Enrolling at university and the social influence of peers

In France, from the second year of high school, students must choose a subject major. Each major gives a different weight to the variety of topics on offer for the Baccalauréat, the high school exit exam held at the end of the third year. High schools propose three possible subject majors: science (S), languages and literature (L), and economics and social sciences (ES). Within each major, students are divided into different classes, and remain with the same classmates throughout the academic year. There is no tracking by ability between the different classes of the same major within a high school.

Each year in April, senior high school students must select their higher education path using a website called Application Post Bac (APB).⁽⁵⁾ On that platform, they can list up to 24 institutions and fields of study in higher education that they are considering for the following academic year. In July of each year, if the student has graduated from Baccalauréat, she is allowed to enroll in university and into the subject field of choice from those listed on the APB selection process.

In 2009, a new policy, called Orientation Active (OA), was enacted with the objective of helping students to select their higher education pathway. For any choice the student has selected on APB, the university must deliver individual feedback on the student's likelihood of graduating from that field of study. This feedback is determined by the student's previous academic records, and is one of the three possible responses: first, a positive response, (henceforth called “A”), stating that the student is encouraged to register in that institution, and is likely to graduate, given their past academic records; and, second, a “B” or neutral response states that the student should succeed but will have to work conscientiously in order to graduate; and third, a negative response (henceforth called “C”), which states that based on the student's academic records, it would be advisable to amend the choice of postsecondary education. Feedback is sent out in May prior to the students graduating from high school. Whatever the feedback received, students are able to register in their choice of university and in their field of choice. In previous work (Hestermann and Pistolesi, 2017; Pistolesi, 2017), we demonstrate the impact of this policy on the students’ choices of higher education: the students receiving C feedback are less likely to register and this relationship is causal. In this article, we investigate whether the share of classmates receiving C feedback from their local university has an impact on the individual probability of enrolling in the same university.

We use administrative records collected by the APB website on all applicants at a large French university for seven consecutive cohorts from 2009 to 2015. The data contains individual characteristics, such as a unique student identifier, gender, age, place of residence, nationality, and whether or not she received a needs-based scholarship.⁽⁶⁾ The data also includes individual schooling records from the last 2 years: numerical grades by topic, high school major, and class identifier. This information is provided by the school. Moreover, the data indicates the name of the high school attended, a unique national high school identifier, and whether it is a public or private institution. The data also lists the feedback each student has received from the university listed on APB. We match these data with the university's internal records in order to determine those students enrolled at a particular institution in the following academic year as a first year undergraduate.

The university that provided the data used in this paper is a large research public institution. Around 25,000 individuals study in this university in the fields of economics, law, management, and computer sciences. At the graduate level, it attracts students from all over the country and from other European and non-European countries. It offers professional and research Master degrees in each of these fields, as well as PhD programs. At the undergraduate level, most students are French and come from within the local district (as is the case for most other French universities).⁽⁷⁾ This university is not in the Paris area and there are no other universities offering these fields of study in the same region. In France, there are 13 regions, and there are 5,800,000 inhabitants in this particular region; therefore, it faces no competition in attracting local students. In France, there is limited competition among universities to attract undergraduate students, since, at that level, most of the programs are similar. Moreover, families are used to sending their children to study at the closest university from their place of residence at the undergraduate level. At the graduate level, however, competition between universities is more intense with each university attempting to differentiate their offerings within each of their different graduate programs. The university providing the data used in this paper is clearly identified at the graduate level, as a research intensive university.

The data sample is restricted to high school students living in the same region as the university providing the data. Those living abroad face very different costs and opportunities. We drop observations from vocational high schools.⁽⁸⁾ As a further restriction, we concentrate on students from high school majors with at least two different classes, as some of our specifications are based on within high school major variation in the proportion of classmates gaining access to university. The data only includes university applicants, and does not include high school students who do not apply to this university. Therefore, our sample is not representative of the population of high school students, since unobserved factors can affect the probability of applying to university and the share of peers receiving C feedback. The sample is representative of the population of students from a general high school applying to university; however, the difference between the two is limited.

