Intergroup Inequality as a Product of Diffusion of Practices with Network Externalities Under Conditions of Social Homophily: Applications to the Digital Divide in the U

Research in social stratification has tended to view intergroup inequality in one of two ways. Work in the status-attainment tradition focuses on individual outcomes and, by implication, views the reproduction of intergroup inequality as a consequence of agents with differing endowments attaining outcomes that vary depending on the level of those endowments. More recent work has deviated from this aggregationist strategy in two ways. First, researchers have introduced social structure, in the sense of ego-centered social networks, as an additional kind of resource upon which actors draw in their efforts to retain privilege or achieve social mobility. Second, other researchers have studied how collective action may alter the terms of competition by changing state policies or the practices of private actors in response to claims by mobilized groups. In this paper, we introduce a third mechanism, which we contend chronically reproduces and, under some conditions, may generate or even efface intergroup inequality. That mechanism is (a) the diffusion of goods, services, and practices that (b) are characterized by strong network externalities under conditions of (c) social homophily. When the value of a good or practice to an agent is a function of the number of persons in that agent’s network who also possess the good or engage in the practice, and when networks are homophilic with respect to certain social characteristics, this mechanism will exacerbate initial individuallevel differences in access to the good or practice and, under some conditions, induce persistent intergroup inequality. We illustrate this claim in two empirical contexts. For the first, the diffusion of access to and use of the Internet, we start with observed data on the relationship between cost and adoption and between adoption levels and price, and produce a computational model that permits us to predict variation in intergroup inequality over time as a function of variation in the strength of network externalities and the extent of social homophily. For the second, the practice of rural-to-urban migration by young people in rural Thailand, we use village-level data on family resources and migration patterns to explore the relationship between information sharing, homophily, and intergroup differences in migration. We conclude with a discussion of the scope conditions of our argument and the range of phenomena to which this mechanism may apply. Introduction We draw on earlier work in several fields to introduce a class of social mechanisms that we believe influence intergroup inequality, usually by making such inequality larger and more durable than it would be in a world without these mechanisms, although potentially effacing inequality as well. These mechanisms come into play when (a) a good, service, or practice influences individual life chances; (b) that good, service or practice is characterized by network externalities, such that the costs to an actor are lower or the benefits higher if persons with whom he or she is socially tied consume the good or service or engage in the practice; and (c) actors’ social networks are characterized by social homophily. We illustrate our argument with examples of two such practices --technology adoption in the U.S. and internal migration in Thailand – to suggest the scope within which we believe these mechanisms operate. This paper’s approach is broadly consistent with the view that sociological explanation can be advanced by the identification of “social mechanisms” that entail (a) goal-directed individual actions and (b) consequent social interactions that (c) yield higher-level outcomes that (i) are emergent (i.e., that cannot be recovered simply by aggregating the individual actions that combine to produce them) and that (ii) vary depending upon the initial social structure (ordinarily depicted in terms of social networks). Although this approach has deep roots in sociology and has become especially prominent in recent years (Hedstrom 2005; Tilly 2006; Watts 2003), it has played a less central role in empirical research on social inequality than one might have expected. Instead, research on social inequality has often tended to depict inequality as the aggreDiMaggio & Garip: Externalities, Homophily and Inequality ---2--gate product of individual efforts to obtain useful educations, good jobs, and adequate incomes. For many years, work in the status attainment tradition in sociology (as well as the human-capital tradition in labor economics) focused on individual attainment of education, jobs, and earnings, treating these as functions of initial endowments and lifecourse events (Featherman and Hauser 1978). The implication of this approach is that intergroup inequality reflects the fact that people with similar initial endowments have similar experiences that lead them to similar outcomes. In response to the evident limitations of such imagery, students of social stratification began introducing structure into research on social stratification in the 1980s. But they often did so by converting social structure into an endowments predicting individual-level success, thus reproducing the individualistic and aggregationist bias of the status-attainment tradition, albeit with sophisticated accounts of the impact of structural position on