# The role of unobservable characteristics in friendship network formation

Pablo Brañas-Garza Universidad de Loyola Andalucía. E-mail:
<EMAIL_ADDRESS>Lorenzo Ductor Universidad de Granada. E-mail:
<EMAIL_ADDRESS>Jaromír Kovářík Universidad del País Vasco UPV/EHU and
University of West Bohemia. Email<EMAIL_ADDRESS>
We acknowledge the financial support of MINECO-FEDER (PGC2018-093506-B-I00,
PID2019-106146GB-I00 and PID2019-108718GB-I00), Excelencia—Andalucía
(PY18-FR-0007), the Basque government (IT1336-19), GAČR (17-25222S) and
Fundación Ramón Areces.

(August 28, 2024)

###### Abstract

Inbreeding homophily is a prevalent feature of human social networks with
important individual and group-level social, economic, and health
consequences. The literature has proposed an overwhelming number of dimensions
along which human relationships might sort, without proposing a unified
empirically-grounded framework for their categorization. We exploit rich data
on a sample of University freshmen with very similar characteristic - age,
race and education- and contrast the relative importance of observable vs.
unobservables characteristics in their friendship formation. We employ
Bayesian Model Averaging, a methodology explicitly designed to target model
uncertainty and to assess the robustness of each candidate attribute while
predicting friendships. We show that, while observable features such as
assignment of students to sections, gender, and smoking are robust key
determinants of whether two individuals befriend each other, unobservable
attributes, such as personality, cognitive abilities, economic preferences, or
socio-economic aspects, are largely sensible to the model specification, and
are not important predictors of friendships.

JEL Codes: D8, D85, J7, J16, O30; Keywords: Homophily; Unobservable individual
characteristics; networks; Bayesian Model Averaging

##  1 Introduction

Individuals tend to interact and form relationships with others who are more
similar to one’s self than randomly chosen members of the population. This
phenomenon, known as homophily or “love of the same” (Lazarsfeld et al.,
1954), is one of the most prevalent and robust features of human social
networks and has been widely studied across fields (Lazarsfeld et al., 1954;
McPherson et al., 2001; Moody, 2001; Kossinets and Watts, 2009). The
ubiquitous presence of homophily directly translates into human interactions
segregated across a variety of dimensions. Since the resulting segregation
patterns have important consequences on behavior, diffusion, inequality, and
social mobility (Glaeser et al., 2000; Ruef et al., 2003; Centola, 2011;
Bramoullé et al., 2012; Jackson et al., 2017; Zeltzer, 2020), it is of utmost
importance to understand the origins, nature, and consequences of homophily.

Rather than analyzing the origins or consequences, the objective of this
article is to test the relative importance of the large set of differing
dimensions of homophily in friendship networks analyzed in previous studies
(see McPherson et al. (2001) for an influential review of the literature).
Abstracting from whether the studies document induced or choice homophily or
rather social influence Kossinets and Watts (2009); Currarini et al. (2010),
there exists large and robust evidence that friendships sort on gender, age,
race, ethnicity, religion, and socio-economic status (Wittek et al., 2020;
Kruse et al., 2016; Ibarra, 1992; Moody, 2001; Marmaros and Sacerdote, 2006;
Kossinets and Watts, 2009; Currarini et al., 2010; Zeltzer, 2020). In the same
vein, meeting constraints–proxied by living in the same neighbourhoods,
belonging to the same club, working in the same firm, studying the same major,
living in the same dorm, and so on–are important predictors of who interacts
with whom (Glaeser et al., 2000; Marmaros and Sacerdote, 2006; Kossinets and
Watts, 2009; Mayer and Puller, 2008). Some studies have focused on more subtle
but still detectable dimensions, such as smoking Christakis and Fowler (2008)
and obesity (Christakis and Fowler, 2007; Valente et al., 2009; De la Haye et
al., 2010); others have analyzed factors imperceptible by a naked eye, such as
political orientation, academic performance, cognitive abilities, behavioral
or personality traits among others (Almack, 1922; Marmaros and Sacerdote,
2006; Conti et al., 2013; Mayer and Puller, 2008).111The number of studies
proposing one or multiple dimensions of homophily in social networks is large
and reviewing all of them is out of scope of this article.

Although the existing work has established the baseline for homophily
theories, the literature has proposed an overwhelming number of dimensions
along which human relationships might sort, without providing a unified
framework according to which we can categorize the different dimensions to
determine their relative importance.222Lazarsfeld et al. (1954) distinguish
between status homophily and value homophily, but this categorization is based
on the nature of the factor rather than on empirical grounds. That is, there
is no systematic analysis assessing how important and robust the proposed
predictors of friendship are from a statistical perspective.

The objective of this paper is to provide a step toward in characterizing the
potential dimensions of homophily based on their empirical relevance. To that
aim, we point out one problem of the existing literature: the typical approach
is to analyze a small and/or exogenously given set of potential dimensions of
homophily, depending on the data and variables at researchers’ disposal.
Nevertheless, these approaches can lead to pre-testing bias and increase the
”researcher’s degrees of freedom” and ”p-hacking” if the estimation is
conducted using multiple combinations of regressors with the aim of obtaining
statistically significant estimates (Simmons et al., 2011). In addition, many
human characteristics are highly correlated in real life: gender is frequently
correlated with self-confidence, prosocial, and risk attitudes (see e.g.
Barber and Odean, 2001; Croson and Gneezy, 2009), while race predicts a large
array of socio-economic outcomes (Guterbock and London, 1983; Altonji and
Blank, 1999).

These correlations in turn generate two classic statistical issues while
estimating homophily using standard approaches. Focusing on a small number of
characteristics increases the probability of accepting a particular
determinant of friendship formation incorrectly (see below for concrete
examples) due to the omitted-variable problem, which leads to biased–and even
inconsistent–estimates.

A converse issue arises if several correlated factors are included into one
model. Such a multicollinearity issue leads to a well known problem regarding
the interpretation of the individual estimates and cast doubts on the
(non-)redundancy of the individual factors. This multicollinearity problem may
result in a loss of efficiency, leading to an incorrect rejection of a
determinant. Thus, both statistical issues can lead to serious
misunderstanding of origins and consequences of homophily.

Using the statistical jargon, the overwhelming variety of potential factors
that might influence network formation generates a problem known as model
uncertainty, arising from the lack of a unified framework for examining the
drivers of friendship. One natural way to think about model uncertainty is to
admit that we do not know which is the “true” model and attach probabilities
to different models (Sala-i Martin et al., 2004a). This is the main idea
behind Bayesian Model Averaging (BMA), which consists in estimating all
possible combinations of the regressors, comparing the performance of all the
models resulting from the different combinations, and taking a weighted
average over all the candidate models, where the weights are the probabilities
that the candidate model is the true model (Hoeting et al., 1999). In our
analysis, we account for uncertainty in the friendship formation model and
identify robust determinants of link formation in friendship networks by using
a BMA panel-data approach.333For the sake of robustness, we also employ the
Weighted Least Squares estimation method to identify the determinants. Our
conclusions are robust to the modeling approach; see Section 4. To the best of
our knowledge, this is the first study that addresses model uncertainty while
identifying the main drivers of friendship.

In this paper, we study potential determinants of friendship formation among
the freshmen of a faculty at a major Spanish University ($n=273$). The data at
our disposal have several particular features. First, we mapped the friendship
networks twice, once at the first week of their freshmen year and once at the
very end of the same academic year. Such timing provides a unique opportunity
to examine the determinants of the emergence of friendships in the group.
Although some links already exist in the beginning, the first-week network
resembles a scarcely connected randomly generated network. Most of the
elicited friendships were established between the two periods and we can
control for preexisting relationships using the first network elicitation.

Second, we collected a rich set of individual characteristics for each
student, enabling to examine the role of homophily on large array of
dimensions. We broadly classify the dimensions under study as observable and
unobservable (or imperceptible) and contrast their importance in friendship
formation. We define an attribute as observable if it can be detected by mere
observation. Examples of such characteristics are race, gender,
geographical/physical proximity, obesity, or whether one smokes. We classify
as unobservable or imperceptible characteristics those attributes that require
more intimate disclosure or a deeper conversation to be detected; these
include family background, cognitive and personality traits, or economic
preferences.