One can wonder whether observing only the university applicants affects the internal and external validity of our study. First, as regards external validity (as explained above) the vast majority of students in France choose to apply to the university within their region of residence. By law, when applying to their local university, students are prioritized for enrollment. Moreover, universities are the single type of higher education institutions that are non-selective.⁽⁹⁾ Therefore, high school students have a strong incentive to list their local university among their 24 choices on APB in order to ensure their admittance to higher education. Second, as regards internal validity, in Section 4.2, we test whether the estimation results change between classes in which everyone applies to university and classes in which there are more class members than university applicants.⁽¹⁰⁾ The test does not reject the null hypothesis of similar peer effects between the classes that are fully observed and the classes that are partially observed.

Table 1 provides descriptive statistics for our sample, which includes 19,181 individual observations. Panel A shows individual observable characteristics: for example male students represent a smaller share (41%) of university applicants in our data; a large majority of students (92%) are French; and in high school, 14% of the students come from families with a low socio-economic background. Several measures of academic level in high school are available. First, the mean numerical score over the different topics can range from 0 (worst) to 20 (best). We observe a large variance in achievement, with low-achievers scoring 3.25, while high achievers score 19.33. Second, 32% are potentially high-achievers.⁽¹¹⁾ In our data, 44% of the candidates come from a high school major in ES, 37% from science, and 18% from language and literature. When applying to university, 27% receive C feedback from this institution. Finally, 50% register at this university.

In panel B, we compute the mean value of various class characteristics, and study their distribution across classes. We observe a median class size of 28 students. The composition of the class varies largely between the different classes: the share of male students varies from 5% to 70% of the class and the share of students from low socio-economic backgrounds varies from 0% to 50% of the class. Importantly, the mean academic level of the class is heterogeneous, since it ranges from 10.10 to 14.17. The last row indicates the distribution, of the share of peers that register in this university. In the classes in the lower part of the class distribution (P25), 42% of the students register at this university, while for classes in the higher part of the class distribution (P75), this proportion increases to 87% of the class. Overall, this panel shows that the composition of the classes changes considerably from one class to another. Peer groups are mostly heterogeneous in this sample.

Table 2 provides descriptive statistics on the type of feedback received and the individual probability to register. Panel A displays the individual probability of attending this university by the type of feedback received: 51% of students receiving A or B feedback are likely to register,⁽¹²⁾ which is 4 percentage points more than those receiving C feedback. The difference is statistically significant at the 5% level. Panel B presents the individual probability of enrolling at university, relative to the share of classmates receiving C feedback. When 20% of the peers receive C feedback, 69% of the class register in the same university; on the other hand, when 80% of the class receive the same negative recommendation, only 35% of students attend this institution in the next following year. There is a clear drop in enrollment with the share of peers receiving C feedback. In the rest of the paper, we investigate whether that relationship can be given a causal interpretation conditional on major-by-high-school-by-year fixed effects.

Figure 2 graphically depicts the relationship between the share of students enrolling in this university and the proportion of classmates receiving C feedback.⁽¹³⁾ It also presents the decreasing pattern of enrollment when the proportion of peers receiving C feedback increases. We observe a continuous drop in enrollment when >20% of the classmates receive C feedback. The next section details our empirical strategy.

Figure 2

Using repeated cross-sectional data, we estimate the following reduced-form equation, in order to explore how the feedback received by classmates in high school affect an individual's choices for post-secondary education:⁽¹⁴⁾ (1) ysmgti=β1C¯smgt(−i)+Xsmgti′β2+X¯smgt(−i)′β3+θsmt+εsmgti {y_{smgti}} = {\beta _1}{{\bar C}_{smgt\left( { - i} \right)}} + {\boldsymbol{X}}_{smgti}^\prime{\beta _2} + {\boldsymbol{\bar X}}_{smgt\left( { - i} \right)}^\prime{\beta _3} + {\theta _{smt}} + {\varepsilon _{smgti}} where sm represents school-major⁽¹⁵⁾, g represents groups of peers measured by classes in high school, t is time and i denotes individuals; y_smgti is a dummy variable taking the value 1 if individual i in high school major sm in class g at time t enrolls in the university and 0 otherwise; C¯smgt(−i) {{\bar C}_{smgt\left( { - i} \right)}} represents the proportion of classmates, excluding individual i, from class g at time t receiving C feedback from their university application; X_smgti is a vector of individual's covariates such as age, gender, nationality, and socio-economic background; X¯smgt(−i) {\boldsymbol{\bar X}}_{smgt\left( { - i} \right)} is a vector of the same characteristics of the peer group, excluding individual i; θ_smt is a high school major-time fixed effect and ɛ_smgti is an error term; the coefficient of interest is β₁, which captures the effect of having a higher proportion of high school classmates receiving C feedback on the decision to enroll at the same institution.

