1. education
2. school

The Pull of Popularity
Explaining Conformity in Student Behaviors
WORKING PAPER
April 6, 2015
Nancy Haskell
University of Dayton
Dept. of Economics & Finance
300 College Park
Dayton, OH 45469
[email protected]
ABSTRACT: In contrast to most existing literature on social interactions, this paper posits a model with endogenously determined popularity that provides a novel,
micro-founded mechanism for explaining conformity to group behavior. Model assumptions and predictions are tested with Add Health data using a multi-step estimation process. The empirical work combines a bivariate probit model of friendship
formation with a two-stage least squares estimation of student behaviors. Results
are consistent with a model in which students use behaviors to gain friendships,
and the model allows for policy-relevant simulations to predict student behaviors in
counterfactual school environments.
This research uses data from Add Health, a program project designed by J. Richard
Udry, Peter S. Bearman, and Kathleen Mullan Harris, and funded by a grant P01HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and
Human Development, with cooperative funding from 17 other agencies. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in
the original design. Persons interested in obtaining Data Files from Add Health
should contact Add Health, The University of North Carolina at Chapel Hill, Carolina Population Center, 206 W. Franklin Street, Chapel Hill, NC 27516-2524 (addhealth [email protected]). No direct support was received from grant P01-HD31921
for this analysis.
1
Introduction
Almost every child in middle or high school has experienced a social situation in which
they were torn between their preferred activity and the popular activity. These behaviors can range from the clothes students wear to the amount of time they spend
studying or partying. A choice must be made as to how to act, and this decision
will affect popularity differently depending on the school environment. As a result, a
person’s social network position is not exogenous to her actions. Behaviors, to some
extent, are a conscious choice with recognized consequences for an individual’s social
status among a group of peers.
This paper introduces the idea that people directly gain utility from being popular. The paper then explores how the desire to gain popularity affects the behavior of
individuals relative to their peers. The assumption is consistent with literature from
sociology and psychology that describes popularity as a measure of status and documents the time and effort that students spend trying to become more popular [Kiefer
and Ryan (2008); Eder (1985)]. In contrast to the existing literature, popularity is
endogenously determined within the model. This provides a novel mechanism for
explaining why students conform to group behaviors.
The model also provides a framework for determining how people choose their
friends. Friendship between an individual and her peer is decided by two factors:
(1) homophily, and (2) whether the peer perceives the individual’s behavior to be
“cool.” The theory of homophily, the idea that people who are more similar to each
other in behaviors and characteristics are more likely to be friends, has been well
documented by sociologists and economists. In this model, being viewed as “cool”
1
by more of one’s peers is associated with an increase in the number of friends, thus
greater popularity. The model, however, places no restrictions on the types of behaviors that are “cool.” Rather, data on the behaviors, characteristics, and reported
friendships of students from a large number of high schools across the United States
are used to estimate a unique, popularity-maximizing level of behavior.
This theory of behaviors directed at achieving social acceptance differs from most
existing work. Many studies by economists and sociologists use rich data on the
structure of social networks to identify the extent to which people affect their close
friends and their more distant acquaintances. These studies overwhelmingly estimate reduced form equations with little discussion of an underlying, micro-founded
framework. Furthermore, existing literature largely ignores the paradigm described
earlier in which students actively choose behaviors with the intent of altering their
social standing. The model and empirical work introduced here allow behaviors to
affect popularity, and use an instrumental variables approach to estimate the extent
to which the desire to gain popularity drives a student’s observed behavior.
The model developed in this paper predicts that each individual will choose an
optimal behavior that is a convex combination of her popularity-maximizing behavior
and the “innate” behavior that she would exhibit in the absence of any preference
for popularity. Both the underlying assumptions and the model’s predictions are
tested using data from the National Longitudinal Study of Adolescent Health (Add
Health). The empirical analysis focuses on four indexes: (1) academic performance,
studying, and effort in school as measured by a student’s grade point average (GPA),
(2) an index of substance use composed of smoking and drinking behavior, (3) an index of unruliness as defined by skipping school, lying, fighting, and doing dangerous
2
things on dares, and (4) an index of interpersonal troubles with teachers and other
students. In the data, good grades, substance use, and general unruliness, tend to
be viewed as “cool” and have a positive influence on a student’s popularity, while
interpersonal problems reduce popularity on average. Consistent with the theoretical predictions, the empirical results show that GPA, substance use, and unruliness
are affected by the popular level of the behavior, with students putting the most
emphasis on popularity-maximization with regard to their effort in school.
The results suggest that altering the perceived “coolness” of certain behaviors can
minimize risky behaviors or improve grades. While not a new idea, these findings
provide an economic motivation for the many school programs and public service
announcements that attempt to change perceptions of which behaviors are “cool”
among youths. This paper further shows that the racial and socioeconomic composition of the school is a strong determinant of which behaviors are socially accepted
because subgroups of the population tend to have different tolerances for the behaviors. Since homophily is a large part of the popularity process, changing the racial,
ethnic, and socioeconomic composition has the potential to change the popularitymaximizing behaviors in a school, thereby altering the actual behavior of students.
This could have implications for policy initiatives such as school-choice programs,
which enable students to change their school and peer group.
The next section discusses relevant literature. A detailed description of the model
is provided in the third section. The fourth section presents data, while the fifth
discusses the empirical methods and results. Finally, the sixth section concludes.
3
2
Literature
A large literature exists on social interactions, but only a handful of studies focus
on the relationship between an individual’s network position and her behavior. Two
network positions, centrality and popularity, have received particular attention. Centrality describes how well-connected an individual is within a network. This measure
includes the number of direct friends, as well as the number of indirect contacts
(friends of friends) thereby capturing information about the local network structure.
On the other hand, popularity is measured by the number of peers who nominate
a particular student as a friend. The direction of friendship matters for defining
popularity, meaning the distinction between nominee and nominator is important.
Centrality and popularity are often correlated, and studies indicate that both
measures of network position are strongly related to behavior. This result has been
shown in theoretical models (Calvo-Armengol, Patacchini, and Zenou, 2009) and in
empirical studies [Babcock (2008), Haynie (2001)] for a variety of data on academic
achievement and delinquency. In all but one paper, however, these studies assume
that centrality and popularity are given features of the network structure. Based on
this assumption, they assess the effects of an individual’s position on her behavior,
but fail to consider how behavior might influence her centrality or popularity.
Rather than examining the causal effects of popularity on behavior, this paper
explores how the desire to increase popularity affects a student’s behavior. If, as
this paper posits, behaviors affect a student’s popularity, then endogeneity will lead
to biased coefficient estimates in regressions of behaviors on popularity. The error
terms in these regressions will be positively correlated with popularity for “cool” be4
haviors because higher levels of such behaviors lead to greater popularity, according
to the model presented in this paper. The correlation between the error term and
popularity suggests that the findings in prior literature, which assume popularity is
exogenous, over-estimate the effects of popularity on “cool” behaviors.
Recent literature on social interactions has attempted to address this possible
endogeneity between friendships and behaviors. A common approach has been to
exploit data on the random assignment of college roommates or military cadets in
order to get a set of exogenous links between students. These papers find varying degrees of peer effects for college roommates on academic outcomes [Sarcedote
(2001), Foster (2001), Zimmerman (2003), Stinebrickcer Stinkbrickner (2006), and
Lyle (2007)]. However, these methods fail to account for differing effects based on the
unique pattern of social interactions that develops endogenously even in randomly
assigned peer groups (Carrell, Sarcerdote, and West, 2013). Foster (2001) further
suggests that peer effects may be heterogeneous across different types of students,
and so average effects may not be very informative. A model of endogenous friendship
formation such as the one presented in this paper, allows for heterogeneous peer effects based on a student’s characteristics relative to the distribution of her classmates.
This is not the first paper to attempt to simultaneously account for endogenous
friendship formation and behavioral outcomes. Conti et. al. (2011) use a more
sophisticated empirical model and estimation strategy to understand the relationship between popularity and labor market outcomes. While the authors show that
popularity is largely determined by a student’s family environment, her personal
characteristics relative to the school’s demographics, and the size of the school, they
do not consider student behaviors as determinants of popularity. Similarly, Mihaly
5
(2009) estimates the effects of popularity on academic achievement, using a student’s
race, gender, and background characteristics relative to the demographic composition
of the grade as instrumental variables for popularity. Goldsmith-Pinkham and Imbens (2014) also estimate endogenous friendship formation as a function of individual
characteristics. Weinberg (2006) models the endogenous selection of individuals into
subgroups within a network. In his model, “peer pressure,” or a change in popularity,
directly enters the utility function of his agents. Yet all of these papers posit that
the relevant factor affecting behavior is the student’s actual popularity or friendships.
The model and empirical findings presented in this paper suggest the relevant
mechanism is not the level of popularity but rather the desire to increase popularity
that drives student behaviors relative to their peers. By assuming popularity directly
enters the utility function, students intentionally behave in a manner that will make
them more popular. This paper is the first to explicitly model students’ desire to
gain popularity through their behaviors, which endogenizes both the behavior and
the network position. The model places no restrictions on the effects of behaviors on
popularity. Rather, popularity-maximizing behaviors are determined from data.
3
Model
This section describes a model of behavior and popularity in the presence of social interactions. In this paper, the model is applied to high schools so agents in the model
will be referred to as students. Each student is defined by her “innate” behavior, y0 ,
which represents how she would behave in an environment without peer effects or
concern for popularity. This “innate” behavior captures the non-social benefits and
costs to engaging in various behaviors. The “innate” behavior is assumed to be a
6
function of an individual’s characteristics such as race, ethnicity, gender, age, and socioeconomic status. For example, students with well-educated parents are expected
to have a higher “innate” level of academic achievement. The effects of parental
education on a student’s academics could operate in part through a preference for
learning passed on from her parents, or through lower costs to studying due to the
student being smarter or having access to more resources at home.
In the model, the students directly derive utility from being popular, but face a
convex-utility cost of deviating from their “innate” behavior. Popularity is itself a
function of an individual’s behavior relative to her peers, and the “coolness” associated with certain behaviors. In choosing an optimal behavior, y ∈ Y , a student
must choose the extent to which she should follow her “innate” behavior and the
extent to which she should act in a manner that will increase her popularity. This
decision is formalized in the utility maximizing problem described below. In the
model, popularity is defined as the probability of the student being nominated as a
friend by a schoolmate, summed across all peers in the group of potential friends.1
maxy U (y, f (·); y0 , x, g(·), s) = αP (y, f (·); x, g(·), s) − β(y − y0 )2
P (y, f (·); x, g(·), s) =
Z Z X
Y
p(x, x
e, s) − θ(y − ye)2 + k(x, x
e)y f (e
y )de
y g(e
x)de
x
(1)
(2)
α, β, θ ∈ R+
1
In this general model, the group of potential friends is defined as all other students in the
individual’s school.
7
The utility function parameters, α and β, are assumed to be positive constants.
A student’s cost of deviating from her “innate” behavior is quadratic, thus the student experiences greater disutility the further she moves from her “innate” behavior.
Students are assumed to know their “innate” behaviors, and the distribution of these
behaviors is exogenous (i.e. the model does not consider any selection into schools).
