Peer effects in college academic outcomes – Gender matters!

Economics of Education Review 31 (2012) 1102–1115

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Peer effects in college academic outcomes – Gender matters! Carlena Cochi Ficano ∗ Department of Economics, 229 Golisano Hall, Hartwick College, Oneonta, NY 13820, United States

a r t i c l e

i n f o

Article history: Received 7 September 2010 Received in revised form 3 July 2012 Accepted 27 July 2012 JEL classification: I21 Keywords: Peer effects Educational economics

a b s t r a c t An extensive literature exploring a range of peer influences on both academic and nonacademic outcomes continues to produce contradictory evidence regarding the existence and magnitude of peer effects. Our results provide no evidence of peer effects in models where peer academic ability is measured in the aggregate. However, models that control for own-gender and other gender peer performance identify strong, positive, and statistically significant male peer influence on male students. In contrast, females are unresponsive to either male or female peer average academic rating. The results highlight the possibility that significant own gendered effects for males may be masked by insignificant effects in the aggregate. © 2012 Elsevier Ltd. All rights reserved.

1. Background and motivation During the transition from high school to college, students encounter new academic challenge. They also struggle to establish their identity in an unfamiliar environment, leaving open the potential for peer influence on behavior. An extensive empirical literature investigates the presence of peer effects in higher education. Studies have addressed the impact of peer academic ability on own academic performance (e.g., Brunello, De Paola, & Scoppa, 2010; Foster, 2006; Han & Li, 2009; Winston & Zimmerman, 2003; Zimmerman, 2003); the effects of other peer characteristics such as family income, leadership ability or fitness on own academic performance (e.g., Carrell, Fullerton, & West, 2008; Stinebrickner & Stinebrickner, 2005); and the effects of peer characteristics on other behaviors such as the decision to join a Greek organization or athletic team or select and persist in a given academic major (e.g., De Giorgi, Pellizzari, & Redaelli, 2010; Lyle, 2007; Ost, 2010; Sacerdote, 2001). An understanding of the operation of peer influences on these outcomes can inform student

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admissions and tracking policy across a range of educational institutions. With respect to the impact of peer academic ability on own academic performance, the literature recognizes a number of distinct transmission mechanisms. In particular, Stinebrickner and Stinebrickner (2005) identify role models with respect to time use, study habits, and class effort as a channel through which peer effects operate. Similarly, Eisenkopf (2010) and Foster and Frijters (2010) identify peer influenced own motivation as a channel through which peer effects operate. Carrell et al. (2008) allude to study group connections to explain stronger peer effects in math and science than humanities courses. Goethals (2001) and Zimmerman (2003) draw heavily upon social comparison theory (Festinger, 1954) to motivate their independent analyses of peer effects on Williams College undergraduates. A majority of the analyses focus on residential peer groupings, usually roommates or floor mates. Some exceptions to this are De Paola and Scoppa (2010) and De Giorgio, Pellizzari, and Redaelli (2010) who use classmate peers; Carrell et al. (2008) and Lyle (2007) whose military peer groups encompass both the academic and residential simultaneously; Hansen, Owan, and Pan (2006) who exploit a natural experiment design in business class project grouping; and Eisenkopf (2010) and Goethals

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(2001) who use random treatment and control group assignment. The existing empirical evidence on peer effects is mixed. Sacerdote (2001), Winston and Zimmerman (2003), and Stinebrickner and Stinebrickner (2005) find that roommate academic ability has a significant and positive effect on own GPA. Brunello et al. (2010) find evidence of roommate peer effects in the hard sciences only while De Paola and Scoppa (2010) identify positive classmate peer effects that correlate with the nature of peer interaction. Zimmerman (2003) finds no effect of roommate total SAT but does find a small but positive and significant effect of roommate verbal SAT score. Carrell et al. (2008) also find significant effects of peer verbal SAT, but unlike Sacerdote and Winston and Zimmerman, they find this at the squadron level and not at the roommate level. Foster (2006) finds weak evidence of peer effects while Lyle (2007) finds no significant effect of peer academic ability on own academic performance. The size of peer effects appear to depend on where one falls in a school’s academic distribution (Ost, 2010; Stinebrickner & Stinebrickner, 2005; Winston & Zimmerman, 2003; Zimmerman, 2003) and the measure of peer academic performance used. In particular, Griffith and Rask (2010) note that in their own and others’ analyses, high school achievement is a consistently stronger peer measure than are standardized test scores. The literature also finds that peer effects vary by gender (Foster, 2006; Goethals, 2001; Griffith & Rask, 2010; Han and Li, 2009; Stinebrickner & Stinebrickner, 2005; Winston & Zimmerman, 2003; Zimmerman, 2003), although studies disagree on which gender is more strongly affected. A potential source of the aforementioned inconsistency in empirical evidence of peer effects may be variation across schools in what constitutes the relevant peer group (Foster, 2006). For example, roommates may represent an effective peer group in some undergraduate settings, while floor-mates or classmates may be more influential in other settings. Further, students may be differentially affected by peers who are more or less similar to themselves in race, ethnicity or ability (Bifulco, Fletcher, & Ross, 2009; Fletcher & Tienda, 2008; Goethals, 2001; Griffith, 2008). For example, studies using roommates frequently identify own gender peer effects – in some instances stronger for women (Han & Li, 2009; Stinebrickner & Stinebrickner, 2005) and in some instances stronger for men (Griffith & Rask, 2010), that might have been diluted if own and other gender peers were considered in aggregate. In this paper, we further explore the hypothesis that peer effects may differ by gender and that students may be differentially affected by own and other gendered peers. Similar to Lyle (2007), we begin by modeling the effect of a student’s classmates’ academic quality on her own academic performance in the first semester of college. Our models use data on two cohorts of students from a small, selective liberal arts college. Consistent with the evidence generated by the Lyle analysis, our results using measures of aggregate classmate academic quality provide no evidence of peer effects. However, acknowledging the well-documented gender gap reversal in which males have underperformed females in college achievement and completion since at least the