Estimating the enrollment equation by OLS regression without the major-by-high-school-by-year fixed effects is unlikely to deliver credible peer effect estimates, since the composition of the peer group is not random. Using major-by-high-school-by-year fixed effects, we focus on the random assignment of students to classes within high school major-year and use the variation between classes of the same major, school, and year. We discuss the validity of this assumption in the next section.

First, we discuss the self-selection of students into peer groups.⁽¹⁶⁾ To correct for the endogeneity of the formation of groups, we introduce major-by-high-school-by-year fixed effects.⁽¹⁷⁾ As explained above, high schools in France offer different types of majors. Within a school and between the different majors, there is a potential selection of students, since many high-achieving students select the science major in high school, even if they do not plan to study in a scientific field at university. Using major-by-high-school-by-year fixed effects and multiple years, we compare different classes within the same major in the same school and during the same academic year. Using this approach we correct for the non-random allocation of students between the different high school majors and therefore between the different high schools, which are the drivers of self-selection at the high school level in France (Ly et al., 2014). Moreover, this empirical strategy controls for unobserved factors that are correlated with high school major and the decision to register at university.

We now present evidence of the validity of the fixed effect identification strategy. First, in Appendix AII, we check that the peers’ mean variables have enough variation within high school majors, schools, and years. Table A1 presents the decomposition within and between high school major by school and by year components and shows that, on average, the within component of the peers’ mean variables represents around 45% of the variance. Second, in Table 3, we test whether the change in the proportion of peers receiving C feedback within a high school major, a school, and a year is correlated with the changes in students’ background characteristics. Figure 3 presents the results graphically. The first column of Table 3 displays the OLS regression coefficients. In this column, we see that several observable characteristics are correlated with the share of peers receiving C feedback: males, individuals with lower academic records, those who have been academically held back in the past, and those with a larger share of peers receiving C feedback. In column (2), we introduce major-by-high-school-by-year fixed effects and find that the coefficients are closer to zero. Only two variables are still significant: the dummy for males and the one for French nationality. In column (3), we add peer mean characteristics and find that none of the coefficients are now significant. From the results of column (3), we conclude that the variation in the share of peers receiving C feedback is exogeneous after taking out major-by-high-school-by-year and peer mean characteristics. Finally, to complement this analysis, in Appendix AII.2, we test whether or not the assignment of students between classes within a high school major, a school, and a year is randomly determined. The empirical test presented here validates this assumption.

Figure 3

Our major-by-high-school-by-year fixed effects strategy controls for the most obvious potential confounding factor: the endogenous sorting of students across majors and across schools based on their socio-economic background. It is still possible that unobservable factors varying across classes and within high school majors that are correlated with the proportion of peers receiving C feedback may generate some spurious correlation within the group of peers. In this respect, the major potential threat to our strategy comes from the potential difference in teacher quality. A class can have a particularly effective teacher, which reduces the share of the class receiving C feedback. Admittedly, our strategy does not completely prevent that threat. However, high school students are allowed to apply to university whatever their score during the high school academic year. The single requirement in applying to university is to succeed at the Baccalauréat exam, which is set at the national level and is assessed anonymously by various teachers, with the results unknown at the time that universities provide feedback. Nonetheless, our analysis relies on the assumption that potential class unobserved shocks are not correlated with the share of peers receiving C feedback. In the empirical analysis below, we present the results with major-by-high-school-by-year fixed effects.