achievement. Thus measures of network position (in-degree or “popularity,” centrality, occupancy of “structural holes,” and so on) are treated as forms of “social capital,” analogous to human capital, that advance individual life chances (Lin 1999; Burt 2000). Similarly, characteristics of the firms and other organizations in which individuals are employed --size, profitability, market power, prestige – are often converted into individual-level variables in income-determination models (Bielby and Baron 1980). There are, of course, many exceptions to the aggregationist tendency in research on social inequality. Classical sociology emphasized the impact of collective action (by elites or subordinate groups) on the degree of intergroup inequality. Marx and Engels (1888 [1966]) famously (if incorrectly) argued that concentrating laborers in factories generates processes of identity formation and social learning that culminate in social DiMaggio & Garip: Externalities, Homophily and Inequality ---3--revolution. In this tradition, Offe and Wiesenthal (1980) argues that the size and social organization of business elites and union members, respectively, influence their strategies of collective action. Weber (1922 [1968]) described how dominant groups use their influence to establish criteria of virtue (“status honor”) that benefit their members. More recently, Karabel (2005) demonstrated how U.S. Protestant elites manipulated criteria of virtue to monopolize admissions to prestigious private universities and documented the effectiveness of collective action by African-Americans in persuading these institutions to adopt affirmative action plans that enhanced opportunity for underrepresented groups. Tilly (1999) likewise emphasizes the role of collective action (“opportunity hoarding”) in reproducing inequality. Institutional research on inequality also departs from the aggregationist bias of the status-attainment tradition by focusing upon supra-individual processes that influence the distribution of opportunity. Political institutionalism has emphasized the ways in which state policies influence inequality by providing structures of opportunity, redistributing income, and establishing the terms of political competition (Western 2006; Gustaffson and Johansson 1999). The application of neoinstitutional theory to the study of inequality has demonstrated the varying efficacy of state mandates and organizational policies in reducing categorical inequality in the workplace (Kalev, Dobbin and Kelly 2006). Such research has to defocalize individual choice, often because it examines cases in which higher-level mechanisms such as incarceration, income transfers, or discrimination operate in ways that constrain the scope of individual action. Only a few studies of inequality focus on the production of higher-level patterns as a consequence of individual choice under varying structural conditions. Simon (1957) DiMaggio & Garip: Externalities, Homophily and Inequality ---4--introduced the idea that inequality was a function of the depth of organizational hierarchies (itself a function of organizational size and span of control) and norms about appropriate compensation differences for employees at different hierarchical levels. White (1970) explored the impact of rates at which positions in hierarchies become vacant on several emergent properties of systems of inequality. Boudon (1973) developed a competitive model of individual decisions about investments in schooling to explain the persistence of intergroup inequality despite unprecedented levels of educational expansion (and see Breen and Goldthorpe 1997). Rosenbaum (1976) demonstrated empirically the production of educational inequality as a function of the structure of opportunities within a large urban high school. More recently, research on neighborhoods has focused on mechanisms generating individual-level behavioral or health outcomes likely to influence socioeconomic outcomes. Such research, which is ably reviewed by Sampson, Morenoff and GannonRowley (2002), examines neighborhood effects on social mechanisms (especially the nature of neighborhood interaction networks or place-specific activity patterns) and emergent consequences at the neighborhood level. Although not all of this research explicitly addresses intergroup inequality per se, much of it addresses multiple interactions among conditions associated with concentrated poverty. At the same time, the authors note that existing studies rely on cross-sectional data and, in many cases, indirect measures of neighborhood level variables, often failing to realizing potential gains from multi-level designs and theoretical attention to social mechanisms. One purpose of this paper is to contribute to the depiction and understanding of the role of mechanisms highlighting the interaction of structure-dependent individual DiMaggio & Garip: Externalities, Homophily and Inequality ---5--choices in generating, reproducing, and effacing intergroup inequality. This effort, however, emerged from the authors’ respective efforts to solve concrete empirical problems --whether diffusion of Internet use would eventually eliminate intergroup differences observed in its first years; and why rural-urban migration in Thailand varies at the level of persons, families, and villages. These two empirical questions, we believe, entail social mechanisms that are analytically quite similar. In each case individual choices (to use the Internet or to migrate) are