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early 1990s (DiPrete & Buchmann, 2006), we extend the base models to allow for gender differences in peer effects. Specifically, we separately consider the effect of male peer academic quality on male and female grade outcomes and female peer academic quality on female and male grade outcomes, under the assumption that the effective peer group may be gender determined. In contrast to the base model results, results from these models indicate that male peer academic quality positively and significantly influences male student performance but not female student performance, while female peer academic quality has no statistically significant effect on either male or female course GPA. In other words, males appear more susceptible to peer influence than females, and they appear to be differentially affected by male and female classmate academic quality. If own and other-gender peer effects have the potential to cancel one another or if positive peer effects for one gender can be diluted by insignificant peer effects for another gender, it becomes important to differentiate own and other-gendered peer effects where data allow. The remainder of the paper is organized as follows. Section 2 presents the empirical techniques employed in the analysis and addresses the means by which we address the multiple sources of endogeneity endemic to this type of analysis. Section 3 introduces our data source and defines the variables used in the regressions. Section 4 presents the results of the analysis and robustness checks and Section 5 concludes. 2. Model We follow a standard education production function model where a student’s academic ability and preparedness (Ai ) and the quality and context of the educational process (Qi ) are the primary production inputs that generate the outcome of interest, student college academic performance (Hanushek, 1979). Recognizing the potential for one’s peers to influence the translation of student ability/preparedness into “produced output” (i.e., a grade) through both “peer mentor” channels (Stinebrickner & Stinebrickner, 2005) and by social comparison (Suls, Martin, & Wheeler, 2002), we extend the model to include peer academic quality (Pi ) as an additional production process input. We estimate regression models of own student first semester course level GPA as a function of peer high school academic performance and other controls: GPAi = ˇ0 + ˇ1 Ai + ˇ2 Ai + ˇ2 Qi + ˇ2 Pi + ei

(1)

2.1. Endogenous peer groupings Interpretation of regression results from (1) as evidence of peer effects introduces two distinct empirical concerns, the first of which is that the peer academic measure must be exogenous to the model. In other words, our specification must address endogeneity from selection of academically similar individuals into the peer group and endogeneity from the simultaneous determination of own and peer performance. Our use of high school academic performance indicators as our peer ability measures removes the potential for simultaneity as peer quality is determined prior to

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college matriculation. Controls for selection endogeneity are less easily addressed. In the literature, instances of random roommate or squadron selection (Carrell et al., 2008; Han & Li, 2009; Lyle, 2007; Sacerdote, 2001; Stinebrickner & Stinebrickner, 2005; Winston & Zimmerman, 2003), controlled experiments (Eisenkopf, 2010; Goethals, 2001; Hansen et al., 2006), instrumental variables techniques (De Paola & Scoppa, 2010), or course fixed effects (Ost, 2010) typically address selection. In this paper, we exploit the fact that first semester course selection, while not completely random, is generally made by the student prior to arriving on campus with little peer input or influence and is thus exogenous conditional upon observed student characteristics. Further, selection into a given section of a course is made by the college and is random conditional upon student schedule constraints. The nature of the freshman course and course section selection process in our sample merits a brief explanation, and our claim of conditional exogeneity of peer groupings from that selection process merits justification. The course selection process in our sample occurs as follows. Guided by a course preference worksheet that prompts student choice of a departmentally based freshman seminar and a distribution of other courses across academic divisions, students select and rank course options, but not course sections, corresponding to their academic interests during the summer prior to their college matriculation. College faculty and staff register students for a subset of the selected course options based upon course availability, major requirements (if the student declares a major or indicates a strong major interest), and incoming mathematics and writing placement scores.1 While freshmen distribute themselves across academic departments, the majority of students takes a composition (607 out of 889) or composition related (125 out of 889) writing course and a freshman seminar within or outside of their major area of interest. When multiple sections of the same course are offered, section selection is determined by the college largely based upon athletic participation (e.g., athletes are unable to take later afternoon sections due to practice conflicts) and lab-course conflicts. Thus, athletes and science majors are likely to congregate in similar sections, while non-science majors and non-athletes distribute more randomly. With this course selection process, the potential for endogeneity at the course level remains but endogeneity at the section level of a given course is unlikely. Thus, we estimate course fixed effects models for the approximately 69% of total courses for which we observe multiple sections of a course offered over the sample period. These courses enroll over 90% of the freshman student academic course load and capture some portion of the course schedule of 873 of the 889 students in the full sample. In other words, we exploit both the implicit panel nature of the data and the

1 The data do not reveal students who, at the time of the census one month into the semester, have switched from their original course selections. Endogenous switching between courses should be corrected by the course fixed effects estimation strategy. However, endogenous switching between sections of a given course remains a potential problem in the model.

