Discussion Paper No. 979

Peer Effects
in Academic Performance

Ryohei Hayashi

September 2016

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Peer Effects in Academic Performance*
Ryohei HAYASHI†

September 20, 2016

Abstract
This paper deals with the data of dormitory students in National Institute of Technology,
Kagoshima College to demonstrate the existence of peer effects in academic performance. The data
have unique advantages to avoid the difficulties of the self-selection problem and reflection problem.
The data shows freshmen’s academic performance and previous year’s junior high school records, androommate’s previous year’s academic performance for using an instrumental variable method. The
results of my findings suggest that peer’s academic performance does not have any effects on
freshmen’s. In spite of considering the asymmetric relationship between roommates, self-selection
bias when choosing subjects, and nonlinearities of effects, there is no significance in any models.

JEL classifications code: J13, J44, C26.
Keywords: learning, reflection problem, instrumental variable method, self-selection bias.

*

This study was supported by the Joint Usage/Research Center at ISER, Osaka University. I thankNaohiro Matsumura, Fumio Ohtake, Masaru Sasaki, Shoko Yamane, Shinji Abematsu, and Anis Ur
Rehman for their very helpful comments. Any remaining errors are the sole responsibility of the author.
†
The Departments of Liberal Arts and Sciences, National Institute of Technology, Kagoshima College,
1460-1 Shinkou Hayato-cho, Kirishima City, Kagoshima, 899-5193, Japan. E-mail: pey@ryohei.info.

1

Introduction

Does dormitory students’ academic performance vary with their peer roommates? No one can haveany choice but to accept the given conditions in which they were born: sex, height, inherent abilities,
family background, race, parental income and many others. However, a peer is one of the sparseselective options. You can choose your peers by yourself, and also your parents, teachers, matrons of
dormitories and managers of workplaces can arrange an opportunity to let you choose your peers byassigning the best peers next to you (Carrell, et al., 2013).
If your performance depends on your peers’ performance, you may be more careful to choose yourpeers. The hypothesis that peers’ performance affects one’s performance has been defined as peer
effects. People, especially parents and teachers, believe this hypothesis strongly. Then parents let theirchildren avoid bad company.
Not only parents but also educational researchers have a keen interest in peer effects1. School
choice, selective admissions, affirmative action, distance learning, class disruption and many othermatters may be affected by peer effects. Educational researchers understand peer effects as the key
issue to solve the problem of equality of education opportunity. It is because of Coleman Report (1966).
While he was attempting to describe the relation of achievement to school characteristics, Coleman
unexpectedly found out the fact that “a pupil’s achievement is strongly related to the educational
backgrounds and aspirations of the other students in the school2.” After this report, numerous research
papers which mention peer effects were published (Foster, 2003; Kremer and Levy, 2003; Sacerdote,
2001; Stinebrickner and Stinebrickner, 2005; Winston and Zimmerman, 2004; Zimmerman, 2003).
These papers discuss whether peer effects are statistically significant or not. If they exist, then peer
effects can be used as the corrective action effectively for gender, family income, or race disparity.
Peer effects are also important issues in labor economics studies. Economists are interested in thesign of peer effects, positive or negative, and also in the magnitude of peer effects. Economists
understand peer effects as one kind of externality. Market with externality will fail. Policy makers,
including classroom teachers, matrons of dormitories and managers of workplaces, have to fix that
failure to put the effective equilibrium into practice. If peers’ performance affects others’ performance
positively, policy makers need to support peers by giving some positive incentive like praising peers,
publishing peers’ svirtues, giving special treatment to assign a single room, or giving money.
Otherwise, if peers’ performance affects others’ performance negatively, policy makers need to punish
peers by a negative incentive like imposing tax, suspension from school, summoning parents, or giving
1
2