As for our starting hypothesis, on the one hand, there is no reason to believe
a priori that the observable characteristics should play a more important role
that the unobservable ones, or viceversa. On the other hand, one may argue
that observable factors are more salient and, hence, the primary drivers of
friendship formation, while homophily on unobservable attributes may only
arise after certain amount of personal interaction. In line with the latter,
McPherson et al. (2001) note that –in contrast to, say, gender or race– socio-
economic indicators are more sensible on the strength of the relationships.
Mayer and Puller (2008) estimate the determinants of friendships using an
array of race and socio-economic indicators both separately and jointly. If
separately considered, most indicators predict friendships. However, once all
indicators are included into one regression, the influence of the socio-
economic attributes weakens and some become insignificant. Similarly, Girard
et al. (2015) report that, although their behavioral indicators all correlate
significantly with friendships, the magnitude, significance, and even the sign
of their estimated impact on friendships in multivariate regressions are
sensible to the set of dependent variables. These issues are akin to the
omitted-variable and collinearity issues discussed above. Therefore, we prefer
not to be inclined toward any of the two–or any other–alternative hypothesis
and let the data speak. The methodology that we employ is explicitly designed
to target such ex-ante ambiguity in the underlying hypothesis. We note that,
in contrast to other studies, our sample is largely homogeneous in term of
race, ethnicity, age, “profession", cohort, major, and religion, all belonging
among the classic determinants of homophily McPherson et al. (2001). We belief
that this is an advantage of our study: such homogeneity in terms of
observable features maximizes the chances that our subjects organize along the
unobservable, imperceptible traits under study.

We briefly summarize our findings in what follows. Applying the BMA uncovers
that the most important determinants of friendship formation are common
gender, common study section (reflecting the importance of geographical
location), and smoking habits.In a stark contrast, none of the unobservable
factors capturing individual preferences, socio-economic indicators, and
individual personality and behavioral traits play any robust role in
friendship formation in our data. Since women and men form networks
differently Ductor et al. (2018), we show that friendship formation differs
between women and men. We found that common gender, smoking habits and common
section are specially important to explain the friendships of women. However,
the only robust determinant for men is common class section among our
candidate factors.

The rest of the paper proceeds as follows. Section 2 describes the data and
lays out the empirical strategy. Section 3 presents our findings. Section 4
assesses the robustness of the results. We discuss the implications of our
findings in Section 5.

##  2 Materials and Methods

We exploit a data set collected from all freshmen ($n=273$) in the Faculty of
Economic and Business Sciences at the Universidad de Granada, Spain, over the
whole academic year 2010-2011. These data contain rich information on
students’ individual characteristics and their social networks.444The data
were previously employed in an analysis of the role of prenatal exposure to
sex hormones and social integration (Kovářík et al., 2017) and altruism
(Branas-Garza et al., 2013), respectively. The data elicitation was approved
by the Ethical Committee of the Universidad de Granada and all subjects
provided informed written consent. Anonymity was also assured according to the
Spanish Law 15/1999 for Personal Data Protection.

We use this database because it exhibits three particular features providing a
unique opportunity to examine the role of both perceptible and imperceptible
determinants of friendship formation, the main question of this study.

###  2.1 Sample and section distribution

The first interesting feature of the data is the homogeneity of the sample in
terms of race, ethnicity, age, religion, major, cohort, and “profession”
(Table 1). By definition, all participants are first-year students (without
any profession), studying Economics. In addition, our subjects are mostly
Caucasian students (99% of them), aged 17-18 (80% of them), and catholic (61%
of them).

Table 1: Participant’s characteristics | (1) | (2)
---|---|---
Variable | Observations | Frequency
Year of birth |  |
$<$1990 | 27 | 14%
1990 | 11 | 6%
1991 | 43 | 22%
1992 | 113 | 58%
Religion |  |
Catholic | 120 | 62%
Non-Believer/Agnostic | 62 | 32%
Other | 9 | 6%
Gender |  |
Male | 136 | 56%
Female | 108 | 44%
Ethnicity |  |
Caucasian | 202 | 99%
Other | 3 | 1%
Study/class sections |  |
A | 61 | 27%
B | 64 | 29%
C | 48 | 21%
D | 51 | 23%
Household Monthly Income |  |
Income $=<$ 1500 | 69 | 36%
1500 $<$Income $=<$ 2500 | 63 | 32%
2500 $<$Income $=<$ 3500 | 35 | 18%
Income $>$ 3500 | 27 | 14%

Therefore, out of the classic determinants of friendships and homophily
(McPherson et al., 2001), we only expect gender, proximity (see below), and
similar socio-economic background to affect who befriends whom. We believe
that, due to such homogeneity, there is a large chance that friendships sort
out by the more imperceptible, unobservable characteristics under scrutiny
(see Section 2.3 and Table 2).

At beginning of their first year, the School distributes the incoming students
randomly into study/class sections555This is the standard procedure and
unrelated to our study.. In the case of the 2010-2011 cohort, the students
were randomly assigned into four sections (labelled as A, B, C, and D). No
student has any ability to self-select into a particular section and they are
explicitly advised to attend the classes of their corresponding section.
Following the previous literature (e.g. Marmaros and Sacerdote, 2006; Carrell
et al., 2013), we use the section distribution as a measure of location or
geographical distance, determining meeting opportunities of students. The
random assignment provides a causal interpretation regarding the role of
meeting opportunity in link formation (Marmaros and Sacerdote, 2002).

###  2.2 Networks

The second advantage of the dataset stems from the fact that networks were
elicited twice, during the first week of the academic year in October 2010
(Period 1) and at the end of the academic year in May 2011 (Period 2). All
students were initially invited to disclose the names of their friends at the
beginning of the first year. This is an important aspect of the data because
it enables us to control for any pre-existing relationships and focus on the
social dynamics taking place within the class during the first academic year.
The students were again surveyed at the end of the school year when one may
expect to observe a standard social network.666See Kovářík et al. (2017) for
more information regarding the network elicitation.

For the analysis, we mapped the elicited friendships in two undirected
networks using subjects as nodes and friendship nominations as links under the
conditions that a link between two individuals exists if both named each other
as a friend. That is, we focus on the network of reciprocal relations. Since
link reciprocity is one of Granovetter’s (Granovetter, 1973) conditions for a
relationship to be considered strong, we focus on reciprocal ties to make sure
that we analyze friendship rather than acquaintances.

As expected, the network in period 1 was sparsely connected, suggesting that
students had very few ties with their peers at the beginning of the school
year. In stark contrast, the end-of-the-year network resembles classic
socially generated networks in most respects (e.g. skewed degree distribution,
high reciprocity of connections, network transitivity, positive assortativity
etc.; see Table 1 and Figure 3 in Kovářík et al. (2017)). This time setting
and the fact that the friendship network was almost empty in period 1 allow us
to evaluate the causal role of observable characteristics (such as gender or
smoking behaviour) and imperceptible features (e.g., personality or economic
preferences) in the link formation process of friendship networks.777The fact
that the initial network is almost empty allows us to consider simple
probability models in the estimation of the formation of ties.

Since participation was voluntary, some subjects were not active in both
periods (similar consideration applies in case of the data introduced in
Section 2.3). The number of students in period 1 and 2 was 204 and 246,
respectively; 168 students participated in both periods. In our empirical
analysis, we focus on the 168 subjects who participated in both periods, since
we can estimate their link formation in Period 2 conditional on the prior
network in Period 1 or focus on people who have not had any link in Period 1
(our robustness check in Section 4).888We are not able to identify friendships
made between period 1 and 2 that were broken before period 2.

We use the 168 subjects to create all possible pairs of potential friendships
among the 168 subjects, removing duplicated pairs. Thus, we have a pairwise
panel data with 8515 observations. The dependent variable of interest is
friendship indicating whether two individuals $i$ and $j$ nominated each other
in Period 2 as friends. This variable $g_{ij,2}=1$ if both $i$ and $j$ did;
$g_{ij,2}=0$ otherwise.999To illustrate the definition of pairwise panel and
our dependent variable, consider the following example. We have a two-column
matrix, where column 1 contains the id of individual $i$ and column 2 the id
of individual $j$. For individual $i=1$, we create $n-1=167$ observations to
indicate whether person 1 is a friend of each $j=2,3,..,168$. The dependent
variable, $g_{1,3}=1$ if individual individuals 1 and 3 mutually nominate each
other as a friend. In addition, the observation $g_{3,1}$ is removed from the
sample, since the friendship relationship between 1 and 3 is already accounted
for in the observation for $i=1$ and $j=3$. We then consider the
(dis)similarity in observable and imperceptible characteristics between $i$
and $j$ as the determinants of their friendship formation.