semi-exogenous course selection process described above in an attempt to identify peer effects within the following framework: GPAijk = ˇ0 + ˇ1 Ai + ˇ2 Qi + ˇ2 Pijk + ∝j + i (∝)j ∗ i + ijk (2) where i represents student, j represents course (e.g., Biology 101), k represents course section (e.g., Biology 101 taught at 9:00 on Tuesdays and Thursdays), ∝j reflects unobserved factors correlated with student performance in a course which vary across courses but remain constant for students enrolled in a given course, and  i represents student schedule constraints likely to influence section choice. Consistent with the course section assignment process described earlier, we define schedule constraints to be one of the following: athletic participation constraints, lab requirement constraints, both athletic and lab requirement constraints, or no constraints (base case). Note that in these models, classmates in a student’s section of a given course constitute the relevant peer group potentially acting upon that student’s performance in the course. Variation in peer ability across multiple sections of a given course identifies the peer effects in the presence of course fixed effects estimation methods.2 A placebo test of the ex post conditional randomness of peer grouping at the course section level examines the correlation between section enrollment propensity and own ability, controlling for enrollment in any section of the course and student schedule constraint as indicated above. If (1) section enrollment propensities are uncorrelated with student academic rating given controls for enrollment in the course and student schedule constraints, and if (2) the parameter estimates on the course enrollment indicators are robust to the inclusion of student level controls, the estimation strategy is likely adequate to identify exogenous peer effects. Fig. 1 presents the significance of own academic ability in linear probability models of section enrollment into each of the different course sections offered over the sample period. Here, the height of the bar represents one minus the p-value on the own academic rating variable. Note that the vast majority of the bar heights, 217 out of 240, are below 0.90, indicating the statistical insignificance of peer academic rating in most of the section selection regressions. In all of these models, the parameter estimates on the course enrollment indicator variables interacted with the student schedule constraint variables are robust to the inclusion of student level controls, and the course enrollment indicators capture the majority of

2 For comparison, results without course fixed effects for all courses offered and parallel results for the relevant subsample of courses with multiple sections are presented in the first and second columns of Appendix Table A1, respectively. These results reveal negative own and other gender peer effects for all groups except men; own male peer effects for men are positive and marginally significant. The results are consistent with selection bias which is stronger for women than men. Student semester GPA models, in which peers are defined as all students sharing any class section with the reference student and in which the outcome of interest is semester rather than course GPA, are presented in the third column of Appendix Table A1. The results are similar to those presented in Table 3 and provide an additional venue for comparison.

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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Fig. 1. Statistical significance of own academic rating in section enrollment propensity regressions (bar height = 1 − p). Note: Each bar represents the significance (1 − p) of the own academic rating variable in a linear probability model of section enrollment for a given course section. Additional model controls include course (as opposed to section) indicator, student schedule constraint, and their interaction. Results are robust to the inclusion of the full set of model controls used in the paper. Of the 240 total course enrollment propensities estimated, academic rating is significant at p < 0.10 in only 23 instances.

the regressions’ explanatory power. Together, these results support a claim of section peer grouping exogeneity necessary for identification of peer effects. 2.2. Relative grading norms A second empirical concern introduced by the model involves relative grading norms (i.e., grading on a curve). Interpretation of the model results as evidence of peer effects requires that own student GPA be measured in an absolute rather than relative (i.e., grading on a curve) terms. The grading policy at the institution from which our data derive is nominally absolute, as indicated by formal description of the grading policy as being based upon depth of mastery and originality of thought.3 However, if faculty members do curve grades, then a student’s own GPA is negatively affected by strong peers and positively affected by weak peers by mathematical definition. Further, if grading norms vary departmentally, the peer-own student performance relationship will vary systematically by a student’s course distribution.4 To test for grading norms, we examine grade distributions by department and

3

Source: Grading Policy, College Catalogue. Our use of controls for the departmental distribution of a student’s courses minimizes this concern. 4

division. These distributions should not vary substantially in the presence of relative grading. Fig. 2 displays the grade distributions in courses that enrolled any freshmen over the sample period by academic department where departments are anonymously identified by the color of the bar. Table 1 provides the departmental and academic division (Social Science, Physical Science and Humanities) average mean, median and standard deviation of course grades over the same period. These data indicate that the Physical Sciences assign slightly lower and the Humanities assign slightly higher grades relative to the Social Sciences, and that there is substantial random variation in grade distributions within and between departments across the college. As such, we assume that no implicit or explicit relative grading norms are in operation in the sample. 3. Data and variables Our analysis dataset was collected from a small selective private liberal arts college. Unless otherwise noted, all data were retrieved from a central college administrative database. The data follow the students who entered in the Fall of 2006 and those who entered in the Fall of 2007 through the end of their first college semester, measuring socio-demographics and high school achievement at the time of admission, measuring course configurations and co-curricular affiliations approximately one month into

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0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

A

A-

B+

B

B-

C+

C

C-

D+

D

D-

F

Fig. 2. Distribution of course grades by academic departments. Note: Academic departments are anonymously identified by the color of the bar. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) Source: College administrative database.

the semester, and measuring realized course GPA after semester completion for each completed course.5 The data contain a rich set of variables for not only each student in the data, but also for each of the peers that they encounter in classroom and residential settings. Following the structure of Eq. (2), our empirical GPA model includes academic rating and original math and writing level to capture a student’s ability level. A student’s academic rating is assigned on a scale of one to five by the Admissions Office and is based on high school GPA, and SAT or ACT scores. A one point increase in academic rating is roughly equivalent to a four point increase in high school GPA and a 70 point increase in the combined verbal and quantitative SAT scores. A student’s writing level is determined by a placement test that students take in the summer before their freshman year. Students scoring a “1” must take a writing tutorial before beginning college composition; students scoring a “2” are immediately eligible

5 An additional empirical concern involves partial observability of the GPA data. We are able to observe course GPA only for those who retain through the first semester. We present results for the 97.5% of the students in the sample who complete their first college semester. Heckman selection models on the full sample yield nearly identical results and are available upon request.