Popularity, P (y, f (·); x, g(·), s), enters the utility function linearly, where ye represents the behavior of an individual’s peer. In the model, an individual’s popularity
is both a function of her behavior relative to her peers, as well as her innate characteristics. Characteristics such as race, gender, or socioeconomic status may make
a student very popular or very unpopular, irrespective of how she behaves. It is
assumed that students cannot reasonably change their characteristics such as gender
or race.2 Thus, students are assumed to start with some baseline level of popularity,
p(x, x
e, s), and become more or less popular as a result of their behaviors relative to
other students in the school. Here, p(x, x
e, s) is a function of the student’s characteristics (x) such as race, gender, and socioeconomic status, the peer’s characteristics
(e
x), and school-specific factors (s) such as the size of the student body.
Popularity is also determined in part by a quadratic loss function in the distance
2
Since students report their own race in the data, it may be more appropriate to think of this
term as “racial identification.” A student could alter her racial identification, particularly if she
is multiracial, depending on her environment. In addition, students could self-identify with a race
other than their true one. The first, selective racial identification based on peers, presents a potential
problem for this paper. However, the empirical work controls for students being multiracial, and
these are the ones most likely to successfully select their racial identification based on their peer
group. The second issue of racial identification being different from a student’s true race is less of
an issue if the relevant factor for friendship formation is racial identification and not genetic lineage.
However, given that racial identification is a choice but genetic heritage is exogenous, this could
lead to problems with the identification strategy in this paper. Using data on the small portion
of the sample with interviewer-reported racial identification, it might be possible to estimate the
extent to which self-reported race differs from the perceptions of an outside observer.
8
between a student’s behavior (y) and the behavior of her peers (e
y ).3 The model
assumes that greater distance between behaviors reduces the probability of receiving
a friendship nomination by θ, where θ is assumed to be a positive constant. This
functional form assumption is made primarily for analytical convenience, and is not
rejected by empirical evidence.4 This portion of the popularity function is also consistent with the concept of homophily, meaning that people prefer friends who are
similar to themselves. The “coolness” factor, k(x, x
e), of behaviors is assumed to enter linearly into the popularity function.5 However, the perception of “coolness” for
any given behavior is allowed to differ based on the gender, race, and socioeconomic
status of both the student and her peer. This allows the tolerance for various behaviors to differ across racial, ethnic, and socioeconomic groups. For instance, drinking
may be viewed as “cool” on average, but specific racial or ethnic subgroups of the
population may view drinking negatively.6
In this framework, the desire to gain popularity draws students away from their
“innate” behaviors and toward the popularity-maximizing behavior. The extent to
which a student deviates from her “innate” behavior is characterized by the optimal
decision rule derived from the utility-maximization problem. The purely popularity3
The probability density function, f (·), denotes the distribution of peers’ behaviors, ye.
Results from a bivariate probit estimation of the probability of two students being friends, as
reported in Table 11, show the distance between the two students’ behaviors, as measured by the
difference between their behaviors squared, decreases the likelihood of them being friends.
5
The function k(x, x
e) is itself assumed to be linear, so integrating over the distribution of student
characteristics (denoted by g(·)), will yield a linear function of the average demographic characteristics in the school k(x, E(e
x)).
6
A negative value of k(x, x
e) indicates that the behavior is “uncool”.
4
9
maximizing behavior is found by solving
∂P
∂y
∗
= E(e
y) +
ypop
= 0, which yields
k(x, E(e
x))
.
2θ
(3)
Taking and solving the first-order condition from the utility-maximization problem
generates the following relationship.
αθ
k(x, E(e
x))
β
y=
E(e
y) +
+
y0
αθ + β
2θ
αθ + β
(4)
Substituting equation (3) into equation (4), we are left with
∗
y ∗ = γypop
+ (1 − γ)y0 ,
where γ =
(5)
αθ
.
αθ + β
Each student’s best response to the behavior of her peers is to choose a convex combination of her “innate” behavior and the popularity-maximizing behavior.7 Assuming
that the utility gains from being popular (α) are constant, students will put more
weight on behaviors for which θ is larger, meaning that friendship nominations are
more affected by homophily in those behaviors. Students will put less weight on
popularity-maximization for behaviors in which deviating from one’s “innate” behavior is particularly costly, a larger β in the model. These effects will be visible in
∗
the empirical results in the size of γ, the coefficient estimate on ypop
.
7
The following simplifying assumptions serve as sufficient conditions for the existence of equilibrium: (1) behaviors and characteristics are independently distributed, (2) the “coolness” factor,
k, is constant, and (3) popularity is only a function of in-degree nominations and no weight is
placed on the connectedness of the nominator. The second simplifying assumption is relaxed in the
empirical work. Proof available upon request.
10
The formulation in equation (4) departs only slightly from a standard Manskimodel in which behavior is a linear function of the group average, E(y). Specifically,
the interaction between individual and group characteristics, k(x, E(e
x)), affects behaviors in this model, unlike in a Manski-model where there is no interaction between
the individual and correlated effects.8 More notably, this model provides a novel,
micro-founded mechanism in which popularity is endogenously determined through
utility-maximizing behavior that can generate a linear-in-means behavioral equation.
The underlying assumption of the model, that popularity increases utility, is consistent with the data. The empirical findings are also consistent with the primary
mechanism of the model; students modify their behaviors to increase popularity.
4
Data
Both the underlying assumptions and the predictions of the model are tested empirically using data from the first wave of Add Health. This study uses the In-School
portion of the survey, which was administered to a nationally representative sample
of more than 90,000 students in grades 7-12 across 132 schools during the 1994-1995
academic year. In this paper, the sample is restricted to only include high school
students, grades 9-12. This study omits schools with available data on fewer than ten
students because of the focus on popularity and friendship networks. After cleaning
the data, and eliminating observations with missing values, 35,490 students across
88 schools remain in the regression sample.9
8
Correlated effects is the term Manski uses to refer to the influence that average group characteristics have on individual behaviors.
9
About one-third of the reduction in sample size is the result of dropping middle school students in grades 7-8. The remainder of the loss of observations is the result of missing data for
characteristics and the behavioral outcomes of interest.
11
The Add Health data set includes a wealth of information on student behaviors,
health outcomes, and interpersonal relationships. In this study, popularity, academic
grades, substance use (drinking and smoking), and general unruliness or delinquency,
are the primary variables of interest. Characteristics such as age, gender, race and
ethnicity, the presence of a father, and the education of the mother are considered
innate and serve as exogenous controls in the regression equations.
Table 1 provides summary statistics for the variables. The sample is evenly split
between male and female students. In the sample, 14% of students are Hispanic.
Approximately 70% of the sample are white, 15% are black, and 7% are Asian. The
racial categories are not, however, mutually exclusive. The data show 6% of the
regression sample reporting multiple races. Three-quarters of the students in the
sample live with their fathers. The mother’s education is coded to correspond to
the average number of years she has spent in school. On average, the mothers’ of
these students have completed 13 years of schooling, meaning they graduated from
high school but do not have a college degree. However, many of these demographic
characteristics vary substantially by school.
4.1
Popularity
The Add Health survey asks students to list their five closest male and five closest female friends. Popularity is defined as the number of in-degree nominations a student
receives, meaning the number of times a student is listed as a friend by others. Since
the survey questionnaire asks for only a student’s top five friends in each gender,
the number of in-degree nominations may be biased downward. A student could be
considered a friend, but she will not receive a nomination unless she is among the top
12
five friends in that gender. While this raises a concern that the measure of popularity
could be biased downward, there is reason to believe that the bias is relatively small.
The majority of students list no more than three close friends of each gender, so the
limit of five friends is rarely binding and it is unlikely to affect the results.10 The
distribution of popularity is heavily right-skewed. The majority of students receive
between one and four in-degree nominations, with only a small handful of students
receiving a substantially larger number of nominations. The average number of indegree nominations is approximately four. Only 5% of students receive more than
ten nominations, and only 1% of students receive 17 or more nominations. However,
the most popular students in the sample receive as many as 30 nominations.
4.2
Behaviors
Study habits and academic achievement are measured using the grade point average
(GPA) from the student’s reported grades in English, Mathematics, Science, and History.11 The distribution of GPA is mostly consistent across schools, with a mean of
2.9 and a median of 3.0 on a 4.0 scale. Grades are approximately normally distributed
around the mean. The bottom ten percent of students have a cumulative GPA that is
lower than a C-average, while the top ten percent of students maintain an A-average.
Data exist on a variety of substance use and other delinquent behaviors. However, many of these behaviors are highly correlated. The degree of collinearity makes
it very difficult to separately identify the relationship between the behaviors and
friendship nominations when trying to control for all of the relevant behaviors si10
The effort of reporting additional friends might still create some downward bias.
If a student does not report grades for all four subjects, the GPA is calculated using only the
subset of classes for which grades are reported.
11
13
multaneously. Instead, indexes are used to represent “types” of behaviors. The
substance-use index is a summation of the number of times in the last month a student smoked, drank alcohol, and got drunk. The substance-use index is extremely
right-skewed, as are the distributions of smoking and drinking. The median student
in the sample smokes, drinks alcohol, or gets drunk once per month. The bottom
25% of high school students report no use of any of these substances. However, a
substantial number of students drink or smoke heavily. A mean of 7 implies that on
average students engage in substance use a little less than twice per week. The top
ten percent of students report smoking, drinking, or getting drunk every day.
The remaining behaviors of interest include fighting, doing dangerous activities
on dares, skipping school, lying, having trouble with teachers, and having trouble
with other students. An exploratory factor analysis provides information on which of
these activities belong in the same grouping or index. The analysis shows two underlying latent variables. The first latent variable corresponds to general unruliness. It
is primarily defined by fighting, doing dangerous activities on dares, skipping school,
and lying. The second latent variable describes interpersonal problems and is defined
by getting into trouble with teachers and other students. Given the results from this
exploratory factor analysis, two behavioral indexes are created to correspond with
the underlying latent variables. The index of unruliness is a summation of the number of times per month a student did something dangerous on a dare, skipped school,
or lied, and the number of times in the last year that the student got into a physical
fight. As with substance use, the unruliness index is very right-skewed. The median
student only engages in two or three of these activities. The bottom ten percent
only participate in one of these activities once or twice per month (or once or twice
per year in the case of fighting). The top ten percent of students, however, engage
14
in three or four of these activities every week. The mean is around 7.5 suggesting
almost two incidences of unruly behavior per week.
The final index describing interpersonal problems is a summation of how many
times per month a student gets in trouble with teachers or other students. The
median student has some sort of interpersonal altercation once a week. A mean of
11 indicates that, on average, students have interpersonal problems every few days.
While the bottom ten percent of students report having no problems with teachers
or other students, the top ten percent of students report having trouble getting along
with teachers and other students more than once a day (40 or more times per month).
Having trouble getting along with peers and teachers is likely the least relevant of
the four behavioral measures for friendship nominations. If anything, one might
expect it to negatively impact a student’s popularity. The regression analysis still
includes this index to minimize potential omitted variable bias. As discussed in the
next section, having interpersonal problems does not increase popularity, and thus
the remainder of the paper focuses primarily on the first three behavioral measures:
academic achievement, substance use, and general unruly behavior.