###  2.3 Non-network variables

The third feature of the data worth mentioning is the richness of the
available information on the subjects. Apart from the network elicitation,
subjects participated in a series of questionnaires, surveys, and incentivized
economic experiments designed to collect data on their heterogeneity over
their whole freshmen year. In this study, we consider 20 characteristics that
might affect the formation of students’ friendships. We broadly classify these
characteristics as observable (O) and unobservable or imperceptible
characteristics (U) and contrast their importance in explaining friendship
formation. Observable characteristics are attributes that can be easily
observed without any deep interaction, whereas we classified as unobservable
or imperceptible those attributes that would require more intimate disclosure
or a deeper conversation to be detected. To assess the (dis)similarity of two
individuals, we either employ the absolute difference between their values for
the characteristic in question or an indicator dummy if they share a
characteristic. Table 2 lists all the characteristics and indicates whether
homophily is assessed in our regressions using an absolute value
(Transformation = A) or an indicator dummy (Transformation = D). In what
follows, we present all the variables in Table 2 one by one:

  * •

Observable characteristics:

    1. 1.

Common gender. Large literature has documented that age, gender, religion,
race, and ethnicity are key determinants of friendship (Patacchini and Zenou,
2016; McPherson et al., 2001; Currarini et al., 2009; Kossinets and Watts,
2009; Currarini et al., 2010). Since our sample is homogeneous in terms of
age, religion, race, and ethnicity, we only study common gender among these
classic observable factors.

    2. 2.

Common section. Geographical location and spatial proximity are crucial for
interaction (Preciado et al. (2012)). For instance, Glaeser et al. (2000) find
that students in university dorms are more likely to interact with their
roommates and dormmates even if they are assigned to dorms and rooms randomly,
Currarini et al. (2010) document that friendship formation is largely
influenced by meeting chances, and Preciado et al. (2012) show that the log-
odds of friendship existence decrease with the geographical distance. In our
setting, all the first-year students were randomly distributed into four
sections at the beginning of the freshman year. We thus expect homophily in
section assignments. We capture such “location” using a dummy variable common
section, which is equal to one if both $i$ and $j$ belong to the same section.

    3. 3.

Body mass index (BMI). Christakis and Fowler (2007) document homophily in BMI
as a driver of the epidemic obesity in the U.S. De la Haye et al. (2010) show
that male friends tended to be similar in their consumption of high-calorie
foods. We thus include the absolute difference in BMI of $i$ and $j$ as a
potential determinant of them becoming friends.

    4. 4.

Smoking. Individuals who smoke have been documented to cluster together
(Christakis and Fowler, 2008; Hsieh and Van Kippersluis, 2018). We therefore
consider a smoking dummy equal to one if both $i$ and $j$ self-report being
smokers.

    5. 5.

Pre-existing friendship. Finally, our regressions control for whether $i$ and
$j$ had been reported each othe as a friend at the first week of their
freshmen year, using a variable Friends Period 1 that indicates whether $i$
and $j$ named each other in Period 1.

  * •

Unobservable characteristics:

    1. 1.

Socio-economic status. Education, occupation, and social class are classic
dimensions on which people sort in social networks (McPherson et al., 2001).
Since our subjects are all students, we include two measures of family
background. First, as in Conti et al. (2013), we consider parental education,
measured for individual $i$ as the average education between the mother and
the father and included for a pair $i$ and $j$ in the analysis as the absolute
difference in the average parental education between $i$ and $j$. Second, we
consider the absolute difference between the self-reported household income of
$i$ and $j$.

    2. 2.

Common interests. Students are more likely to become friends if they share
interests, as documented in (Marmaros and Sacerdote, 2002). Therefore, we
include two variables related to preferences regarding the field of study.
First, STEM best is a dummy equal to 1 if $i$ and $j$ have received the
highest grade in their final high-school exam in the scientific track (that
includes topics from science, technology, engineering, or mathematics (STEM)
subjects), rather than in humanities or social sciences. Second, STEM
preference is a dummy variable equal to 1 if both individuals report a STEM
subject as the most preferred, irrespective of their grades.

    3. 3.

Prosocial attitudes. There exists large evidence that prosocial attitudes
correlate with network positioning, including with who befriends whom (Girard
et al., 2015; Branas-Garza et al., 2010; Apicella et al., 2012; Kovářík et
al., 2012). We first use the behavior in the Dictator game (DG) elicited
together with the networks in Periods 1 and 2 to measure subjects’ altruism.
DG is a classic experimental protocol, in which a “Dictator" splits a fixed
amount of money between herself and another anonymous individual, the
Recipient. Dictators rarely keep all the money for themselves; on average, 20%
of the money is donated to the recipient, despite the anonymity of the
transfers. The donated quantity is usually interpreted as an instance of
altruistic behavior. As a measure of altruism, we employ the amount donated in
the DG in Period 2, which–we believe–reflects better the social dynamics in
the groups under study. Once again, the variable included in the regressions
is the absolute difference between the altruism exhibited by $i$ and $j$. In
addition, since the amount donated in the DG by an individual generally
differs across the two periods and, in general, decreased between the two time
periods, we define altruism learning as equal to one if the amount given in
Period 2 is lower than in Period 1 for both $i$ and $j$ (and zero otherwise).
This variable enables to test whether there can be homophily in learning. We
additionally measure reciprocity from the answer to the following survey
question: “I am willing to do a boring job to return previous help”. The
answers vary from 1 (minimum willingness to help) to 7 (maximum reciprocity)
and we construct the variable reciprocity between $i$ and $j$ by taking the
absolute difference between their answers to the survey question. Last,
volunteering was elicited from the answer to the question “Are you a member of
a voluntary organization (e.g., Red Cross, NGO, Political Party, Sports Club,
Church Choir, economic association,…)?”. We assess homophily in volunteering
using a dummy equal to 1 if both $i$ and $j$ answered yes to this question.

    4. 4.

Self-confidence. One’s self-confidence is an important determinant of her
socio-economic outcomes in a range of domains (Sharot, 2011). We measure self-
confidence from the answer to the question “When I face a problem I usually
trust that I will solve it”, the answer could take values from 1 (minimum
self-confidence) to 7 (maximum self-confidence). Homophily in self-confidence
is captured by the absolute difference between both individuals’ self-
confidence scores.

    5. 5.

Risk and time preferences. Common attitudes to risk and delays may affect who
befriends whom. Indeed, Kovářík and Van der Leij (2014) document a correlation
between the clustering coefficient and risk aversion in college friendship
networks and Girard et al. (2015) detects homophily on time but not risk
preferences. In our data, both risk preferences and time preferences were
elicited using multiple price lists (see Andersen et al. (2006) for a review).
As for risk, participants made 10 binary decisions between two lotteries with
different amounts and probabilities. This elicitation was incentivized. In
case of time preferences, they faced 11 binary decisions between a lower
immediate or earlier amount of money and a later but higher quantity.101010The
elicitation of time preferences was hypothetical. However a recent paper shows
that hypothetical and incentivized time preferences are the same (see Brañas-
Garza et al. (2020)). Following the literature, we use the number of times an
individual selects the less risky option and the number of decisions, in which
she chooses the immediate or earlier amount, as the measures of risk aversion
and impatience, respectively. In both cases, homophily in preferences is
reflected in the absolute difference between both individuals’ risk and time
scores.

    6. 6.

Cognitive characteristics. Students in the same class frequently engage in
group activities and sorting on intelligence is probably the earliest evidence
of homophily in the literature Almack (1922). More recently, Conti et al.
(2013) suggest that IQ and other cognitive variables might condition the
formation of social networks or groups in certain contexts, Kretschmer et al.
(2018) show that students tend to befriend peers with similar academic
achievement. We employ two measures of cognitive abilities in our analysis.
First, we generate a variable reflective taking value of 1 if two individuals
scored a positive amount in the Cognitive Reflection Test by Frederick (2005)
– see Brañas-Garza et al. (2019) for a meta-analysis. Second, we include the
absolute difference in CRT between $i$ and $j$, labeled as CRT. Both variables
reflect whether two individuals have a similar cognitive style, but CRT
captures it more precisely.