for college composition; students scoring a “3” place out of composition and are immediately eligible for a writing across the curriculum course; and students scoring a “4” satisfy the college writing requirement upon entry. A student’s math level is determined in a similar manner and determines the range of math courses a student is eligible to take. High school quality variables capture student preparedness for college. Specifically, we include dummy variables indicating whether a student’s high school offered fewer than 3 AP courses or 3 or more6 and whether the student attended a public high school (private or parochial represent the base case). We include demographic variables to account for a student’s gender, race, and home community’s degree of urbanization (metropolitan area represents the base case) that might further influence preparedness. Finally, we include measures of a student’s financial need and level of financial aid receipt likely to both influence preparedness prior to enrollment and student level access to academic and co-curricular inputs after matriculation. To capture the quantity and quality of the academic and co-curricular inputs in the production function more

6 Data used was drawn from the College Board’s Enrollment Planning Service (EPS® ).

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Table 1 Grade distribution statistics for freshmen courses by academic department and division. Academic department (anonymously identified by number)

Departmental/divisional average mean grade

Departmental/divisional average median grade

Departmental/divisional average grade standard deviation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

2.433 3.115 3.188 2.504 2.848 2.498 3.049 2.466 3.196 2.963 2.912 2.582 2.805 2.638 3.216 2.654 3.105 3.180 3.013 2.979 2.808 2.919 2.691 2.913 2.578 2.937 2.715 3.329

2.540 3.317 3.400 2.595 3.000 2.655 3.327 2.570 3.370 3.135 3.240 2.715 3.100 2.793 3.400 2.738 3.289 3.250 3.188 3.185 2.940 3.063 2.858 3.000 2.700 3.018 2.873 3.527

1.222 0.905 0.813 1.049 0.713 1.123 1.071 1.070 0.797 0.855 1.003 0.988 1.040 0.973 0.692 1.063 0.815 0.869 0.850 0.973 0.918 0.869 0.925 0.937 1.090 0.825 1.065 0.775

Social science Physical science Humanities

2.812 2.678 3.011

2.955 2.821 3.199

0.927 1.037 0.884

Source: College administrative database. Note: Numbers in the table represent grade mean, median, and standard deviation at the course section level averaged by department and division across all course sections enrolling freshmen students.

directly, we include whether or not a student participated in the college’s honors program, a student’s academic credit load, and the average class size encountered by the student. To capture the influence of one’s peers, we create a series of classmate peer average academic achievement variables. We begin with aggregate measures that reflect the mean academic rating of one’s classmates in the course section. Then, recognizing the potential for gender differences in the norms of mentoring and social comparison, we distinguish between the course section mean academic ratings of males and females. Finally, we allow students to be differentially affected by own-gender academic rating and other gender academic rating by interacting the genderdifferentiated academic rating variables with a student’s own gender. Table 2 provides an overview of the background characteristics, college experience variables, and own and peer academic quality for students in the sample, both overall and by gender, and highlights important gender differences. Female students are more likely to have attended public high schools and come from small towns. They are on average financially needier than males, but they have a smaller proportion of that need met through aid than do males. Nonetheless, relative to male students, female students exhibit stronger academic aptitude as indicated by statistically significant higher mean academic rating,

honors program participation and college GPA. They generally carry more credits and are less likely to major in business or be “undeclared” than males. They are also less likely to be schedule constrained by athletics but more likely to be schedule constrained by lab requirements than are their male counterparts. On average, they are in courses with lower proportions of male students, but their male classmates are more highly rated academically than the male classmates of the average male student. Fig. 3A–C provides a more complete picture of relevant gender differences in own and peer academic rating. As is evident from the first histograms, the distribution of class female academic ratings lies to the right of the corresponding distribution for males. Further, as shown in Fig. 2B, women encounter a slightly stronger but more variable set of male peers than do men (p-value for difference in subsample mean = 0.000) while men and women encounter similar distributions of females in classes. Thus, women are both academically stronger and are, on average, in class with academically stronger male peers than are men. This gender difference in exposure to male and female peers may in part explain differences in peer sensitivity. For this reason, we run models that incorporate a variety of distributional peer academic rating measures (i.e., mean, minimum, maximum, median, inter-quartile range and standard deviation) but present only those

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Table 2 Estimation sample descriptive statistics. Full sample

Male sample

Female sample

Outcome variable Own GPA*** Pre-matriculation characteristics High school offers fewer than 3 AP courses Attended a public high school*** Home residence (omitted category = urban) Micropolitan area Small town*** Rural area Gender (1 if male) Race (1 if white)

2.746 (0.875)

2.511 (0.941)

2.919 (0.779)

0.143 (0.350) 0.832 (0.374)

0.137 (0.345) 0.792 (0.406)

0.147 (0.355) 0.861 (0.347)

0.094 (0.292) 0.064 (0.245) 0.078 (0.268) 0.425 (0.495) 0.654 (0.476)

0.081 (0.273) 0.035 (0.184) 0.094 (0.293) 1.000 (0.000) 0.652 (0.477)

0.104 (0.305) 0.086 (0.280) 0.066 (0.248) 0.000 (0.000) 0.655 (0.476)

0.090 (0.287) 0.174 (0.379) 0.145 (0.353) 0.078 (0.268) 0.385 (0.487) 13.801 (1.560) 0.159 (0.366) 0.247 (0.431) 0.055 (0.228) 26.246 (9.335) 0.110 (0.313)

