- Email: [email protected]
The positive influence of female college students on their male peers
Labour Economics 44 (2017) 151–160
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Labour Economics journal homepage: www.elsevier.com/locate/labeco
The positive influence of female college students on their male peers Andrew J. Hill
MARK
1
University of South Carolina, United States
A R T I C L E I N F O
A BS T RAC T
JEL Codes: I21 J16
Female college students improve the academic outcomes of their male peers. Using within-college across-cohort variation in freshman enrollment at US colleges, a one standard deviation increase in the proportion of females in a freshman cohort is associated with a half percentage point increase in graduation rates for males in that cohort, while there is no effect for females. Effects are more evident in colleges where student interactions are likely more intense – colleges with higher shares of students living on campus, in college housing, and without cars – suggesting that effects operate through changes in the college learning environment.
Keywords: College Peer effects Gender
1. Introduction The nature and intensity of interactions across genders on college campuses continues to change both inside and outside the college classroom. The proportion of females enrolled in institutions of higher education levelled off in the 2000s after increasing through much of the twentieth century. In the US, females are now more likely than males to enroll in four-year colleges. Furthermore, females are also more likely to choose college majors that were considered the domain of males in the past, although there are still marked gender differences in coursetaking behavior (Dickson, 2000). Outside of the class environment, universities have responded to evolving student preferences by increasing the number of mixed gender residences, and some universities have even begun to allow opposite gender roommates (Gordon, 2010). This paper takes a step towards understanding some of the implications of these changes by estimating the effect of freshman cohort gender composition on college graduation rates. I exploit within-college across-cohort variation in freshman composition to show that there are statistically and economically significant cohort gender peer effects on graduation rates at public four-year colleges in the US. A ten percentage point increase in the share of female freshman students increases the subsequent graduation rate of male students in that cohort by about two percentage points, while there is no effect on female graduation rates. Effects are concentrated in colleges where students are more likely to interact outside the classroom: colleges with higher shares of students living on campus, in college housing, and without cars. This suggests that college peer gender composition affects student behavior through the college environment.
A secondary analysis using individual level administrative data from a small subset of institutions supports the above findings. For male students, both accumulated total credit hours and the probability of graduation are positively correlated with the share of female students in their freshman cohorts. These effects are evident when controlling for individual college admission scores. This indicates that they are not driven by changes in ability composition that may be correlated with cohort female shares, specifically more able females being admitted and enrolled at the expense of less able males. In addition, there is no convincing evidence that gender composition effects operate inside the college classroom as there is no correlation between course gender composition and course achievement. This lends further support to college peer effects operating through a general college environment mechanism rather than in the classroom. There is clear potential for college students to be affected by the gender composition of their peers, especially given the existing evidence on peer gender composition effects in other school settings. When students leave their homes to attend college, they not only take classes with their peers, but are likely to reside with them, too. This increases the opportunities for freshman peers to exert influence on each other. At the same time, college classes are likely to be larger and less interactive than classes in elementary and high schools, reducing the possibility of students in the same cohort affecting each other's academic achievement. The overall extent to which cohort composition matters in college is therefore an empirical question. College gender peer effects on academic achievement could operate through compositional or behavioral channels. A change in the graduation rate caused by a change in the proportion of female
E-mail address: [email protected]. I am grateful to Louis-Philippe Beland, Nicole Fortin, Nick Huntington-Klein, Daniel Jones, Craig Riddell, anonymous referees, and seminar participants at the University of South Carolina and the annual meetings of the Southern Economic Association (2015), Association for Education Finance and Policy (2016) and Society of Labor Economists (2016) for helpful comments and discussions. Errors remain my own. 1
http://dx.doi.org/10.1016/j.labeco.2017.01.005 Received 26 July 2016; Received in revised form 25 January 2017; Accepted 28 January 2017 Available online 01 February 2017 0927-5371/ © 2017 Elsevier B.V. All rights reserved.
Labour Economics 44 (2017) 151–160
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The paper is organized as follows. The empirical strategy, data and estimation results using the aggregate data are presented in Sections 2–4, respectively, while the discussion and analysis using the individual student data forms Section 5.
students may come about because the change in gender composition simply reflects a change in the ability composition of the cohort. For example, consider a marginally admitted male student being replaced by a female student in a particular freshman cohort. This increases the female share of that cohort. If the marginally admitted male student was less likely to graduate than other admitted males in the cohort, the removal of that male student from the male subsample would increase the male graduation rate, and we would observe a positive correlation between the cohort female share and cohort male graduation rate. This would be a purely compositional effect and not necessarily reflect any actual peer influence. Alternatively, college peers may affect incentives and actions. Behavioral mechanisms are broadly grouped into effects operating inside and outside the college classroom. Inside the classroom, gender composition could affect the learning environment through changes in student participation and class atmosphere. For example, females may promote class engagement if they are generally more focused than their male peers. Lavy and Schlosser (2011) find that gender peer effects at the school level operate through mechanisms such as classroom disruption and student-teacher relationships that would broadly fall into this class. Outside the classroom, peer gender composition may affect students’ study efforts, attitudes towards class, and socializing behavior. For example, if females are more academically oriented than males, a higher proportion of female students in a cohort may increase the general importance given to studies by students in that cohort. Alternatively, it is also possible that female students mitigate excessive college partying and drinking. Kremer and Levy (2008) find negative spillovers from alcohol consumption among male college roommates, and Eisenberg et al. (2014) provide evidence of peer effects in binge drinking at college. College peer gender composition may affect the propensity to engage in risky behaviors of this type, which may affect academic achievement. My paper is related to a few strands of the existing peer effects literature. We know that peer gender affects educational outcomes in kindergarten (Whitmore, 2005), elementary school (Hoxby, 2000), middle school (Hu, 2015; Lee et al., 2014; Lu and Anderson, 2015) and high school (Lavy and Schlosser, 2011; Jackson, 2012; Hill, 2015). The subset of this literature investigating the effects of variation in cohort gender composition in mixed gender school environments typically finds that school performance is positively associated with the proportion of female students in the cohort. The effect found in this paper for male college students goes in the same direction. Importantly, however, school peer gender composition effects are typically considered to be stronger inside the classroom (Burke and Sass, 2013), while evidence presented in this paper indicates that college peer gender composition effects operate outside the classroom. Outside of K-12 education, the potential for college peers to influence outcomes has been explored in a variety of settings, such as roommates (Sacerdote, 2001; Zimmerman, 2003; Stinebrickner and Stinebrickner, 2006; Jain and Kapoor, 2015), air force academy squadrons (Carrell et al., 2009), and residences (Garlick, 2014). There is some evidence that college peer effects differ by gender. Fischer (2016) finds that class ability composition affects the likelihood that females choose and complete degrees in STEM, while Ficano (2012) and Griffith and Rask (2014) find that males are more susceptible to ability peer effects than females. In a more directly related study, Feld and Zölitz (2016b) finds that the gender composition of randomly assigned teaching sections at a university in the Netherlands affects achievement and major choice, although a related study by Oosterbeek and van Ewijk (2014) does not find evidence of substantial peer gender composition effects in randomly assigned college study groups. My paper differs from these by looking at the effects of the gender composition of larger freshman cohorts and considering an arguably more representative sample consisting of the majority of public four-year colleges in the US.
2. Empirical strategy I investigate the effect of college freshman cohort gender composition on students’ academic outcomes by estimating the following reduced form equation:
yct = αc + βt + γct + πPct + εct
(1)
yct is the gender-specific aggregate graduation rate for the cohort of freshman students in college c in year t , αc is a college fixed effect, βt is a cohort or year fixed effect, and γct is a college-specific time trend (which is included in some specifications and is either linear or quadratic). Pct is the proportion of female students in the freshman cohort in college c in year t . The parameter π measures the relationship between the share of female freshman students in the college cohort and the aggregate graduation rate for male or female freshman students in that college cohort. In order for π to have a causal interpretation, the unobserved component of the cohort graduation rate must be uncorrelated with the cohort female share. College fixed effects capture the endogenous sorting of students into colleges. This controls for colleges that consistently have higher shares of female students and higher or lower graduation rates, for example. There may also be unobserved time-varying factors that are correlated with both changes in the proportion of female students and aggregate graduation rates. In particular, a potential upward trend in the female share of college students due to a widening female-male achievement gap combined with a potential upward trend in college graduation rates due to grade inflation or higher administrative costs associated with student failure would generate a positive estimate of the parameter π , but would not indicate a causal relationship. The cohort fixed effects and college-specific time trends control confounding factors of this type. Identification therefore relies on college-specific deviations in cohort female shares and cohort graduation rates from their long-term trends. Essentially, we are comparing the graduation rates of cohorts at the same college who are exposed to different cohort female shares by purely idiosyncratic factors. Sources of variation may include (1) fluctuations in the gender composition of applicants caused by either natural variation in the gender composition of the local college-going population or the college preferences of applying students, (2) changes in the gender composition of admitted students, and, (3) idiosyncratic shocks to the college preferences of admitted students in terms of if and where they choose where to enroll. I show in the data section that these factors generate a sufficient amount of variation in female shares across cohorts within colleges for the identification strategy to work. Angrist (2014) shows that models that rely solely on chance variation in peer groups may be complicated by bias from weak instruments. Feld and Zölitz (2016a) consider precisely how classical measurement error impacts the estimation of compositional peer effects in these contexts, ultimately showing that estimates will only be attenuated by measurement error when assignment to peer groups is random. Although assignment to freshman cohort groups is not random, measurement error is likely to be a much smaller concern in my study given we are considering a fixed, well-measured peer characteristic – gender – rather than peer traits such as ability or smoking that are harder to measure. The primary specification above considers gender peer effects at the college cohort level using aggregate data. The majority of college students primarily interact with other students who entered college in the same year that they did. Freshman students in college are likely to live, attend classes and socialize with other students in their cohorts. The preferences and actions of students in all three settings are likely to 152
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If the college characteristic is binary, for example, the coefficient πj on the interaction term between the college characteristic Xcj and the female share πj reveals whether the effect of the proportion of female students in the freshman cohort is more evident in colleges that display this characteristic than colleges that do not. Pure ability compositional effects are unlikely to systematically vary across colleges, so if students are affected by peer composition only in certain environments, then effects are likely to be driven by behavioral responses to freshman cohort gender composition.4 Note that the effect of the actual college characteristic on graduation rates cannot be identified given the inclusion of college fixed effects. The college characteristics I consider are from the US News Academic Insights dataset. I look at college characteristics that describe both how peers may interact outside the classroom - the share of students in college housing, the share of students who live off campus, and the share of students with cars on campus – and college characteristics that describe the extent to which peers may interact inside the classroom – the share of small classes and large classes in the college. Separating characteristics into these two categories helps determine whether peer gender composition effects are likely to occur inside or outside the college classroom (or both), which is important when considering university policies that may reinforce positive peer effects or mitigate negative ones. The set of college characteristics are necessarily limited, and any individual college characteristic could be correlated with other factors that are the underlying drivers of gender peer effects. We cannot argue that any of the college characteristics cause college gender peer effects, but we can use the results to restrict our interpretations to those consistent with observed correlations.