See Sacerdote (2011)’s survey.
Coleman (1966) also pointed out as follows:
An important part of a child’s school environment consists not of the physical facilitiesof the school, the curriculum, and the teachers, but of his fellow-students. A child’s fellowstudents provide challenges to achievement and distractions from achievement; they provide
the opportunities to learn outside the classroom, through association and casual discussions(p.183).
1

additional homework. Moreover, for the internalization of the spillover of peer effects, the amount of
the incentive must be the same as that of the spillover of peer effects. That is the reason why
economists are interested in the sign and a magnitude of peer effects. They are also interested in thenature and the process of affecting peer effects. It could be possible for peer effects to affect the result
directly, indirectly, or both ways. There are many economists suspecting the nonlinearities in the peer
effects (Duncan et al, 2005; Sacerdote, 2001; Hoxby and Weingarth, 2005).
As detailed in Brock and Durlaf (2001), social interaction, which includes peer effects, is roughly
divided into two structures. One is local interaction where individuals face of one or a small number
of appropriately defined peers. The other is global interaction where individuals face the mean of areference group. In school classmate data, there is a tendency to show a strong significant relationshipbetween global interaction models3. But on the contrary, there is a tendency to show a weak significant
relationship or an insignificant relationship between local interaction models.
Peer effect is a familiar topic, but there are difficulties to demonstrate it. To say “demonstration ofpeer effect” inevitably connotes demonstrating the causal relationship of peer effect in which peers
affect others. There are four well-known difficulties4. One is called an endogenous problem5, in which
we could not know whether an individual’s outcome is affected by peer’s outcome or vice versa fromcorrelated data. Another is called an exogenous problem, in which individual’s outcome is affected bypeer’s background characteristics6 (e.g. sex, height, family background, race, and parental income).
A third is called a contextual effect, in which both individual’s outcome and peer’s outcomes are
simultaneously affected by their shared social and environmental factors (e.g. neighborhood,classroom teacher, school curriculum, social norm). The other is called a selection problem, in which
individuals generally self-select peers. To avoid these problems, a few methods have been suggested.
Steglich et al. (2010) show the stochastic actor-oriented model using dynamic network data. Others
are experimental methods of using random assignment data (Sacerdote, 2001; Falk and Ichino, 2006)
or partial assignment of random interventions (Duflo and Saez, 2003; An, 2011). The stochastic actororiented model relies on strong parametric assumptions, and the contextual confounding problem of
biased network. The experimental methods are problematic when experiments are unethical to conduct
randomization.
The results of literature are confusing. Most of the literature insist that there are strong effects ofpeers (Sacerdote, 2001; Hasan and Bagde, 2013; Angrist and Lang, 2004; Carrell at el., 2009;
Rumberger and Palardy, 2005) or small limited effects (Stinebbrickner and Stinebrickner, 2006;
3

The effects of peer-group characteristics on individual outcomes are easily confounded with theeffects of students’ unobserved, individual characteristics (Evans et al., 1992; Moffitt, 2001).
4
An (2015) detailed these problems effectively by using directed acyclical graphs (DAGs) figure.
5This problem is also called as a reflection problem.
6
Betts and Morell (1999) report that there are significant relations between students’ grade point
averages and their gender, ethnicity, potential income and SAT score.
2

Zimmerman, 2003). Unlike them, McEwan and Soderberg (2006) and Angrist (2014) show there areno effects.
The Instrumental variable (IV) methods have been argued to be useful as alternatives in identifying
endogenous peer effects. The advantage of IV’s can be used to obtain consistent estimators in thepresence of omitted variables to solve the errors-in-variables problem (Woodlridge, 2015).
There have only been a few studies using IV methods to estimate peer effects (Duncan et al., 1968;
Bramoulle et al., 2009; O’Malley et al., 2014; An, 2014; Hoxby, 2000). However, these few studies
suggest that the former methods of peer effects studies were overestimated because of unobserved
variables influence on the analysis. For example, Angrist (2014) reanalyzed Sacerdote (2011)’s datain the IV method and pointed out that Sacerdote’s estimate was likely to be statistically insignificant.
In this paper, peer effects of local interaction using dormitory students’ data is demonstrated. I use
previous year’s data, like school records of junior high school or previous year’s GPA, to control one’s
and peers’ unobserved ability. And my data have the advantage to avoid a reflection problem because
they are limited to use two-pair rooms with one freshman and one sophomore student. Two-pair rooms
dataset is also good to define one’s peer because a freshman has only a sophomore in his/her room.
These controls make it easier to demonstrate clean peer effects of local interaction.
2