Finally, Chapman et al. (2018) estimate that choice consistency in tasks
similar to our risk and time preference elicitation procedure is positively
correlated with cognitive abilities, education, and income. Therefore, we
generate a variable inconsistency and set it equal to 2 if an individual
exhibits inconsistent preferences in both risk and time preferences (i.e.,
switches between the risk averse/patient to risk loving/impatient options more
than once; see Andersen et al. (2006) or Amador-Hidalgo et al. (2021) for a
recent review), equal to 1 if she exhibit inconsistent preferences either in
the risk or time elicitation, and 0 if she answer the task consistently.
Again, we compute homophily in inconsistency as the absolute difference
between both individuals’ inconsistency scores.

    7. 7.

Political attitudes. Common political orientation has shown to be correlated
with friendship formation McPherson et al. (2001); Marmaros and Sacerdote
(2006); Mayer and Puller (2008). We elicit political orientation of the
individual from the answer to the question “Do you think the size of the
public sector in Spain is too large?” and define a dummy variable political
orientation equal to one if both individuals state a positive answer. It is a
indirect measure of political orientation.

Table 2: Potential determinants of Friendship

Variable | Transformation | Description
---|---|---
Observable |  |
Gender | D | 1 = Both individuals are of the same gender.
Smoking | D | 1 = Both individuals are smokers.
Common section | D | 1 = Both individuals in the same section.
BMI | A |  Absolute difference between the BMI of $i$ and $j$.
Friends Period 1 | D |  1= If $i$ and $j$ were friends in Period 1.
Unobservable |  |
Parental education | A |  Absolute difference between the average parental education of $i$ and $j$.
STEM best | D | 1 = Both individuals obtained their highest mark in a STEM subject.
STEM preference | D | 1 = Both individuals selected a STEM subject as their most preferred
|  | subject.
Reflective | D | 1 = Both individuals scored more than 0 in the CRT.
CRT | A |  Absolute difference in cognitive reflection test scores between $i$ and $j$.
Household Income | A |  Absolute difference between the household income of $i$ and $j$.
Altruism learning | D | 1= Both individuals give less in the dictator game of period 2 than
|  | in period 1.
Altruism | A | Absolute difference between individuals’ amount given in the dictator
|  | game of period 2.
Reciprocity | A | Absolute difference between individuals’ willingness to return help,
|  | previously given.
Kindness | D | 1= Both individuals were members of a voluntary organization.
Self-confidence | A | Absolute difference between both individuals’ self-confidence score.
Risk preferences | A | Absolute difference between both individuals’ risk score.
Time preferences | A | Absolute difference between both individuals’ patience score.
Inconsistency | A | Absolute difference between both individuals’ inconsistency score.
Political orientation | D | 1= Both individuals have a ‘right-wing’ political orientation.

Transformation=D if a variable is a dummy equal to 1 if $i$ and $j$ share the
same characteristic; Transformation=A if the variable is ordinal and the
absolute difference between the characteristics of $i$ and $j$ employed.

Table 3 summarizes all the individual characteristics in our sample. We
observe that 44% of the participants are female, 22% are smokers, 44% belief
that the public sector is too large (suggesting relatively more right-wing
political orientation), and 30% state a science-oriented (STEM) fields as the
most preferred. We also note that the average CRT and altruism are relatively
low, 0.55 and 1.07, respectively. On the other hand, the average self-
confidence index is high, 5.7.

Table 3: Summary statistics Variable | N | Mean | Std. Dev. | Min. | Max.
---|---|---|---|---|---
Observable |  |  |  |  |
Female | 244 | 0.44 | 0.50 | 0 | 1
Smoking | 186 | 0.22 | 0.42 | 0 | 1
BMI | 186 | 22.53 | 3.23 | 15.60 | 41.87
Friends Period 1 | 204 | 2.7 | 2.1 | 0 | 11
Friends Period 2 | 246 | 7.3 | 4.5 | 0 | 18
Unobservable |  |  |  |  |
Parental education | 186 | 2.73 | 1.53 | 0 | 5
STEM best | 217 | 0.28 | 0.45 | 0 | 1
STEM preference | 217 | 0.30 | 0.46 | 0 | 1
Reflective | 274 | 0.54 | 0.50 | 0 | 1
CRT | 217 | 0.55 | 0.73 | 0 | 3
Household Income | 185 | 2.39 | 1.21 | 0 | 5
Altruism learning | 274 | 0.38 | 0.49 | 0 | 1
Altruism | 168 | 1.07 | 1.06 | 0 | 5
Reciprocity | 186 | 3.57 | 1.81 | 1 | 7
Volunteering | 186 | 0.17 | 0.38 | 0 | 1
Self-confidence | 186 | 5.74 | 1.23 | 1 | 7
Risk preferences | 195 | 4.94 | 1.43 | 0 | 10
Time preferences | 168 | 5.60 | 2.54 | 0 | 11
Inconsistency | 202 | 0.15 | 0.36 | 0 | 1
Political orientation (right) | 186 | 0.44 | 0.50 | 0 | 1

###  2.4 Friendship model

Our aim is to detect the main determinants of frienship formation and estimate
their importance in the friendship formation process. The specification of our
friendship model relies on homophily theories, positing that individuals
prefer to befriend with individuals who are similar to them. As a result, we
expect that two individuals are more likely to be friends if they share
personal characteristics. However, there is no agreement in the literature
about the importance of the different characteristics in explaining link
formation nor whether observable characteristics, such as gender or race,
should matter more than features invisible to the naked eye, such as cognitive
or personality traits. As a result, a priori, we have no specific empirical
model and little guidance as to which factors are likely to be influential in
the friendship formation process. We deal with this problem, known as model
uncertainty in the literature, using a Bayesian Model Averaging (BMA) approach
Hoeting et al. (1999). In this section, we present the friendship formation
model and the BMA methodology.

Our friendship model starts with a basic pairwise probability model that
relates the probability that individuals $i$ and $j$ are friends in Period 2,
may 2011, with their similarity in the characteristics presented and explained
in Section 2.3, $X_{ij}$, conditioning on the probability of being friends in
Period 1. Such specification follows standard approaches of modelling network
formation in the literature (see e.g. the friendship formation in Marmaros and
Sacerdote (2006); Mayer and Puller (2008) or the co-authorship model of
Fafchamps et al. (2010)). Formally,

$P(g_{ij,2}=1/X_{ij})=\beta_{0}+\beta_{1}|X_{i}-X_{j}|+\beta_{2}D_{ij}+\beta_{3}g_{ij,1}+u_{ij},$
(1)

where $|X_{i}-X_{j}|$ is the vector of absolute differences between the non-
binary measures of individuals $i$ and $j$, while $D_{ij}$ is a vector
containing all dummy variables that capture common dichotomous characteristics
as specified in Table 2. The variable $g_{ij,t}=1(0)$ if $i$ and $j$ were
(not) friends in Period $t\in\\{1,2\\}$ and $u_{ij}$ is the disturbance term.
Below, we also estimate this model for females and males separately to analyse
whether the friendship determinants differ across genders.

###  2.5 Methodology

We consider two different approaches to identify the underlying factors
explaining link formation in the network: BMA and, mostly for robustness,
Weighted average least squares (WALS; see Section 4).

Our benchmark estimation method is the BMA reported in Section 3. BMA is
specifically designed to address model uncertainty by estimating model (1) for
all possible combinations of the regressors and taking a weighted average over
all the candidate models, where the weights are determined by applying Bayes’
rule. In simple terms, BMA only selects the determinants of link formation
that are not too sensitive to the inclusion or removal of other factors into
the model specification. Therefore, it explicitly accounts for the omitted-
variable and multicollinearity issues discussed in Section 1. The probability
that model $j$, $M_{j}$, is the "true" model given the data, $y$ (i.e., the
posterior model distribution given a prior model probability) is defined as

$P(M_{j}|y)=\frac{P(y|M_{j})P(M_{j})}{\Sigma_{i=1}^{2^{k}}P(y|M_{i})P(M_{i})},$
(2)

where $P(y|M_{j})$ is the marginal likelihood of Model $j$, $P(M_{i})$ is the
prior model probability, and $\Sigma_{i=1}^{2k}P(y|M_{i})P(M_{i})$ is the
integrated likelihood of model $j$. We employ the priors specified in Magnus
et al. (2010). In particular, they consider uniform priors on the model space,
so each model has the same probability of being the true one. Moreover, they
use a Zellner’s g-prior structure for the regression coefficients and set the
hyperparameter $g=\frac{1}{max(N,K^{2})}$ as in Fernandez et al. (2001), where
$K$ is the number of regressors and $N$ the number of observations. This
hyperparameter measures the degree of prior uncertainty over the coefficients.
For robustness, we also consider ’random theta’, ’fixed’ and ’uniform’ priors
for the model space.