affect their academic performance. Defining the peer group as the college cohort captures several dimensions of peer influence that may not be captured by narrower peer groups. Investigating peer effects at the cohort rather than class level also eliminates concerns related to endogenous sorting into college classes, such as gender differences in the extent to which expected course or class composition or achievement affects course or class selection. For example, female students may avoid a course if they expect it to be particularly male-dominated in a given term. This motivation for using college cohorts rather than college classes is similar to the motivation for using within-school grade composition rather than within-school class composition in the school compositional peer effects literature (Hoxby, 2000; Lavy and Schlosser, 2011). Using the freshman cohort rather than cohorts in subsequent years has the added advantage of not being subject to biases introduced by student failure and course repetition (Ciccone and Garcia-Fontes, 2015). The disadvantage of using this broad definition of the peer group is that cohort gender composition may only be weakly correlated with the gender composition of some of the narrower peer groups in which students interact, such as college residences and classes. Using a noisy proxy for potentially more influential peer groups attenuates estimated effects. This may be particularly true in larger colleges. I explore whether estimated effects differ in magnitude or precision across college size by estimating the primary model on five subsamples based on college size quintiles. After estimating the primary effect using the strategy just outlined, I consider a variety of models to check the effect's robustness and understand its mechanism. College students interact across cohorts, so the gender composition of adjacent cohorts may affect students’ academic outcomes in similar ways to the gender composition of their own cohort.2 I report results from separate models relating cohort graduation rates to the gender composition of cohorts two years ahead, one year ahead, one year behind, and two years behind (denoted by s∈{t − 2, t − 1, t + 1, t + 2} in the below specification) to explore this.
yct = αc + βt + γct + πsPcs + εct
3. Data Two datasets are used in the first section of the paper. The primary analysis uses publicly-available data from the Integrated Postsecondary Education Data System (IPEDS). IPEDS collects information from every college that participates in federal student financial aid programs. I focus on public four-year colleges for which data is available over all the years in the study sample, a sample of 525 colleges. Freshman cohort gender composition is computed from gender-specific aggregate enrollment counts for each institution. Graduation information is available for cohorts that entered between 1996 and 2006. I consider overall six-year graduation rates – the share of students who graduate in six or fewer years – as the primary outcome variable.5 Fig. 1 displays freshman cohort gender composition and graduation rates over time. The upper panel plots the average cohort female share both in the cohort's freshman year – the composition measure used in this paper – and upon the cohort's graduation. The average freshman female share is constant at 54 percent through the study sample, indicating that the female-male gender gap in college attainment was already present and stable by the mid-1990s. This is broadly consistent with existing literature (Fortin et al., 2015). The average cohort female share at graduation is higher, indicating that admitted females are more likely to graduate than their male counterparts. This is also evident in the lower panel of Fig. 1, which shows that female graduation rates are consistently above male graduation over time. Both are trending upward, possibly due to grade inflation or higher
(2)
In addition to providing information on the types of peers that affect outcomes in college, results from this model also provide a loose assessment of the empirical strategy. In particular, evidence of peer effects of a similar or larger magnitude for student's adjacent cohorts rather than the actual cohort to which the student belongs would be unexpected and problematic for the given peer effect interpretation without a clear reason why adjacent cohorts could be more influential. The impact of college peers may depend on the college environment. Students at commuter campuses, for example, are surrounded by their peers for a much lower share of their time than students at residential campuses or in college towns. I investigate heterogeneity in peer gender composition effects along this dimension by estimating a series of specifications that include both the proportion of female students in the freshman cohort and this proportion interacted with a fixed3 college characteristic Xcj that describes the college environment, such as the share of students in college housing.
yct = αc + βt + γct + πPct + πj (Xcj ×Pct )+εct
(3)
2 In the appendix, I report and discuss the effects of freshman cohort gender composition on a related outcome that is less likely to be affected by adjacent freshman cohorts to the same extent as graduation rates, one-year retention rates. The pattern of effects is very similar to those reported in the results section. 3 There are insufficient years of college characteristics data to allow the college characteristic to be time varying in the model, which would naturally be more informative as effects would be identified from within college variation in the college characteristic over time that is less likely correlated with unobservable factors. At the same time, though, it would be difficult to assign year-specific college characteristics to cohorts given students in each cohort attend college for multiple years.
4 There is an alternative hypothesis in which purely compositional effects at a subset of colleges drive the result. If different types of colleges have marginal students of different abilities, then compositional effects could still vary by college type. There are no ex ante reasons why the college characteristics I consider would be systematically correlated with college selectivity or the ability distribution of admitted students, so I consider this to be a less likely explanation for non-zero estimates on the interaction term, but I cannot rule it out. 5 Results are similar using other definitions of graduation rates (see Appendix Table 1).
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Share female .5 .52 .54 .56 .58 .6
Freshman cohort gender composition: US public 4-year colleges
1996
1998
2000
2002
2004
2006
Cohort Freshman year
At graduation
.55 .5 .45
Graduation rate
.6
Freshman cohort graduation rates: US public 4-year colleges
1996
1998
2000
2002
2004
2006
Cohort
Male graduation rate
Female graduation rate
Fig. 1. Freshman cohort gender composition and graduation rates over time.
administrative costs associated with student failure.6 The median freshman cohort consists of about 1000 students. We may be concerned that idiosyncratic shocks to composition across cohorts in the same college generate insufficient variation for the empirical strategy to be effective. The left panel in Fig. 2 – a plot showing the distribution of freshman cohort gender composition – shows considerable variation in cohort female shares across colleges and cohorts; the interquartile range is about 20 percentage points. Identifying variation, however, comes from within-college acrosscohort variation in gender composition. The distribution of this is shown in the right panel. The standard deviation of the within-college female share is 2.5 percentage points. Gender composition shocks of this magnitude will be considered when interpreting whether estimated effects on outcomes are of an economically meaningful magnitude. The distributions of college graduation rates for males and females are plotted in Fig. 3. Both the distributions across colleges and cohorts (left panel) and within colleges (right panel) are shown. The left panel shows that there are very large differences in college graduation rates across colleges. This is expected given the large differences in college and student quality across the US. The right panel shows the expected smaller differences in cohort graduation rates when considering within-college variation; a standard deviation of almost 5 percentage points for both males and females. The second data source in the first part of the paper is the US News Academic Insights dataset used to construct the popular US News and World Report college rankings. I use college characteristics from this dataset to explore heterogeneity in gender peer effects by college type. I construct time invariant measures of these characteristics for each college by computing means for years in which the data is available. Colleges are manually matched using the name of the institution across the two datasets, resulting in a reduced sample of 165 public four-year colleges. The number of colleges is smaller than in the original sample because satellite campuses are often excluded from Academic Insights, which focuses on flagship schools, and some college characteristics being missing for a small subset of schools. The main sample of colleges and the smaller US News sample of colleges are compared in Table 1, showing that colleges in the US News sample are
generally larger and have higher graduation rates. The original model is estimated on this smaller sample of colleges to confirm that the sample restriction does not affect the primary results. Means and distributions of the college characteristics are plotted in Appendix Fig. 1, showing a considerable amount of variation in these dimensions of the college environment across the US. 4. Results Table 2 reports estimates of the parameter of interest π from Eq. (1). Using variation in cohort composition across colleges – the specifications without college fixed effects in Columns 1 and 5 – an increase in the female share is associated with a reduction in both male and female graduation rates. The coefficients of −0.36 and −0.35 indicate that a 10 percentage point increase in the female cohort share is associated with a 3.6 and 3.5 percentage point reduction in male and female graduation rates, respectively. Colleges with higher shares of female freshman students have lower graduation rates, on average. However, given that colleges with consistently different gender shares are likely different in several other dimensions, these estimates cannot be given a causal interpretation. The remaining columns in Table 2 include college fixed effects; the within-college variation identifies the causal effects of freshman cohort gender composition on graduation rates. Using no college-specific time trends, linear trends or quadratic trends (Columns 2, 3 or 4 and Columns 6, 7 or 8), there is a positive effect of the proportion of female students on male graduation rates and no effect on female graduation rates. The coefficient of 0.2 means that a 10 percentage point increase in the female cohort share is associated with a 2 percentage point increase in male graduation rates. The pattern of effects is not affected by the inclusion or functional form of the college-specific time trend; subsequent specifications use the most flexible (quadratic) trend, but results are not sensitive to this. Table 3 shows that the positive effect on male graduation rates is evident in colleges of almost all sizes. The concern that in large colleges cohort gender composition may be too weakly correlated with the gender composition of the narrower peer groups in which students interact (such as college residences) is unfounded. The magnitude of the estimated effect of the female share on male graduation rates in Tables 1–3 is consistently around 0.2. The economic significance of this effect is interpreted by considering a one standard deviation composition shock to a representative college
6 In contrast, Bound et al. (2010) document declining college completion rates between the high school classes of 1972 and 1992. The difference is likely explained by my study covering a more recent period and only including four-year colleges.
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10
4
15
6
20
25
8
A.J. Hill
Within-college standard deviation: .025
0
0
5
2
Mean share female: .54
0
.2
.4
.6
.8
-.1
1
0
.1
.2
Freshman cohort composititon: share female (within-college variation from mean)
Freshman cohort composititon: share female
1
10
1.5
2
15
Fig. 2. Distribution of freshman cohort gender composition.