a function of previous choices by members of ego’s social network; and intergroup inequality (in technology use or in the benefits of migration) is likely to be amplified to the extent that ego’s social network is homophilous with respect to socioeconomic status. To develop this model, we combine elements from three well-developed socialscience literatures: on network externalities; on innovation diffusion under conditions of interdependent choice; and on homophily in social networks. Before presenting our cases, we briefly (and incompletely) review work in each field. Network externalities, diffusion models, and social homophily In 1892, John F. Parkinson, owner of a hardware and lumber business, became the first telephone subscriber in Palo Alto, California. (This account is taken from Fischer 1992: 1 To our knowledge, this hypothesis – that inequality is exacerbated when adoption of goods and practices that can promote status attainment is governed by network effects under conditions of homophily – has neither been posed nor tested previously. The only shard of relevant evidence we could find is Van den Bulte and Stremersch’s (2004) finding that adoption processes in countries with high levels of income inequality reveal stronger choice interdependence (“contagion effects”) than processes in societies with lower levels of inequality. This result admits to many alternative interpretations (including the author’s own, that it merely reflects heterogeneous and normally distributed reservation prices). The authors contend that their result is inconsistent with a contagion account of innovation adoption, but this contention is based on an implausible assumption that local homophily is negatively correlated with global inequality and on an untested assumption that inequality is the cause rather than the outcome of variation in adoption processes. In any case, the fact that the contagion parameter is based on overall adoption and not on adoption by network peers makes the finding a weak test of our argument. DiMaggio & Garip: Externalities, Homophily and Inequality ---6--130-34.) Parkinson, an entrepreneur who contributed much to the economic development of the town he would eventually serve as mayor, placed the phone in his business. A line to the Menlo Park telephone exchange a few miles away connected him to other businesses in the Bay Area. By 1893, he was joined by a realtor and a butcher. Shortly thereafter, the local pharmacy took a subscription, placing their phone in a quiet room and permitting residents to use it on a pay basis. By 1897, after a reduction in monthly charges, Palo Alto had nineteen telephone subscribers, including several – Parker, two physicians and two newspaper editors – who had telephones in their homes. It is no accident that the early subscribers were businessmen and professionals for whom the telephone was a means of staying in contact with suppliers, customers, and clients – nor that many citizens used telephones (when they used them) at locations outside their home or place of business (just as many early Internet users inhabited Internet cafes). It did not make much sense to get a phone for social reasons unless you could call the family and friends with you socialized. And it was not at all obvious how social (as opposed to business) telephone use would reach critical mass for takeoff. Indeed, it was years before even the telephone companies recognized the potential of the telephone as an instrument of sociability (Fischer 1992: chapter 3). Not until 1920 percent did telephone subscription rates approach 50 percent even in prosperous Palo Alto (with rates considerably less in neighboring communities) (ibid.: 141). Naturally, telephones were more common in professionals and business households, whose members were more likely to have friends and relatives who also resided in telephone households. By 1930, blue-collar households caught up in Palo Alto (where many blue-collar workers were DiMaggio & Garip: Externalities, Homophily and Inequality ---7--independent tradesmen whose clients had phone service) but not in neighboring towns where blue-collar residents were more likely to work in factories (ibid. 146-47). Even after the takeoff of the telephone, inequality in access was tenacious. The United States did not approach universal service (i.e., approximately 90 percent household penetration) until 1970. And even in 1990, the least advantaged Americans often went without, with service close to universal at incomes of $20,000 or more (in 1990 dollars) and declining precipitously below that. Thus 50 percent of mothers living below the poverty line had no telephone service, as did 35 percent of all families receiving public assistance. Race and ethnicity had independent effects on telephone service even controlling for income: overall, 16 percent of African-American households and 18 percent of Hispanic households did not have telephones (these figures are all from Schement 1995). The independent effect of race, and the nonlinear effect of poverty, suggest (but do not prove) that something other than income – perhaps interaction effects related to network composition -may be driving these differences. Now consider a very different case: social class and advanced placement (AP) course enrollments in contemporary high schools. Imagine a high school class with 300 students, divided into three hierarchically arrayed tiers. Each of these students must decide whether or not to take an advanced