5
Empirical Methods and Results
The empirical strategy and results described in this section provide evidence that students engage in some behaviors in order to gain popularity. The theoretical model is
based on the assumption that students gain utility from being popular, and that a
student’s popularity is a function of her behavior, particularly her behavior relative
to her peers. The decision rule derived from the model implies that students will
choose an optimal behavior that is a convex combination of their innate behavior
15
and their popularity-maximizing behavior. The empirical work can be divided into
a pre-stage estimation of popularity, followed by a standard two-stage least squares
(2SLS) estimation of the behavioral equation. The pre-stage estimation determines
how behaviors influence popularity, and uses these results to predict a popularitymaximizing behavior for every student. The first stage of the 2SLS estimation uses a
student’s socioeconomic and racial characteristics relative to the demographic characteristics of her schoolmates as instrumental variables for her popularity-maximizing
behavior. This removes endogeneity between the popularity-maximizing behavior
and the student’s observed behavior. The second stage of the 2SLS estimation determines the relative weight that students place on popularity-maximization when
choosing their optimal behavior. The coefficient estimate from this last step corresponds directly with the parameter γ from equation (5).
5.1
Popularity
In the data, popularity is determined by the number of in-degree nominations a
student receives.12 For the purposes of estimation, predicted popularity is defined
as the sum of the predicted probability of receiving an in-degree nomination across
all other students in the school.13 The probability that two students nominate one
another is assumed to follow a bivariate probit model, which controls for unobserved
correlation in the likelihood of each student nominating the other.
14
The theoretical model directly informs the specification of the bivariate probit.
12
“In-degree” refers specifically to a student being listed as a friend by another student.
A school is the boundary for friendship nominations because the data record friendship nominations made between students in the same school.
14
For instance, two students may name each other as friends, irrespective of characteristics or
behaviors, because they happen to be next door neighbors.
13
16
The probability of receiving a friendship nomination depends on the distance between
the nominee and nominator’s behavior, thereby capturing the effects of homophily
in behaviors. The functional form allows for additional flexibility in the effect of
similarity in behaviors on the likelihood of a friendship by also including an interaction term between the nominee’s and nominator’s behavior. The probability of a
nomination is also dependent on the perceived “coolness” of the potential nominee’s
behavior, which is given a flexible functional form. “Coolness” enters the equation
as a quadratic to account for homophily, and perceptions of “cool” behaviors are allowed to differ by demographic group through interactions between the nominator’s
characteristics and the nominee’s behaviors. The probability of a friendship forming
is also a function of the nominee’s characteristics, the distance between the nominee
and the nominator’s characteristics, and school fixed effects. The bivariate probit
model takes the following functional form:
Pr(nomij = 1, nomji = 1) = Φ2 (Zij β, Zji β, ρ)
Zij β = b0 +
L
X
2
[b1l yjl + b2l yjl
+ b3l (yil − yjl )2 + b4l yil yjl ]
|l=1
+
M
X
{z
}
behaviors
2
[b5m zjm + b6m zjm
+ b7m (zim − zjm )2 + b8m zim zjm ]
|m=1
+
(6)
{z
}
characteristics
M1 X
L
X
[b9ml zim yjl + b10ml zim zjm yjl ] +
m=1 l=1
|
{z
perceptions of “cool” behaviors
}
sij.
|{z}
school fixed effects
(7)
17
In the equations above, ρ refers to the correlation between the probability that person “i” and person “j” in a pair nominate each other. The vector Zij is composed of
the vectors Zi , Zi0 Zi , Zj , Zj0 Zj , and Zi0 Zj . The vector Zj includes the set of innate
characteristics, zjm , and behaviors, yjl , exhibited by the nominee “j.” The vector Zi
includes linear terms for the characteristics and behaviors of the nominator “i” (zim
and yil ). The term sij is an indicator for the school attended by the pair of students.
The characteristics indexed by m include age, number of years attending the school,
grade, gender, mother’s education, presence of a father, and indicator variables for
being white, black, Asian, Indian, another race, and Hispanic.15 The behaviors y,
indexed by l, refer to the four behavioral indexes described in the data section: GPA,
substance use, unruliness, and trouble getting along with others. The interactions
between characteristics and behaviors allow the perceptions of the relative “coolness”
of a behavior to differ across types of students. The index M1 is a subset of M that
refers only to gender, indicators for being white, black, Asian, Indian, another race,
and Hispanic, the mother’s education, and the presence of a father. The vector Zji
follows the same formulation as Zij . It is random whether a given student is indexed
as an “i” or a “j” in the pair, so behaviors and characteristics are restricted to have
the same effect on the probability of a nomination for both bivariate probit equations.
In order to estimate the bivariate probit, each student is paired with every other
student in his or her school and it is recorded whether one, both, or neither student
in the pair nominates the other, as well as the direction of the nomination (i.e. which
student is the nominator and which student is the nominee). The vast majority of
student pairs in a school show neither student nominating the other as a friend. A
15
Of these characteristics, quadratic terms are only included for age, the number of years at
school, and the mother’s education, because the other characteristics are binary.
18
random 5% sample of these pairs with no nominations in either direction are retained
using choice-based sampling.16 The bivariate probit is estimated using more than
69,000 student pairs across the 88 schools. The results show that the probability
of receiving a nomination is heavily driven by similarity in characteristics between
students who are in the same grade.17 In contrast, the marginal effects of behaviors
on the probability of a nomination are relatively small.
Table 2 provides the marginal effects of each of the four behaviors on the probability of receiving a friendship nomination for students of different genders and races,
with an average level of maternal education and a father present. These marginal
effects are calculated assuming that the student’s peers are representative of the sample averages for all of the behaviors and characteristics.18 Specifically, from equation
(7), at the mean the marginal effect of behavior l on the unconditional probability of
receiving a friendship nomination for a student with a given race, ethnicity, gender,
and socioeconomic status is defined as
"
#
M1
X
∂Pr(nomij = 1)
b9ml z m + b10ml z m zjm .
= φ(Z ij β) b1l + 2b2l y l + 2b3l (yil − yjl ) + b4l y l +
∂yjl
m=1
The first column and row of Table 2 indicates that the marginal effect of GPA on
the probability of receiving a friendship nomination for a white male whose mother
has the sample-average level of education, and who lives with his father, is equal to
16
Creating every possible student pair in the school, for every school in the sample, increases
the sample size exponentially, and most of these pairs have no friendship nominations in either
direction. To increase statistical efficiency and focus on understanding the process of friendship
formation, choice-based sampling is used on these pairs without nominations.
17
These findings are consistent with Foster (2005), who estimates the probability of college students choosing to live together.
18
A full set of coefficient estimates from the bivariate probit are reported in the appendix.
19
133x10−6 . This implies that a one standard deviation increase in GPA for such a
student will increase his probability of a friendship nomination by 0.01 percentage
points (0.0001 points, or approximately 0.0013 standard deviations). As noted in the
data section, predicted popularity is defined as the predicted probability of receiving
a friendship nomination from another student, summed over all other students in the
school. With an average school size of approximately 1,000 students, this marginal
effect corresponds to a 0.10 point (0.03 standard deviation) increase in a student’s
predicted popularity. The results are similar for the other student types and behaviors. Although the magnitudes are small, the positive effects of GPA and substance
use on popularity are statistically significant. Unruliness has a positive effect while
interpersonal trouble has a negative marginal effect on popularity, but the effects are
generally statistically insignificant for both behaviors.
The coefficient estimates from the bivariate probit are used to predicted the
probability that a student receives a friendship nomination from any other student.
Summing these predicted probabilities across all other students in the school yields
a predicted level of popularity for the student.19 However, the goal is to find the
popularity-maximizing level of behavior, which is likely not the same as the actual level of behavior exhibited by the student. In order to find this popularitymaximizing level of behavior, the parameters of the bivariate probit are used to calculate the predicted popularity for a student across a grid of possible behavior levels.
Specifically, holding all else constant for the student pair, the probability of receiving
a nomination is calculated while varying one of the potential nominee’s behaviors.
At each possible grid value of the behavior, the unconditional probability of receiv19
Results show the model predicts a slightly lower average popularity than found in the data.
20
ing a friendship nomination from every other student in the school is calculated.20
These predicted probabilities are summed to get a predicted popularity at each grid
value. Searching across the grid, the behavior that yields the highest popularity is
the popularity-maximizing behavior. For the three behaviors, GPA, substance use,
and unruliness, that have on average a positive but diminishing marginal effect on
popularity, an interior solution for the local popularity-maximizing level of behavior
can be expected for most students. The same assumption does not hold for the index
of interpersonal trouble, which has a negative effect on popularity for most students.
Table 3 reports descriptive statistics for the popularity-maximizing levels of each
behavior, which are larger on average than the observed levels of the behaviors.
Substance use shows the greatest difference, with the average popularity-maximizing
level being around 29 (smoking, drinking, or getting drunk almost every day). This
is in contrast to the average level of 7 for observed behaviors, indicating substance
use two or three times per week. Unruly behavior shows a similar discrepancy, with
the average popularity-maximizing level being around 23, in contrast to an average of 7.5 for actual unruliness. For interpersonal problems and GPA, the average
popularity-maximizing levels are only about 15% and 30% larger, respectively, than
the averages for the observed behaviors. The large differences between observed and
popularity-maximizing behaviors are not necessarily unreasonable. The popularitymaximizing behaviors represent how students would act absent any costs to engaging
in these various activities. These costs will reduce actual behaviors relative to the
popularity-maximizing levels, and are captured in students’ “innate” behaviors.
20
The predicted probability of a nomination is unconditional on whether the nomination is reciprocated because it is impossible to know whether the nomination would have been reciprocated
at any grid value other than the observed behavior.
21
Consistent with equation (3) in the theoretical model, the popularity-maximizing
behavior is closely related to the average behavior in the school for all but unruliness. The correlation coefficient between the average behavior in the school and the
popularity-maximizing behaviors of each student is highest for GPA (approximately
0.93), lowest for unruly behavior (approximately 0.46), and equal to 0.75 and 0.77 for
substance use and interpersonal trouble, respectively. The relationship between the
school average and the popularity-maximizing behavior is driven largely by the importance of homophily in determining popularity. These results suggest that students
are more concerned with a similarity in substance use, GPA, and interpersonal trouble, and less concerned with matching levels of unruliness when forming friendships.
The correlation coefficients between popularity-maximizing and actual behaviors at
the individual level are lower, ranging from 0.25 for GPA to 0.04 for interpersonal
troubles, and approximately equal to 0.10 for substance use and unruliness. These
lower correlation coefficients are the function of more noise and other unobserved
factors at the individual level. While popularity-maximizing behaviors are heavily a
function of students’ peers, costs are determined at the individual level as a function
of characteristics, which also helps to explain the lower individual-level correlation
between observed and popularity-maximizing behaviors.
The underlying assumption of the model is that students derive utility from being
popular. Table 4 provides suggestive evidence that this assumption holds true in the
data. A student’s reported mental state is regressed on her predicted popularity,
controlling for her characteristics, all possible interactions between her individual
characteristics and average characteristics in the school, and school effects. The predicted popularity from the bivariate probit is positively associated with a student
22
“feeling happy at school” and negatively related to a student feeling depressed.21
While these regression results show no causal relationship, data are consistent with
the theory that popularity increases a student’s utility, or happiness.