5
Within-college standard deviation: Males: .046 Females: .049
.5
Mean male graduation rate: 0.50
0
0
Mean female graduation rate: 0.56
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
-.4
1
-.2
0
.2
.4
Graduation rate (within-college variation from mean)
Graduation rate Males
Males
Females
Females
Fig. 3. Distribution of college cohort graduation rates.
the female-male college graduation gap. I now turn to the results checking the robustness of the effect and probing its mechanism, starting with exploring whether the peer gender composition of adjacent cohorts affects outcomes in Table 4. The sample is smaller because the first and last two freshman cohorts for each college are excluded from the analysis as they do not have the full set of adjacent cohorts. Note that each cell in the table reports an estimate from a separate model. The results in Column 1 show that peer gender composition effects for male students are most strikingly evident – both in terms of magnitude and precision – within a student's own cohort. The other rows of Column 1 reveal that the gender composition of adjacent cohorts does not affect male graduation rates, and Column 2 shows no peer gender composition effects for females (consistent with the main result in Table 2). Overall, I interpret the results in this table as (1) showing that college peer gender composition effects are strongest within one's own cohort, and (2)
freshman cohort with 1000 male students and 1000 female students. The within-college standard deviation in the female share – the relevant variation for the empirical strategy – is 2.5 percentage points (shown in Fig. 2). Replacing 50 male students with 50 female students would increase the female share by 2.5 percentage points. Assume that these 50 male students randomly substitute away from the given college (choose to attend another college, for example) and 50 female students randomly substitute towards the given college. The increase in the female share increases the male graduation rate by 0.5 percentage points (0.025*0.2) according to the estimate from Table 2. If the initial male graduation rate were 50 percent (the mean male graduation rate in the sample), 475 of the 950 male students would graduate. The 0.5 percentage point increase in the graduation rate causes 480 male students to graduate: five additional male students obtain a college degree, a small but meaningful effect. A one standard deviation increase in the cohort female share closes about one tenth of 155
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unlikely to depend systematically on the college environment. The first column of Table 5 confirms that the overall effect of freshman cohort gender composition in the smaller US News sample of colleges is similar to the overall effect for all colleges reported in Table 2. Columns 2 to 4 of Panel A show that freshman peer gender composition has more of an effect on male graduation rates in colleges with higher shares of students in college housing, colleges with higher shares of students living on campus, and colleges with higher shares of students without cars on campus. For example, in colleges with 10 percent of students living in college housing, the effect of the proportion of female peers on the male graduation rate is only 0.09 (−0.04+0.96*0.1), while it is 0.28 and 0.46 in colleges with 30 and 50 percent of students living in college housing, respectively. Interestingly, and contrasting somewhat with previous estimates, the cohort female share also exerts positive effects on female graduation rates in colleges with these characteristics (Columns 2 to 4 of Panel B). The magnitudes of the estimates are smaller for females, explaining the absence of an average treatment effect when considering all colleges combined in Column 1. However, these results for females provide
Table 1 Descriptive statistics (snapshot of colleges in 2001).
Total number of freshman students Males Females Female share Total number of undergraduate students Males Females Female share Male graduation rate Female graduation rate Number of colleges
Main sample
US News sample
Mean
(Standard deviation)
Mean
(Standard deviation)
1,509
(1,332)
2,753
(1,553)
690 819 0.543 7,241
(639) (715) (0.003) (6,326)
1,293 1,460 0.530 13,207
(760) (828) (0.005) (6,973)
6,280 6,927 0.524 0.569 0.632
(3,529) (3,589) (0.004) (0.013) (0.012)
3,319 (3,099) 3,923 (3,313) 0.539 (0.003) 0.496 (0.008) 0.562 (0.008) 525
165
Table 2 Effect of freshman cohort composition on cohort college graduation rates.
Mean
Male graduation rates
Female graduation rates
0.50
0.56
1
2
3
4
5
6
7
8
Share females
−0.36** (0.11)
0.25** (0.05)
0.19** (0.04)
0.17** (0.04)
−0.35** (0.12)
0.02 (0.05)
−0.00 (0.04)
−0.01 (0.04)
College fixed effects College-specific time trend Number of observations Number of colleges
No No
Yes No
Yes Lin.
Yes Quad.
No No
Yes No
Yes Lin.
Yes Quad.
5775 525
Notes. Regressions weighted by gender-specific college cohort size. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
providing some validation of the empirical strategy given that the estimated effects are largest and most precise where we expect them to be. Table 5 explores whether gender peer effects are affected by the college environment. I report effects on male and female graduation rates in Panels A and B, respectively. As discussed in the empirical methodology section, in addition to providing information about potential mechanisms, heterogeneity in the effect by college type is considered evidence against ability composition effects as these are
Table 4 Effect of lagged and leading freshman cohort composition on cohort college graduation rates. Male graduation rates
Female graduation rates
0.50
0.56
1
2
Share females (t-2)
−0.07 (0.04)
−0.03 (0.05)
Share females (t-1)
0.06 (0.04)
0.07 (0.04)
Mean
Table 3 Effect of freshman cohort composition on cohort college graduation rates by college size. Male graduation rates College size quintile
1
2
3
4
5
Share females (t)
0.17** (0.04)
−0.01 (0.04)
Mean freshman cohort Mean share male
343 0.34
679 0.36
1147 0.43
1871 0.39
4075 0.61
Share females (t+1)
−0.00 (0.04)
0.02 (0.04)
Share females
0.06 (0.06)
0.16* (0.07)
0.20* (0.08)
0.21 (0.12)
0.19* (0.08)
Share females (t+2)
−0.06 (0.04)
−0.05 (0.04)
Number of observations Number of colleges
1155 105
1155 105
1155 105
1155 105
1155 105
Number of observations Number of colleges
Notes. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and quadratic college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
3675 525
Notes. Each cell reports an estimate from a separate regression. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and quadratic college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
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large. The absence of heterogeneity in the class size dimension is interpreted as suggestive evidence that effects are not operating inside the college classroom as we would expect stronger peer gender composition effects in colleges with smaller classes if so. Taking these results as a whole, we see that female students exert positive externalities in colleges in which students are more likely to interact with their college peers outside of class. This is interpreted as support for mechanisms operating through the broader college learning environment.7 The advantage of using college-specific aggregate data from a relatively wide time frame and a large number of public four-year colleges is that estimated effects are representative of the US. This approach has limitations, however, particularly if we are concerned about other dimensions of peer group composition that may vary with gender composition. I therefore complement the above specifications with an analysis using individual level data; specifically, student transcript data aggregated to the semester level from the Texas Higher Education Opportunity Project.
Table 5 Effect of freshman cohort gender composition interacted with college characteristics. 1
2
3
4
5
6
0.22** (0.07)
−0.04 (0.12)
−0.04 (0.13)
0.10 (0.12)
−0.03 (0.34)
0.26 (0.18)
Panel A: Male graduation rates (Mean: 0.57) Share females
Share females interacted with: Share of students in college housing
0.96* (0.43)
Share of students who live on campus
0.93* (0.43)
Share of students without cars on campus
0.80* (0.32)
Share of classes that are small ( < 20)
0.65
5. Effects of freshman cohort composition using individual student data
(0.81)
5.1. Empirical strategy −0.29
Share of classes that are large ( > 50)
I test whether the findings from the primary specification can be replicated in the individual level data by constructing a repeated crosssection with one observation per student where the relevant outcome variable is either a measure of a student's accumulated total credit hours when leaving college or an indicator for whether the student graduated, and the relevant explanatory variable is the student's freshman cohort female share. The specification is otherwise similar to Eq. (1), and is estimated separately for males and females.
(1.12)
Panel B: Female graduation rates (Mean: 0.64) Share females
−0.03 (0.07)
−0.25* (0.13)
−0.25 (0.13)
0.02 (0.12)
−0.15 (0.40)
−0.06 (0.16)
yict = αic + βit + γict + πPict + g(Aict ) + εict
Share females interacted with: Share of students in college housing
(0.39) Share of students who live on campus
0.88* (0.40)
Share of students without cars on campus
0.43 (0.28)
Share of classes that are small ( < 20)
0.33 (0.96)
Share of classes that are large ( > 50)
0.32 (1.00)
Number of observations Number of colleges
1815 165
1782 162
1749 159
935 85
1815 165
(4)
yict is the outcome variable for student i in college c in year t , αic and βit are indicators for student i ’s college and cohort, γict is a college-specific time trend for student i , and Pict is the proportion of female students in student i ’s freshman cohort. I include an additional control for student i ’s college admissions score (SAT or ACT) Aict . The inclusion of a flexible admissions score control means that the parameter π identifies the effect of freshman cohort gender composition for students of approximately equal ability (upon admission). This speaks to whether effects arise from compositional or behavioral changes. If effects are purely coming about because changes in gender composition reflect changes in ability composition, there would be no effect of freshman cohort gender composition on the probability of graduation for students of the same ability. In addition, I investigate whether gender peer effects operate within the college classroom by defining an alternative peer group as the set of students likely in the same set of college classes together (rather than the freshman cohort). I model the semester-specific average GPA (there is no course-specific GPA) for student i in college c , department d , semester (time period) s and cohort t as a function of the departmentspecific female share in that semester Pcdst .
0.90*
1815 165
Notes. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and linear college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
yicdst = αcd + βs + θt + γcdt + πPcdst + εicst
(5)
College-department fixed effects αcd , semester fixed effects βs , cohort fixed effects θt and a college-department trend γcdt are included in the model. The variation for identifying the parameter of interest π comes from deviations in department female shares and department average
further support for the proposed college environment mechanism; if females improve the general learning environment, then there is reason to expect that these changes should improve outcomes for both males and females (even if not to the same extent). Results in Columns 5 and 6 show that gender peer effects do not depend on the average sizes of college classes in a statistically significant way, although the standard errors of these estimates are
7 An alternative interpretation of results worth noting is that male students are negatively affected by exposure to more male “competitors” in college. This hypothesis cannot be ruled out with the available data, although the existing literature on gender and competition typically finds that females are more prone to adverse effects from competition than males (Niederle and Vesterlund, 2011), which is not what is found.
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Table 6 Effect of freshman cohort composition on individual student college outcomes. Males 1
Females 2
3
4
5
6
7
8
5.06 (19.85)
−16.39 (29.16)
−0.74 (18.82)
Panel A: Total credit hours
Mean: 94.79
Mean: 96.26
Share females
−99.16 (143.55)
Panel B: Graduation rates
Mean: 0.59
Share females
−0.12 (1.23)
0.95 (0.56)
0.50 (0.41)
1.10* (0.31)
−0.81 (1.33)
0.31 (0.57)
−0.10 (0.20)
0.29 (0.28)
College fixed effects College-specific time trend Number of students Number of colleges
No No
Yes No
Yes Lin.