Table 4 reports the results of regressions of individual enrollment at university on the proportion of high school classmates receiving C feedback from their application in the same institution during the same year. The dependent variable is a dummy taking the value 1 if the individual registers and 0 otherwise. These regressions are linear probability models. In any of these regressions, standard errors are clustered at the major-by-high-school-by-year level.⁽¹⁸⁾ The table displays different specifications using the proportion of peers receiving C feedback as the main variable of interest. The first column shows a negative correlation of −0.153 of this variable with the probability to enroll at university. The second column adds students’ individual characteristics: age, gender, whether the individual is French, whether she attends optional courses at high school (such as Latin or Greek), whether she receives a high school scholarship (a proxy for coming from a low socio-economic background), and a dummy for whether she has been academically held back in the past. It also includes an indicator variable if the high school is public and 6-year dummy variables. The coefficient drops slightly in absolute value to −0.094. In the third column, we add the mean of the peers’ same observables. The estimated coefficient remains significant and similar at −0.095. In columns (4)–(6), we repeat the same exercise adding major-by-high-school-by-year fixed effects. The peer effect estimates are identified by comparing different classes within the same major, within the same school, and during the same year. In column (6), the coefficient drops in absolute value to −0.068 and is significant at the 10% level. The drop in the peer coefficient when using major-by-high-school-by-year fixed effects can be interpreted as a consequence of the non-random allocation of students between the different high school majors.

From the regression in column (6), we document that an increase of 10 percentage points of the share of peers receiving C feedback is associated with a smaller probability to register at university of around 0.68 percentage points, indicating that there is a negative peer effect of being in a group of academically weaker students on the choice of gaining access to university. While the effect may seem modest, the average probability to register to university is 0.5, and therefore we need alternative ways to measure its importance. Alternatively, we compute standardized coefficients: the effect of a one standard deviation change in the share of peers receiving C feedback. These regressions indicate that an increase by a one standard deviation of the share of peers receiving C feedback results in a decrease in individual registration of around −0.01 in standard deviation unit, compared to −0.02 with the OLS coefficients with the fixed effects.⁽¹⁹⁾ Admittedly, the effect is small from a policy perspective.

It is difficult to compare our estimates to the literature, since we are not aware of any study of the effect of academically low achieving peers on the choice to enroll at university, as previously mentioned. Most of the literature on peer effects in higher education estimates peer effects in the choice of field of study, conditional on enrollment. In the next section, we test whether the previous estimates are homogeneous over the population.

Heterogeneous effects of the proportion of peers receiving C feedback are explored in Table 5. In this table, we report the results of OLS regressions of individual enrollment on the share of peers receiving C feedback for different subsamples. In panel A, we study whether there are heterogeneous effects by gender. Columns (1) and (2) show the results for male students, columns (3) and (4) display results for female students, and column (5) presents results for male and female students together. We provide mean peer effects’ estimates as well as estimates distinguishing female and male peers.

From these regressions, we see that mean peer effects are larger for males than for females (−0.122 vs. −0.034); the estimated coefficient for males is significant, while the one for females is not. The difference between the two is not statistically significant.⁽²⁰⁾ In columns (2) and (4), we split the peers into two groups: first, the male classmates and second, the female classmates, and we compute the proportion receiving C feedback for each of these two groups. We see that for the sample of males, the estimated peer effect is larger with male peers than with female peers (−0.110 vs. −0.032). In column (4), when we study female students, we obtain a symmetric result: peer effects by female peers are larger than peer effects by male peers, even if the coefficients are not statistically significant. In column (5), we pool the sample of males and the sample of females and define two groups of peers; the first group includes peers of the same gender as the individual, and the second group includes peers of a different gender. Only the same gender variable, estimated at −0.044, is significant at 10%, while the different gender variable is not. These results are indicative that within groups of students of the same gender, peer effects within the group are more important than those between the groups. A vast literature on ability peer effects shows that a large proportion of females in a class improves overall achievement levels (Hoxby, 2000; Whitmore, 2005; Lavy and Schlosser, 2011). Other studies conclude that a large proportion of male students negatively affects classroom outcomes (Figlio, 2007; Carrell and Hoekstra, 2010). Zölitz and Feld (2018) study gender peer effects and find that a larger proportion of female students affects the choices of education of males and females differently. Anelli and Peri (2017) find a positive effect on males but not on females. Brenøe and Zölitz (2020) study gender peer effects on the choice on STEM participation. They find a greater number of female peers widens the gender gap. While our results cannot directly be compared to these studies, since we consider a different outcome and do not measure the direct effect of the gender composition, we still find that males and females have asymmetric effects on their fellow classmates. Moreover, in addition to most of the papers outlined in this literature, we provide the estimated cross effects between the two gender groups.