Empirical Strategy
2.1

Data and Dataset

I use the academic records of dormitory students’ in National Institute of Technology, Kagoshima
College in Japan. The advantage of this data is that the students are assigned to two-pair rooms with afreshman and a sophomore at random, and also that the students have almost no choice in selecting
their subjects.
Randomly assigned data is good for avoiding the self-selection problem. I use only the data of therooms with two students; one student is a freshman and the other is a sophomore. The dorm warden
uses the following protocol in assigning rooms. First, the students must submit application forms andthe warden decides to accept or reject before the new semester begins. According to the policy of thiscollege, all the freshmen are supposed to stay in the dormitory7, which the warden does not reject.
Thus, totally around 200 freshmen enter the dormitory every year 8 . Second, the warden makes adecision whether to accept or reject the sophomores by using the data of students’ penalty points list9
7

The requirement for all freshmen to stay in the dormitory is good for avoiding the selection problem.
In the case of using college dormitory data, it is possible that dormitory students are potentially biased,
for the students who apply for entering the dormitory do not mind staying with other roommates. It
follows that dormitory students consist of students who have cooperative characteristics.
8
As of May 2015, freshman students in the dormitory are 195 (91.5% of all 213 freshman students
including 7 repeated students) and include 17 female students (73.9% of 23 female freshman students
including 0 repeated students).
9
The dorm warden records the points of student’s life and study attitude. Warden increase the points
3

of the previous year 10 . Third, the warden assigns one freshman and one sophomore of the sameengineering course to one room. Both freshmen and sophomores could not express the preference of
their roommate to the warden. There is no possibility of the self-selection problem occurring in thiscondition. Two-pair assigned data which have a freshman and a sophomore is good for avoiding thereflection problem and the endogenous problem. I use sophomores’ records of the previous year as
instrumental variables. Freshmen and sophomores were not acquainted with each other in the previous
year. Therefore, there is no reason to correlate freshmen’s records of this semester and of the previous
year, though the sophomores’ records of the previous year indirectly affect those of this semester.
The students have no choice in selecting their subjects because the 1st and 2nd grade subjects are
fixed by school curriculums except art or music credits11. This condition is good for avoiding the selfselection problem. Consider that there is an unusually easy class in which all the students take 100
points. The sophomores took this class in the previous year, tell the freshmen how this class is easy,
and then some freshmen will take this class. In this case, freshmen’s and sophomores’ previous year’s
average points and GPA will be correlated. This correlation is not from academic performance but the
selection of their subjects. The data of this paper do not allow this bias.
This paper deals with the model of local interaction. In the local interaction model, it is necessary
to clarify one’s appropriately defined peers (Brock and Durlauf, 2001). The data define peers easily.
The freshman’s peer is a sophomore student in a room. In the dormitory, the students have to sit attheir desks and concentrate on studying from 8 p.m. to 11 p.m. except for 40 minutes’ break during
the school days, 5 days a week. And no one is allowed to leave the dormitory from 8 p.m. to 6 a.m.
These rules make the roommates very close to each other. The freshmen often ask sophomores, theirroommates, about the study, because the sophomores already passed that class in the previous year.
Thus there are good opportunities to communicate with each other.
The summary of variables for the dataset used is shown in Table 1. The data for the classes of 2008
through 2014 are used. I use only freshmen’s and sophomores’ data12. In the beginning, there are awhen the students break the rules. For example, absence from the roll call, bringing prohibited goods,
entering the prohibited area, late staying, bringing non-dormmates into the dormitory, stealing,
drinking, smoking, violence, leaving the room door unlocked while at school, wasting electricity,
incorrect waste segregation, breaking properties, carelessness of fire, etc. In the study attitude, leavingfrom their own rooms, chatting, dispersion, visiting other students’ rooms in the study hour, etc.
Dormitory students will be forced to leave the dormitory when these points exceed a standard. And
permission to enter the dormitory will be given to students with low points.
10
As of May 2015, sophomore students in the dormitory are 132 (67.0% of all 197 sophomore
students including 3 repeated students) and include 12 female sophomore students (66.6% of 18 female
sophomore students including 0 repeated students).
11
Students can select from Music or Art.
12
There are freshman students to 5th grade students, and post graduate students in this dormitory. As
for over the 3rd grade, 55.9% of all the students are away from the dormitory, and staying at boarding
single houses or come from their parents’ home. In addition, over the 3rd grade dormitory students canchoose their pair students to be group leaders in the dormitory. It could not able to avoid a self-selection
problem. Thus, I do not use the data over 3rd grade students.
4