Yes Quad.
No No
Yes No
Yes Lin.
Yes Quad.
65.53* (23.12)
12.66 (18.18)
38.87* (12.01)
−124.37 (138.18)
Mean: 0.66
44,561 8
46,015 8
Notes. Regressions weighted by gender-specific college cohort size and include controls for admissions scores. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
GPA scores from their long-term trends.8 Students at the same college, entering in the same freshman cohort, and declaring the same major are not necessarily in the same academic peer group. I restrict the sample in two ways to ensure that the set of peers included in the definition are likely to be taking the same courses. First, freshman and sophomore students are excluded as they are typically not yet in classes with peers who declared the same major. And, second, the sample is restricted to students who are deemed to be on-schedule, which is defined as completing at least 12 credit hours per a semester. This is because a junior who has completed only 16 credit hours is unlikely to be taking the same courses as a junior who has completed 24 credit hours even if they entered in the same freshman cohort and declared the same major.
students is computed by summing their obtained credit hours across all semesters in which the student is observed. The THEOP data used in the paper contains information on a little over 80,000 students. Graduation rates are slightly higher than in those reported in the IPEDS data: 59 percent for males and 66 percent for females, although the gender gap is similar. The number of departments per institution in the sample ranges from 29 at Rice University to 53 at Texas Tech University. Average department female shares range from around 20 percent in Computer Science and Engineering to above 90 percent in Nursing and Social Work, although recall that the empirical strategy to estimate within-classroom gender peer effects relies on variation across cohorts within the same department rather than across departments.
5.2. Data
5.3. Results
The individual level data comes from the Texas Higher Education Opportunity Project (THEOP), a dataset containing information on the universe of students who applied to eight Texas four-year colleges during the 1990s and early 2000s. Longitudinal transcript data are available at the student-semester level rather than the student-course level. I observe students’ aggregate GPAs for all semesters in which the student was enrolled, the course credits obtained in these semesters, as well as their current departments and fields of study. Note that there is no course-specific information, so course-specific peers cannot be directly identified. The sample is restricted to students who intended to be admitted and were admitted during a fall semester (regular admission) to ensure that freshman cohorts are well-defined. Observations from summer terms are excluded from the analysis. Indicators for graduation and time-to-graduation are constructed from the recorded graduation year. I restrict the sample to cohorts who entered college between 1995 and 1999 because graduation rates for earlier and later cohorts are based on selected samples and vary considerably from the relatively stable graduation rates of about 60 percent observed for each of the five included cohorts. The total number of credit hours obtained by
Table 6 shows that the effect on graduation found in Tables 1–3 can be replicated using individual level data from THEOP, although estimates are more sensitive to the inclusion and functional form of the college-specific trends than the primary results in Table 2. Interpreting the estimates in Column 4, a 10 percentage point increase in the share of female freshman students increases accumulated total credit hours by 3.9 h (4 percent relative to the mean of 94.8 total credit hours) and the probability of graduation by 11 percentage points (18 percent relative to the mean graduation rate of 0.59) for male students. Columns 6 to 8 reveal no evidence of peer gender composition effects for females.9 These models include flexible controls for admissions scores, so identifying variation comes from comparing students with the same ability (as proxied by admissions scores). I show in Appendix Fig. 2 that effects for male students are evident across much of the ability distribution. Overall, these findings indicate that effects are not driven by pure ability composition changes. If we were simply capturing the effect of more able females being admitted at the expense of less able males, we would not observe positive spillovers from female peers controlling for ability or for infra-marginally admitted male students. 9 The results for this part of the paper are presented with the caveat that when clustering at the college level – as is done in the analysis – there are fewer than ten clusters. Webb (2014) provides a bootstrap procedure for improving the reliability of inference under these particular circumstances; it has better properties – and is more stringent – than conventional wild bootstrap-based tests. When implementing this procedure, the parameter of interest is no longer statistically significantly different from zero at conventional levels; the p-value is 0.16. Although this suggests a one in six chance that the result is due to random sampling error, the very robust effects in the first part of the paper negate some of this concern.
8
Note that the cohort effects are not specific to college departments, so only capture cohort shocks across college departments. The inclusion of college department-specific cohort fixed effects would result in identifying variation coming from fluctuations in peer gender composition across semesters for students in the same college departmentcohort. This would be a concern because variation in gender composition across semesters for students in the same department and cohort is endogenous to the model given that it is likely generated by student failure or students changing majors, which may happen in response to either peer gender composition or GPA.
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Table 7 Effect of college-cohort-term-department (academic peer group) gender composition on individual student term GPA. Males
Females
All junior and senior terms
First junior term only
All junior and senior terms
First junior term only
3.09
3.05
3.26
3.22
1
2
3
4
5
6
Share females
0.17** (0.03)
0.10 (0.05)
0.03 (0.03)
−0.01 (0.03)
0.02 (0.05)
0.05 (0.03)
Semester fixed effects Lagged cumulative GPA fixed effects Number of students Mean semesters per student Number of college-departments Number of colleges
Yes No 56,695 2.8 311 8
No No 46,278 1 302 8
No Yes 45,602 1 302 8
Yes No 65,328 2.8 323 8
No No 55,149 1 315 8
No Yes 54,311 1 315 8
Mean
Notes. All regressions include college-department fixed effects, cohort fixed effects and linear college-department-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
The final table probes whether course gender composition affects course performance. Estimates in Table 7 show a very small positive effect on male course achievement from course female share, and no effect on female course achievement. From Column 1, a 10 percentage point increase in the share of females majoring in the same department causes a (very small) 0.02 increase in average semester GPA per semester for male junior or senior students. In Column 2, the sample is restricted to students in their first junior semester to mitigate biases arising from changes to academic peer group composition that occur in the final two years of college. The estimated effect is less precise. The inclusion of controls for lagged GPA in Column 3 removes the effect for males. Overall, I interpret these results as indicating that within classroom effects are at most responsible for only a very small component of the overall freshman cohort gender composition effect. Finally, an alternative explanation put forward by Feld and Zölitz (2016b) is that college peer gender composition affects major choice. If so, and if major choice subsequently affects graduation rates, this could explain some of the observed effect. I cannot find convincing evidence of this phenomenon (see the Appendix for a more detailed discussion), although some specifications suggest an inverse relationship between the probabilities with which females pursue STEM and the female share of their cohorts, which, interestingly, is broadly consistent with Feld and Zölitz.
I am unable to find evidence of economically meaningful gender peer effects using a proxy for course gender composition rather than cohort gender composition, indicating that effects do not appear to be operating inside the college classroom. Kremer and Levy (2008) and Eisenberg et al. (2014) find negative spillovers in alcohol consumption among college students. This offers a potential class of channels through which the estimated college gender peer effects may affect the general college learning environment: for example, a higher share of female peers may reduce the frequency or intensity of “fraternity-type” parties characterized by binge drinking, improving academic outcomes. In terms of more direct policy implications, males may actually benefit from mixed gender residences rather than the conventional wisdom that females distract males from their academic pursuits. Extrapolating from these results, universities may be able to improve graduation rates – particularly for males – with interventions targeting the college environment.
6. Conclusion
Angrist, Joshua D., 2014. The perils of peer effects. Labour Econ. 30, 98–108. Bound, John, Michael, F. Lovenheim, Turner, Sarah, 2010. Why have college completion rates declined? An analysis of changing student preparation and collegiate resources.. Am. Econ. J. Appl. Econ. 2.3, 129. Burke, Mary A., Tim, R. Sass, 2013. Classroom peer effects and student achievement. J. Labor Econ. 31 (1), 51–82. Carrell, S., Fullerton, R., West, J., 2009. Does your cohort matter? Measuring peer effects in college achievement. J. Labor Econ. 27, 439–464. Ciccone, A., and Garcia-Fontes, W., 2015. Peer Effects When Boys And Girls Learn Together: A Birth Cohort Approach, unpublished manuscript. Dickson, Lisa, 2010. Race and gender differences in college major choice. Ann. Am. Acad. Political Social. Sci. 627.1, 108–124. Eisenberg, Daniel, Golberstein, Ezra, Whitlock, Janis L., 2014. Peer effects on risky behaviors: new evidence from college roommate assignments. J. Health Econ. 33, 126–138. Feld, Zölitz, 2016a. Understanding peer effects – on the nature, estimation and channels of peer effects. J. Labor Econ., (forthcoming). Feld, Zölitz2016b. Majors, Math & Marks: Gender Peer Effects in Higher Education, unpublished manuscript. Ficano, Carlena Cochi, 2012. Peer effects in college academic outcomes–gender matters!. Econ. Educ. Rev. 31.6, 1102–1115. Fischer, S., 2016. The Downside of Good Peers: How Classroom Composition Differentially Affects Men’s And Women’s STEM Persistence. unpublished manuscript. Fortin, N.M., Oreopoulos, P., Phipps, S., 2015. Leaving boys behind. J. Human. Resour. 50 (3). Garlick, R., 2014. Academic Peer Effects with Different Group Assignment Policies:
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.labeco.2017.01.005. References
This paper provides new evidence on the effects of college peer gender composition on academic achievement. In particular, I find that female students improve college outcomes for their male peers. An increase in the freshman cohort female share increases the cohort graduation rate for males at public four-year colleges in the US, while there is no overall effect for females. I provide suggestive evidence that effects are (1) driven by behavioral responses to peer gender composition rather than changes in ability composition, and (2) generated outside of the college classroom. A set of secondary findings supports these claims. First, there is heterogeneity in the effect by college type. Generally, freshman cohort effects are more evident in colleges in which students are more likely to interact outside class. This suggests a broad college environment mechanism. Second, estimates using individual level data show that controlling for individual student ability does not affect the pattern of results. A male student of any ability is more likely to graduate if he is exposed to a higher share of females in his freshman cohort, which is not consistent with a pure ability composition mechanism driven by marginally admitted students only. And, third, 159
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The Impact of School and Classroom Gender Composition on Effort and Academic Achievement. National Bureau of Economic Research. Lu, Fangwen, Anderson, Michael L., 2015. Peer effects in microenvironments: the benefits of homogeneous classroom groups. J. Labor Econ. 33 (1), 91–122. Niederle, Muriel, Vesterlund, Lise, 2011. Gender and competition. Annu. Rev. Econ. 3.1, 601–630. Oosterbeek, Hessel, Ewijk, Reyn Van, 2014. Gender peer effects in university: evidence from a randomized experiment. Econ. Educ. Rev. 38, 51–63. Sacerdote, B., 2001. Peer effects with random assignment: results for Dartmouth roommates. Q. J. Econ. 116, 681–704. Stinebrickner, R., Stinebrickner, T., 2006. What can be learned about peer effects using college roommates? Evidence from new survey data and students from disadvantaged backgrounds. J. Public Econ. 90, 1435–1454. Webb, M., 2014. Reworking Wild Bootstrap Based Inference for Clustered Errors. Technical Report, Queen׳s Economics Department Working Paper No. 1315. Whitmore, Diane, 2005. Resource and peer impacts on girls' academic achievement: evidence from a randomized experiment. Am. Econ. Rev., 199–203. Zimmerman, D., 2003. Peer effects in academic outcomes: evidence from a natural experiment. Rev. Econ. Stat. 85, 9–23.