Understanding the effects of various behaviors on the probability of receiving a
friendship nomination is interesting in and of itself. However, the coefficient estimates
from this bivariate probit are only a first step toward understanding the behavior of
students relative to their peers. Moreover, the results from the bivariate probit should
be interpreted with care. Endogeneity exists between popularity (the probability of
receiving a friendship nomination) and behaviors. Much of the literature assumes
the friendship link is exogenous and estimates the effects of friendship on behavior,
but fails to control for the effects of behaviors on friendships. The bivariate probit
estimation here does the opposite. The effects of behavior on popularity are estimated without controlling for the influence that friendship nominations could have
on behavior. This omission would be of greater concern if the coefficient estimates
from the bivariate probit were meant to be interpreted as a final results. Instead,
the purpose of the bivariate probit in this paper is merely to provide a framework
that can be used to search for the popularity-maximizing level of behavior. The use
of an instrumental variables approach in estimating the behavioral equation helps to
remove remaining endogeneity between the popularity-maximizing behavior and the
observed behavior, which may have resulted from biased coefficient estimates in the
21
The Add Health survey asks students how often they felt “blue” or depressed in the past year.
Their answers are reported on a scale of 0 to 4, where 0 corresponds to “never” feeling depressed,
and 4 corresponds to “feeling down every day.” Data are coded such that 1 corresponds to an
answer of “rarely”, 2 corresponds to “occasionally,” and 3 corresponds to “often” feeling depressed.
Happiness is measured by students’ responses to the statement “I am happy to be at this school.”
Responses have been coded with values ranging from 0 for an answer of “strongly disagree” to 4
for students who “strongly agree” with feeling happy at school.
23
bivariate probit as the result of endogeneity between popularity and behaviors.
5.2
Behavioral Equations
The behavioral equation from the theoretical model predicts that students should
choose a convex combination of their “innate” behavior and the popularity-maximizing
behavior. In order to test this result, the observed behavior is regressed on the predicted popularity-maximizing behavior and the student’s characteristics, controlling
for school fixed effects. For any student “i” in grade “g” and school “s”, the main
behavioral equation takes the form
pop
yigs = γyigs
+ Xigs δ + λg + ηs + igs .
(8)
pop
Here, yigs
refers to the popularity-maximizing behavior for individual i in school s
and grade g that was calculated from the bivariate probit results using the search
algorithm described in the previous subsection. The coefficient γ refers to the weight
that students place on the popularity-maximizing behavior relative to their “innate”
behavior, and corresponds to the same parameter in equation (5). The vector of
characteristics, Xigs , includes a constant, the student’s age, gender, and years at the
school, indicators for the student being white, black, Asian, Indian, another race, or
Hispanic, the mother’s education, and whether the father is present. The regressions
also control for a set of grade fixed effects, λg , and school fixed effects, ηs .22 Finally,
the equation includes a random error term, igs .
22
Robustness checks have considered specifications that also control for school-grade fixed effects.
However, the school-grade effects soak up most of the variation in the instrumental-variables in the
first stage of the 2SLS procedure. Weak first stage results then make it very difficult to precisely
estimate coefficient estimates for equation (8) in the second stage.
24
Due to concerns over endogeneity between the observed behavior and the popularitymaximizing behavior, as discussed above, the behavioral equations are estimated
using a two-stage least squares (2SLS) procedure.23 Different racial, ethnic, and socioeconomic groups tend to have different views of certain behaviors. For example,
substance use, particularly drinking, is viewed as “cool” by most students. However,
Asians on average are much less likely to choose friends who exhibit heavy substance
use. The different preferences for behaviors across racial, ethnic, and socioeconomic
groups provide an exogenous source of variation in the popularity-maximizing level of
behavior across students and schools. This paper makes use of two sets of instrumental variables. A student’s racial, ethnic, and socioeconomic status interacted with the
average racial, ethnic, and socioeconomic composition of the student’s school serve as
the first set of instrumental variables. Under the assumptions of the model presented
earlier, these interactions between student characteristics and average school characteristics directly affect the popularity-maximizing behavior, but do not directly
affect a student’s observed behavior. Specifically, the first stage equation for the
2SLS estimation takes the following form,
pop
0
= Xigs
yigs
X s π + Xigs θ + ψg + φs + νigs .
(9)
The vector of characteristics, Xigs , refers to the same set of characteristics as in
0
equation (8). The excluded instruments in equation (9), Xigs
X s , are composed
of student characteristics interacted with the average composition of the student’s
school. Specifically, the set of racial and ethnic variables used as instruments include
23
The following assumptions are sufficient to guarantee that the 2SLS estimator is consistent:
pop
(1) the instrumental variables are valid, and (2) any bias in the measurement of yi,g,s
from the
bivariate probit procedure is linear and uncorrelated with the instrumental variables. This second
assumption is admittedly very strong and difficult to justify. Proof available upon request.
25
indicators for the student being white, black, Asian, or Hispanic, interacted with
the average level of the same racial or ethnic group in the school.24 Whether the
student’s father is present interacted with the average share of students in the school
who have a father present, and the mother’s education interacted with the average
level of maternal education in the school serve as the instrumental variables that
control for different perceptions of “cool” behaviors across socioeconomic groups.
The second set of instrumental variables used in this paper is composed of a
student’s racial, ethnic, and socioeconomic status interacted with the average racial,
ethnic, and socioeconomic composition of the student’s grade within the school. The
first stage equation under these instrumental variables takes the form,
pop
0
0
= Xigs
yigs
X gs π
e + Xigs θe + Xigs
X −gs ξ + ψeg + φes + νeigs .
(10)
These grade-level instrumental variables require less stringent assumptions to justify
their exogeneity, as they exploit variation in the demographic composition across
grades within a school. Even if students select into schools based on unobserved
parental traits that are also correlated with a student’s “innate” behavior, it is unlikely that this selection would occur at the grade level.25 However, these instrumental variables come at a cost. There is less variation in student characteristics relative
to grade-specific demographics within a school, which weakens the first-stage results.
24
As mentioned previously, the data on racial and ethnic group are not mutually exclusive. A
student can report being both black and white, thus there is no need to omit a category. Indian and
other race are not used as instrumental variables because the share of students in these categories
is extremely small, leading to weak instruments.
25
To remove any selection effects, the first-stage regression controls for school fixed effects, as
well as for interactions between student characteristics and the average characteristics of students
from other grades in the school.
26
5.2.1
First Stage Results
Table 5 shows coefficient estimates from the first stage of the 2SLS procedure for all
four behaviors using the first set of instrumental variables. The coefficient estimates
on the excluded instruments are sensible. As mentioned before, Asians tend to view
delinquent behaviors least favorably. Asians in schools with a greater Asian population have much lower levels of popularity-maximizing substance use and unruliness.
In general, a good GPA is viewed more favorably by every racial/ethnic group when
that group comprises a larger share of the school. The popularity-maximizing levels
of unruliness are lower among students of high socioeconomic status (better educated
mothers and a father present) who attend schools with an overall higher socioeconomic status. Although white students tend to have higher popularity-maximizing
levels of substance use, these levels decrease when whites make up a greater share of
the student body. Similarly, blacks tend to have lower levels of substance use, but
these increase among blacks in more heavily black schools. Overall, the excluded
instruments are strong. The joint F-statistics for the six excluded instruments
26
range from 26 to 1,000 and are always statistically significant at the 5% -level.
Table 6 provides coefficient estimates from the first stage of the 2SLS procedure
using the second set of instrumental variables. The coefficient estimates on the excluded instruments are similar to those from the first IV strategy, but a few differences
exist. A student’s socioeconomic status relative to the average socioeconomic status of her grade has stronger effects on the popularity-maximizing level of behaviors
than previously estimated. Students with better educated mothers in grades with a
26
The instruments are indicators for whether the student is white, black, Hispanic, Asian, interacted with the average share of the racial/ethnic group in the school, as well as the mom’s education
and whether the father is present interacted with the school average of each, respectively.
27
higher average level of mothers’ education have a higher popularity-maximizing level
of GPA, and a lower popularity-maximizing level of substance use, unruliness, and
interpersonal trouble. The same pattern holds for students whose father is present in
grades with more students living with their fathers in this second IV strategy. Some
of these coefficient estimates have the reverse sign or are statistically insignificant
in the first IV strategy. The coefficient estimates for a student’s race and ethnicity
interacted with the average race and ethnicity in the grade generally have a smaller
magnitude and are less statistically significant in the second IV strategy relative
to the first. The joint F-statistics range from about 7 for substance use to 86 for
unruliness, and are less than 30 for both GPA and interpersonal troubles. Overall,
these joint F-statistics on the excluded instruments indicate that this second set of
instrumental variables is weaker than the first.
5.2.2
Second Stage Results
Results for the behavioral equations can be found in Tables 7-10. The first and second
columns of each table show the results from ordinary least squares (OLS) estimation
of the behavioral equation with and without school fixed effects, respectively. The
third column of each table reports coefficient estimates for the 2SLS estimation of
equation (8), which controls for potential endogeneity of the popularity-maximizing
behavior using interactions between student characteristics and average characteristics in the school. The fourth column of the tables reports coefficient estimates
for the 2SLS estimation using the second set of instrumental variables, which rely
on interactions between student characteristics and school-grade averages. For three
of the four behaviors, in all specifications, the coefficient estimate on popularitymaximizing behaviors (γ) falls between zero and one as predicted by the model.
28
Column 1 of Table 7 shows a coefficient estimate of 0.26 in the OLS specification, which indicates that a one point increase (approximately 2 standard deviations)
in the popularity-maximizing GPA will increase a student’s studying and academic
achievement, as measured by a 0.26 point (approximately one-third of a standard
deviation) increase in her GPA. Interestingly, the coefficient estimate in column 2,
controlling for school-fixed effects but not endogeneity, is only 0.09. This suggests
that among students within the same school, the popularity-maximizing behavior
explains only a small portion of the actual GPA students achieve. The substantial
reduction in the coefficient estimate after controlling for school-fixed effects could be
explained if teachers grade on a curve. Within a school, even if everyone tries to
get good grades because academic achievement is popular, some students will still
receive lower marks on the grading scale. Thus, a student’s ability to modify her
GPA in an attempt to gain popularity is more limited when looking only at variation in academic outcomes among students in the same school. The instrumental
variables procedure breaks this relationship between good grades by other students
making academic achievement more “cool,” and it being more difficult for a student
to attain a high GPA since her classmates are studying hard too.
Controlling for school effects and using the first set of instrumental variables
to eliminate endogeneity yields a coefficient estimate of 0.21 on the popularitymaximizing level of GPA, as reported in column 3. This suggests that the OLS
estimate in column (1) is slightly biased upward. To put the result in perspective, a
one standard deviation increase in the popularity-maximizing GPA yields the same
increase in academic achievement, on average, as the student’s mother having 5 additional years (two standard deviations) of educational achievement.