0.162 (0.369) 0.146 (0.353) 0.146 (0.353) 0.016 (0.126) 0.458 (0.499) 13.534 (1.458) 0.240 (0.428) 0.159 (0.364) 0.043 (0.204) 25.919 (8.683) 0.059 (0.237)

0.038 (0.191) 0.195 (0.397) 0.145 (0.353) 0.124 (0.329) 0.331 (0.471) 13.998 (1.603) 0.100 (0.300) 0.313 (0.464) 0.064 (0.245) 26.487 (9.790) 0.147 (0.355)

21.657 (15.123) 15.710 (7.326)

18.834 (15.620) 14.311 (7.155)

23.744 (14.409) 16.744 (7.287)

2.716 (1.336) 2.024 (0.514) 3.451 (1.416)

2.423 (1.257) 1.995 (0.493) 3.501 (1.401)

2.932 (1.352) 2.046 (0.529) 3.414 (1.427)

0.434 (0.134) 2.818 (0.320) 2.654 (0.430) 2.988 (0.341) 2.519 (0.534) 2.985 (0.449)

0.526 (0.109) 2.768 (0.315) 2.582 (0.389) 2.970 (0.327) 2.402 (0.503) 2.989 (0.409)

0.367 (0.108) 2.855 (0.319) 2.707 (0.451) 3.001 (0.351) 2.606 (0.541) 2.983 (0.477)

Academic and co-curricular activities Business major*** Social science major (not

business)*

Science major (not nursing) Nursing major*** Undecided major*** Total academic credits*** Athletic participation constraint alone*** Lab course constraint alone*** Multiple schedule constraints Average class size Membership in college honor’s program*** Financial considerations Student need*** Student aid*** Student college ability level Own academic rating*** Own writing level Own math level Peer effects Proportion of class that is male*** Average class AR*** Average class male AR*** Average class female AR Median class male AR*** Median class female AR Sample size

Asterisks indicate significant mean differences by gender. ** p < 0.05. *** p < 0.01. * p < .10.

873

371

502

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distributional measures that significantly impact upon own student course GPA. Controls for the proportion of peers who are male are included in all regressions. 4. Regression results Table 3 presents coefficients from the course fixed effects models that estimate student grade point average (GPA) in a given section of a course as a function of covariates measuring pre-matriculation student socio-demographics, student academic and co-curricular activities during the freshman fall semester, own student academic ability, and an increasingly specific set of course section level peer academic controls. A brief discussion of the non-peer covariate results follows the presentation of the peer results below. 4.1. The role of gender in peer effects Panel A of Table 3 presents the coefficients on the peer variables. Consistent with the results of Lyle (2007), the base GPA models using overall and gender differentiated peer academic rating provide no evidence of aggregate peer effects as shown by the lack of statistical significance on the “Class AR,” “Class Male AR,” and “Class Female AR” parameter estimates in columns 1 and 2. However, interesting patterns arise when we separately control for the performance of one’s male and female peers and interact these gendered peer variables with a student’s own gender. Columns 3–5 present the results from an empirical specification that includes measures of male peer academic rating and female peer academic rating and their interaction with a student’s own gender. Each column uses a different distributional measure of peer academic rating, namely peer mean (column 3), peer median (column 4), and peer mean standardized against the college-wide mean (column 5). Column 6 presents the gendered and interacted mean academic rating results separately for the roughly 90% of the course sections that passed the placebo test described earlier and serves as a robustness check. In columns 3–6, note the consistently significant positive coefficient on the interaction of “Male” and “Class Male AR” and the individually and jointly insignificant coefficient estimates on the remaining peer variables. This evidence that males are both responsive to peer influence and that they are responsive to male peers parallels the positive roommate peer effects identified for males by Griffith and Rask (2010). It also highlights the possibility that significant peer influence may be obscured when peers are defined in the aggregate. Tables 4–7 convert the results from panel A of Table 3 into own and cross-gendered effects for ease of interpretation. Table 4 indicates that a one point increase in the mean academic rating of one’s male peers correlates with a 0.103 point increase in predicted course GPA for males (standard error = 0.059) but has no impact

Fig. 3. (A) Distribution of class average gendered academic rating, by gender. (B) Distribution of class male average academic rating, by own gender. (C) Distribution of class female average academic rating, by own gender.

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Table 3 GPA regression results. 1 (A) Peer academic performance variables Proportion of class that is male Average class AR

2 0.279 (0.176) −0.001 (0.052)

3 0.290 (0.240)

0.286 (0.252)

0.271 (0.266)

0.286 (0.252)

0.265 (0.256)

0.018 (0.037) −0.012 (0.039)

−0.031 (0.030) −0.045 (0.044) 0.109** (0.045) 0.044 (0.059) 0.082

−0.024 (0.029) −0.020 (0.038) 0.101** (0.044) 0.028 (0.044) 0.145

−0.030 (0.048) −0.017 (0.062) 0.150** (0.063) 0.050 (0.072) 0.155

0.872

−0.203*** (0.054) 0.302*** (0.053) 0.196*** (0.040) 0.028 (0.062) 0.131* (0.102) −0.216*** (0.054) 0.114*** (0.041)

−0.204*** (0.054) 0.303*** (0.053) 0.197*** (0.040) 0.028 (0.062) 0.131* (0.068) −0.217*** (0.048) 0.113*** (0.041)

−0.203*** (0.054) 0.299*** (0.053) 0.191*** (0.039) 0.027 (0.062) 0.125* (0.068) −0.433*** (0.157) 0.112*** (0.041)

−0.203*** (0.054) 0.308*** (0.053) 0.187*** (0.040) 0.027 (0.061) 0.127* (0.068) −0.359*** (0.159) 0.111*** (0.041)