total of 2,275 freshmen and sophomores with 1,527 unique students. And a total of 1,143 pairs with
1,143 unique pairs exist. To set the condition, I remove the rooms whose peer students’ data are notobtained (147 cases). Then I remove the single rooms data (7 cases) and the three pair rooms data (110cases). After that, I also remove the cases of the rooms which have paired with over 3rd grade students(125 cases), the same grade students (180 cases) and repeated students (0 cases). Then next, I remove
the cases of the rooms with another engineering courses’ students (9 cases). Now the dataset is filledwith pure cases of freshmen and sophomores of the same engineering course (565 cases). Finally, I
remove the cases of leaving from the dormitory or exchanging pairs in midterm (11 cases). I use 554
two-pair rooms: ones with a freshman and a sophomore and ones where both are in the sameengineering course.
Table 2 presents the estimation result of the robustness check. To make sure that freshmen’s
academic performance is not related with sophomores’ before they became roommates, I regress theestimation model as(i=1, … , N, j=1, … , N).
The dependent variable

is previous year’s school records points of junior highschool for freshman i.

is the 2-year-ago school records points of junior high schoolfor sophomore j who is a freshman’s peer.

is the vector of freshman’s covariates which include a

department dummy and year dummy. And

is a random error term. Table 2 shows that there isstatically no significance between freshmen’s performance and sophomores’ before they becameroommates. This result means that roommates are assigned randomly.
2.2

Estimation Models

Instrumental variable (IV) methods have been argued to be useful in identifying peer effects. Using
IVs is one of the effective ways to cope with omitted variable bias, simultaneity bias, and measurement
error (An, 2015). To demonstrate peer effects in the dormitory, I specify the estimation model as(i=1, … , N, j=1, … , N).
The dependent variable

is the academic performance for freshman i which was measured as astandardized average score, GPA of the summer semester, or percentile in his/her class.
constant variable.

is ais the academic performance of the sophomore student who is a freshman’s peer.

is the vector of freshman’s covariates which include school record points of junior high school, adepartment dummy value, a dorm building dummy and a year dummy. And
The coefficientis a random error term.

is the interested measure of peer effect.

In this model, the regression errors

are assumed to be correlated withbecause ofendogenous repressors. This correlation leads to the OLS estimator inconsistent for. Therefore, I

5estimate the model by two stage least squares (2SLS). At the first stage, all the covariates of j () are used to predict the sophomore

and j’s previous year’s academic performance (student’s academic performance (
E( |

).

logically satisfies the assumption that)=0. At the second stage, the predicted sophomore student’s academic performance( ) is used to predict the freshman student’s academic performance instead ofand.

satisfies

the assumption that E( | )=0. Shown formally,
the first stage equation is:(j=1, … , N),
where

is the vector of sophomore’s covariates.

And the second stage equation is:(i=1, … , N, j=1, … , N).
In summary, I regress freshman’s academic performance on sophomore’s performance using
instruments sophomore’s previous year’s academic performance.
3

Results

Table 3 reports the results of regression in OLS and 2SLS for four different measures of academic
performance. The coefficients ofare not statistically significant at the 10% level in every measure.

And also the signs of coefficients point in inconsistent directions. The larger value in Average Point(AVG), Standardized Average Point (STDAVG), and Grade Point Average (GPA), the higher inacademic performance. On the other hand, the larger value in relative rank in his/her class (Percentile),
the lower in academic performance. Every coefficient of sophomore’s performance is positive in the
results of regression. These results suggest there were no peer effects from sophomore to freshman.
The coefficient of peer’s performance significantly affects himself/herself in most previous
research. For example, in the study of Dartmouth College by Sacerdote (2001), they showed strong
evidence for the existence of peer effects in student outcomes. And also Zimmerman (2003) used thedata from Williams College, to show the results of suggesting that peer effects are not large, but
statistically significant in their models. Against these studies, my data presented in this paper, there
were no significant coefficients of peer’s performance.
I thought out the reason sophomores’ influences are negligible for freshmen. For example, in thecase of the sophomores’ helps, such as giving the past questions, giving the lecture notes, advice on
the evaluated attitude in the class, and information on teachers’ hidden classification criteria, they seemnot to be used in the year. To make this possibility clear, I divided the subjects into common anduncommon ones. Common subjects are taught both freshmen and sophomores by the same teachers,
while uncommon subjects are taught by different teachers, even though they have the same subject
titles. The summary of variables is shown in Tables 4 and 5. Table 6 shows that the regression resultof 2SLS for common subjects and uncommon subjects. Both common subjects and uncommon
6subjects, the coefficients ofare not statistically significant at the 10% level except uncommon

