We develop a model of friendship formation that sheds light on segregation patterns observed in social and economic networks. Individuals have types and see typedependent benefits from friendships. We examine the properties of a steady-state equilibrium of a matching process of friendship formation. We use the model to understand three empirical patterns of friendship formation: (i) larger groups tend to form more same-type ties and fewer other-type ties than small groups, (ii) larger groups form more ties per capita, and (iii) all groups are biased towards same-type relative to demographics, with the most extreme bias coming from middle-sized groups. We show how these empirical observations can be generated by biases in preferences and biases in meetings. We also illustrate some welfare implications of the model.
Homophily, the tendency of people to associate with others similar to themselves, is observed in many social networks, ranging from friendships to marriages to business relationships, and is based on a variety of characteristics, including race, age, gender, religion, and education. We present a technique for distinguishing two primary sources of homophily: biases in the preferences of individuals over the types of their friends and biases in the chances that people meet individuals of other types. We use this technique to analyze racial patterns in friendship networks in a set of American high schools from the Add Health dataset. Biases in preferences and biases in meeting rates are both highly significant in these data, and both types of biases differ significantly across races. Asians and Blacks are biased toward interacting with their own race at rates >7 times higher than Whites, whereas Hispanics exhibit an intermediate bias in meeting opportunities. Asians exhibit the least preference bias, valuing friendships with other types 90% as much as friendships with Asians, whereas Blacks and Hispanics value friendships with other types 55% and 65% as much as same-type friendships, respectively, and Whites fall in between, valuing other-type friendships 75% as much as friendships with Whites. Meetings are significantly more biased in large schools (>1,000 students) than in small schools (<1,000 students), and biases in preferences exhibit some significant variation with the median household income levels in the counties surrounding the schools.friendships | high schools | homophily | segregation | social networks F riendship networks from a sample of American high schools in the Add Health national survey † exhibit a strong pattern: students tend to form friendships with other students of their same ethnic group at rates that are substantially higher than their population shares ( Fig. 1) (1-4). This feature, referred to as "homophily" in the sociological literature (5), is prevalent across many applications and can have important implications for behaviors (6-9). The widespread presence of homophily indicates that friendship formation differs substantially from a process of uniformly random assortment. Two key sources of homophily are (i) biases in individual preferences for which relationships they form and (ii) biases in the rates at which individuals meet each other. It is important to identify whether homophily is primarily due to just one of these biases or to both because, for instance, this can shape policies aimed at producing more integrated high schools. In this article, we present a technique for identifying these two biases, we apply this technique to the Add Health dataset, and we estimate how preference and meeting biases differ across races.Although there is substantial evidence that race is a salient feature in how people view each other (10), such evidence does not sort out the sources of homophily, other than indicating that student preferences could be a factor. Without detailed and reliable d...
We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is “long-run integration”, whereby the composition of types in sufficiently old nodesʼ neighborhoods approaches the global type-distribution, provided that the network-based search is unbiased. However, younger nodesʼ connections still reflect the biased meetings process. We derive the type-based degree distributions and group-level homophily patterns when there are two types and location-based biases. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals
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