placement class. Each one knows that advanced placement courses will help her or him gain admission to selective colleges and may even reduce the time it takes them to earn a college degree. Each also knows that to 2 The spread of cellular telephony rendered data on household use less informative, because by the nid1990s, some Americans, including young, affluent Americans, were beginning to substitute cell phone service for land lines. Thus by 2000, household penetration actually declined for the first time since the Depression, but the decline appears to have been the result of cell-phone substitution, not a reduction in telephone access. DiMaggio & Garip: Externalities, Homophily and Inequality ---8--take advantage of this benefit, he or she will have to learn enough to pass the AP exam, and that this will require a substantial investment of time. The students’ decisions will be influenced by a number of factors: whether they expect to go to college or can afford to attend a selective college, whether they have the preparation to be admitted into AP courses or to have a realistic chance of passing them, whether they have competing demands (for example team sports or after-school work) that reduce the hours available for study, and so on. Based on inequality in financial and other endowments, let us posit that the probability of choosing to take an AP course is 80 percent for those in the top tier, 50 percent for those in the middle tier, and 20 percent for those in the bottom tier. Now, consider the network externalities that are associated with taking an AP course. If your friends also take the course, it may make more sense for you to take it as well: You can study together (which is fun [increasing the benefits] and efficient [reducing the costs]); and perhaps collaborate on homework; and help each other review; and share the cost of a scientific calculator, or use your friend’s high-speed Internet connection to prepare presentations. Such considerations will increase the benefit to you of taking the course (you will learn more), reduce the rate at which you discount expected benefits (you will be more likely to pass the AP exam), and also reduce the cost of taking the course in both time and money. If friendships are distributed at random – if a top-tier kid is as likely to have a friend in the bottom tier as one in his own group – then, on average half of each student’s friends will plan to take an AP course. Assuming that kids in each tier have the same number of friends, and assuming that the effect of friends taking AP courses on your own DiMaggio & Garip: Externalities, Homophily and Inequality ---9--decision is additive, then a lot more students will take AP courses than if their decision were entirely isolated. Moreover, because lower-tier kids will know as many AP-coursetakers as upper-tier kids, there is a good chance that the outcome will be a little more equal than if the choices did not interact. The problem with this scenario is that high-school friendships are never randomly distributed. Real-world nets are homophilic: kids in each tier hang out with one another more than with kids from other groups (Kandel 1978; Shrum, Cheek and Hunter 1988; Quillian and Campbell 2003). If we build such homophily into our example, externalities will exacerbate inequality, not reduce it. Most of the positive effect of mutual influence will accrue to students in the top tier, because their friends disproportionately enroll in AP courses. By contrast, kids in the bottom tier will have only a few friends in AP courses, so externalities will affect their choices less. Put these influences together – big effects on the most advantaged students’ choices, small ones on the choices of the least advantaged – and the result amplifies initial inequalities. The point of these examples is to convey the intuitions behind, and to suggest the scope of applicability of, the models we describe more systematically in the remainder of the paper. Each example has three elements: a choice (purchasing telephone service, signing up for an AP test); network externalities (your telephone is more valuable if you can all your friends with it; you can get more out of the AP course with less effort if your friends take it, too); and social homophily (which makes the benefits of externalities redound more decisively to those groups that possess an initial advantage). Put these three elements – choice, externalities, and homophily – together in a diffusion process (which is to say a lot of people observing one another making choices over time) and the result is DiMaggio & Garip: Externalities, Homophily and Inequality ---10--a pattern of interactions that often exacerbates social inequality. In the remainder of this section, we look more closely at these elements (externalities, homophily, and systems of choice) and describe some literature that has informed or anticipated our work. Network Externalities A product, service, or behavior possesses network externalities in so far as its value to an actor is conditional upon the number of other actors who consume the product or service or engage in the activity. The term derives from work in communications economics and the economics of innovation, which has focused on the aggregate value of a network as a nonlinear function of scale (and the difficulty of internalizing that value) (Katz and Shapiro 1985; Arthur 1989; Shy 2001). By contrast, we focus on network effects from the standpoint of individual