−0.203*** (0.054) 0.299*** (0.053) 0.191*** (0.039) 0.027 (0.062) 0.125* (0.068) −0.212*** (0.046) 0.112*** (0.046)

−0.192*** (0.054) 0.261*** (0.056) 0.169*** (0.040) 0.013 (0.071) 0.101 (0.075) −0.424** (0.182) 0.111** (0.043)

0.081 (0.062) −0.057 (0.085) 0.109 (0.091) 0.026 (0.077) 0.369 (0.250) 0.048*** (0.014) 0.000 (0.002) 0.141** (0.057)

0.081 (0.062) −0.056 (0.084) 0.108 (0.091) 0.026 (0.077) 0.377 (0.352) 0.047*** (0.014) 0.000 (0.003) 0.139** (0.058)

0.083 (0.063) −0.051 (0.084) 0.108 (0.091) 0.023 (0.077) 0.359 (0.252) 0.047*** (0.014) 0.000 (0.003) 0.146** (0.058)

0.080 (0.062) −0.058 (0.082) 0.112 (0.091) 0.017 (0.076) 0.344 (0.257) 0.049*** (0.014) 0.000 (0.003) 0.148** (0.059)

0.083 (0.063) −0.051 (0.084) 0.109 (0.091) 0.023 (0.077) 0.359 (0.252) 0.047*** (0.014) 0.000 (0.003) 0.146** (0.058)

0.098 (0.068) −0.067 (0.092) 0.104 (0.099) 0.014 (0.087) 0.421 (0.255) 0.039*** (0.014) 0.000 (0.003) 0.110* (0.061)

0.261*** (0.022) 0.033** (0.015) 0.150*** (0.031)

0.262*** (0.020) 0.032** (0.015) 0.150*** (0.031)

0.264*** (0.020) 0.031** (0.015) 0.151*** (0.030)

0.258*** (0.021) 0.032** (0.015) 0.151*** (0.030)

0.264*** (0.020) 0.031** (0.015) 0.151*** (0.030)

0.280*** (0.018) 0.028* (0.017) 0.148*** (0.035)

Male * average class male AR Female * average class female AR

Attended a public high school Micropolitan area Small town Rural area Gender (1 if male) Race (1 if white) (C) Academic and co-curricular activities Undecided major Business major Science major (not nursing) Social science major (not business) Nursing major Total academic credits Average class size Membership in college honor’s program (D) Student college ability level Own academic rating Own math level Own writing level E. Financial Financial need Financial aid Sample size – students Sample size – student course sections

6

0.992

Average class female AR

(B) Pre-matriculation High school offers <3 AP courses

5

−0.032 (0.038) −0.031 (0.061) 0.135** (0.059) 0.045 (0.070) 0.145

Average class male AR

Joint significance of peer (p-value)

4

−0.002 (0.002) −0.001 (0.004) 873 3439

−0.002 (0.002) 0.001 (0.004) 873 3439

−0.001 (0.002) −0.001 (0.004) 873 3439

−0.002 (0.002) 0.001 (0.004) 873 3439

−0.001 (0.001) 0.001 (0.004) 873 3439

−0.001 (0.002) 0.002 (0.004) 871 3100

Standard errors presented in parentheses. All models include additional controls for departmental distribution of courses and are estimated with course X student schedule constraint fixed effects on a sample of courses where multiple sections are offered. * p < 0.10. ** p < 0.05. *** p < 0.01.

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Table 4 Gendered peer effects on own student GPA, peer variable = mean class academic rating. Level effect

Incremental own gender effect

Total effect

(bacademic rating )

(bacademic rating×gender )

On male student GPA

On female student GPA

Average class mean male academic rating

−0.032 −0.038

0.135** −0.059

0.103* −0.059

−0.032 −0.038

Average class mean female academic rating

−0.031 −0.061

0.045 −0.07

−0.031 −0.061

0.014 −0.045

√ Note: Standard error of the total effect in all models presented in Tables 4–7 calculated as follows: se (total effect) = var(bacademic rating ) + var(bacademic rating×gender ) + 2cov(bacademic rating ,bacademic rating×gender ). All models include the following additional covariates: gender, race, public high school attendance, indicator of whether the high school offered less than three advanced placement courses, student’s community of origin (suburban, small town, and rural), indicator of student participation in the college honors program, student writing level, student academic rating, student financial need and aid receipt, student major (business, science, social science, nursing, and humanities), and distribution of the student’s courses across departments. Models are estimated with course X student schedule constraint fixed effects. ** p < 0.05. * p < 0.10. *** p < 0.01. Table 5 Gendered peer effects on own student GPA, peer variable = median class academic rating. Level effect

Incremental own gender effect

Total effect

(bacademic rating )

(bacademic rating×gender )

On male student GPA

On female student GPA

Average class median male academic rating

−0.031 −0.03

0.109** −0.045

0.078 −0.052

−0.031 −0.03

Average class median female academic rating

−0.045 −0.044

0.044 −0.059

−0.045 −0.044

−0.001 −0.037

√ Note: Standard error of the total effect in all models presented in Tables 4–7 calculated as follows: se (total effect) = var(bacademic rating ) + var(bacademic rating×gender ) + 2cov(bacademic rating ,bacademic rating×gender ). All models include the following additional covariates: gender, race, public high school attendance, indicator of whether the high school offered less than three advanced placement courses, student’s community of origin (suburban, small town, and rural), indicator of student participation in the college honors program, student writing level, student academic rating, student financial need and aid receipt, student major (business, science, social science, nursing, and humanities), and distribution of the student’s courses across departments. Models are estimated with course X student schedule constraint fixed effects. * p < 0.10 ** p < 0.05. *** p < 0.01.