In the next section, we present the estimates of the posterior inclusion
probability (PIP) of an explanatory factor, which can be interpreted as the
probability that a particular regressor belongs to the true model of
friendship. We also present results for the posterior mean, the coefficients
averaged over all models, and the posterior standard deviation, which
describes the uncertainty in the parameters and the model. In the robustness
section, we will present results of the WALS (Section 4), a recent model
average approach, which takes an intermediate position between frequentist and
Bayesian methods.

##  3 Results

Table 4 reports our main estimation results, obtained using the BMA approach
described in Section 2.5 over the 168 students who participated in all the
surveys and economic games troughout the whole academic year. The table lists
all the determinants of friendship formation under scrutiny ranked by their
estimated inclusion probability ($PIP$). The first column lists the different
dimensions of homophily and the second column presents the $PIP$ of each
potential determinant of friendship formation in May 2011. As a rule of thumb,
a factor is considered a very robust predictor of friendship if $PIP\geq
0.80$.111111This is a relatively conservative threshold as compared to the
literature, but note from Tables 4 \- 8 that all our conclusions hold for any
threshold $PIP\geq 0.3$.

We find that the most robust determinants for the full sample are the
variables capturing common gender, common smoking habits, belonging to the
same section, and being already friends before entering into the college. The
only observable dimension under study that does not predict friendship
robustly is BMI.

Moreover, all the robust determinants affect friendship with the expected sign
(see the posterior mean in the third column of Table 4). More precisely,
people are 1.7 percentage points more likely to befriend each other if they
have the same gender. Smoking is even a stronger driver of friendship than
gender: if two individuals smoke, they have a 3.4 percentage points higher
probability of forming a tie in our network. This is consistent with
Christakis and Fowler (2008), Hsieh and Van Kippersluis (2018) and Lorant and
Tranmer (2019) who report evidence of strong peer effects in the uptake of
smoking. Last, although people were assigned into the study sections randomly,
being assigned to the same section plays a important role in link formation of
students’ networks, increasing the probability of being friends by 6.4%. This
corroborates the existing evidence regarding the key role of meeting
opportunities in network formation. Unsurprisingly, being friend in October
2010 is the strongest predictor of friendship in May 2011.

Table 4: Determinants of link formation in students’ network

| PI prob. | Pt. Mean | Pt. Std.
---|---|---|---
Common Gender | 1 | 0.017 | 0.003
Common Section | 1 | 0.064 | 0.003
Friendst-1 | 1 | 0.435 | 0.023
Both Smokers | 0.97 | 0.034 | 0.010
Inconsistent diff. | 0.22 | -0.022 | 0.005
Altruism diff. | 0.08 | -0.003 | 0.001
CRT diff. | 0.04 | -0.0001 | 0.0008
Both Reflective | 0.03 | 0.0002 | 0.011
Time pref. diff. | 0.02 | -0.0000 | 0.0001
Income diff. | 0.02 | -0.0000 | 0.0003
Risk diff. | 0.01 | 0.0000 | 0.0001
Reciprocity diff. | 0.01 | 0.0000 | 0.0002
Self-confidence diff. | 0.01 | -0.0000 | 0.0002
BMI diff. | 0.01 | -0.0000 | 0.0001
Parent educ. diff. | 0.01 | -0.0000 | 0.0001
Both volunteers | 0.01 | -0.0000 | 0.0012
Both STEM best grade | 0.01 | 0.0000 | 0.0006
Both STEM pref. | 0.01 | 0.0000 | 0.0006
Both altruism learner | 0.01 | -0.0000 | 0.0003
Both right | 0.01 | 0.0000 | 0.0004
Observations | 8515 | 8515 | 8515

Notes: Column 1 presents the posterior inclusion probability ($PIP$). Robust
determinants are those with $PIP\geq 0.8$ in bold. Column 2 shows the
posterior mean. Column 3 reports the posterior standard deviation. The
dependent variable is equal to 1 if $i$ and $j$ are friends in Period 2, 0
otherwise. The results are obtained by using a uniform prior for the prior
model probability and a BRIC prior for the hyperparameter that measures the
degree of prior uncertainty on coefficients, $g=1/max(N,K^{2})$.

In contrast to the observable dimensions, none of the imperceptible
characteristics matter for friendship formation in our data. Inconsistent risk
and time preferences are the best predictor with $PIP=0.22$, relatively low
inclusion probability that cannot rival with the $PIP$’s estimated for the
observable features. The remaining unobservable characteristics exhibit an
estimated $PIP<0.1$.

Hence, the first conclusions of our analysis is that, if we focus on the whole
sample under study, only observable dimensions matter for friendships, while
none of the unobservable factors play an robust role in the friendship
formation process in our data.

To understand whether the friendship formation processes differ across
genders, we reestimate the friendship model separately for the male and female
participants. The results are presented in Tables 7 and 8 in the appendix,
respectively. In line with the pooled estimates, common gender, smoking
habits, and belonging to a common section are important drivers of friendship
for women; these factors have the associated $PIP=1$.

In a stark contrast, the only robust predictors determining friendship
formation in men is belonging to the same study section that increases the
probability of forming a link by 6.8% with $PIP=1$.

The gender differences notwithstanding, the gender-specific estimates
corroborate that observable characteristics are important drivers of
friendship formation while imperceptible features play a minor role.

##  4 Robustness

In this section, we check the robustness of the results to (i) the employment
of different priors in the BMA model, (ii) applying a different estimation
method designed to identify the most robust drivers of friendship formation,
and (iii) removing the students who have already had friends in Period 1
(October 2010). The first two tests check whether our results are not a
consequence of our estimation procedure, while the third case allows to see
whether our results are not driven by preexisting social ties in the group.

As for (i), we present results for an analysis using two alternative priors
for the model probability: the “random theta” prior proposed by Ley and Steel
(2009) who advocate for a binomial-beta hyperprior on the a priori inclusion
probability; and fixed common prior inclusion probabilities for each regressor
as in Sala-i Martin et al. (2004b). Figure 1 shows that our main findings are
largely robust to the specification of the model priors: the most important
drivers of link formation in our data are the same regardless of the prior
specification.

Figure 1: Determinants of link formation in students’ network: PIP using
different model priors

---

Note: The random prior corresponds to the ’random theta’ prior by Ley and
Steel (2009), who suggest a binomial-beta hyperprior on the a priori inclusion
probability. The fixed is the fixed common prior inclusion probabilities for
each regressor as in Sala-i Martin et al. (2004b). Unif corresponds to the
uniform model prior. The sample includes 8,515 observations.

Second, we test whether the findings hold while using alternative methods
dealing with model uncertainty. To that end, we apply the WALS method
introduced by Magnus et al. (2010). The rule of thumb with this method is that
an explanatory factor is considered robust if the absolute value of the
$t$-statistic is higher than 2. The results for the full sample, presented in
Table 5, show that the most robust drivers are the same as in Table 4.
Nonetheless, this alternative method suggest an additional determinant of
friendship formation: altruism with a $t$-statistic of -2.79. The weighted
average coefficient of the absolute difference of the amount donated in the DG
between both individuals is 0.004, implying that homophily on altruism is
associated with an increase of the probability that two individuals befriend
each other by 0.4 percentage points. This does not affect our conclusions that
observable features are considerably more relevant than imperceptible
characteristics, but it suggests that some of the latter should still be
considered and future work should determine which observable features robustly
predict tie formation across contexts and cultures (see the next section for a
discussion of this and other issues).

