Segregation in Friendship Networks

• Author: Yves Zenou,Joan de Martí
• DOI: http://doi.org/10.1111/sjoe.12178
• Published date: 01 July 2017
• Date: 01 July 2017

Scand. J. of Economics 119(3), 656–708, 2017

DOI: 10.1111/sjoe.12178

Segregation in Friendship Networks∗

Joan de Mart´

ı

Pompeu Fabra University, 08005 Barcelona, Spain

joan.demarti@upf.edu

Yves Zenou

Monash University, Caulfield, VIC 3145, Australia

yves.zenou@monash.edu

Abstract

We analyze a network-formation model where agents belong to different communities. Both

individual benefits and costs depend on direct as well as indirect connections. Benefits of an

indirect connection decrease with distance in the network, while the cost of a link depends on

the type of agents involved. Two agents from the same community always face a low linking

cost, while the cost of forming a relationship between two agents from different communities

diminishes with the rate of exposure of each of them to the other community. We find that

socialization among the same type of agent can be weak even if the cost of maintaining links

within one’s own type is very low. Our model also suggests that policies aimed at reducing

segregation are socially desirable only if they reduce the within-community cost differential

by a sufficiently large amount.

Keywords: Homophily; segregation; social networks; social norms

JEL classification:J15; Z13

I. Introduction

In social and economic contexts, individuals generally have relevant at-

tributes, such as ethnicity, gender, age, education, income, etc., and these

attributes are often related to their interaction patterns. Are individuals

more likely to be linked to others who have similar characteristics? This

∗We are grateful to two anonymous referees for very helpful comments. We also thank the

participants of the 13th Coalition Theory Network Workshop, of the seminars at IFN, IIES,

and Duke University, in particular, Andrea Galeotti, Guillaume Haeringer, Rachel Kranton,

and Karl Schlag for helpful comments, and we thank Willemien Kets for a thorough dis-

cussion. J. de Marti gratefully acknowledges financial support from the Spanish Ministry

of Education, through the project SEJ2006-09993/ECON and a Juan de la Cierva fellow-

ship (co-financed by the European Social Fund), from the Spanish Ministry of Science and

Innovation through grant ECO2011-28965, from the Comissionat per a Universitats i Re-

cerca del Departament d’Innovaci´

o, Universitats i Empresa de la Generalitat de Catalunya

through Beatriu de Pin´

os 2009 BP-A 00116 postdoctoral grant, and from Barcelona GSE and

the Government of Catalonia. Y. Zenou (also affiliated with IFN) gratefully acknowledges

financial support from the French National Research Agency grant ANR-13-JSH1-0009-01.

CThe editors of The Scandinavian Journal of Economics 2016.

J. de M ar t´

ı and Y. Zenou 657

Fig. 1. Distribution of black students (left) and white students (right) byshare of same-race

friends in integrated schools [Colour figure can be viewed at wileyonlinelibrary.com]

is a phenomenon known as homophily, and it refers to the fairly pervasive

observation in working with social networks that having similar character-

istics is often a strong and significant predictor of two individuals being

connected (McPherson et al., 2001). This means that social networks can,

and often do, exhibit strong segregation patterns. Segregation can occur be-

cause of the decisions of the people involved and/or by forces that affect the

ways in which they meet and have opportunities to interact (Currarini et al.,

2009, 2010; Tarbush and Teytelboym, 2012). Clearly, capturing homophily

requires one to model, or at least explicitly account for, characteristics of

nodes that exhibit a dimension of heterogeneity across the population.

The aim of this paper is to develop a network-formation model where

agents are heterogeneous in some observable characteristics (such as eth-

nicity), which imply different interaction costs between communities, and

where homophily behavior and segregation emerge in equilibrium.

Consider, for example, Figure 1, taken from Patacchini and Zenou

(2016), which depicts a friendship network among US high-school students

(using data from the National Longitudinal Study of Adolescent to Adult

Health, Add Health). It turns out that the (self-reported) friendships are

strongly related to ethnicity, with students of the same ethnicity being

significantly more likely to be connected to each other than students of

different ethnicities. To be more precise, Patacchini and Zenou (2016) use

the homophily index Hiof individual iproposed by Coleman (1958) to

analyze the exposure of individuals of white and black ethnicity to own

and other ethnicities. If the homophily index Hiof a student iis equal

to 0, this means that the percentage of same-race friends of this individual

equals the share of same-race students in the school. Negative values of

the index imply an underexposure to same-race students, while positive

values imply an overexposure to same-race students compared to the mean.

Figure 1 displays their results for mixed schools (i.e., schools with a

CThe editors of The Scandinavian Journal of Economics 2016.

658 Segregation in friendship networks

percentage of black and white students between 35 and 75 percent). Most

of the white students have white friends as roughly 40 percent of them are

associated with values of the homophily index greater than 0.4, denoting

a clear deviation from the assumption of random choice of friends by

race. Black students appear to be more heterogeneous in their choice

of friends than white students. The clear bimodality in the distribution

(corresponding to values of Hibetween −0.6 and −0.8 and between 0.6

and 0.8) reveals that there are, mainly, two types of black students: those

who have mostly white friends and those choosing mostly black friends.1

In this paper, we propose a network-formation model that can explain the

socialization patterns observed in Figure 1. For this, we consider a finite

population of individuals composed of two different communities. These

two communities are categorized according to some exogenous factor such

as, for example, their gender, race, or ethnic and cultural traits. Individuals

decide with whom they want to form a link, according to a utility function

that weights the costs and benefits of each connection. This results in a

network of relationships where a link between two different individuals

represents a friendship relationship. The utility of each individual depends

on the geometry of this friendship network.

To model the benefits and costs of a given network, we consider a varia-

tion of the connections model introduced by Jackson and Wolinsky (1996),

a workhorse model in the analysis of strategic network formation.2From

the standard connections model, we keep the property that an individual

benefits from their direct and indirect connections, and that this benef it

decays with distance in the network. This can be interpreted as positive

externalities derived from information transmission (of trends and fashion

for adolescents, of job offers for workers, etc.). However, in the standard

connections model, each link is equally costly, irrespective of the pair of

agents that is connected. We depart from this assumption as follows.

Consider the case where communities are defined according to ethnicity,

which might entail differences in language and social norms. When

two individuals of different communities interact, they might initially

experience a disutility because of the attachment to their original culture.

This discomfort can, however, be mitigated if individuals are frequently

exposed to the other community. Indeed, when someone spends time

1Marmaros and Sacerdote (2006) and Patacchini et al. (2015) show that the main determi-

nants of friendship formation are geographical proximity and race. Also, using administrative

data and information from Facebook.com, Mayer and Puller (2008) find that race is strongly

related to social ties, even after controlling for a variety of measures of socio-economic

background, ability, and college activities.

2See Goyal (2007), Jackson (2008), de Mart´

ı and Zenou (2011), Jackson and Zenou (2015),

and Jackson et al. (2017) for overviews of the growing body of literature on social and

economic networks.

CThe editors of The Scandinavian Journal of Economics 2016.