In panel B, we repeat the same exercise, but split the sample by social background.⁽²¹⁾ First, the effect of peers is relatively more important for students from families with a low socio-economic background (−0.105 vs. −0.027); however, the standard errors are too large for the difference to be significant⁽²²⁾. Second, in columns (2) and (4) we consider the cross effects of these two groups of peers. Only the proportion of lower social background individuals receiving C feedback is significant for the students of the low socio-economic group. These results are somewhat parallel to those of Angrist and Lang (2004), who find that the presence of minority students has little effect on non-minority students’ academic outcomes.

In Table 6, we study peer effects for different groups of students defined by ability level⁽²³⁾. This is defined by the within-classroom percentile in the score distribution, ranging from 0 for the student with the lowest numerical score in her class to 1 for the student with the highest score in her peer group. In column (2), we add a dummy variable taking the value 1 if the individual's score is above the 50 percentile of the ability distribution. The results do not change. In column (3), we add the interaction between the dummy and the proportion of peers receiving C feedback to study whether the effect of the peer variable changes between individuals above or below the median of the ability distribution. The coefficient is not significant and close to zero.

Finally in column (5), we interact the dummy variables for the first and last quartile of the ability distribution with the proportion of peers receiving C feedback. The coefficient of the interaction is positive and significant for the high academic ability students. For this group, the negative effect of having academically low performing peers represents two-thirds of the effect estimated for the overall sample: these results, therefore, provide some insight into how social interactions impact individual enrollment. A larger fraction of academically low performing peers is less detrimental to the students that are in the higher quartile of the ability distribution. A potential explanation could be that those receiving C feedback interact less with their academically high achieving peers.

In Table 7, we investigate whether the peer effects’ estimates change with the number of observed peers. The first column presents our main result from Table 4 for comparison. In column (2), we add a dummy variable taking the value 1 if the number of observed peers in the class of individual i is above the median number of observed peers in the data and 0 otherwise, and we interact this dummy variable with the proportion of peers receiving C feedback. The interaction coefficient measures if there are differences in the peer effect estimate between the high and low number of observed peers: results show that it is positive but not significant. From this regression, we conclude that there are no differences in the peer effect estimate, irrespective of whether the group of observed peers is small or large.

So far, the peer groups have been defined in relation to university applicants only. In this setting, the group of peers is partially observed when some students in the class do not apply to this university; however, it is fully observed when every student in the class does so. To test if the peer effects estimate changes between these two groups, we use the information provided in the data for each applicant on the total number of students in the class. We define a dummy variable taking the value 1 if the number of observed peers plus one is equal to the total number of students in the class⁽²⁴⁾ and 0 otherwise, and we interact the dummy with the proportion of peers receiving C feedback. In column (3), the estimated coefficient of the interaction term is negative at −0.057 and not significant. We conclude that there are no differences in the effect of the proportion of peers receiving C feedback between the groups of peers that are fully observed and the groups of peers that are partially observed.

In Table 8, we perform some falsification tests, changing the proportion of students that register at university in cohort t by the proportion of enrolled peers from the same school and the same major in younger cohorts: the individuals of the cohort (t + 1) in columns (1) and (2), and those of the cohort (t + 2) in columns (3) and (4).

The results of these four regressions point to no clear relationship between the adjacent cohorts and the university enrollment choices of the current cohort. None of the four estimated coefficients is significant at the usual levels. We interpret the estimates from these regressions as evidence that the results from Tables 4–7 do not come from a correlation between the share of students enrolling at university and time-varying high school major unobserved characteristics.