Proximity Similarity and Friendship Formation Theory and Evidence A. Arda GitmezrRom an Andr es Z arate

2025-04-26 0 0 820.36KB 26 页 10玖币
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Proximity, Similarity, and Friendship Formation:
Theory and Evidence∗
A. Arda Gitmez†r
○Rom´an Andr´es Z´arate‡
October 14, 2022
Abstract
Can proximity make friendships more diverse? To address this question, we
propose a learning-driven friendship formation model to study how proximity
and similarity influence the likelihood of forming social connections. The model
predicts that proximity affects more friendships between dissimilar than similar
individuals, in opposition to a preference-driven version of the model. We use
an experiment at selective boarding schools in Peru that generates random vari-
ation in the physical proximity between students to test these predictions. The
empirical evidence is consistent with the learning model: while social networks
exhibit homophily by academic achievement and poverty, proximity generates
more diverse social connections.
∗The “ r
○” symbol indicates that the authors’ names are in certified random order, as described by
Ray r
○Robson (2018). We are grateful to Nicol´as Fajardo and Linda Maokomatanda for their superb
research assistance. We also thank Nicol´as de Roux, Robert McMillan, Clementine Van Effenterre,
Tatiana Velasco, David Zarruk, and participants at NEUDC and Toronto JAMS for valuable com-
ments and suggestions. Funding for this project was generously provided by the Weiss Family Fund
and the NAEd/Spencer dissertation fellowship. The experiment was approved by the MIT IRB (ID
1702862092), and is registered at the AEA RCT Registry (ID 0002600).
†Department of Economics, Bilkent University. E-mail: arda.gitmez@bilkent.edu.tr.
‡Department of Economics, University of Toronto. E-mail: ra.zarate@utoronto.ca.
arXiv:2210.06611v1 [econ.GN] 12 Oct 2022
1 Introduction
The social connections that students form when they are young are known to affect
them later in life (Chetty et al.,2022a;Zimmerman,2019). This fact motivates one
popular approach to improving social mobility in the form of school integration policies.
School integration policies aim to help underprivileged students succeed by exposing
them to peers from different backgrounds, thereby allowing them to make more diverse
connections. Yet, as Chetty et al. (2022b) suggest, increasing exposure at the school
level does not necessarily result in more diverse friendships. This is due to friending
bias: even when exposed to a diverse set of peers, students tend to form social ties with
peers of the same race, income, or academic level (Chetty et al.,2022b;Currarini et al.,
2010;Carrell et al.,2013). The operation of this bias casts doubt on whether school
integration policies can counter the segregating tendency in friendship networks, and
actually succeed in bringing about more diverse friendships for underprivileged students.
For instance, Mele (2020) shows that race-based reallocation of students across schools
does not necessarily decrease segregation by race in friendship networks.
As an alternative policy instrument, within-school policies offer a mean to tackle
friending bias and foster diverse interactions. They do so by changing students’ within-
school exposure to specific peers through their allocation of classrooms, desks, and
dormitories. Ultimately, within-school policies manipulate students’ physical proximity,
which is a central factor in forming friendships (Marmaros and Sacerdote,2006). The
overall effect of such policies depends on the underlying structure of the friending bias. If
the friending bias is strong enough, proximity will not overcome homophily. Conversely,
when proximity fosters friendships, within-school policies can improve the diversity of
friendships by placing dissimilar students close to each other.
Such a policy has a hidden cost, however. As there are only a finite number of phys-
ically close locations, when school authorities place two dissimilar students together,
they implicitly forgo putting two similar students together. If the effect of proximity on
friendships for dissimilar pairs is positive but smaller than the effect for similar pairs, a
within-school policy leads to a lower number of friendships (an efficiency loss). Under-
standing the link between friending bias and proximity is critical for designing policies
that reduce segregation in friendship networks while not sacrificing the total number of
friendships.
In this paper, we propose a model of friendship formation to explore the role of
proximity and similarity in the diversity of friendships. We also provide an empirical test
based on an experiment that randomly varies proximity between students at selective
boarding schools in Peru.
Our model is an application of the theory of exponential bandits (Keller et al.,2005).
In the model, a student decides whether to maintain interactions with a peer, where
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the value of maintaining the interaction is initially uncertain and is revealed over time.
The optimal strategy prescribes an exploration phase, where a student engages with a
peer to “test the waters”. If she receives a signal that the interaction is valuable within
the exploration phase, she maintains the interactions; otherwise, she stops engaging
with that peer. The crucial assumption of the model is that when a student engages
with a peer from a similar background, learning about the interaction’s value occurs
faster. Then, students end up being friends with similar peers more often than with
dissimilar peers. That is, friendship patterns exhibit homophily, which is a common
empirical feature of social networks.
The model also explores the role of physical proximity. When a student engages
with a peer in physical proximity, the cost of maintaining interactions is lower. A lower
cost allows the student to explore the value of maintaining interactions longer, which
translates into a higher friendship rate with proximate peers than with remote peers.
That is, proximity fosters friendships.
The model’s distinguishing prediction is that the effect of physical proximity is
stronger for dissimilar peers: proximity fosters diversity. Intuitively, this is because
proximity and similarity are substitutes in this model. When two peers have similar
characteristics, the value of interaction is already explored even when the cost is high.
In this case, a lower cost due to proximity has little impact on the outcome. By
contrast, when two peers are dissimilar, the reduction in the interaction cost extends
the exploration phase, allowing individuals to form new and more diverse friendships.
The distinguishing prediction contrasts with an alternative version of the model we
explore, where preferences are the main driver of homophily. In the alternative model,
individuals derive a higher payoff from interacting with similar peers in expectation. In
that case, the effect of proximity on friendships is higher for similar pairs, which is the