29
The results are similar for substance use and unruliness in Tables 8 and 9, respectively. Overall, popularity-maximization plays a smaller role in determining these
behavior levels. The coefficient estimates indicate that a one unit increase in the
popularity-maximizing level of substance use or unruliness leads to an 0.5-0.10 point
increase in the actual behavior.27 While these coefficient estimates appear small, a
one standard deviation increase in the popularity-maximizing level is associated with
the same magnitude increase in substance use, on average, as the mother having 2.5
(one standard deviation) fewer years of education.
Table 10 provides results for the index of personal problems with teachers and
other students. While the OLS and fixed effects results are similar in magnitude to
the other behaviors, the 2SLS results using interactions between individual characteristics and average school characteristics as instrumental variables show that the
popularity-maximizing behavior has a negative effect on actual behaviors. This runs
contrary to the theoretical model, which predicts that true behaviors will be a convex
combination of “innate” and popularity-maximizing behaviors. These results are not
entirely surprising given that interpersonal trouble has a negative marginal effect on
popularity for many students. It is natural to think that an inability to get along
well with others is unlikely to have a substantial, positive impact on popularity.28
27
Although the IV estimate in column 3 of 8 for smoking is a bit larger than the OLS estimate in
column 1, the standard error bands are such that the two coefficient estimates are not statistically
different from each other.
28
It remains important to include the index of interpersonal problems at least in the initial
bivariate probit in order to minimize any omitted variable bias from entering coefficient estimates on
other behaviors, particularly substance use and lack of good grades, that are correlated with getting
in trouble with students and teachers. The results are, however, robust to dropping interpersonal
troubles from the bivariate probit. In particular, the second-stage coefficient estimates have very
similar magnitudes but slightly larger standard errors.
30
The results from the 2SLS estimation of behavioral equations with the second set
of instrumental variables that use interactions between individual characteristics and
school-grade averages are reported in column 5 of all the tables. These results are
similar to those reported in column 4. For GPA and unruliness, the coefficient estimates are slightly larger but not statistically different from those found with the first
set of instrumental variables. The coefficient estimates on the popularity-maximizing
level of behavior for substance use and interpersonal troubles are substantially larger
using the second instrumental variables strategy. For substance use, the difference
in second-stage results is likely the result of a very weak first-stage. The coefficient
estimate on the popularity-maximizing level of interpersonal troubles reverses sign,
but remains statistically insignificant. While this change in the magnitude of the
coefficient estimate is difficult to explain, the effect is imprecisely estimated and interpersonal troubles already have an unclear relationship with popularity.
Disregarding the behavioral results for interpersonal trouble, the empirical results match the theoretical predictions well. For GPA, substance use, and general
unruliness, students place some positive weight on the popularity-maximizing level
of behavior when choosing their optimal behavior. It is not necessarily surprising
that popularity-maximization accounts for about 20% of students’ decisions regarding academic success but only accounts for 5-10% of their decision to engage in
delinquent behaviors such as smoking, drinking, skipping school, lying, fighting, or
taking dangerous dares. The most compelling explanation for these results is that a
student’s grade point average is a proxy for behaviors such as time spent studying
relative to hanging out with friends, and participation in extracurricular activities.
It seems natural that the allocation of time between studying and other activities is
31
sensitive to the time-use of one’s peers, as well as to the extent to which studying
and academic achievement is perceived favorably in the school environment.29
5.3
Policy Simulation
The model and empirical results provide a framework for understanding the behavior
of students not just within their own school, but also for predicting the behavior of
these students if placed in different environments. To illustrate, this paper considers
three hypothetical students in the 10th grade.30 The first archetypical student is a
white female with high socioeconomic status. The student’s father is present in the
household, and her mother holds a master’s degree or higher, placing her in the top
5% for education among white mothers. The second representative student is a white
male with average socioeconomic status.31 The third student type is a black male
who also has average socioeconomic status.32 Results from the empirical work are
used to predict how these students would behave in different schools in the sample.
29
An alternative explanation posits that time use is an intensive margin response, and thus may
be easier for students to alter in order to gain popularity. Engaging in substance use or unruly
behavior in order to gain popularity first requires an extensive margin change for many students.
Almost 50% of students report no substance use or unruly behavior. For the majority of students,
the popularity-returns to substance use or unruly behavior may not be large enough to meet the
threshold needed to start smoking, drinking, or fighting. Furthermore, the utility cost (β in the
theoretical model) of initially engaging in substance use or delinquent behavior may be much higher
than the utility cost of spending more or less time in the library relative to the amount of time you
would have spent studying absent any concerns over popularity. This could explain why, on average,
students place less weight on popularity-maximizing levels of substance use and unruly behavior
than grades. However, re-estimating the results using an indicator for whether students engage in
substance use and unruly behaviors, and using a linear probability model for behaviors, shows no
increase in the coefficient estimates on the popularity-maximizing levels of these behaviors.
30
The students are 15 years of age and have attended the school for 2 years. These represent the
median age and years of attendance among 10th grade students in the sample.
31
His father is present, and his mother holds a high school degree but only attended a vocational
school or some college, which represents the median education level among white mothers.
32
His father is present in the household and his mother completed high school but only attended
a vocational school or some college. As with the other hypothetical students, both of these qualities
represent the median among parents of black students in the sample.
32
The first step to predicting behaviors requires finding the popularity-maximizing
level of all four behaviors. Each archetypical student is paired with every student in
the data for a given school. For a set of behaviors,33 the coefficient estimates from the
bivariate probit are used to predict the probability of the hypothetical student being
nominated as a friend by every student in the school. The sum of these predicted
probabilities of receiving a nomination is the hypothetical student’s predicted popularity in the school. Searching over a 4-dimensional grid representing all possible
combinations of the different levels of each behavior yields the set of behaviors that
would maximize the student’s popularity in a given school in the sample. Once the
popularity-maximizing behaviors have been found, the coefficient estimates from the
second-stage of the 2SLS estimation of the behavioral equations are used to predict
behaviors for the hypothetical students. The set of estimates used for this simulation
exercise come from the first instrumental variables strategy, which relies on variation
in a student’s characteristics relative to the demographic composition of the school.34
Figures 1-3 show the results of the simulation exercise for the three hypothetical
students described above when placed in three very distinct school environments.
The first figure illustrates the results for academic performance, the second for substance use, and third for unruly behavior.35 The student types and school charac33
The behaviors are academic performance (GPA), substance use, unruliness, and having interpersonal trouble with teachers and other students.
34
The results are not drastically different when using the coefficient estimates from the second
IV strategy that relies on variation in a student’s characteristics relative to the demographic composition of the grade. However, the first stage regressions from the first IV strategy are stronger,
and the behavioral equation results from the first IV strategy relying on school-composition are the
focus of most of the discussion in this paper.
35
A figure for interpersonal troubles is not reported here since that behavior has an unusual relationship with popularity and the coefficient estimates from the behavioral equation are inconsistent
with the theoretical model.
33
teristics are listed along the horizontal axis. The first panel of each graph represents
an urban school located in the southern United States. The school is composed of
93% black students and 3% white students, and the students have average socioeconomic characteristics. The average mother in the school completed high school but
not college, and fathers are present in 60% of the students’ households. The second
panel represents a suburban Midwestern school in which 95% of the students are
white and 3% of the students are black. The school has above average socioeconomic
status, with the median mother completing college and 90% of fathers living in the
students’ homes. Finally, the third panel shows predicted behaviors in a racially diverse, urban, Midwestern school with average socioeconomic characteristics. In this
school, 33% of students are black and 62% of students are white. On average, the
mothers have completed high school but have no additional education, and 64% of
students live with their fathers.
In the figures, diamonds represent the predicted behavior for each student type.
The small circles illustrate the actual behaviors observed for students in the data
attending the given school who have identical characteristics to the hypothetical student. By the nature of the in-sample simulation, the predicted behaviors fall near
the average of observed behaviors across student types and schools. For some combinations of student type and school, however, the data have no observations matching
the student description in attendance at the school. In such cases, the model developed in this paper can predict how a specific type of student is likely to behave when
placed in a demographic environment that is very different from the type of school
in which she is usually found in the data.
Across all of the schools, the white female with high socioeconomic status earns
34
better grades and engages in less substance use and unruliness than the other two
student types. In each of the schools, black students engage in less substance use than
white students from similar socioeconomic backgrounds. Furthermore, in Figure 1
it is clear that academic achievement for the three student types is highest in the
suburban school in which the students come from families with high socioeconomic
status. The effects of average school characteristics on all student types is consistent
with the correlated effects in a standard Manski-model. Students of all types exhibit
better academic performance when placed among peers with higher socioeconomic
characteristics. However, the results differ from the standard Manski-result in that
the effects of the group demographics on student behavior differ by student type.
Specifically, the popularity-maximizing and thus the actual behavior depend on interactions between student characteristics and average-group characteristics.
Academic performance (Figure 1), shows some differences in the effects of average
group characteristics on each type of student. Socioeconomic status plays a relatively
larger role than race in determining the “coolness” of academic achievement. The
male students with average socioeconomic status attain similar GPAs in the heavily
black and the racially diverse schools that have average socioeconomic characteristics. However, both of these student types exhibit higher academic achievement
in the suburban school with high socioeconomic characteristics. Between the two,
the white student experiences a larger increase in academic achievement than the
black student when they move from the diverse school to the heavily white school.
This result stems from the fact that both white and black students view academic
achievement more favorably when forming friendships with peers of the same race.36
36
See the panel for “Varying Perceptions of “Coolness” for Behaviors by Characteristics of the
Nominator - GPA” in the appendix. Similar interactions between student characteristics and the
35
In Figure 2, substance use is lowest in the heavily black school and highest in the
racially diverse school among all three student types. Substance use by these representative students more than doubles when the students move from a heavily black
school to a school with more racial diversity but similar socioeconomic characteristics.
These findings can be explained by the fact that white students view substance use
more favorably than black students when nominating friends. However, the predicted
behaviors in the suburban school show that increasing the socioeconomic status of
the peer group while also increasing the share of white students in the school will
decrease substance use by more for the white students than for the black student.
This effect is derived from the fact that substance use is viewed as less “cool” by
white students when they are nominating a friend of the same race as a opposed to
when they are nominating a friend of a different race.
The varying effects of group characteristics on students of different types is also
visible in Figure 3. Unruly behavior is lowest among all three types of students in
the heavily black, urban school. However, the black student engages in the highest level of unruliness in the heavily white, high socioeconomic school, while both
white students engage in the most unruly behavior in the third, racially diverse
school. The different effects on the white and black students between these schools
can be explained by the finding that unruliness is viewed least favorably by students
considering whether to nominate a peer who has similar racial and socioeconomic
characteristics. In contrast, unruly behavior does not reduce the probability of a
friendship nomination by as much when the nominee has a different race and socioeconomic background from the nominator.
other behaviors can be found in the other panels of the bivariate probit results.
36
A simulation of this nature illustrates the possible uses of the model and empirical
results for predicting the behavior of students when placed in a variety of different
environments. While group characteristics increase achievement and reduce delinquency for all students in the expected manner, the magnitude of these effects differs
depending on the characteristics of each student. For instance, moving a black student with average socioeconomic characteristics into a heavily white school with high
socioeconomic status does not always lead to beneficial outcomes on all dimensions.