subject’s GPA. In the same way as Table 3, the signs of coefficients point in inconsistent directions.
However, the group leader dummy shows a meaningful result. The group leader dummy is a proxyvariable of peer’s influence power. The group leader plays a part in role-calling once every morningand twice every night. And he/she also gives orientation for the rules of the dormitory, for example,
separation of garbage and time schedules. The group leaders can be influential as stronger peers thanordinary students. In Table 6, the coefficients of group leader dummy on AVG, STDAVG, andPercentile are statistically significant at not less than 5% level only about a common subject. This
result suggests that group leaders play the role of the middleman to exchange information. To sum up,
to be sophomores is negligible on freshmen’s performance, but to be group leaders is influential
enough to affect freshmen’s performance.
Next, I suspect that unobserved variables brought about overestimation because of the reflection
problem. Though the student i’s performance affects j’s, vice versa at the same time. These two
phenomena are not distinguishable in view of one-period data. In case i and j affect each other, thosevariables correlate more closely, compared with the case in which j affects i one way. However, thereverse causation effect of i on j must be omitted to demonstrate peer effects. To do that, additionaldata, such as j’s previous year’s performance record as an instrumental variable, are required.
In Scaredote (2001)’s framework, he assumed that i and j’s background ability is not measured
with error. He did not use instrumental variables and estimated only one-period data. Then, Angrist(2014) pointed out that Sacerdote’s estimation possibly had been overestimated. Angrist usedadditional data from an entrance examination, SAT data, as instrumental variables to control potential
ability of j’s. According to his re-estimation using data of Dartmouth College, a strong correlation inroommate GPAs seems to be driven solely by common variance components in outcomes. As a resultof the IV method, there was statistically no significance in the coefficient of peer effects.
In the same way as Angrist’s IV method, I used school record points of junior high school to control
freshman’s potential ability, and previous year’s academic performance to control sophomore student’s
potential ability in our model. Our case that there was no significance in the coefficient of peer effects
supports Angrist’s argument. Similarly, at Wellesley College MacEwan and Soderberg (2006) reports
there were no peer effects using the additional data of freshmen’s SAT scores.
As the third point, the present literature are used as co-worker data. For example, classmates in thesame class and roommates of the same grade. However, in my case, the two students are not coworkers, but one is an assistant, and the other is assisted. This asymmetric relationship possibly makes
peer effects weaker.
To confirm this hypothesis, I made one more dataset that both roommates are freshmen. According
to the same formula shown above, sophomore’s performance is changed into peer freshman’s school
record points of junior high school. Tables 7 and 8 show the summary of variables and results,
7respectively. In spite of the hypnosis, there are not significant coefficients of peer effects. The signs ofcoefficients point in inconsistent directions.
At last, peer effects might affect nonlinearities from peers. McEwan and Soderberg (2006) reportthat there are no peer effects on students’ grade point averages in linear specifications. And there issome evidence that students’ SAT scores have nonlinear effects on their roommates’ achievement, but
the results are not robust.
Then I separate data bottom 25%, top 25% and middle 50% by using data of the entrance
examination. To separate categories, I calculate freshman’s percentile rank in his/her own class byschool record points of junior high school. And also I calculate sophomore’s percentile rank in his/herclass by previous year’s average point. The combined result of the analysis is shown in Table 9. In
every case, there were not significant peer effects. I do same analysis in the cases of {5%, 90%, 5%},
{10%, 80%, 10%}, there were not significant peer effects in any case.
4

Conclusion and discussion
Roommate peer effects in the local interaction model are not statistically significant in academic

performance in this study. Also, nonlinear roommate peer effects were not found in this study. The
data used are strictly controlled to demonstrate clean peer effects. And students have good
opportunities to affect each other. However, I couldn’t find out the evidence of the existence of peer
effects. This result does not coordinate with most of the former literature.
It is suspected that the former literature overestimated peer effects because of self-selection
problem and reflection problem. Random assigned room data is not enough to avoid the self-selection
problem. Because students arbitrarily choose subjects after they are randomly assigned to their rooms.
The effect of roommates, when choosing the subjects, can be regarded as one kind of peer effects.
However, it does not affect their academic performance but the value of the index to measure theiracademic performance. My data have the advantage of not contaminating this self-selection bias.
As Anglist (2014) pointed out that it is required to use IV method to avoid the reflection problem.
I strictly control the reflection problem using previous year’s data. I assert that the analysis of theformer literature should be demonstrated again with control the reflection problem.
The data used in this paper was obtained only for a short period of time, one semester (5 months).
To elucidate the peer effects, especially measuring learning effects, a longer period of time may berequired for investigation.