Residential Tracking Versus Random Assignment. unpublished manuscript. Gordon, Larry, 2010. Mixed-gender dorm rooms are gaining acceptance. LA Times. Griffith, Amanda L., Kevin, N. Rask, 2014. Peer effects in higher education: a look at heterogeneous impacts. Econ. Educ. Rev. 39, 65–77. Hill, Andrew J., 2015. The girl next door: the effect of opposite gender friends on high school achievement. Am. Econ. J.: Appl. Econ. 7 (3), 147–177. Hoxby, Caroline, 2000. Peer Effects in the Classroom: Learning From Gender and Race Variation. National Bureau of Economic Research. Hu, Feng, 2015. Do girl peers improve your academic performance? Econ. Lett. 137, 54–58. Jackson, C. Kirabo, 2012. Single-sex schools, student achievement, and course selection: evidence from rule-based student assignments in Trinidad and Tobago. J. Public Econ. 96 (1), 173–187. Jain, Tarun, Kapoor, Mudit, 2015. The impact of study groups and roommates on academic performance. Rev. Econ. Stat. 97 (1), 44–54. Kremer, Michael, Levy, Dan, 2008. Peer effects and alcohol use among college students. J. Econ. Perspect. 22 (3), 189–189. Lavy, V., Schlosser, A., 2011. Mechanisms and impacts of gender peer effects at school. Am. Econ. J.: Appl. Econ. 3, 1–33. Lee, Soohyung, Lesley, J. Turner, Woo, Seokjin, Kim, Kyunghee, 2014. All or Nothing?
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Labour Economics journal homepage: www.elsevier.com/locate/labeco
The positive influence of female college students on their male peers Andrew J. Hill
MARK
1
University of South Carolina, United States
A R T I C L E I N F O
A BS T RAC T
JEL Codes: I21 J16
Female college students improve the academic outcomes of their male peers. Using within-college across-cohort variation in freshman enrollment at US colleges, a one standard deviation increase in the proportion of females in a freshman cohort is associated with a half percentage point increase in graduation rates for males in that cohort, while there is no effect for females. Effects are more evident in colleges where student interactions are likely more intense – colleges with higher shares of students living on campus, in college housing, and without cars – suggesting that effects operate through changes in the college learning environment.
Keywords: College Peer effects Gender
1. Introduction The nature and intensity of interactions across genders on college campuses continues to change both inside and outside the college classroom. The proportion of females enrolled in institutions of higher education levelled off in the 2000s after increasing through much of the twentieth century. In the US, females are now more likely than males to enroll in four-year colleges. Furthermore, females are also more likely to choose college majors that were considered the domain of males in the past, although there are still marked gender differences in coursetaking behavior (Dickson, 2000). Outside of the class environment, universities have responded to evolving student preferences by increasing the number of mixed gender residences, and some universities have even begun to allow opposite gender roommates (Gordon, 2010). This paper takes a step towards understanding some of the implications of these changes by estimating the effect of freshman cohort gender composition on college graduation rates. I exploit within-college across-cohort variation in freshman composition to show that there are statistically and economically significant cohort gender peer effects on graduation rates at public four-year colleges in the US. A ten percentage point increase in the share of female freshman students increases the subsequent graduation rate of male students in that cohort by about two percentage points, while there is no effect on female graduation rates. Effects are concentrated in colleges where students are more likely to interact outside the classroom: colleges with higher shares of students living on campus, in college housing, and without cars. This suggests that college peer gender composition affects student behavior through the college environment.
A secondary analysis using individual level administrative data from a small subset of institutions supports the above findings. For male students, both accumulated total credit hours and the probability of graduation are positively correlated with the share of female students in their freshman cohorts. These effects are evident when controlling for individual college admission scores. This indicates that they are not driven by changes in ability composition that may be correlated with cohort female shares, specifically more able females being admitted and enrolled at the expense of less able males. In addition, there is no convincing evidence that gender composition effects operate inside the college classroom as there is no correlation between course gender composition and course achievement. This lends further support to college peer effects operating through a general college environment mechanism rather than in the classroom. There is clear potential for college students to be affected by the gender composition of their peers, especially given the existing evidence on peer gender composition effects in other school settings. When students leave their homes to attend college, they not only take classes with their peers, but are likely to reside with them, too. This increases the opportunities for freshman peers to exert influence on each other. At the same time, college classes are likely to be larger and less interactive than classes in elementary and high schools, reducing the possibility of students in the same cohort affecting each other's academic achievement. The overall extent to which cohort composition matters in college is therefore an empirical question. College gender peer effects on academic achievement could operate through compositional or behavioral channels. A change in the graduation rate caused by a change in the proportion of female
E-mail address: [email protected]. I am grateful to Louis-Philippe Beland, Nicole Fortin, Nick Huntington-Klein, Daniel Jones, Craig Riddell, anonymous referees, and seminar participants at the University of South Carolina and the annual meetings of the Southern Economic Association (2015), Association for Education Finance and Policy (2016) and Society of Labor Economists (2016) for helpful comments and discussions. Errors remain my own. 1
http://dx.doi.org/10.1016/j.labeco.2017.01.005 Received 26 July 2016; Received in revised form 25 January 2017; Accepted 28 January 2017 Available online 01 February 2017 0927-5371/ © 2017 Elsevier B.V. All rights reserved.
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The paper is organized as follows. The empirical strategy, data and estimation results using the aggregate data are presented in Sections 2–4, respectively, while the discussion and analysis using the individual student data forms Section 5.
students may come about because the change in gender composition simply reflects a change in the ability composition of the cohort. For example, consider a marginally admitted male student being replaced by a female student in a particular freshman cohort. This increases the female share of that cohort. If the marginally admitted male student was less likely to graduate than other admitted males in the cohort, the removal of that male student from the male subsample would increase the male graduation rate, and we would observe a positive correlation between the cohort female share and cohort male graduation rate. This would be a purely compositional effect and not necessarily reflect any actual peer influence. Alternatively, college peers may affect incentives and actions. Behavioral mechanisms are broadly grouped into effects operating inside and outside the college classroom. Inside the classroom, gender composition could affect the learning environment through changes in student participation and class atmosphere. For example, females may promote class engagement if they are generally more focused than their male peers. Lavy and Schlosser (2011) find that gender peer effects at the school level operate through mechanisms such as classroom disruption and student-teacher relationships that would broadly fall into this class. Outside the classroom, peer gender composition may affect students’ study efforts, attitudes towards class, and socializing behavior. For example, if females are more academically oriented than males, a higher proportion of female students in a cohort may increase the general importance given to studies by students in that cohort. Alternatively, it is also possible that female students mitigate excessive college partying and drinking. Kremer and Levy (2008) find negative spillovers from alcohol consumption among male college roommates, and Eisenberg et al. (2014) provide evidence of peer effects in binge drinking at college. College peer gender composition may affect the propensity to engage in risky behaviors of this type, which may affect academic achievement. My paper is related to a few strands of the existing peer effects literature. We know that peer gender affects educational outcomes in kindergarten (Whitmore, 2005), elementary school (Hoxby, 2000), middle school (Hu, 2015; Lee et al., 2014; Lu and Anderson, 2015) and high school (Lavy and Schlosser, 2011; Jackson, 2012; Hill, 2015). The subset of this literature investigating the effects of variation in cohort gender composition in mixed gender school environments typically finds that school performance is positively associated with the proportion of female students in the cohort. The effect found in this paper for male college students goes in the same direction. Importantly, however, school peer gender composition effects are typically considered to be stronger inside the classroom (Burke and Sass, 2013), while evidence presented in this paper indicates that college peer gender composition effects operate outside the classroom. Outside of K-12 education, the potential for college peers to influence outcomes has been explored in a variety of settings, such as roommates (Sacerdote, 2001; Zimmerman, 2003; Stinebrickner and Stinebrickner, 2006; Jain and Kapoor, 2015), air force academy squadrons (Carrell et al., 2009), and residences (Garlick, 2014). There is some evidence that college peer effects differ by gender. Fischer (2016) finds that class ability composition affects the likelihood that females choose and complete degrees in STEM, while Ficano (2012) and Griffith and Rask (2014) find that males are more susceptible to ability peer effects than females. In a more directly related study, Feld and Zölitz (2016b) finds that the gender composition of randomly assigned teaching sections at a university in the Netherlands affects achievement and major choice, although a related study by Oosterbeek and van Ewijk (2014) does not find evidence of substantial peer gender composition effects in randomly assigned college study groups. My paper differs from these by looking at the effects of the gender composition of larger freshman cohorts and considering an arguably more representative sample consisting of the majority of public four-year colleges in the US.