Although the move is predicted to increase the academic achievement, it also leads
to slightly more substance use and substantially more unruliness such as fighting,
lying, and skipping school. Furthermore, the increase in academic achievement is
not as large as it could be if the student were moved to a school with equally high
socioeconomic status as well as greater racial diversity. These comparisons across
schools and student types have implications for policies that allow students to move
to alternative schools through programs such as public school choice. The results
suggest that moving students from a low-performing school to the opposite extreme
may not generate the largest possible gains in all behavioral outcomes.
6
Conclusion
The paper presents a novel mechanism for explaining conformity in student behavior.
Prior literature generally takes a student’s position in a network of friends as exogenous and uses the information to understand how her network position affects behaviors. This paper focuses on a specific network position, popularity, and endogenizes
it within the model. The model provides a micro-foundation for a linear-in-means
behavioral equation. Empirical results show the assumptions and implications of the
37
model are consistent with data. Students are found to consider the popularity implications of their actions when deciding how to act in different school environments.
High school students derive utility from being well-liked by their peers, and strive
to gain this popularity through behaving appropriately. The empirical findings from
estimating the probability of a friendship nomination using a bivariate probit model
show that popularity is a function of students’ behaviors and characteristics relative
to their peers (homophily), as well as the general “coolness” associated with certain
actions and types of students. A unique popularity-maximizing level of behavior
for each student is predicted using coefficient estimates from the bivariate probit.
Two instrumental variables approaches are then used to estimate the effect of these
popularity-maximizing levels on actual behaviors. The coefficient estimates show
that students place some positive consideration on the popularity-maximizing level
of GPA, substance use, and unruliness, although perhaps unsurprisingly the results
do not hold for the index of interpersonal trouble with teachers and students.
Studying the endogenous formation of subgroups, as well as popularity or social
acceptance within those groups, is an important extension of this work. It may be the
case that the desire to be accepted by a specific subgroup (clique) of students drives
behaviors much more than any concern over the total number of nominations.37 A
richer model in which students are only concerned with popularity in endogenously
determined subgroups of peers also generates important differences from the linearin-means Manski-model. Most notably, the weight placed on the average group be37
However, Goldsmith-Pinkham and Imbens (2013) find that both direct and peers who are a
number of links removed have a substantial effect on student behaviors, which suggests students
care about social acceptance among a wider group of peers than their immediate clique.
38
havior differs with the student’s location in the distribution of group behaviors and
characteristics. If a student is very dissimilar from her peers, the popularity-returns
to conforming will be too small to substantially change the student’s behavior.
From a policy perspective, the results in this paper suggest that the desire to
gain popularity may have a substantial effect on improving a student’s grades if she
were moved to a school in which academic success was viewed favorably by peers.
Similar effects hold to a lesser extent for substance use and unruliness. However, the
school environments that are best for some types of students will not be optimal for
other types of students. For instance, academic achievement leads to greater popularity among students of higher socioeconomic status, and also among peers with the
same racial characteristics. The benefits of moving a student to a school with higher
socioeconomic status can be mitigated by racial differences between the student and
her peers. Additionally, in schools with a greater share of white students there is
a greater incentive to engage in substance use, particularly for non-white students.
These effects, as discussed in the previous section, can be seen in Figures 1-3. Since
the perception of behaviors varies by race, ethnicity, and socioeconomic status, public programs that alter the demographic composition of schools may have substantial
effects on student behavior by changing the returns to popularity of certain actions.
39
Table 1: Summary Statistics
Variable
Mean Standard Deviation
Popularity
4.20
3.74
GPA
2.87
0.77
Substance Use
7.10
14.04
Unruliness
7.54
12.82
Interpersonal Trouble 11.50
16.80
Age
15.72
1.20
Male
0.47
0.50
Hispanic
0.14
0.34
White
0.69
0.46
Black
0.15
0.35
Asian
0.07
0.25
American Indian
0.04
0.20
Other Race
0.07
0.26
Years at School
2.56
1.41
Lives with Dad
0.81
0.39
Mom’s Education
13.68
2.48
N. Observations
35,490
Median
3
3
1
2.5
4
16
0
0
1
0
0
0
0
2
1
14
a) Summary statistics are reported for the behavioral equation
regression sample. The bivariate probit regression uses the same
set of students, but by pairing each student with every schoolmate
the sample size increases exponentially.
40
Table 2: Marginal Effects of Behaviors on Popularity by
Gender & Race/Ethnicity
GPA
White
Black
Hispanic
Asian
Substance Use
White
Black
Hispanic
Asian
Unruliness
White
Black
Hispanic
Asian
Interpersonal Trouble
White
Black
Hispanic
Asian
Male
133***
(9.75)
135***
(16.3)
124***
(16.5)
105***
(16.7)
Male
4.87***
(0.77)
7.49***
(1.16)
6.61***
(1.16)
6.02***
(1.16)
Male
0.427
(0.80)
1.15
(1.12)
1.10
(1.14)
1.39
(1.15)
Male
0.34
(0.63)
-1.08
(0.81)
-0.75
(0.82)
-1.02
(0.83)
Female
157***
(10.2)
158***
(16.4)
148***
(16.7)
129***
(16.9)
Female
4.46***
(0.78)
7.08***
(7.08)
6.20***
(1.15)
5.61***
(1.15)
Female
0.70
(0.83)
1.42
(1.12)
1.38
(1.14)
1.67
(1.15)
Female
0.67
(0.64)
-0.75
(0.82)
-0.41
(0.83)
-0.68
(0.84)
a) Marginal effects are calculated for students with the average level of
each behavior whose mothers have the sample average level of education and who live with their father, in schools that exhibit the sample
average level of all behaviors and demographic characteristics, as reported in Table 1. Standard errors are reported in parentheses. One,
two, and three asterisks indicate statistical significance at the 10-, 5-,
and 1-percent level, respectively. Coefficient estimates and standard
errors reported here have been scaled by a factor of 106 .
41
Table 3: Summary Statistics for Popularity-Maximizing Behaviors
Popularity-Maximizing
Behaviors
Mean
Observed
Behaviors
Mean
(s.d.)
(s.d.)
GPAp
3.64
(0.48)
GPA
2.87
(0.77)
Substance Usep
28.73
(24.82)
Substance Use
7.10
(14.04)
Unrulinessp
23.41
(25.55)
Unruliness
7.54
(12.82)
Interpersonal Troublep
13.17
(8.28)
Interpersonal Trouble
11.50
(16.80)
Observations
35490
Observations
35490
a) A superscript p indicates the predicted, popularity-maximizing level of each behavior.
b) Standard deviations are reported in parentheses beside the means for each popularitymaximizing and observed behavior.
c) For comparison, the summary statistics for observed behaviors are repeated in this
table.
42
Table 4: Relating Utility and Popularity
Variable
Happy at School
Depressed
0.04***
(0.01)
-0.05***
(0.01)
0.16***
(0.02)
0.01
(0.03)
0.07*
(0.04)
-0.22***
(0.05)
-0.05
(0.04)
-0.15***
(0.04)
-0.04*
(0.02)
0.02*
(0.01)
0.02***
(0.004)
0.08***
(0.02)
0.02
35,167
88
-0.03***
(0.01)
0.02*
(0.01)
-0.58***
(0.02)
0.04
(0.03)
0.11***
(0.02)
-0.12***
(0.03)
0.11***
(0.03)
0.22***
(0.03)
0.08***
(0.03)
-0.000
(0.01)
-0.001
(0.003)
-0.12***
(0.02)
0.07
35,357
88
Predicted Popularity
Age
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Mother’s Education
Lives with Dad
R-squared
N. Observations
N. Schools
a) The regressions also control for school and grade fixed
effects, as well as all possible interactions between individual
characteristics and the average characteristics in the school.
Standard errors are listed in parentheses. One, two, and
three asterisks indicate statistical significance at the 10-, 5-,
and 1-percent level, respectively.
b) The table reports bootstrap standard errors
43
Table 5: First Stage Results From 2SLS Estimation of Behavioral Equations
(First IV Strategy: School-Composition)
White*W hite
Black*Black
Hispanic*Hispanic
Asian*Asian
Mom’s Edu*M om0 sEdu
With Dad*W ithDad
Age
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Mother’s Education
Lives with Dad
Constant
R-squared
N. Observations
N. Schools
F-statistic on Excluded IV’s
F(6, 35382)
GPAp
Substance Usep
Unrulinessp
Interpersonal Troublep
0.12***
(0.02)
0.34***
(0.03)
0.20***
(0.03)
0.02
(0.05)
-0.003***
(0.001)
0.03
(0.05)
-0.02***
(0.003)
-0.07***
(0.004)
-0.04***
(0.01)
-0.01
(0.02)
-0.08***
(0.01)
-0.001
(0.01)
0.02**
(0.01)
-0.01
(0.01)
-0.001
(0.002)
0.04***
(0.01)
-0.05
(0.04)
3.88***
(0.06)
0.03
35,490
88
44.66***
-14.04***
(1.48)
14.10***
(2.13)
4.47**
(2.11)
-17.56***
(3.17)
-0.01
(0.06)
-5.10
(3.40)
0.84***
(0.20)
2.54***
(0.24)
2.05***
(0.65)
5.01***
(1.05)
-2.77***
(0.80)
-3.93***
(0.84)
-1.60***
(0.59)
-1.24**
(0.53)
-0.14
(0.13)
0.43
(0.81)
1.10
(2.70)
17.49***
(3.72)
0.03
35,490
88
26.34***
-42.14***
(0.98)
-28.67***
(1.42)
-55.21***
(1.40)
-19.76***
(2.11)
-1.01***
(0.04)
-53.04***
(2.26)
0.29**
(0.14)
-2.88***
(0.16)
-1.43***
(0.43)
9.26***
(0.70)
-15.67***
(0.53)
0.16
(0.56)
4.86***
(0.39)
-5.88***
(0.35)
0.05
(0.09)
6.63***
(0.54)
27.25***
(1.79)
155.62***
(2.47)
0.65
35,490
88
1271.30**
10.76***
(0.39)
-4.72***
(0.56)
11.28***
(0.56)
-15.93***
(0.84)
0.06***
(0.02)
0.79
(0.90)
0.19***
(0.05)
-2.83***
(0.06)
-0.23
(0.17)
-0.19
(0.28)
4.73***
(0.21)
-1.53***
(0.22)
-5.00***
(0.16)
3.45***
(0.14)
-0.05
(0.04)
0.15
(0.21)
0.26
(0.71)
-10.34***
(0.98)
0.34
35,490
88
262.78***
a) Behaviors are estimated, popularity-maximizing levels for each student. Excluded IV’s are interactions between the student’s own characteristic and the school average, denoted with a bar over them.
Regressions control for school and grade fixed effects (12th grade is excluded). Standard errors are
listed in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and
1-percent level, respectively.