8

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11

Table 1: Summary of variables.
Variable

Obs.

Mean

Std. Dev.

Min

Max

Year15

554

2012

1.69

2009

2014

Dormitory

554

3.41

2.81

1

9

Class

554

2.91

1.37

1

5

Summer semester average points

554

80.1

6.83

37.6

95.7

Summer semester standardized average points

554-0.00403

0.66

-3.29

1.56

Summer semester GPA

554

1.55

0.39

0

2.48

Summer semester percent rank in class

554

0.51

0.287

0.0222

1

School records points of junior high school

554

74

7.59

55

90

Summer semester average points

554

77.8

8.04

48

96.9

Summer semester standardized average points

554

0.163

0.649

-1.82

1.87

Summer semester GPA

554

1.39

0.454

0.36

2.58

Summer semester percent rank in class

554

0.454

0.275

0.0222

1

School records points of junior high school

554

75

7.87

52

90

Previous year’s average points

554

81.3

6.19

61.2

95.6

Previous year’s standardized average points

554

0.12

0.62

-2.11

1.52

Previous year’s GPA

554

1.61

0.372

0.56

2.57

Previous year’s percentile rank in class

554

0.46

0.283

0.0233

1

Group leader dummy (leader to 1, otherwise 0)554

0.00361

0.06

0

1

Freshmen

Sophomores

15

N.B. The whole data is used from 2008 to 2014. The data in 2008 are used as instrumental variables. This summary is analyzed intended for freshmen. Therefor, the data in 2008 is
not shown in this summary, because of a time lag.

12

Table 2: The result of regression before freshman and his/her peer became roommates.
Freshman’s
School records points of JH
Sophomore’s School records points of JH

0.047

Control
Department

yes

Year

yes

constant

68.361 ***

N

554

r2

0.088

Standard errors in parentheses (* p<0.1, ** p<0.05, *** p<0.01) , cluster
robust by year, class.

13

Table 3: The results of regression using four measures of academic performance.
OLS
Variable

2SLS

AVG

STDAVG

GPA

Percentile

AVG

STDAVG

GPA

Percentile

0.45 ***

0.0472 ***0.0426 ***-0.0189 ***0.45 ***

0.0472 ***0.0426 ***-0.0189 ***Freshman
School records points of
JH
Sophomore
Performance

0.03320.02540.03080.02460.03090.02960.02990.0296

Group leader dummy-2.66-0.217-0.2430.153 ***

-2.59

-0.211-0.2420.153 ***

Control
Department

Yes

yes

yes

yes

yes

yes

yes

yes

Dorm building

yes

yes

yes

yes

yes

yes

yes

yes

Year

yes

yes

yes

yes

yes

yes

yes

yes

Constant

42.5 ***-3.44 ***

-0.828 **1.87 ***

42.7 ***-3.45 ***

-0.817 **

N

554

554

554

554

554

554

554

554

r2

0.324

0.285

0.34

0.239

0.325

0.285

0.34

0.239

Standard errors in parentheses (* p<0.1, ** p<0.05, *** p<0.01), cluster robust by year, class14

1.87 ***

Table 4: Summary of variables calculated about only common subjects.
Variable
Freshmen

Obs.

Mean

Std. Dev.

Min

Max

Summer semester average points

554

80.4

6.73

35.8

96.5

Summer semester standardized average points

554-0.00543

0.679

-3.38

1.85

Summer semester GPA

554

1.63

0.394

0

2.56

Summer semester percent rank in class

554

0.509

0.288

0.0222

1

554

81.4

6.2

58.5

95.1

Previous year’s standardized average points

554

0.125

0.658

-2.47

1.76

Previous year’s GPA

554

1.68

0.368

0.75

2.56

Previous year’s percentile rank in class

554

0.455

0.28

0.0233

1

Mean

Std. Dev.