on GPA for females. The average academic rating of one’s female peers has no statistically significant effect on GPA for either gender. Similar results obtain using median and standardized mean peer measures as shown

in Tables 5 and 6, respectively. Specifically, a one point increase in the median academic rating of one’s male peers associates with a 0.078 point increase in predicted course GPA for males (standard error = .052) but not for

Table 6 Gendered peer effects on own student GPA, peer variable = standardized mean class academic rating. Level effect

Incremental own gender effect

Total effect

(bacademic rating )

(bacademic rating×gender )

On male student GPA

On female student GPA

Average class std mean male academic rating

−0.024 −0.029

0.101** −0.044

0.077* −0.043

−0.024 −0.029

Average class std mean female academic rating

−0.02 −0.038

0.028 −0.044

−0.02 −0.038

0.008 −0.028

√ Note: Standard error of the total effect in all models presented in Tables 4–7 calculated as follows: se (total effect) = var(bacademic rating ) + var(bacademic rating×gender ) + 2cov(bacademic rating ,bacademic rating×gender ). All models include the following additional covariates: gender, race, public high school attendance, indicator of whether the high school offered less than three advanced placement courses, student’s community of origin (suburban, small town, and rural), indicator of student participation in the college honors program, student writing level, student academic rating, student financial need and aid receipt, student major (business, science, social science, nursing, and humanities), and distribution of the student’s courses across departments. Models are estimated with course X student schedule constraint fixed effects. * p < 0.10. ** p < 0.05. *** p < 0.01.

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Table 7 Gendered peer effects on own student GPA, peer variable = mean class academic rating on subsample of exogenously selected courses. Level effect

Incremental own gender effect

Total effect

(bacademic rating )

(bacademic rating×gender )

On male student GPA

On female student GPA

Average class std mean male academic rating

−0.03 −0.048

0.150** −0.063

0.120* −0.063

−0.03 −0.048

Average class std mean female academic rating

−0.017 −0.062

0.05 −0.072

−0.017 −0.062

0.033 −0.043

√ Note: Standard error of the total effect in all models presented in Tables 4–7 calculated as follows: se (total effect) = var(bacademic rating ) + var(bacademic rating×gender ) + 2cov(bacademic rating ,bacademic rating×gender ). All models include the following additional covariates: gender, race, public high school attendance, indicator of whether the high school offered less than three advanced placement courses, student’s community of origin (suburban, small town, and rural), indicator of student participation in the college honors program, student writing level, student academic rating, student financial need and aid receipt, student major (business, science, social science, nursing, and humanities), and distribution of the student’s courses across departments. Models are estimated with course X student schedule constraint fixed effects. * p < 0.10. ** p < 0.05. *** p < 0.01.

females. Having male peers one standard deviation above the male sample mean associates with a 0.077 point course GPA increase for males (standard error = .043) but not for females. Note that these results derive from course fixed effects models on a sample of multiple section courses in the presence of controls for distribution of student courses across departments and proportion of classmates that are male, minimizing the chance for spurious correlation based upon course selection. Table 7 presents results from the subsample of courses into which selection bias was least evident based upon the placebo test. These results, which indicate a total male peer effect of 0.120 (p = 0.063), are larger than but consistent with those from the full sample analysis and provide further evidence that course level selection is not biasing the identification of peer effects. It bears mention that endogenous section level selection remains a possibility in the model, and that results should be treated as suggestive rather than definitive.

GPA in all models. Specifically, a one point increase in academic rating, which roughly equates to a 4 point increase in high school GPA (on a 100 point scale) and a 70 point increase in SAT score, associates with a 0.26 point increase in predicted course GPA. Students with stronger assessed writing skills exhibit an additional 0.15 point course GPA gain, even controlling for own academic ability. Women outperform men academically, consistent with numerous peer effects papers that identify gender differences in higher education performance (e.g., Betts & Morrell, 1998; Stinebrickner & Stinebrickner, 2005; Winston & Zimmerman, 2003; Zimmerman, 2003), and non-minorities outperform minorities. Ceteris paribus, GPA does not vary systematically by major, but does vary somewhat by course distribution (results available upon request) and course load. Each additional credit hour correlates with an approximate 0.05 point course GPA gain.

4.2. Non-peer determinants of own student GPA

5. Conclusion

The coefficients on the non-peer covariates from the course GPA models, presented in panels B through D of Table 3 are stable across the various model specifications and consistent with results generated elsewhere. In all models, characteristics of the high school from which a student graduated impact student college performance. Students from high schools offering fewer than three advanced placement (AP) courses score approximately 0.20 points lower in courses during their first college semester than do those from high schools offering three or more AP courses while students from public schools or schools located in suburban areas score approximately 0.30 and 0.19 points higher, respectively, than those from private/parochial schools or schools located in urban centers. These coefficient estimates point to the role that high school quality likely plays in college success (Betts & Morrell, 1998). Not surprisingly, own academic ability, measured through an index of high school GPA and SAT scores correlates positively and significantly with first semester

An extensive literature exploring a range of peer influences on both academic and non-academic outcomes continues to produce contradictory evidence regarding the existence and sign of peer effects. The diversity of results may be linked to inconsistency across settings in what constitutes the effective peer group or inconsistency across settings in the influence that peer groups exert on student outcomes. This analysis is distinctive in that we further the investigation of own gendered peer effects implicit in the residential peer literature by distinguishing between the academic ratings of male and female peers and allowing students to be differentially affected by own-gender and other-gender peers in academic settings. Our results provide no evidence of peer effects when peer academic ability is measured in the aggregate. However, regressions that control for own-gender and other gender average peer performance consistently identify positive and statistically significant male peer influence on males but no significant male or female peer effect on