44
Table 6: First Stage Results From 2SLS Estimation of Behavioral Equations (Second IV
Strategy: Grade-Composition)
White*W hitegs
Black*Blackgs
Hispanic*Hispanicgs
Asian*Asiangs
Mom’s Edu*M om0 sEdugs
With Dad*W ithDadgs
Age
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Mother’s Education
Lives with Dad
White*W hite−gs
Black*Black−gs
Hispanic*Hispanic−gs
Asian*Asian−gs
Mom’s Edu*M om0 sEdu−gs
With Dad*W ithDad−gs
Constant
Observations
R-squared
Number of Schools
F-statistic on Excluded IV’s, F(6, 35382)
GPAp
Substance Usep
Unrulinessp
Interpersonal Troublep
-0.05
(0.05)
0.47***
(0.07)
-0.02
(0.10)
0.05
(0.12)
0.004***
(0.001)
0.14***
(0.05)
-0.02***
(0.003)
-0.07***
(0.004)
-0.04***
(0.01)
-0.01
(0.02)
-0.09***
(0.01)
-0.002
(0.01)
0.02**
(0.01)
-0.01
(0.01)
-0.0004
(0.002)
0.05***
(0.01)
-0.07
(0.04)
0.17***
(0.05)
-0.13*
(0.07)
0.21**
(0.10)
-0.04
(0.12)
-0.01***
(0.001)
-0.09
(0.06)
3.87***
(0.06)
35,490
0.04
88
17.74***
2.06
(2.90)
-11.85***
(4.48)
-3.73
(6.15)
-9.61
(7.56)
-0.20***
(0.04)
-5.25*
(3.11)
0.82***
(0.20)
2.52***
(0.24)
2.20***
(0.65)
4.68***
(1.05)
-2.09***
(0.79)
-3.80***
(0.85)
-1.53***
(0.59)
-1.22**
(0.53)
-0.15
(0.13)
0.62
(0.80)
0.27
(2.70)
-15.45***
(2.95)
23.69***
(4.39)
7.72
(6.09)
-7.95
(7.90)
0.17***
(0.05)
1.23
(3.79)
17.68***
(3.71)
35,490
0.03
88
7.55***
-19.80***
(1.92)
-23.00***
(2.98)
-41.08***
(4.08)
-14.42***
(5.02)
-0.21***
(0.02)
-19.35***
(2.07)
0.30**
(0.14)
-2.87***
(0.16)
-1.23***
(0.43)
9.03***
(0.70)
-14.98***
(0.53)
0.32
(0.56)
4.91***
(0.39)
-5.85***
(0.35)
0.04
(0.09)
6.76***
(0.53)
25.58***
(1.79)
-21.66***
(1.96)
-7.90***
(2.91)
-13.84***
(4.05)
-5.42
(5.25)
-0.81***
(0.04)
-31.51***
(2.52)
155.48***
(2.47)
35,490
0.65
88
86.51***
4.15***
(0.76)
2.55**
(1.18)
5.06***
(1.62)
-6.57***
(1.99)
-0.10***
(0.01)
-1.78**
(0.82)
0.19***
(0.05)
-2.83***
(0.06)
-0.23
(0.17)
-0.14
(0.28)
4.53***
(0.21)
-1.55***
(0.22)
-5.02***
(0.16)
3.44***
(0.14)
-0.05
(0.04)
0.21
(0.21)
0.77
(0.71)
6.50***
(0.78)
-6.42***
(1.15)
6.24***
(1.60)
-9.18***
(2.08)
0.16***
(0.01)
1.94*
(1.00)
-10.42***
(0.98)
35,490
0.34
88
29.11***
a) The behaviors are the estimated, popularity-maximizing levels for each student. The excluded IV’s are interactions between the student’s own characteristic and the school-grade average characteristic, denoted here with a
bar over them. A subscript of “-g” indicates an average taken over all other grades in the school. The regressions
also control for school fixed effects and grade fixed effects (12th grade is the excluded category). Standard errors
are listed in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and 1-percent
level, respectively.
45
Table 7: Behavioral Results – GPA
GPA
GPAp
Age
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Mom’s Education
Lives with Dad
Constant
R-squared
N. Observations
N. Schools
OLS
School FE
0.26***
(0.01)
-0.15***
(0.01)
-0.10***
(0.01)
-0.12***
(0.01)
0.02*
(0.02)
-0.20***
(0.02)
0.21***
(0.02)
-0.10***
(0.02)
-0.04***
(0.02)
0.02***
(0.003)
0.05***
(0.002)
0.15***
(0.01)
3.78***
(0.12)
0.15
35,490
88
0.09***
(0.01)
-0.15***
(0.01)
-0.13***
(0.01)
-0.10***
(0.02)
0.04***
(0.02)
-0.20***
(0.02)
0.26***
(0.02)
-0.11***
(0.02)
-0.04**
(0.02)
0.01
(0.004)
0.05***
(0.002)
0.14***
(0.01)
4.36***
(0.13)
0.09
35,490
88
2SLS
(IV-Strategy 1)
2SLS
(IV-Strategy 2)
0.21*
(0.12)
-0.15***
(0.01)
-0.12***
(0.01)
-0.10***
(0.02)
0.03**
(0.02)
-0.20***
(0.02)
0.26***
(0.02)
-0.11***
(0.02)
-0.04**
(0.02)
0.01
(0.004)
0.05***
(0.002)
0.14***
(0.01)
3.88***
(0.50)
0.34*
(0.20)
-0.014***
( 0.01)
-0.12***
(0.02)
-0.13***
(0.02)
-0.01
(0.03)
-0.13***
(0.03)
0.30***
(0.03)
-0.11***
(0.02)
-0.04**
(0.02)
0.01
(0.004)
0.03
(0.03)
-0.18**
(0.08)
3.37***
(0.78)
35,490
88
35,490
88
a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks
indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure
controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p
denotes the popularity-maximizing level of the behavior.
b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the
excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification.
46
Table 8: Behavioral Results – Substance Use
Substance Use
OLS
Substance Usep
0.05***
(0.003)
Age
1.78***
(0.12)
Male
1.07**
(0.15)
Hispanic
-1.13***
(0.27)
White
2.27***
(0.29)
Black
-2.98***
(0.33)
Asian
-0.44
(0.37)
Indian
3.13***
(0.37)
Other Race
1.04***
(0.33)
Years at School
0.02
(0.06)
Mom’s Education -0.21***
(0.03)
Lives with Dad
-2.14***
(0.19)
Constant
-21.10***
(2.24)
R-squared
0.04
N. Observations
35,490
N. Schools
88
2SLS
School FE
0.03***
(0.003)
1.81***
(0.13)
1.04***
(0.15)
0.35
(0.30)
2.01***
(0.29)
-3.28***
(0.35)
-0.27
(0.38)
3.13***
(0.37)
1.17***
(0.33)
-0.004
(0.08)
-0.21***
(0.03)
-2.29***
(0.19)
-20.93***
(2.32)
0.03
35,490
88
2SLS
(IV-strategy 1) (IV-strategy 2)
0.11**
(0.05)
1.74***
(0.13)
0.83***
(0.20)
0.07
(0.34)
2.33***
(0.35)
-3.35***
(0.36)
0.33
(0.53)
3.23***
(0.37)
1.26***
(0.34)
0.01
(0.09)
-0.24***
(0.04)
-2.04***
(0.25)
-22.33***
(2.48)
0.28***
(0.10)
1.60***
(0.16)
0.39
(0.30)
1.29***
(0.48)
2.76***
(0.85)
-3.45***
(0.58)
-0.29
(0.69)
3.39***
(0.42)
1.50***
(0.37)
0.04
(0.09)
0.23
(0.50)
3.22*
(1.72)
-24.38***
(3.06)
35,490
88
35,490
88
a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks
indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure
controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p
denotes the popularity-maximizing level of the behavior.
b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the
excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification.
47
Table 9: Behavioral Results – Unruliness
Unruliness
OLS
Unrulinessp
0.06***
(0.004)
Age
0.34***
(0.11)
Male
3.09***
(0.14)
Hispanic
2.28***
(0.26)
White
1.06***
(0.27)
Black
1.68***
(0.32)
Asian
-0.28
(0.33)
Indian
2.49***
(0.34)
Other Race
1.13***
(0.30)
Years at School
-0.07
(0.06)
Mom’s Education 0.25***
(0.04)
Lives with Dad
-0.27
(0.19)
Constant
-6.76***
(2.13)
R-squared
0.03
N. Observations
35,490
N. Schools
88
School FE
0.06***
(0.004)
0.36***
(0.12)
3.18***
(0.14)
2.11***
(0.28)
1.29***
(0.28)
1.28***
(0.33)
0.17
(0.35)
2.38***
(0.34)
1.11***
(0.30)
-0.002
(0.08)
0.28***
(0.04)
-0.23
(0.19)
-7.95***
(2.22)
0.03
35,490
88
2SLS
(IV-strategy 1)
2SLS
(IV-strategy 2)
0.06***
(0.01)
0.37***
(0.12)
3.17***
(0.14)
2.06***
(0.30)
1.22***
(0.31)
1.19***
(0.38)
0.17
(0.35)
2.41***
(0.35)
1.09***
(0.31)
-0.002
(0.08)
0.25***
(0.08)
-0.29
(0.23)
-7.289***
(2.57)
0.08**
(0.04)
0.36***
(0.12)
3.22***
(0.18)
2.39***
(0.38)
2.06***
(0.66)
0.42
(0.73)
-0.43
(0.48)
2.31***
(0.39)
1.23***
(0.37)
-0.002
(0.08)
0.70
(0.45)
-0.362**
(1.63)
-10.08
(6.28)
35,490
88
a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks
indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure
controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p
denotes the popularity-maximizing level of the behavior.
b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the
excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification.
48
Table 10: Behavioral Results – Interpersonal Trouble
Interpersonal Trouble
Interpersonal Troublep
Age
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Mom’s Education
Lives with Dad
Constant
R-squared
N. Observations
N. Schools
OLS
School FE
0.13***
(0.01)
2.42***
(0.15)
2.52***
(0.18)
1.28***
(0.33)
-3.01***
(0.35)
1.68***
(0.40)
2.05***
(0.44)
2.08***
(0.44)
-0.05
(0.39)
-0.03
(0.08)
-0.59***
(0.04)
-1.06***
(0.23)
-24.63***
(2.67)
0.05
35,490
88
0.04***
(0.02)
2.39***
(0.15)
2.28***
(0.18)
1.13***
(0.36)
-2.51***
(0.36)
2.23***
(0.42)
1.61***
(0.46)
1.64***
(0.44)
0.13
(0.40)
0.07
(0.10)
-0.43***
(0.04)
-0.79***
(0.23)
-26.22***
(2.77)
0.03
35,490
88
2SLS
(IV-strategy 1)
2SLS
(IV-strategy 2)
-0.28***
(0.07)
2.45***
(0.15)
1.36***
(0.27)
1.83***
(0.39)
-0.43
(0.58)
3.22***
(0.48)
-0.003
(0.58)
-0.09
(0.58)
1.28***
(0.47)
0.06
(0.10)
-0.12
(0.08)
-0.48**
(0.24)
-28.87***
(2.84)
0.29
(0.22)
2.33***
(0.157)
2.96***
(0.63)
2.59***
(0.48)
-2.50***
(0.77)
1.93*
(1.13)
0.46
(0.73)
2.82**
(1.17)
-0.66
(0.84)
0.08
(0.10)
-0.87
(0.56)
2.52
(1.91)
-22.94***
(3.56)
35,490
88
35,490
88
a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks indicate
statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure controls for school
fixed effects. All specifications also control for grade fixed effects. A superscript p denotes the popularitymaximizing level of the behavior.
b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the excluded
instruments. IV-strategy 2 uses interaction terms between individual characteristics and grade-school specific
averages for identification.