Sophomores Previous year’s average points

Table 5: Summary of variables calculated about only uncommon subjects.
Variable
Freshmen

Obs.

Min

Max

Summer semester average points

554

80.2

8.47

42

98.8

Summer semester standardized average points

554

0.00751

0.742

-3.05

1.67

Summer semester GPA

554

1.48

0.469

0

2.71

Summer semester percent rank in class

554

0.501

0.289

0.0222

1

554

81.3

7.36

54.8

96.8

Previous year’s standardized average points

554

0.115

0.641

-1.74

1.49

Previous year’s GPA

554

1.59

0.443

0.4

2.75

Previous year’s percentile rank in class

554

0.468

0.283

0.0233

1

Sophomores Previous year’s average points

15

Table 6: The results of regression separated for common and uncommon subjects using four measures of academic performance.
Common Subject (2SLS)
Variable

Uncommon Subject (2SLS)AVG

STDAVG

GPA

Percentile

AVG

STDAVG

GPA

Percentile

0.436 ***

0.0473 ***0.0435 ***-0.0184 ***0.511 ***

0.0476 *** 0.0279 ***-0.0171 ***Performance

0.01310.02950.02190.02240.0661

0.04480.0835 *0.0127

Group leader dummy-3.85 **

-0.304 ***-0.2810.135 ***

1.83

0.038

0.155

-0.0945

Department

yes

yes

yes

yes

yes

yes

yes

yes

Dorm building

yes

yes

yes

yes

yes

yes

yes

yes

Year

yes

yes

yes

yes

yes

yes

yes

yes

constant

45.3 ***-3.48 ***

-0.6 *

1.83 ***

34.9 ***-3.46 ***

-1.46 ***

1.72 ***

N

554

554

554

554

554

554

554

554

r2

0.301

0.269

0.323

0.219

0.334

0.239

0.353

0.204

Freshman
School records points of
JH
Sophomore

ControlStandard errors in parentheses (* p<0.1, ** p<0.05, *** p<0.01), cluster robust by year, class.

16

Table 7: Summary of variables of freshman-freshman pair rooms data.
Variable

Obs.

Year

290

2011

1.62

2009

2014

Dormitory

290

3.56

2.75

1

9

Class

290

3.02

1.43

1

5

Summer semester average points

290

79.5

7.09

40.6

93.2

Summer semester standardized average points

290-0.0806

0.692

-3.08

1.49

Summer semester GPA

290

2.52

0.657

0

3.83

Summer semester percent rank in class

290

0.548

0.286

0.02381School records points of junior high school

290

73.2

8.24

28

90

One self

Peer

Mean

Std. Dev.

Same as above.

17

Min

Max

Table 8: The results of regression using freshman-freshman rooms data.
OLS
Variable

AVG

STDAVG2SLSGPAPercentile

AVG

STDAVG

GPA

Percentile

0.0427 ***-0.0188 ***0.456 ***

0.0465 ***0.0426 ***-0.0187 ***Freshman
School records points of
JH

0.456 ***

0.0466 ***Peer Freshman
School records points of

0.00317-0.00297

0.001820.000912

0.00696-0.06360.0426-0.0486

Department

yes

yes

yes

yes

yes

yes

yes

yes

Dorm building

yes

yes

yes

yes

yes

yes

yes

yes

Year

yes

yes

yes

yes

yes

yes

yes

yes

constant

44 ***-3.18 ***

N

290

290

r2

0.338

0.313

JH
Control-0.954

1.82 ***

43.7 ***-3.39 ***

290

290

290

290

290

290

0.349

0.306

0.339

0.305

0.356

0.301

Standard errors in parentheses (* p<0.1, ** p<0.05, *** p<0.01), cluster robust by year, class.

18-0.913

1.91 ***

Table 9: Interaction between one’s own background and roommate’s background. (OLS)
Sophomore’s academic index16
Own academic index17

Bottom25%

Middle 50%

Top 25%

Bottom 25%-0.3060.349-0.572

Middle 50%-0.561-0.083

0.272

Top 25%-0.3290.0269-0.35

Standard errors in parentheses (* p<0.1, ** p<0.05, *** p<0.01),
cluster robust by year, class.

16
17

Percentile rank in his/her class by previous year’s average point.
Percentile rank in his/her own class by school record points of junior high school.

19