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Table A1 OLS Results without fixed effects controls. 1 Peer academic performance variables Proportion of class that is male Average class male AR Average class female AR Male * average class male AR Female * average class female AR Pre-matriculation High school offers fewer than 3 AP courses Attended a public high school Metropolitan area Small town Rural area Gender (1 if male) Race (1 if white) Academic and co-curricular activities Undecided major Business major Science major (not nursing) Social science major (not business) Nursing major Total academic credits Average class size Membership in college honor’s program Student college ability level Own academic rating Own math level Own writing level Financial Financial need Financial aid Sample size – students Sample size – student course sections

2

3

−0.034 (0.096) −0.054 (0.029)* −0.070 (0.044) 0.090 (0.051)* 0.022 (0.056)

−0.024 (0.096) −0.054 (0.030)* −0.064 (0.044) 0.088 (0.051)* 0.017 (0.056)

0.178 (0.304) 0.003 (0.089) −0.204 (0.132) 0.231 (0.145)* 0.122 (0.167)

−0.193 (0.065)*** 0.293 (0.079)*** 0.193 (0.060)*** 0.051 (0.090) 0.133 (0.094) −0.378 (0.187)** 0.116 (0.049)**

−0.184 (0.066)*** 0.292 (0.079)*** 0.201 (0.060)*** 0.056 (0.091) 0.127 (0.095) −0.388 (0.187)** 0.113 (0.049)***

−0.227 (0.068)*** 0.266 (0.062)*** 0.157 (0.079)** 0.053 (0.094) 0.065 (0.086) −0.424 (0.479) 0.089 (0.047)*

0.038 (0.085) −0.098 (0.118) 0.058 (0.122) −0.008 (0.093) 0.684 (0.336)* 0.050 (0.018)*** −0.003 (0.004) 0.182 (0.065)***

0.047 (0.086) −0.087 (0.118) 0.067 (0.123) 0.001 (0.093) 0.703 (0.360)* 0.048 (0.018)*** −0.003 (0.004) 0.182 (0.065)***

0.030 (0.083) −0.110 (0.121) 0.134 (0.118) −0.037 (0.093) 0.240 (0.666) 0.048 (0.018)*** −0.002 (0.004) 0.206 (0.089)**

0.266 (0.025)*** 0.020 (0.020) 0.132 (0.045)***

0.264 (0.025)*** 0.023 (0.020) 0.138 (0.045)***

0.249 (0.025)*** 0.022 (0.018) 0.147 (0.047)***

−0.001 (0.002) −0.002 (0.005) 873 3492

−0.002 (0.002) −0.002 (0.005) 873 3439

Standard errors presented in parentheses. All models include additional controls for departmental distribution of courses. *** p < 0.01. ** p < 0.05. * p < 0.10 † .

−0.002 (0.002) 0.003 (0.005) 867 N/A

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Table A2 Test of the exogeneity of peer grouping (dependent variable = own academic rating). Peer variablea

Male sample (n = 371)

Female sample (n = 502)

OLS model

Course FE model

OLS model

Course FE model

Average class male academic rating

0.163** −0.067

−0.326*** −0.082

0.245*** −0.052

0.388*** −0.07

Average class female academic rating

0.269*** −0.067

0.088 −0.1

0.213*** −0.07

−0.267*** −0.08

Average class academic rating

0.103 −0.086

−0.917*** −0.159

0.182** −0.073

−0.387*** −0.115

Note: “OLS model” refers to a regression of a student’s own academic rating on only a constant and either the gender specific academic ratings for males and females or the aggregate average class academic rating. “Course FE model” refers to a course fixed effects model that includes either the gender specific academic ratings for males and females or the aggregate average class academic rating, controlling for course by schedule constraint fixed effects. The same fixed effects specification is used in the regression models presented in Table 4. a Average Class Male Academic Rating” and “Average Cass Female Academic Rating” are included together in a single regression model that does not include “Average Class Academic Rating.” “Average Class Academic Rating” is included in a separate regression model where it acts as an alternative to the male and female average academic rating variables. * p < 0.100 ** p < 0.05. *** p < 0.01.

females. Specifically, for each point increase on a five point scale in the average academic rating of one’s male classmates, the predicted male student course GPA increases by approximately 0.10 points. In contrast, females are unresponsive to either male or female peer average academic rating. Our results highlight the importance of differentiating between own and other-gendered peer effects where data will allow and demonstrate that significant own or other gendered effects that differ by gender may be masked by insignificant effects in the aggregate. These results also have important implications for admissions policy and for the assignment of freshmen students to classes based upon gender and prior achievement. The implications for the former are obvious. Granting admission to marginally qualified students, in particular males, has the potential to generate negative academic performance spillovers that draw down classmate academic performance. As discussed extensively in Winston and Zimmerman (2003), this justifies the college selectivity to which most institutions of higher education aspire. In regards to the latter, while roommate match has received attention for some time as an important driver of academic and social success at college, classmate match and class assignment have largely ignored peer implications. Going forward, college orientation staff and first year academic advisors might do well to consider the optimal mix of students in regular and honor classes with an eye towards male on male peer influence, in particular. Appendix A. See Tables A1 and A2. References Betts, J. R., & Morrell, D. (1998). The determinants of undergraduate grade point average. The Journal of Human Resources, 34(2), 268–293.

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