49
Figure 1: Predicted & Actual Academic Grades Across Student Types & Schools
a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds
indicate the predicted behavior for the three types of students across the schools. Small circles represent observations
in the data for students in the school who match the description of the hypothetical student.
b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The
race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High
socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father
present in the household. Median socioeconomic status refers to a having a mother who has completed high school
but does not have a college degree, and having a father present.
50
Figure 2: Predicted and Actual Substance Use Across Student Types and Schools
a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds
indicate the predicted behavior for the three types of students across the schools. Small circles represent observations
of behaviors in the data for students in the school who match the description of the hypothetical student.
b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The
race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High
socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father
present in the household. Median socioeconomic status refers to a having a mother who has completed high school
but does not have a college degree, and having a father present.
51
Figure 3: Predicted and Actual Unruly Behavior Across Student Types and Schools
a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds
indicate the predicted behavior for the three types of students across the schools. Small circles represent observations
of behaviors in the data for students in the school who match the description of the hypothetical student.
b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The
race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High
socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father
present in the household. Median socioeconomic status refers to a having a mother who has completed high school
but does not have a college degree, and having a father present.
52
7
Appendix: Bivariate Probit Results
Table 11: Bivariate Probit Results
Probability that Person j Nominates Person i
General “Coolness” in Behaviors
Behaviors (yi , yi2 )
GPA
-0.14233211***
(0.017)
0.00354063***
(0.001)
0.00038622
(0.001)
0.00111946*
(0.001)
0.01551107***
(0.002)
0.00000983*
(0.000)
0.00000429
(0.000)
-0.00000246
(0.000)
Substance Use
Unruliness
Interpersonal Trouble
GPA2
Substance Use2
Unruliness2
Interpersonal Trouble2
Homophily in Behaviors
Distance in Behaviors ((yi − yj )2 )
GPA-distance
-0.05503049***
(0.002)
-0.00008118***
(0.000)
-0.00001013***
(0.000)
-0.00001517***
(0.000)
Substance Use-distance
Unruliness-distance
Interpersonal Trouble-distance
Interactions in Behaviors (yi ∗ yj )
GPA-interaction
0.01362604***
(0.001)
0.00013761***
(0.000)
0.00000732
(0.000)
-0.00000146
(0.000)
Substance Use-interaction
Unruliness-interaction
Interpersonal Trouble-interaction
(CONTINUED)
53
Table 1.11 Continued: Bivariate Probit Results
Probability that Person j Nominates Person i
Characteristics of the Nominee
Characteristics (xi , x2i )
Age
0.04870483
(0.031)
0.05380015***
(0.014)
-0.04275485*
(0.025)
-0.07837962***
(0.027)
-0.08066360**
(0.037)
0.00856091
(0.037)
-0.05710053*
(0.030)
-0.04606534*
(0.027)
0.07843586***
(0.006)
0.03763856**
(0.019)
0.00202729
(0.006)
-0.00154896
(0.001)
-0.00976036***
(0.001)
0.00056820***
(0.000)
Male
Hispanic
White
Black
Asian
Indian
Other Race
Years at School
Lives With Dad
Mother’s Education
Age2
Years at School2
Mom’s Education2
(CONTINUED)
54
Table 1.11 Continued: Bivariate Probit Results
Probability that Person j Nominates Person i
Homophily in Characteristics
Distance in Characteristics ((xi − xj )2 )
Grade-distance
-0.04185820***
(0.002)
-0.01648061***
(0.001)
-0.13381297***
(0.015)
0.02085278
(0.026)
-0.04073913
(0.028)
-0.25858481***
(0.037)
-0.10304419***
(0.037)
0.04920090*
(0.029)
0.03929546
(0.027)
-0.00673962***
(0.001)
-0.03822054*
(0.020)
-0.00292635***
(0.000)
Age-distance
Male-distance
Hispanic-distance
White-distance
Black-distance
Asian-distance
Indian-distance
Other Race-distance
Years at School-distance
Lives with Dad-distance
Mom’s Education-distance
Interactions in Characteristics (xi ∗ xj )
Age-interaction
-0.00075587***
(0.000)
-0.07089025***
(0.023)
0.24070085***
(0.046)
0.14308518***
(0.048)
0.30389580***
(0.058)
0.35002329***
(0.070)
0.12764530
(0.116)
0.09444958
(0.065)
0.00547474***
(0.000)
-0.01162758
(0.031)
-0.00038033**
(0.000)
0.76549501***
(0.008)
0.67152154***
(0.006)
0.60153644***
(0.006)
0.58258758***
(0.008)
Male-interaction
Hispanic-interaction
White-interaction
Black-interaction
Asian-interaction
Indian-interaction
Other Race-interaction
Years at School-interaction
Lives with Dad-interaction
Mom’s Education-interaction
9th Grade-interaction
10th Grade-interaction
11th Grade-interaction
12th Grade-interaction
55
(CONTINUED)
Table 1.11 Continued: Bivariate Probit Results
Probability that j Nominates i
Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - GPA
Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi )
Male-GPA
0.02295788***
(0.004)
Hispanic-GPA
-0.02015993**
(0.008)
White-GPA
-0.02046619**
(0.008)
Black-GPA
-0.03629561***
(0.011)
Asian-GPA
0.00742348
(0.011)
Indian-GPA
-0.02007624**
(0.009)
Other Race-GPA
-0.00523329
(0.008)
Lives with Dad-GPA
0.01188473**
(0.006)
Mom’s Education-GPA
0.00456669***
(0.001)
Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi )
Male-Male-GPA
-0.01482142***
(0.005)
Hispanic-Hispanic-GPA
0.02512044**
(0.011)
White-White-GPA
0.00891471
(0.006)
Black-Black-GPA
0.04419077***
(0.011)
Asian-Asian-GPA
-0.03195628*
(0.017)
Indian-Indian-GPA
0.05809285*
(0.035)
Other Race-Other Race-GPA
0.00346160
(0.020)
Lives with Dad-Lives with Dad-GPA
-0.00370797
(0.005)
Mom’s Education-Mom’s Education-GPA
-0.00001416
(0.000)
(CONTINUED)
56
Table 1.11 Continued: Bivariate Probit Results
Probability that j Nominate i
Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Substance Use
Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi )
Male-Substance Use
-0.00054331**
(0.000)
Hispanic-Substance Use
-0.00020388
(0.001)
White-Substance Use
0.00026357
(0.001)
Black-Substance Use
-0.00176891**
(0.001)
Asian-Substance Use
-0.00165487**
(0.001)
Indian-Substance Use
0.00086756
(0.001)
Other Race-Substance Use
0.00085307
(0.001)
Lives with Dad-Substance Use
-0.00005873
(0.000)
Mom’s Education-Substance Use
-0.00024887***
(0.000)
Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi )
Male-Male-Substance Use
0.00025390
(0.000)
Hispanic-Hispanic-Sustance Use
0.00096450
(0.001)
White-White-Substance Use
-0.00054887
(0.000)
Black-Black-Substance Use
0.00268157***
(0.001)
Asian-Asian-Substance Use
-0.00063008
(0.001)
Indian-Indian-Substance Use
-0.00400246*
(0.002)
Other Race-Other Race-Substance Use
-0.00112316
(0.001)
Lives with Dad-Lives with Dad-Substance Use
-0.00026279
(0.000)
Mom’s Education-Mom’s Education-Substance Use
0.00000577*
(0.000)
(CONTINUED)
57
Table 1.11 Continued: Bivariate Probit Results
Probability that j Nominates i
Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Unruliness
Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi )
Male-Unruliness
0.00033803
(0.000)
Hispanic-Unruliness
-0.00029864
(0.001)
White-Unruliness
-0.00031634
(0.001)
Black-Unruliness
-0.00072003
(0.001)
Asian-Unruliness
-0.00014430
(0.001)
Indian-Unruliness
-0.00062938
(0.001)
Other Race-Unruliness
-0.00040016
(0.001)
Lives with Dad-Unruliness
0.00000532
(0.000)
Mom’s Education-Unruliness
0.0015907**
(0.000)
Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi )
Male-Male-Unruliness
-0.00017156
(0.000)
Hispanic-Hispanic-Unruliness
-0.00083765
(0.001)
White-White-Unruliness
-0.00045553
(0.000)
Black-Black-Unruliness
-0.00069326
(0.001)
Asian-Asian-Unruliness
-0.00045232
(0.001)
Indian-Indian-Unruliness
0.00065168
(0.002)
Other Race-Other Race-Unruliness
-0.00093372
(0.001)
Lives with Dad-Lives with Dad-Unruliness
-0.00028295
(0.000)
Mom’s Education-Mom’s Education-Unruliness
-0.00000889***
(0.000)
(CONTINUED)
58
Table 1.11 Continued: Bivariate Probit Results
Probability that j Nominates i
Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Trouble
Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi )
Male-Interpersonal Trouble
-0.00012521
(0.000)
Hispanic-Interpersonal Trouble
0.00008857
(0.000)
White-Interpersonal Trouble
-0.00034147
(0.000)
Black-Interpersonal Trouble
0.00073576
(0.001)
Asian-Interpersonal Trouble
0.00013171
(0.001)
Indian-Interpersonal Trouble
0.00093555**
(0.000)
Other Race-Interpersonal Trouble
-0.00073496*
(0.000)
Lives with Dad-Interpersonal Trouble
-0.00021189
(0.000)
Mom’s Education-Interpersonal Trouble
-0.00011108**
(0.000)
Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi )
Male-Male-Interpersonal Trouble
-0.00020825
(0.000)
Hispanic-Hispanic-Interpersonal Trouble
0.00026008
(0.000)
White-White-Interpersonal Trouble
0.00051352**
(0.000)
Black-Black-Interpersonal Trouble
-0.00043573
(0.000)
Asian-Asian-Interpersonal Trouble
-0.00066907
(0.001)
Indian-Indian-Interpersonal Trouble
-0.00304771*
(0.002)
Other Race-Other Race-Interpersonal Trouble
0.00085060
(0.001)
Lives with Dad-Lives with Dad-Interpersonal Trouble
0.00006204
(0.000)
Mom’s Education-Mom’s Education-Interpersonal Trouble
0.00000331
(0.000)
Constant
-3.20359793***
(0.255)
ρ
Observations
0.82
643,293
a) Standard errors are listed in parenthesis below the coefficient estimates. One, two, and
three asterisks indicate statistical significance at the 10- , 5- , and 1-percent level, respectively.
b) It is random whether a student is indexed with an i or a j. Both equations in the bivariate
probit have identical specifications, as noted in equation (7). As a result, the coefficient
estimates for the probability of person i nominating person j have been constrained to be
identical to those reported in the above table.
59
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