2. Empirical strategy I investigate the effect of college freshman cohort gender composition on students’ academic outcomes by estimating the following reduced form equation:
yct = αc + βt + γct + πPct + εct
(1)
yct is the gender-specific aggregate graduation rate for the cohort of freshman students in college c in year t , αc is a college fixed effect, βt is a cohort or year fixed effect, and γct is a college-specific time trend (which is included in some specifications and is either linear or quadratic). Pct is the proportion of female students in the freshman cohort in college c in year t . The parameter π measures the relationship between the share of female freshman students in the college cohort and the aggregate graduation rate for male or female freshman students in that college cohort. In order for π to have a causal interpretation, the unobserved component of the cohort graduation rate must be uncorrelated with the cohort female share. College fixed effects capture the endogenous sorting of students into colleges. This controls for colleges that consistently have higher shares of female students and higher or lower graduation rates, for example. There may also be unobserved time-varying factors that are correlated with both changes in the proportion of female students and aggregate graduation rates. In particular, a potential upward trend in the female share of college students due to a widening female-male achievement gap combined with a potential upward trend in college graduation rates due to grade inflation or higher administrative costs associated with student failure would generate a positive estimate of the parameter π , but would not indicate a causal relationship. The cohort fixed effects and college-specific time trends control confounding factors of this type. Identification therefore relies on college-specific deviations in cohort female shares and cohort graduation rates from their long-term trends. Essentially, we are comparing the graduation rates of cohorts at the same college who are exposed to different cohort female shares by purely idiosyncratic factors. Sources of variation may include (1) fluctuations in the gender composition of applicants caused by either natural variation in the gender composition of the local college-going population or the college preferences of applying students, (2) changes in the gender composition of admitted students, and, (3) idiosyncratic shocks to the college preferences of admitted students in terms of if and where they choose where to enroll. I show in the data section that these factors generate a sufficient amount of variation in female shares across cohorts within colleges for the identification strategy to work. Angrist (2014) shows that models that rely solely on chance variation in peer groups may be complicated by bias from weak instruments. Feld and Zölitz (2016a) consider precisely how classical measurement error impacts the estimation of compositional peer effects in these contexts, ultimately showing that estimates will only be attenuated by measurement error when assignment to peer groups is random. Although assignment to freshman cohort groups is not random, measurement error is likely to be a much smaller concern in my study given we are considering a fixed, well-measured peer characteristic – gender – rather than peer traits such as ability or smoking that are harder to measure. The primary specification above considers gender peer effects at the college cohort level using aggregate data. The majority of college students primarily interact with other students who entered college in the same year that they did. Freshman students in college are likely to live, attend classes and socialize with other students in their cohorts. The preferences and actions of students in all three settings are likely to 152
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If the college characteristic is binary, for example, the coefficient πj on the interaction term between the college characteristic Xcj and the female share πj reveals whether the effect of the proportion of female students in the freshman cohort is more evident in colleges that display this characteristic than colleges that do not. Pure ability compositional effects are unlikely to systematically vary across colleges, so if students are affected by peer composition only in certain environments, then effects are likely to be driven by behavioral responses to freshman cohort gender composition.4 Note that the effect of the actual college characteristic on graduation rates cannot be identified given the inclusion of college fixed effects. The college characteristics I consider are from the US News Academic Insights dataset. I look at college characteristics that describe both how peers may interact outside the classroom - the share of students in college housing, the share of students who live off campus, and the share of students with cars on campus – and college characteristics that describe the extent to which peers may interact inside the classroom – the share of small classes and large classes in the college. Separating characteristics into these two categories helps determine whether peer gender composition effects are likely to occur inside or outside the college classroom (or both), which is important when considering university policies that may reinforce positive peer effects or mitigate negative ones. The set of college characteristics are necessarily limited, and any individual college characteristic could be correlated with other factors that are the underlying drivers of gender peer effects. We cannot argue that any of the college characteristics cause college gender peer effects, but we can use the results to restrict our interpretations to those consistent with observed correlations.
affect their academic performance. Defining the peer group as the college cohort captures several dimensions of peer influence that may not be captured by narrower peer groups. Investigating peer effects at the cohort rather than class level also eliminates concerns related to endogenous sorting into college classes, such as gender differences in the extent to which expected course or class composition or achievement affects course or class selection. For example, female students may avoid a course if they expect it to be particularly male-dominated in a given term. This motivation for using college cohorts rather than college classes is similar to the motivation for using within-school grade composition rather than within-school class composition in the school compositional peer effects literature (Hoxby, 2000; Lavy and Schlosser, 2011). Using the freshman cohort rather than cohorts in subsequent years has the added advantage of not being subject to biases introduced by student failure and course repetition (Ciccone and Garcia-Fontes, 2015). The disadvantage of using this broad definition of the peer group is that cohort gender composition may only be weakly correlated with the gender composition of some of the narrower peer groups in which students interact, such as college residences and classes. Using a noisy proxy for potentially more influential peer groups attenuates estimated effects. This may be particularly true in larger colleges. I explore whether estimated effects differ in magnitude or precision across college size by estimating the primary model on five subsamples based on college size quintiles. After estimating the primary effect using the strategy just outlined, I consider a variety of models to check the effect's robustness and understand its mechanism. College students interact across cohorts, so the gender composition of adjacent cohorts may affect students’ academic outcomes in similar ways to the gender composition of their own cohort.2 I report results from separate models relating cohort graduation rates to the gender composition of cohorts two years ahead, one year ahead, one year behind, and two years behind (denoted by s∈{t − 2, t − 1, t + 1, t + 2} in the below specification) to explore this.
yct = αc + βt + γct + πsPcs + εct
3. Data Two datasets are used in the first section of the paper. The primary analysis uses publicly-available data from the Integrated Postsecondary Education Data System (IPEDS). IPEDS collects information from every college that participates in federal student financial aid programs. I focus on public four-year colleges for which data is available over all the years in the study sample, a sample of 525 colleges. Freshman cohort gender composition is computed from gender-specific aggregate enrollment counts for each institution. Graduation information is available for cohorts that entered between 1996 and 2006. I consider overall six-year graduation rates – the share of students who graduate in six or fewer years – as the primary outcome variable.5 Fig. 1 displays freshman cohort gender composition and graduation rates over time. The upper panel plots the average cohort female share both in the cohort's freshman year – the composition measure used in this paper – and upon the cohort's graduation. The average freshman female share is constant at 54 percent through the study sample, indicating that the female-male gender gap in college attainment was already present and stable by the mid-1990s. This is broadly consistent with existing literature (Fortin et al., 2015). The average cohort female share at graduation is higher, indicating that admitted females are more likely to graduate than their male counterparts. This is also evident in the lower panel of Fig. 1, which shows that female graduation rates are consistently above male graduation over time. Both are trending upward, possibly due to grade inflation or higher
(2)
In addition to providing information on the types of peers that affect outcomes in college, results from this model also provide a loose assessment of the empirical strategy. In particular, evidence of peer effects of a similar or larger magnitude for student's adjacent cohorts rather than the actual cohort to which the student belongs would be unexpected and problematic for the given peer effect interpretation without a clear reason why adjacent cohorts could be more influential. The impact of college peers may depend on the college environment. Students at commuter campuses, for example, are surrounded by their peers for a much lower share of their time than students at residential campuses or in college towns. I investigate heterogeneity in peer gender composition effects along this dimension by estimating a series of specifications that include both the proportion of female students in the freshman cohort and this proportion interacted with a fixed3 college characteristic Xcj that describes the college environment, such as the share of students in college housing.
yct = αc + βt + γct + πPct + πj (Xcj ×Pct )+εct
(3)
2 In the appendix, I report and discuss the effects of freshman cohort gender composition on a related outcome that is less likely to be affected by adjacent freshman cohorts to the same extent as graduation rates, one-year retention rates. The pattern of effects is very similar to those reported in the results section. 3 There are insufficient years of college characteristics data to allow the college characteristic to be time varying in the model, which would naturally be more informative as effects would be identified from within college variation in the college characteristic over time that is less likely correlated with unobservable factors. At the same time, though, it would be difficult to assign year-specific college characteristics to cohorts given students in each cohort attend college for multiple years.
4 There is an alternative hypothesis in which purely compositional effects at a subset of colleges drive the result. If different types of colleges have marginal students of different abilities, then compositional effects could still vary by college type. There are no ex ante reasons why the college characteristics I consider would be systematically correlated with college selectivity or the ability distribution of admitted students, so I consider this to be a less likely explanation for non-zero estimates on the interaction term, but I cannot rule it out. 5 Results are similar using other definitions of graduation rates (see Appendix Table 1).
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Share female .5 .52 .54 .56 .58 .6
Freshman cohort gender composition: US public 4-year colleges
1996
1998
2000
2002
2004
2006
Cohort Freshman year
At graduation
.55 .5 .45
Graduation rate
.6
Freshman cohort graduation rates: US public 4-year colleges
1996
1998
2000
2002
2004
2006
Cohort
Male graduation rate
Female graduation rate
Fig. 1. Freshman cohort gender composition and graduation rates over time.
administrative costs associated with student failure.6 The median freshman cohort consists of about 1000 students. We may be concerned that idiosyncratic shocks to composition across cohorts in the same college generate insufficient variation for the empirical strategy to be effective. The left panel in Fig. 2 – a plot showing the distribution of freshman cohort gender composition – shows considerable variation in cohort female shares across colleges and cohorts; the interquartile range is about 20 percentage points. Identifying variation, however, comes from within-college acrosscohort variation in gender composition. The distribution of this is shown in the right panel. The standard deviation of the within-college female share is 2.5 percentage points. Gender composition shocks of this magnitude will be considered when interpreting whether estimated effects on outcomes are of an economically meaningful magnitude. The distributions of college graduation rates for males and females are plotted in Fig. 3. Both the distributions across colleges and cohorts (left panel) and within colleges (right panel) are shown. The left panel shows that there are very large differences in college graduation rates across colleges. This is expected given the large differences in college and student quality across the US. The right panel shows the expected smaller differences in cohort graduation rates when considering within-college variation; a standard deviation of almost 5 percentage points for both males and females. The second data source in the first part of the paper is the US News Academic Insights dataset used to construct the popular US News and World Report college rankings. I use college characteristics from this dataset to explore heterogeneity in gender peer effects by college type. I construct time invariant measures of these characteristics for each college by computing means for years in which the data is available. Colleges are manually matched using the name of the institution across the two datasets, resulting in a reduced sample of 165 public four-year colleges. The number of colleges is smaller than in the original sample because satellite campuses are often excluded from Academic Insights, which focuses on flagship schools, and some college characteristics being missing for a small subset of schools. The main sample of colleges and the smaller US News sample of colleges are compared in Table 1, showing that colleges in the US News sample are
generally larger and have higher graduation rates. The original model is estimated on this smaller sample of colleges to confirm that the sample restriction does not affect the primary results. Means and distributions of the college characteristics are plotted in Appendix Fig. 1, showing a considerable amount of variation in these dimensions of the college environment across the US. 4. Results Table 2 reports estimates of the parameter of interest π from Eq. (1). Using variation in cohort composition across colleges – the specifications without college fixed effects in Columns 1 and 5 – an increase in the female share is associated with a reduction in both male and female graduation rates. The coefficients of −0.36 and −0.35 indicate that a 10 percentage point increase in the female cohort share is associated with a 3.6 and 3.5 percentage point reduction in male and female graduation rates, respectively. Colleges with higher shares of female freshman students have lower graduation rates, on average. However, given that colleges with consistently different gender shares are likely different in several other dimensions, these estimates cannot be given a causal interpretation. The remaining columns in Table 2 include college fixed effects; the within-college variation identifies the causal effects of freshman cohort gender composition on graduation rates. Using no college-specific time trends, linear trends or quadratic trends (Columns 2, 3 or 4 and Columns 6, 7 or 8), there is a positive effect of the proportion of female students on male graduation rates and no effect on female graduation rates. The coefficient of 0.2 means that a 10 percentage point increase in the female cohort share is associated with a 2 percentage point increase in male graduation rates. The pattern of effects is not affected by the inclusion or functional form of the college-specific time trend; subsequent specifications use the most flexible (quadratic) trend, but results are not sensitive to this. Table 3 shows that the positive effect on male graduation rates is evident in colleges of almost all sizes. The concern that in large colleges cohort gender composition may be too weakly correlated with the gender composition of the narrower peer groups in which students interact (such as college residences) is unfounded. The magnitude of the estimated effect of the female share on male graduation rates in Tables 1–3 is consistently around 0.2. The economic significance of this effect is interpreted by considering a one standard deviation composition shock to a representative college
6 In contrast, Bound et al. (2010) document declining college completion rates between the high school classes of 1972 and 1992. The difference is likely explained by my study covering a more recent period and only including four-year colleges.