Table 5: Determinants of link formation in students’ network: A Weighted
Average Least Squares approach (WALS). Full sample.

| Coef. | Std. | t-stat.
---|---|---|---
Common Section | 0.059 | 0.003 | 20.20
Friendst-1 | 0.420 | 0.021 | 19.81
Common Gender | 0.016 | 0.003 | 6.04
Both Smokers | 0.031 | 0.008 | 3.89
Altruism diff. | -0.004 | 0.001 | -2.79
CRT diff. | -0.003 | 0.002 | -1.81
Inconsistent diff. | -0.007 | 0.004 | -1.75
Both Reflective | 0.005 | 0.003 | 1.47
Parent educ. diff. | -0.001 | 0.0010 | -1.18
Reciprocity diff. | 0.0008 | 0.0008 | 1.01
Time pref. diff. | -0.0005 | 0.0006 | -0.81
Both altruism learner | -0.0018 | 0.0026 | -0.71
Both right | 0.002 | 0.0033 | 0.59
Risk diff. | 0.0005 | 0.0009 | 0.57
Income diff. | -0.0006 | 0.0013 | -0.43
Both volunteers | -0.0034 | 0.0087 | 0.39
BMI diff. | 0.0002 | 0.0005 | 0.32
Both STEM pref. | 0.0007 | 0.0044 | 0.16
Self-confidence diff. | -0.0001 | 0.0012 | -0.05
Both STEM best grade | -0.0001 | 0.0051 | -0.03
Observations | 8515 | 8515 | 8515

Notes: The results are obtained by using the Weighted Average Least Squares
approach introduced by Magnus et al. (2010). Determinants with a $t>2$ are
considered robust.

Finally, to focus on the pure formation process (free of any pre-college
influences), we reestimate our benchmark model excluding all the students who
have already had at least one friend in the first week of their first academic
year (Period 1). This decreases the number of potential pairs to 8483
observations, but the results presented in Table 6 are both quantitatively and
qualitatively similar to those obtained using the full sample.

Table 6: Determinants of link formation in students’ network: Excluding
students with friends in period 1.

| PI prob. | Pt. Mean | Pt. Std.
---|---|---|---
Common Gender | 1 | 0.015 | 0.003
Common Section | 1 | 0.064 | 0.003
Both Smokers | 0.87 | 0.026 | 0.013
Inconsistent diff. | 0.07 | -0.0006 | 0.0023
Altruism diff. | 0.06 | -0.0002 | 0.0007
CRT diff. | 0.05 | -0.0002 | 0.0008
Time pref. diff. | 0.03 | -0.0000 | 0.0002
Both Reflective | 0.03 | 0.0001 | 0.0010
Both volunteers | 0.02 | -0.0001 | 0.0016
Income diff. | 0.02 | -0.0000 | 0.0002
Risk diff. | 0.01 | 0.0000 | 0.0001
Reciprocity diff. | 0.01 | 0.0000 | 0.0001
Self-confidence diff. | 0.01 | -0.0000 | 0.0002
BMI diff. | 0.01 | 0.0000 | 0.0001
Parent educ. diff. | 0.01 | -0.0000 | 0.0001
Both STEM best grade | 0.01 | 0.0000 | 0.0006
Both STEM pref. | 0.01 | 0.0000 | 0.0006
Both altruism learner | 0.01 | -0.0000 | 0.0003
Both right | 0.01 | 0.0000 | 0.0005
Observations | 8483 | 8483 | 8483

Notes: Column 1 presents the posterior inclusion probability ($PIP$). Robust
determinants are those with $PIP\geq 0.8$ in bold. Column 2 shows the
posterior mean. Column 3 reports the posterior standard deviation. The
dependent variable is equal to 1 if $i$ and $j$ are friends in Period 2, 0
otherwise. The results are obtained by using a uniform prior for the prior
model probability and a BRIC prior for the hyperparameter that measures the
degree of prior uncertainty on coefficients, $g=1/max(N,K^{2})$.

##  5 Discussion

In this study, we argue that the literature has proposed a large array of
dimensions of homophily without accounting for the model uncertainty problem
inherent in the identification of the determinants of friendship formation.
This research aims at initializing such a research line. Focusing on 20
particular individual characteristics that cover a large share of the
determinants of segmentation of heterogeneous populations analyzed so far, we
find that the robust determinants of friendship formation are gender, smoking
habits, and geographical/spatial proximity. Hence, our data suggest that, in
our context of an emerging social structure, all robust predictors of
friendships are directly visible by a naked eye. Due to the homogeneity of our
sample, we do not consider other observable attributes such as race,
ethnicity, and religion, but the literature shows that these characteristics
are key predictors of links in many contexts (Lazarsfeld et al., 1954; Ibarra,
1995; McPherson et al., 2001; Moody, 2001; Marmaros and Sacerdote, 2006;
Currarini et al., 2010). We thus positions them among the robust predictors of
friendships generally. In contrast, we find little evidence for unobservable
features to predict who befriends whom in an emerging social network among
University freshmen. Neither political orientation, family background, nor
cognitive and behavioral traits survive our robustness tests.

Our findings corroborate some existing findings and contradict others. First,
gender belongs among the most robust findings and we are no exception. Since
gender segregation might have contributed to e.g. the gender wage and output
gaps (Ductor et al., 2018; Lindenlaub and Prummer, 2019), we corroborate that
policies aiming at a large gender integration in social and professional
networks could reduce gender inequalities. As for smoking, we corroborate
Hsieh and Van Kippersluis (2018) and Christakis and Fowler (2008) that smoking
influences friendship formation. However, our results suggest that this factor
is more important for women. If corroborated in other studies, this finding
calls for gender-specific policies combating smoking. Last, we confirm that
friendship formation can be to a large extend malleable and shaped by policy
interventions as random distribution of people into groups have large
consequences on who befriends whom (see also Marmaros and Sacerdote (2006);
Girard et al. (2015)).

In contrast, the fact that the unobservable factors under scrutiny, like
personality, economic preferences, family background, political orientation
are not robust predictors of link formation in the students’ networks
contradict others studies (e.g. Almack (1922); Marmaros and Sacerdote (2006);
Christakis and Fowler (2007); Mayer and Puller (2008); Girard et al. (2015)).
We do not argue that none of them is correlated with friendship. Rather, we
argue that whether they can predict friendship depends on other covariates in
the link formation model, suggesting that the unobservable, imperceptible
attributes are not the primary reason for how people become friends.

Our results have implications for several strands of network literature.
First, it is well documented that friendship networks have far-reaching and
long-lasting socio-economic consequences in human life (see Burt (1997);
Christakis and Fowler (2007, 2008); Cohen et al. (2008); Conti et al. (2013);
Jackson et al. (2017) for a few examples of the large literature on the
topic). We contribute to this literature by emphasizing which individual
attributes robustly predict who befriends whom. Understanding the determinants
of friendship and segregation patterns is crucial to evaluate diffusion of
information, behaviors, and diseases in general populations and to design
optimal policies aimed at maximizing or minimizing the diffusion, targeting
integration of minorities, and combating gender and race inequalities.

Second, our results deliver an important message for the estimation of network
effects. One of the main empirical challenges for causal estimation of network
effects is to account for all factors that influence friendship and network
formation (Manski, 1993; Boucher and Fortin, 2016; Jackson et al., 2017).
Nevertheless, many individual characteristics are typically not observed by
the researchers or policy-makers and they are believed to influence both the
outcomes under study and the link formation. These concerns have motivated a
series of methodological contributions enabling the estimation of network
effects causally, each under different assumptions (examples include Bramoullé
et al. (2009); De Giorgi et al. (2010); Hsieh and Lee (2016)). It is commonly
assumed that people exhibit homophily in the unobserved attributes. Our
results suggest that such concerns might be less serious than expected and
that one can account for the endogeneity of the network structure by
controlling for observable personal attributes, at least in the context of
friendship networks. Future research should determine to what extent our
results replicate in other data and contexts.

Third, we may also indirectly inform the literature on the origins of
homophily by testing the relevance of different classes of attributes in
friendship formation. In particular, our results suggest that observable
characteristics might be the primary driving force behind homophilous
interactions, while unobservable, imperceptible features might be solely a by-
product of the many correlations between the observable and imperceptible
attributes. Naturally, this claim requires further analysis using different
data, contexts, and definitions of links before one can widely accept its
validity.