opposite of our distinguishing prediction.
We verify the theoretical predictions with an experiment at selective boarding
schools in Peru. The details of the experiment are in Z´arate (2021) that studies how
more central and higher-achieving peers affect social and academic outcomes. Here, we
exploit the fact that the peer assignment generates random variation in the physical
proximity between a pair of students in the allocation to dormitories. Our empirical
strategy leverages this variation to explore the effects of proximity on social interactions.
Our empirical analysis starts by exploring homophily in three dimensions: poverty
status, baseline academic achievement, and baseline centrality level.1Our findings show
that social networks exhibit homophily along these three characteristics. On average,
poor students have 0.66 fewer non-poor friends (p-value <0.01) than non-poor students.
1We use eigenvector centrality that measures a student’s influence within their social network. High
values of this measure indicate that a student is connected to other individuals with high values of
eigenvector centrality.
2
Likewise, compared to higher-achieving students, lower-achieving students have, on
average, 1.05 more interactions with other lower-achieving students and 1.26 fewer
interactions with higher-achieving students. The results by other social skills variables
(measured by centrality at baseline) also exhibit homophily. Compared to high central
students, less central students have around 1.07 fewer connections (p-value <0.01) with
more central peers.
Next, we study the effect of proximity on social interactions. As part of the exper-
iment, students’ names were randomly organized on a list that school administrators
used to assign students to specific beds and dormitories. Conditional on students’ char-
acteristics, the distance on the list is random, and it is a strong predictor of the physical
distance between two students. We show that distance on the list is unrelated to so-
cial interactions before the intervention, as expected from this random variation. The
effect of distance on social interactions after the intervention is high and statistically
significant. Two adjacent students on the list are 16.6 percentage points more likely
to become friends. This effect is 23.6 percentage points higher for first-year students,
which is intuitive as they have no prior friendships with their peers.
Finally, we explore the main theoretical prediction of the model: heterogeneous
effects of proximity on social interactions by student characteristics. Our empirical
findings are consistent with the predictions of the learning-driven homophily model.
The impact of proximity on social connections is higher for students with different
achievement levels (around 2.4 percentage points, p-value 0.028) and poverty statuses
(around 3.4 percentage points, p-value <0.01 ). These results suggest that policies that
increase within-school exposure across both characteristics can succeed in generating
more diverse connections.
Related literature. This paper contributes to three branches of literature.
First, we contribute to the literature on social networks in schools. While there
has been extensive work estimating homophily by type in the formation of direct and
indirect friendships (Currarini et al.,2010;Mele,2020;Paula et al.,2018), less is known
about the effects of mixing students of different types within a school. We show that
even though students prefer friends similar to them, these differences are less prevalent
when students are physically close to each other. This finding is an essential factor to
consider when designing policies for school integration. Our results suggest that within-
school policies that mix students by poverty status or different academic achievement
levels can generate more diverse social connections.
Second, we contribute to the literature that examines how exposure to peers of a
different type changes attitudes towards that group. When two students have different
poverty statuses and academic achievement levels, the effect of exposure is stronger than
when they have similar characteristics. These results add to the evidence of contact
on attitudes and preferences such as race (Boisjoly et al.,2006), poverty (Rao,2019),
3
caste (Lowe,2021), and religion (Mousa,2020). Our results also align with those of
Gallen and Wasserman (2022), who show that while there is homophily by gender in
the selection of mentors, this homophily disappears once information about mentors is
provided to students.
On the theoretical front, we propose a novel model of friendship formation. As in
Currarini et al. (2009), our model also predicts homophily. In our model, faster learning
(rather than preferences) is the driver of homophily. Kets and Sandroni (2019) also
propose an information-driven theory, where homophily alleviates strategic uncertainty
because similar individuals receive correlated impulses. In comparison, our model makes
predictions on the effects of proximity on friendship patterns. Peski (2008) and Baccara
and Yariv (2013) propose models of homophily where group formation is a critical part
of the argument; in contrast, our model considers the isolated instance of a student
choosing whether to interact with a peer.
2 The Model
We model the friendship process as a game of experimentation with exponential bandits.
The model is based on Keller et al. (2005) and our treatment is closest to Bardhi
et al. (2020).2The model allows us to decompose the effects of proximity (a design
variable) and similarity (students’ exogenous characteristics) on friendship patterns and
understand their interaction.
2.1 The Friendship Formation Process
There is a finite set of students I. At any point in time, each student i∈Idecides
whether to maintain interactions with the remaining students in I\ {i}. All the inter-
actions between all pairs occur independently and simultaneously. In what follows, we
describe interactions between a representative pair (i, j)∈I×(I\ {i}).
There is a finite set of categories K. Each category k∈ K represents a binary
classification based on observable characteristics (poverty levels, academic achievement,
etc.) Student i’s characteristic in category kis given by:
τik ∈ {0,1}
For instance, when krepresents poverty status, τik = 1 means ihas high poverty, and
τik = 0 means low poverty. Student i’s type is τi≡ {τik}k∈K.
Consider a pair of students (i, j). Based on students’ types, we can introduce a
2For other models of experimentation, see Keller and Rady (2010), Keller and Rady (2015), and
Strulovici (2010).
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摘要：

Proximity,Similarity,andFriendshipFormation:TheoryandEvidence*A.ArdaGitmez„rORomanAndresZarate…October14,2022AbstractCanproximitymakefriendshipsmorediverse?Toaddressthisquestion,weproposealearning-drivenfriendshipformationmodeltostudyhowproximityandsimilarityinuencethelikelihoodofformingsocialcon...

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