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10
4
15
6
20
25
8
A.J. Hill
Within-college standard deviation: .025
0
0
5
2
Mean share female: .54
0
.2
.4
.6
.8
-.1
1
0
.1
.2
Freshman cohort composititon: share female (within-college variation from mean)
Freshman cohort composititon: share female
1
10
1.5
2
15
Fig. 2. Distribution of freshman cohort gender composition.
5
Within-college standard deviation: Males: .046 Females: .049
.5
Mean male graduation rate: 0.50
0
0
Mean female graduation rate: 0.56
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
-.4
1
-.2
0
.2
.4
Graduation rate (within-college variation from mean)
Graduation rate Males
Males
Females
Females
Fig. 3. Distribution of college cohort graduation rates.
the female-male college graduation gap. I now turn to the results checking the robustness of the effect and probing its mechanism, starting with exploring whether the peer gender composition of adjacent cohorts affects outcomes in Table 4. The sample is smaller because the first and last two freshman cohorts for each college are excluded from the analysis as they do not have the full set of adjacent cohorts. Note that each cell in the table reports an estimate from a separate model. The results in Column 1 show that peer gender composition effects for male students are most strikingly evident – both in terms of magnitude and precision – within a student's own cohort. The other rows of Column 1 reveal that the gender composition of adjacent cohorts does not affect male graduation rates, and Column 2 shows no peer gender composition effects for females (consistent with the main result in Table 2). Overall, I interpret the results in this table as (1) showing that college peer gender composition effects are strongest within one's own cohort, and (2)
freshman cohort with 1000 male students and 1000 female students. The within-college standard deviation in the female share – the relevant variation for the empirical strategy – is 2.5 percentage points (shown in Fig. 2). Replacing 50 male students with 50 female students would increase the female share by 2.5 percentage points. Assume that these 50 male students randomly substitute away from the given college (choose to attend another college, for example) and 50 female students randomly substitute towards the given college. The increase in the female share increases the male graduation rate by 0.5 percentage points (0.025*0.2) according to the estimate from Table 2. If the initial male graduation rate were 50 percent (the mean male graduation rate in the sample), 475 of the 950 male students would graduate. The 0.5 percentage point increase in the graduation rate causes 480 male students to graduate: five additional male students obtain a college degree, a small but meaningful effect. A one standard deviation increase in the cohort female share closes about one tenth of 155
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unlikely to depend systematically on the college environment. The first column of Table 5 confirms that the overall effect of freshman cohort gender composition in the smaller US News sample of colleges is similar to the overall effect for all colleges reported in Table 2. Columns 2 to 4 of Panel A show that freshman peer gender composition has more of an effect on male graduation rates in colleges with higher shares of students in college housing, colleges with higher shares of students living on campus, and colleges with higher shares of students without cars on campus. For example, in colleges with 10 percent of students living in college housing, the effect of the proportion of female peers on the male graduation rate is only 0.09 (−0.04+0.96*0.1), while it is 0.28 and 0.46 in colleges with 30 and 50 percent of students living in college housing, respectively. Interestingly, and contrasting somewhat with previous estimates, the cohort female share also exerts positive effects on female graduation rates in colleges with these characteristics (Columns 2 to 4 of Panel B). The magnitudes of the estimates are smaller for females, explaining the absence of an average treatment effect when considering all colleges combined in Column 1. However, these results for females provide
Table 1 Descriptive statistics (snapshot of colleges in 2001).
Total number of freshman students Males Females Female share Total number of undergraduate students Males Females Female share Male graduation rate Female graduation rate Number of colleges
Main sample
US News sample
Mean
(Standard deviation)
Mean
(Standard deviation)
1,509
(1,332)
2,753
(1,553)
690 819 0.543 7,241
(639) (715) (0.003) (6,326)
1,293 1,460 0.530 13,207
(760) (828) (0.005) (6,973)
6,280 6,927 0.524 0.569 0.632
(3,529) (3,589) (0.004) (0.013) (0.012)
3,319 (3,099) 3,923 (3,313) 0.539 (0.003) 0.496 (0.008) 0.562 (0.008) 525
165
Table 2 Effect of freshman cohort composition on cohort college graduation rates.
Mean
Male graduation rates
Female graduation rates
0.50
0.56
1
2
3
4
5
6
7
8
Share females
−0.36** (0.11)
0.25** (0.05)
0.19** (0.04)
0.17** (0.04)
−0.35** (0.12)
0.02 (0.05)
−0.00 (0.04)
−0.01 (0.04)
College fixed effects College-specific time trend Number of observations Number of colleges
No No
Yes No
Yes Lin.
Yes Quad.
No No
Yes No
Yes Lin.
Yes Quad.
5775 525
Notes. Regressions weighted by gender-specific college cohort size. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
providing some validation of the empirical strategy given that the estimated effects are largest and most precise where we expect them to be. Table 5 explores whether gender peer effects are affected by the college environment. I report effects on male and female graduation rates in Panels A and B, respectively. As discussed in the empirical methodology section, in addition to providing information about potential mechanisms, heterogeneity in the effect by college type is considered evidence against ability composition effects as these are
Table 4 Effect of lagged and leading freshman cohort composition on cohort college graduation rates. Male graduation rates
Female graduation rates
0.50
0.56
1
2
Share females (t-2)
−0.07 (0.04)
−0.03 (0.05)
Share females (t-1)
0.06 (0.04)
0.07 (0.04)
Mean
Table 3 Effect of freshman cohort composition on cohort college graduation rates by college size. Male graduation rates College size quintile
1
2
3
4
5
Share females (t)
0.17** (0.04)
−0.01 (0.04)
Mean freshman cohort Mean share male
343 0.34
679 0.36
1147 0.43
1871 0.39
4075 0.61
Share females (t+1)
−0.00 (0.04)
0.02 (0.04)
Share females
0.06 (0.06)
0.16* (0.07)
0.20* (0.08)
0.21 (0.12)
0.19* (0.08)
Share females (t+2)
−0.06 (0.04)
−0.05 (0.04)
Number of observations Number of colleges
1155 105
1155 105
1155 105
1155 105
1155 105
Number of observations Number of colleges
Notes. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and quadratic college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
3675 525
Notes. Each cell reports an estimate from a separate regression. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and quadratic college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
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large. The absence of heterogeneity in the class size dimension is interpreted as suggestive evidence that effects are not operating inside the college classroom as we would expect stronger peer gender composition effects in colleges with smaller classes if so. Taking these results as a whole, we see that female students exert positive externalities in colleges in which students are more likely to interact with their college peers outside of class. This is interpreted as support for mechanisms operating through the broader college learning environment.7 The advantage of using college-specific aggregate data from a relatively wide time frame and a large number of public four-year colleges is that estimated effects are representative of the US. This approach has limitations, however, particularly if we are concerned about other dimensions of peer group composition that may vary with gender composition. I therefore complement the above specifications with an analysis using individual level data; specifically, student transcript data aggregated to the semester level from the Texas Higher Education Opportunity Project.
Table 5 Effect of freshman cohort gender composition interacted with college characteristics. 1
2
3
4
5
6
0.22** (0.07)
−0.04 (0.12)
−0.04 (0.13)
0.10 (0.12)
−0.03 (0.34)
0.26 (0.18)
Panel A: Male graduation rates (Mean: 0.57) Share females
Share females interacted with: Share of students in college housing
0.96* (0.43)
Share of students who live on campus
0.93* (0.43)
Share of students without cars on campus
0.80* (0.32)
Share of classes that are small ( < 20)
0.65
5. Effects of freshman cohort composition using individual student data
(0.81)
5.1. Empirical strategy −0.29
Share of classes that are large ( > 50)
I test whether the findings from the primary specification can be replicated in the individual level data by constructing a repeated crosssection with one observation per student where the relevant outcome variable is either a measure of a student's accumulated total credit hours when leaving college or an indicator for whether the student graduated, and the relevant explanatory variable is the student's freshman cohort female share. The specification is otherwise similar to Eq. (1), and is estimated separately for males and females.
(1.12)
Panel B: Female graduation rates (Mean: 0.64) Share females
−0.03 (0.07)
−0.25* (0.13)
−0.25 (0.13)
0.02 (0.12)
−0.15 (0.40)
−0.06 (0.16)
yict = αic + βit + γict + πPict + g(Aict ) + εict
Share females interacted with: Share of students in college housing
(0.39) Share of students who live on campus
0.88* (0.40)
Share of students without cars on campus
0.43 (0.28)
Share of classes that are small ( < 20)
0.33 (0.96)
Share of classes that are large ( > 50)
0.32 (1.00)
Number of observations Number of colleges
1815 165
1782 162
1749 159
935 85
1815 165
(4)
yict is the outcome variable for student i in college c in year t , αic and βit are indicators for student i ’s college and cohort, γict is a college-specific time trend for student i , and Pict is the proportion of female students in student i ’s freshman cohort. I include an additional control for student i ’s college admissions score (SAT or ACT) Aict . The inclusion of a flexible admissions score control means that the parameter π identifies the effect of freshman cohort gender composition for students of approximately equal ability (upon admission). This speaks to whether effects arise from compositional or behavioral changes. If effects are purely coming about because changes in gender composition reflect changes in ability composition, there would be no effect of freshman cohort gender composition on the probability of graduation for students of the same ability. In addition, I investigate whether gender peer effects operate within the college classroom by defining an alternative peer group as the set of students likely in the same set of college classes together (rather than the freshman cohort). I model the semester-specific average GPA (there is no course-specific GPA) for student i in college c , department d , semester (time period) s and cohort t as a function of the departmentspecific female share in that semester Pcdst .