## References

  * Almack (1922) Almack, J. C. (1922).  The influence of intelligence on the selection of associates.  School and Society 16(410), 529–530.
  * Altonji and Blank (1999) Altonji, J. G. and R. M. Blank (1999).  Race and gender in the labor market.  Handbook of Labor Economics 3, 3143–3259.
  * Amador-Hidalgo et al. (2021) Amador-Hidalgo, L., P. Brañas-Garza, A. M. Espín, T. García-Muñoz, and A. Hernández-Román (2021).  Cognitive abilities and risk-taking: Errors, not preferences.  European Economic Review 134, 103694.
  * Andersen et al. (2006) Andersen, S., G. W. Harrison, M. I. Lau, and E. E. Rutström (2006).  Elicitation using multiple price list formats.  Experimental Economics 9(4), 383–405.
  * Apicella et al. (2012) Apicella, C. L., F. W. Marlowe, J. H. Fowler, and N. A. Christakis (2012).  Social networks and cooperation in hunter-gatherers.  Nature 481(7382), 497–501.
  * Barber and Odean (2001) Barber, B. M. and T. Odean (2001).  Boys will be boys: Gender, overconfidence, and common stock investment.  The Quarterly Journal of Economics 116(1), 261–292.
  * Boucher and Fortin (2016) Boucher, V. and B. Fortin (2016).  Some challenges in the empirics of the effects of networks.  Handbook on the Economics of Networks.
  * Bramoullé et al. (2012) Bramoullé, Y., S. Currarini, M. O. Jackson, P. Pin, and B. W. Rogers (2012).  Homophily and long-run integration in social networks.  Journal of Economic Theory 147(5), 1754–1786.
  * Bramoullé et al. (2009) Bramoullé, Y., H. Djebbari, and B. Fortin (2009).  Identification of peer effects through social networks.  Journal of Econometrics 150(1), 41–55.
  * Branas-Garza et al. (2010) Branas-Garza, P., R. Cobo-Reyes, M. P. Espinosa, N. Jiménez, J. Kovářík, and G. Ponti (2010).  Altruism and social integration.  Games and Economic Behavior 69(2), 249–257.
  * Branas-Garza et al. (2013) Branas-Garza, P., J. Kovářík, and L. Neyse (2013).  Second-to-fourth digit ratio has a non-monotonic impact on altruism.  PLoS ONE 8(4), e60419.
  * Brañas-Garza et al. (2020) Brañas-Garza, P., D. Jorrat, A. M. Espín, and A. Sánchez (2020).  Paid and hypothetical time preferences are the same: Lab, field and online evidence.  Technical report, arXiv:2010.09262.
  * Brañas-Garza et al. (2019) Brañas-Garza, P., P. Kujal, and B. Lenkei (2019).  Cognitive reflection test: Whom, how, when.  Journal of Behavioral and Experimental Economics 82, 101455\.
  * Burt (1997) Burt, R. S. (1997).  The contingent value of social capital.  Administrative Science Quarterly, 339–365.
  * Carrell et al. (2013) Carrell, S. E., B. I. Sacerdote, and J. E. West (2013).  From natural variation to optimal policy? the importance of endogenous peer group formation.  Econometrica 81(3), 855–882.
  * Centola (2011) Centola, D. (2011).  An experimental study of homophily in the adoption of health behavior.  Science 334(6060), 1269–1272.
  * Chapman et al. (2018) Chapman, J., E. Snowberg, S. Wang, and C. Camerer (2018).  Loss attitudes in the us population: Evidence from dynamically optimized sequential experimentation (dose).  Technical report, National Bureau of Economic Research.
  * Christakis and Fowler (2007) Christakis, N. A. and J. H. Fowler (2007).  The spread of obesity in a large social network over 32 years.  New England Journal of Medicine 357(4), 370–379.
  * Christakis and Fowler (2008) Christakis, N. A. and J. H. Fowler (2008).  The collective dynamics of smoking in a large social network.  New England Journal of Medicine 358(21), 2249–2258.
  * Cohen et al. (2008) Cohen, L., A. Frazzini, and C. Malloy (2008).  The small world of investing: Board connections and mutual fund returns.  Journal of Political Economy 116(5), 951–979.
  * Conti et al. (2013) Conti, G., A. Galeotti, G. Mueller, and S. Pudney (2013).  Popularity.  Journal of Human Resources 48(4), 1072–1094.
  * Croson and Gneezy (2009) Croson, R. and U. Gneezy (2009).  Gender differences in preferences.  Journal of Economic Literature 47(2), 448.
  * Currarini et al. (2009) Currarini, S., M. O. Jackson, and P. Pin (2009).  An economic model of friendship: Homophily, minorities, and segregation.  Econometrica 77(4), 1003–1045.
  * Currarini et al. (2010) Currarini, S., M. O. Jackson, and P. Pin (2010).  Identifying the roles of race-based choice and chance in high school friendship network formation.  Proceedings of the National Academy of Sciences 107(11), 4857–4861.
  * De Giorgi et al. (2010) De Giorgi, G., M. Pellizzari, and S. Redaelli (2010).  Identification of social interactions through partially overlapping peer groups.  American Economic Journal: Applied Economics 2(2), 241–75.
  * De la Haye et al. (2010) De la Haye, K., G. Robins, P. Mohr, and C. Wilson (2010).  Obesity-related behaviors in adolescent friendship networks.  Social Networks 32(3), 161–167.
  * Ductor et al. (2018) Ductor, L., S. Goyal, and A. Prummer (2018).  Gender & collaboration.  Technical report, Working Paper.
  * Fafchamps et al. (2010) Fafchamps, M., S. Goyal, and M. J. van der Leij (2010).  Matching and network effects.  Journal of the European Economic Association 8(1), 203–231.
  * Frederick (2005) Frederick, S. (2005).  Cognitive reflection and decision making.  Journal of Economic perspectives 19(4), 25–42.
  * Girard et al. (2015) Girard, Y., F. Hett, and D. Schunk (2015).  How individual characteristics shape the structure of social networks.  Journal of Economic Behavior & Organization 115, 197–216.
  * Glaeser et al. (2000) Glaeser, E. L., B. Sacerdote, et al. (2000).  The social consequences of housing.  Journal of Housing Economics 9(1-2), 1–23.
  * Granovetter (1973) Granovetter, M. (1973).  The Strength of Weak Ties.  American Journal of Sociology, 1360–1380.
  * Guterbock and London (1983) Guterbock, T. M. and B. London (1983).  Race, political orientation, and participation: An empirical test of four competing theories.  American Sociological Review, 439–453.
  * Hoeting et al. (1999) Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky (1999).  Bayesian model averaging: a tutorial.  Statistical Science, 382–401.
  * Hsieh and Lee (2016) Hsieh, C.-S. and L. F. Lee (2016).  A social interactions model with endogenous friendship formation and selectivity.  Journal of Applied Econometrics 31(2), 301–319.
  * Hsieh and Van Kippersluis (2018) Hsieh, C.-S. and H. Van Kippersluis (2018).  Smoking initiation: Peers and personality.  Quantitative Economics 9(2), 825–863.
  * Ibarra (1992) Ibarra, H. (1992).  Homophily and differential returns: Sex differences in network structure and access in an advertising firm.  Administrative Science Quarterly, 422–447.
  * Ibarra (1995) Ibarra, H. (1995).  Race, opportunity, and diversity of social circles in managerial networks.  Academy of Management 38(3), 673–703.
  * Jackson et al. (2017) Jackson, M. O., B. W. Rogers, and Y. Zenou (2017).  The economic consequences of social-network structure.  Journal of Economic Literature 55(1), 49–95.
  * Kossinets and Watts (2009) Kossinets, G. and D. J. Watts (2009).  Origins of homophily in an evolving social network.  American Journal of Sociology 115(2), 405–450.
  * Kovářík et al. (2012) Kovářík, J., P. Brañas-Garza, R. Cobo-Reyes, M. P. Espinosa, N. Jiménez, and G. Ponti (2012).  Prosocial norms and degree heterogeneity in social networks.  Physica A: Statistical mechanics and its Applications 391(3), 849–853.
  * Kovářík et al. (2017) Kovářík, J., P. Branas-Garza, M. W. Davidson, D. A. Haim, S. Carcelli, and J. H. Fowler (2017).  Digit ratio (2d: 4d) and social integration: an effect of prenatal sex hormones.  Network Science 5(4), 476–489.
  * Kovářík and Van der Leij (2014) Kovářík, J. and M. J. Van der Leij (2014).  Risk aversion and social networks.  Review of Network Economics 13(2), 121–155.
  * Kretschmer et al. (2018) Kretschmer, D., L. Leszczensky, and S. Pink (2018).  Selection and influence processes in academic achievement—more pronounced for girls?  Social Networks 52, 251–260.
  * Kruse et al. (2016) Kruse, H., S. Smith, F. van Tubergen, and I. Maas (2016).  From neighbors to school friends? how adolescents’ place of residence relates to same-ethnic school friendships.  Social Networks 44, 130–142.
  * Lazarsfeld et al. (1954) Lazarsfeld, P. F., R. K. Merton, et al. (1954).  Friendship as a social process: A substantive and methodological analysis.  Freedom and Control in Modern Society 18(1), 18–66.
  * Ley and Steel (2009) Ley, E. and M. F. Steel (2009).  On the effect of prior assumptions in bayesian model averaging with applications to growth regression.  Journal of Applied Econometrics, 651–674.
  * Lindenlaub and Prummer (2019) Lindenlaub, I. and A. Prummer (2019).  Network structure and performance.  The Economic Journal.
  * Lorant and Tranmer (2019) Lorant, V. and M. Tranmer (2019).  Peer, school, and country variations in adolescents’ health behaviour: A multilevel analysis of binary response variables in six european cities.  Social Networks 59, 31–40.
  * Magnus et al. (2010) Magnus, J. R., O. Powell, and P. Prüfer (2010).  A comparison of two model averaging techniques with an application to growth empirics.  Journal of Econometrics 154(2), 139–153.
  * Manski (1993) Manski, C. F. (1993).  Identification of endogenous social effects: The reflection problem.  The Review of Economic Studies 60(3), 531–542.
  * Marmaros and Sacerdote (2002) Marmaros, D. and B. Sacerdote (2002).  Peer and Social Networks in Job Search.  European Economic Review 46(4), 870–879.
  * Marmaros and Sacerdote (2006) Marmaros, D. and B. Sacerdote (2006).  How do friendships form?  The Quarterly Journal of Economics 121(1), 79–119.
  * Mayer and Puller (2008) Mayer, A. and S. L. Puller (2008).  The old boy (and girl) network: Social network formation on university campuses.  Journal of Public Economics 92(1-2), 329–347.
  * McPherson et al. (2001) McPherson, M., L. Smith-Lovin, and J. M. Cook (2001).  Birds of a feather: Homophily in social networks.  Annual Review of Sociology 27(1), 415–444.
  * Moody (2001) Moody, J. (2001).  Race, school integration, and friendship segregation in america.  American Journal of Sociology 107(3), 679–716.
  * Patacchini and Zenou (2016) Patacchini, E. and Y. Zenou (2016).  Racial identity and education in social networks.  Social Networks 44, 85–94.
  * Preciado et al. (2012) Preciado, P., T. A. Snijders, W. J. Burk, H. Stattin, and M. Kerr (2012).  Does proximity matter? distance dependence of adolescent friendships.  Social networks 34(1), 18–31.
  * Ruef et al. (2003) Ruef, M., H. E. Aldrich, and N. M. Carter (2003).  The structure of founding teams: Homophily, strong ties, and isolation among us entrepreneurs.  American Sociological Review, 195–222.
  * Sala-i Martin et al. (2004a) Sala-i Martin, X., G. Doppelhofer, and R. I. Miller (2004a).  Determinants of long-term growth: A bayesian averaging of classical estimates (bace) approach.  The American Economic Review, 813–835.
  * Sala-i Martin et al. (2004b) Sala-i Martin, X., G. Doppelhofer, and R. I. Miller (2004b).  Determinants of long-term growth: A bayesian averaging of classical estimates (bace) approach.  The American Economic Review, 813–835.
  * Sharot (2011) Sharot, T. (2011).  The optimism bias.  Current Biology 21(23), R941–R945.
  * Simmons et al. (2011) Simmons, J. P., L. D. Nelson, and U. Simonsohn (2011).  False-positive psychology: Undisclosed flexibility in data collection and analysis allows presenting anything as significant.  Psychological Science 22(11), 1359–1366.
  * Valente et al. (2009) Valente, T. W., K. Fujimoto, C.-P. Chou, and D. Spruijt-Metz (2009).  Adolescent affiliations and adiposity: a social network analysis of friendships and obesity.  Journal of Adolescent Health 45(2), 202–204.
  * Wittek et al. (2020) Wittek, M., C. Kroneberg, and K. Lämmermann (2020).  Who is fighting with whom? how ethnic origin shapes friendship, dislike, and physical violence relations in german secondary schools.  Social Networks 60, 34–47.
  * Zeltzer (2020) Zeltzer, D. (2020).  Gender homophily in referral networks: Consequences for the medicare physician earnings gap.  American Economic Journal: Applied Economics, forthcoming.

