.229)
                                             -0.102       0.048
                                            (0.175)      (0.168)
% minority * above median SAT * minority     -0.384       0.009
Above median SAT                            (0.809)      (0.265)
                                             0.0143      -0.0002
Grade in DWC 101                            (0.0139)     (0.0138)
                                           -0.047 ***   -0.045 ***
Observations                                (0.008)      (0.008)
                                             3,969        4,066
[R.sup.2]                                    0.058        0.054
% minority for nonwhites
% minority for nonwhites, low SAT            0.182        0.0469
% minority for nonwhites, high SAT          (0.587)      (0.190)
                                             -0.304       0.104
% minority for whites, low SAT              (0.930)      (0.355)
                                             0.243        -0.166
% minority for whites, high SAT             (0.301)      (0.173)
                                             0.141        -0.118
                                            (0.316)      (0.114)

Notes: Regressions also include team fixed effects
and the full set of control variables from Table 4.
Robust standard errors clustered by DWC 101
section in parentheses.

*** p< .01, ** p < .05, * p<.1.

TABLE 8
Effect of Racial Composition of DWC 101 on
Probability of Switching Teams for DWC 102

                                              (1)          (2)
                                            Nonwhite      Black

% minority                                   2.076        2.386
                                            (1.357)      (2.254)
% minority * minority                        -0.284       -0.426
                                            (0.367)      (0.891)
% minority * above median SAT
% minority * above median SAT * minority
Above median SAT

Grade in DWC 101                           -0.069 ***   -0.069 ***
                                            (0.012)      (0.012)
DWC 101 grade easiness                     1.402 ***    1.315 ***
                                            (0.176)      (0.318)
Observations                                 4,435        3,969
[R.sup.2]                                    0.385        0.376
% minority for nonwhites                     1.792        1.960
                                            (1.245)      (2.457)
% minority for nonwhites, low SAT
% minority for nonwhites, high SAT
% minority for whites, low SAT
% minority for whites, high SAT

                                              (3)          (4)
                                            Hispanic     Nonwhite

% minority                                  3.243 *       2.159
                                            (1.796)      (1.319)
% minority * minority                        -0.394       -0.341
                                            (0.726)      (0.376)
% minority * above median SAT                             -0.148
                                                         (0.167)
% minority * above median SAT * minority                  0.0248
                                                         (0.225)
Above median SAT                                         0.00248
                                                         (0.0313)
Grade in DWC 101                           -0.070 ***   -0.069 ***
                                            (0.010)      (0.0118)
DWC 101 grade easiness                     1.752 ***    1.405 ***
                                            (0.166)      (0.176)
Observations                                 4,066        4,435
[R.sup.2]                                    0.396        0.385
% minority for nonwhites                     2.849
                                            (1.974)
% minority for nonwhites, low SAT                         1.818
                                                         (1.222)
% minority for nonwhites, high SAT                        1.695
                                                         (1.350)
% minority for whites, low SAT                            2.159
                                                         (1.319)
% minority for whites, high SAT                           2.011
                                                         (1.386)

                                              (5)          (6)
                                             Black       Hispanic

% minority                                   2.113       3.205 *
                                            (2.219)      (1.749)
% minority * minority                        -0.213       -0.372
                                            (0.893)      (0.739)
% minority * above median SAT                0.516        0.0586
                                            (0.492)      (0.256)
% minority * above median SAT * minority     -1.950      -0.0107
                                            (1.569)      (0.619)
Above median SAT                            -0.0415      -0.0224
                                            (0.0299)     (0.0230)
Grade in DWC 101                           -0.069 ***   -0.070 ***
                                            (0.0124)     (0.0103)
DWC 101 grade easiness                     1.311 ***    1.753 ***
                                            (0.317)      (0.166)
Observations                                 3,969        4,066
[R.sup.2]                                    0.377        0.396
% minority for nonwhites
% minority for nonwhites, low SAT            1.900        2.833
                                            (2.451)      (1.954)
% minority for nonwhites, high SAT           0.466        2.881
                                            (3.004)      (2.123)
% minority for whites, low SAT               2.113       3.205 *
                                            (2.219)      (1.749)
% minority for whites, high SAT              2.629       3.263 *
                                            (2.297)      (1.831)

Notes: Regressions also include team fixed effects
and the full set of control variables from Table 4.
Robust standard errors clustered by DWC 101
section in parentheses.

*** p < .01, ** p < .05, * p < .1.