0.90*
1815 165
Notes. Regressions weighted by gender-specific college cohort size and include college fixed effects, cohort fixed effects and linear college-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
yicdst = αcd + βs + θt + γcdt + πPcdst + εicst
(5)
College-department fixed effects αcd , semester fixed effects βs , cohort fixed effects θt and a college-department trend γcdt are included in the model. The variation for identifying the parameter of interest π comes from deviations in department female shares and department average
further support for the proposed college environment mechanism; if females improve the general learning environment, then there is reason to expect that these changes should improve outcomes for both males and females (even if not to the same extent). Results in Columns 5 and 6 show that gender peer effects do not depend on the average sizes of college classes in a statistically significant way, although the standard errors of these estimates are
7 An alternative interpretation of results worth noting is that male students are negatively affected by exposure to more male “competitors” in college. This hypothesis cannot be ruled out with the available data, although the existing literature on gender and competition typically finds that females are more prone to adverse effects from competition than males (Niederle and Vesterlund, 2011), which is not what is found.
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Table 6 Effect of freshman cohort composition on individual student college outcomes. Males 1
Females 2
3
4
5
6
7
8
5.06 (19.85)
−16.39 (29.16)
−0.74 (18.82)
Panel A: Total credit hours
Mean: 94.79
Mean: 96.26
Share females
−99.16 (143.55)
Panel B: Graduation rates
Mean: 0.59
Share females
−0.12 (1.23)
0.95 (0.56)
0.50 (0.41)
1.10* (0.31)
−0.81 (1.33)
0.31 (0.57)
−0.10 (0.20)
0.29 (0.28)
College fixed effects College-specific time trend Number of students Number of colleges
No No
Yes No
Yes Lin.
Yes Quad.
No No
Yes No
Yes Lin.
Yes Quad.
65.53* (23.12)
12.66 (18.18)
38.87* (12.01)
−124.37 (138.18)
Mean: 0.66
44,561 8
46,015 8
Notes. Regressions weighted by gender-specific college cohort size and include controls for admissions scores. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
GPA scores from their long-term trends.8 Students at the same college, entering in the same freshman cohort, and declaring the same major are not necessarily in the same academic peer group. I restrict the sample in two ways to ensure that the set of peers included in the definition are likely to be taking the same courses. First, freshman and sophomore students are excluded as they are typically not yet in classes with peers who declared the same major. And, second, the sample is restricted to students who are deemed to be on-schedule, which is defined as completing at least 12 credit hours per a semester. This is because a junior who has completed only 16 credit hours is unlikely to be taking the same courses as a junior who has completed 24 credit hours even if they entered in the same freshman cohort and declared the same major.
students is computed by summing their obtained credit hours across all semesters in which the student is observed. The THEOP data used in the paper contains information on a little over 80,000 students. Graduation rates are slightly higher than in those reported in the IPEDS data: 59 percent for males and 66 percent for females, although the gender gap is similar. The number of departments per institution in the sample ranges from 29 at Rice University to 53 at Texas Tech University. Average department female shares range from around 20 percent in Computer Science and Engineering to above 90 percent in Nursing and Social Work, although recall that the empirical strategy to estimate within-classroom gender peer effects relies on variation across cohorts within the same department rather than across departments.
5.2. Data
5.3. Results
The individual level data comes from the Texas Higher Education Opportunity Project (THEOP), a dataset containing information on the universe of students who applied to eight Texas four-year colleges during the 1990s and early 2000s. Longitudinal transcript data are available at the student-semester level rather than the student-course level. I observe students’ aggregate GPAs for all semesters in which the student was enrolled, the course credits obtained in these semesters, as well as their current departments and fields of study. Note that there is no course-specific information, so course-specific peers cannot be directly identified. The sample is restricted to students who intended to be admitted and were admitted during a fall semester (regular admission) to ensure that freshman cohorts are well-defined. Observations from summer terms are excluded from the analysis. Indicators for graduation and time-to-graduation are constructed from the recorded graduation year. I restrict the sample to cohorts who entered college between 1995 and 1999 because graduation rates for earlier and later cohorts are based on selected samples and vary considerably from the relatively stable graduation rates of about 60 percent observed for each of the five included cohorts. The total number of credit hours obtained by
Table 6 shows that the effect on graduation found in Tables 1–3 can be replicated using individual level data from THEOP, although estimates are more sensitive to the inclusion and functional form of the college-specific trends than the primary results in Table 2. Interpreting the estimates in Column 4, a 10 percentage point increase in the share of female freshman students increases accumulated total credit hours by 3.9 h (4 percent relative to the mean of 94.8 total credit hours) and the probability of graduation by 11 percentage points (18 percent relative to the mean graduation rate of 0.59) for male students. Columns 6 to 8 reveal no evidence of peer gender composition effects for females.9 These models include flexible controls for admissions scores, so identifying variation comes from comparing students with the same ability (as proxied by admissions scores). I show in Appendix Fig. 2 that effects for male students are evident across much of the ability distribution. Overall, these findings indicate that effects are not driven by pure ability composition changes. If we were simply capturing the effect of more able females being admitted at the expense of less able males, we would not observe positive spillovers from female peers controlling for ability or for infra-marginally admitted male students. 9 The results for this part of the paper are presented with the caveat that when clustering at the college level – as is done in the analysis – there are fewer than ten clusters. Webb (2014) provides a bootstrap procedure for improving the reliability of inference under these particular circumstances; it has better properties – and is more stringent – than conventional wild bootstrap-based tests. When implementing this procedure, the parameter of interest is no longer statistically significantly different from zero at conventional levels; the p-value is 0.16. Although this suggests a one in six chance that the result is due to random sampling error, the very robust effects in the first part of the paper negate some of this concern.
8
Note that the cohort effects are not specific to college departments, so only capture cohort shocks across college departments. The inclusion of college department-specific cohort fixed effects would result in identifying variation coming from fluctuations in peer gender composition across semesters for students in the same college departmentcohort. This would be a concern because variation in gender composition across semesters for students in the same department and cohort is endogenous to the model given that it is likely generated by student failure or students changing majors, which may happen in response to either peer gender composition or GPA.
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Table 7 Effect of college-cohort-term-department (academic peer group) gender composition on individual student term GPA. Males
Females
All junior and senior terms
First junior term only
All junior and senior terms
First junior term only
3.09
3.05
3.26
3.22
1
2
3
4
5
6
Share females
0.17** (0.03)
0.10 (0.05)
0.03 (0.03)
−0.01 (0.03)
0.02 (0.05)
0.05 (0.03)
Semester fixed effects Lagged cumulative GPA fixed effects Number of students Mean semesters per student Number of college-departments Number of colleges
Yes No 56,695 2.8 311 8
No No 46,278 1 302 8
No Yes 45,602 1 302 8
Yes No 65,328 2.8 323 8
No No 55,149 1 315 8
No Yes 54,311 1 315 8
Mean
Notes. All regressions include college-department fixed effects, cohort fixed effects and linear college-department-specific time trends. Robust standard errors clustered at the college level. ** Significant at 1% level. * Significant at 5% level.
The final table probes whether course gender composition affects course performance. Estimates in Table 7 show a very small positive effect on male course achievement from course female share, and no effect on female course achievement. From Column 1, a 10 percentage point increase in the share of females majoring in the same department causes a (very small) 0.02 increase in average semester GPA per semester for male junior or senior students. In Column 2, the sample is restricted to students in their first junior semester to mitigate biases arising from changes to academic peer group composition that occur in the final two years of college. The estimated effect is less precise. The inclusion of controls for lagged GPA in Column 3 removes the effect for males. Overall, I interpret these results as indicating that within classroom effects are at most responsible for only a very small component of the overall freshman cohort gender composition effect. Finally, an alternative explanation put forward by Feld and Zölitz (2016b) is that college peer gender composition affects major choice. If so, and if major choice subsequently affects graduation rates, this could explain some of the observed effect. I cannot find convincing evidence of this phenomenon (see the Appendix for a more detailed discussion), although some specifications suggest an inverse relationship between the probabilities with which females pursue STEM and the female share of their cohorts, which, interestingly, is broadly consistent with Feld and Zölitz.
I am unable to find evidence of economically meaningful gender peer effects using a proxy for course gender composition rather than cohort gender composition, indicating that effects do not appear to be operating inside the college classroom. Kremer and Levy (2008) and Eisenberg et al. (2014) find negative spillovers in alcohol consumption among college students. This offers a potential class of channels through which the estimated college gender peer effects may affect the general college learning environment: for example, a higher share of female peers may reduce the frequency or intensity of “fraternity-type” parties characterized by binge drinking, improving academic outcomes. In terms of more direct policy implications, males may actually benefit from mixed gender residences rather than the conventional wisdom that females distract males from their academic pursuits. Extrapolating from these results, universities may be able to improve graduation rates – particularly for males – with interventions targeting the college environment.
6. Conclusion
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Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.labeco.2017.01.005. References
This paper provides new evidence on the effects of college peer gender composition on academic achievement. In particular, I find that female students improve college outcomes for their male peers. An increase in the freshman cohort female share increases the cohort graduation rate for males at public four-year colleges in the US, while there is no overall effect for females. I provide suggestive evidence that effects are (1) driven by behavioral responses to peer gender composition rather than changes in ability composition, and (2) generated outside of the college classroom. A set of secondary findings supports these claims. First, there is heterogeneity in the effect by college type. Generally, freshman cohort effects are more evident in colleges in which students are more likely to interact outside class. This suggests a broad college environment mechanism. Second, estimates using individual level data show that controlling for individual student ability does not affect the pattern of results. A male student of any ability is more likely to graduate if he is exposed to a higher share of females in his freshman cohort, which is not consistent with a pure ability composition mechanism driven by marginally admitted students only. And, third, 159
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