## Appendix

Table 7: Determinants of link formation in students’ network: female sample

| PI prob. | Pt. Mean | Pt. Std.
---|---|---|---
Common Gender | 1 | 0.025 | 0.004
Common Section | 1 | 0.061 | 0.005
Friendst-1 | 1 | 0.395 | 0.036
Both Smokers | 0.99 | 0.049 | 0.012
Altruism diff. | 0.22 | -0.001 | 0.003
Inconsistent diff. | 0.22 | -0.003 | 0.006
Parent educ. diff. | 0.09 | -0.0003 | 0.0011
CRT diff. | 0.07 | -0.0004 | 0.0016
Both Reflective | 0.09 | 0.0011 | 0.0037
Time pref. diff. | 0.03 | -0.0000 | 0.0003
Reciprocity diff. | 0.05 | 0.0000 | 0.0005
Both altruism learner | 0.04 | -0.0002 | 0.0013
Both STEM best grade | 0.03 | 0.0002 | 0.0017
Risk diff. | 0.02 | -0.0000 | 0.0002
Income diff. | 0.02 | -0.0000 | 0.0003
Self-confidence diff. | 0.02 | 0.0000 | 0.0003
BMI diff. | 0.02 | 0.0000 | 0.0001
Both volunteers | 0.02 | 0.0000 | 0.0021
Both STEM pref. | 0.02 | 0.0000 | 0.0010
Both right | 0.02 | -0.0000 | 0.0009
Observations | 4092 | 4092 | 4092

Notes: Column 1 presents the posterior inclusion probability ($PIP$). Robust
determinants are those with $PIP\geq 0.8$ in bold. Column 2 shows the
posterior mean. Column 3 reports the posterior standard deviation. The
dependent variable is equal to 1 if $i$ and $j$ are friends in Period 2, 0
otherwise. The results are obtained by using a uniform prior for the prior
model probability and a BRIC prior for the hyperparameter that measures the
degree of prior uncertainty on coefficients, $g=1/max(N,K^{2})$.

Table 8: Determinants of link formation in students’ network: Male sample

| PI prob. | Pt. Mean | Pt. Std.
---|---|---|---
Common Section | 1 | 0.068 | 0.005
Friendst-1 | 1 | 0.457 | 0.030
Both right | 0.08 | 0.0008 | 0.003
Common Gender | 0.07 | 0.005 | 0.002
Both altruism learner | 0.05 | 0.0003 | 0.0017
Parent educ. diff. | 0.05 | 0.0001 | 0.0006
Self-confidence diff. | 0.04 | -0.0001 | 0.0006
BMI diff. | 0.04 | -0.0000 | 0.0003
Reciprocity diff. | 0.02 | -0.0000 | 0.0004
CRT diff. | 0.02 | -0.0000 | 0.0004
Risk diff. | 0.02 | 0.0000 | 0.0002
Both Smokers | 0.02 | 0.0002 | 0.0025
Altruism diff. | 0.02 | -0.0000 | 0.0003
Time pref. diff. | 0.02 | -0.0000 | 0.0001
Income diff. | 0.02 | -0.0000 | 0.0003
Both volunteers | 0.02 | -0.0001 | 0.0017
Inconsistent diff. | 0.02 | 0.0000 | 0.0008
Both Reflective | 0.02 | 0.0000 | 0.0009
Both STEM best grade | 0.02 | -0.0001 | 0.0014
Both STEM pref. | 0.02 | -0.0000 | 0.0008
Observations | 4423 | 4423 | 4423

Notes: Column 1 presents the posterior inclusion probability ($PIP$). Robust
determinants are those with $PIP\geq 0.8$ in bold. Column 2 shows the
posterior mean. Column 3 reports the posterior standard deviation. The
dependent variable is equal to 1 if $i$ and $j$ are friends in Period 2, 0
otherwise. The results are obtained by using a uniform prior for the prior
model probability and a BRIC prior for the hyperparameter that measures the
degree of prior uncertainty on coefficients, $g=1/max(N,K^{2})$.