decision-makers (to whom the value of action increases with network size). DiMaggio and Cohen (2004) distinguish between general network externalities (when each user’s perceived benefit from adoption of a good or practice is influenced only by the number and not by the identities of other adopters) and specific network externalities (where each user’s benefit is a function of the identities of those who adopt). Specific, or identity-based, network externalities can be status-based (e.g., positive when users are higher-status than oneself and negative when they are lowerstatus) or network-based (when changes in perceived benefit are a function of the percentage of members of one’s network who have already adopted a good or practice). Whereas the economic literature has emphasized general network externalities, we are exclusively concerned with specific externalities, because these have especially signif3 The idea, if not the term, goes back considerably further, at least to Leibenstein (1950: 189), who described a class of goods for which “the utility derived from the commodity is enhanced or decreased owing to the fact that others are purchasing and consuming the same commodity,” DiMaggio & Garip: Externalities, Homophily and Inequality ---11--icant implications for social inequality. In order to make the notion of network externalities useful for the study of social inequality, then, we narrow it by considering only identity-specific externalities but broaden it by applying to practices and behaviors as well as to goods and services. As our example of telephone use indicates, network are endemic to communications technologies and utilities: telephones, fax machines, e-mail clients, instant messaging, and so on. Network effects also characterize any kind of software that produces files that consumers want to exchange with one another (text files, spreadsheets, graphic files, and so on). “Social networking” sites like Myspace or Facebook similarly increase in value in proportion to the number of one’s associates who are already on them. But as our AP-course example suggests, we hypothesize that network externalities characterize a much broader range of choices: choice between public, secular private, and religious secondary schools (kids like to go to the same schools as their friends and parents benefit from car-pooling and information-sharing with other parents); fertility (raising children is a lot easier if your friends have kids [or if you can make friends with people who do]) (Buhler and Fratczak 2007); divorce (the more divorces in one’s social network, the more people will be available for support and companionship and the larger the pool of potential mates) (Booth, Edwards and Johnson 1991); and migration (the more migrants one knows, the easier it is to get vital information about the place to which one is migrating and the more available will be social support once one gets there) (Curran, Garip, Chung and Tangchonlatip 2005; Uhlig 2006); religious choice (Shy 2007); and bilingualism (Church and King 1983). DiMaggio & Garip: Externalities, Homophily and Inequality ---12--Other things equal, network externalities tend to produce dual equilibria in diffusion: very low levels of adoption until some takeoff threshold, after which adoption increases rapidly (Shy 1971). But in many cases the takeoff threshold is easily reached because a critical mass of initial adopters is motivated by intrinsic returns. Under these conditions, network externalities tend to increase adoption levels across the board. But where externalities are identity-specific and ego-network-based, and where ego networks are homophilous, externalities can become a potent source of increased inequality. Social Homophily Social networks are homophilous with respect to a social trait to the extent that connected pairs of actors in a network share the characteristic in question. In other words, social homophily exists to the extent that people are similar to their friends and associates. Since Lazarsfeld and Merton (1954) coined the term, research has found homophily to be a ubiquitous characteristics of social networks in many different contexts. Studies in numerous societies and organizations demonstrate pervasive homophily with respect to race and ethnicity, gender, age, educational attainment, occupation, religion, and other factors (McPherson, Smith-Lovin, and Cook 2001). Many researchers have studied the impact of homophily on diffusion processes and information flows. Rogers (2003:307) depicts homophily as a barrier to the diffusion of innovation, arguing that where homophily is strong, adoption of innovations is more 4 McPherson, Smith-Lovin and Cook (2001) note that observed homophily reflects both “baseline homophily,” which produces homophily even in random networks based on the distribution of characteristics of the nodes, and “inbreeding homophily,” which reflects patterns of similarity between tied agents above what one would expect if ties were distributed at random. These authors also usefully distinguish between “inbreeding homophily” and “choice homophily,” noting that greater-than-random levels of homophily may result not only from choice but also from institutional factors (e.g., occupational gender segregation) and from correlations among different personal characteristics. These are critical distinctions if one is concerned with the causes of homophily, but they are less critical given our focus on homophily’s consequences. DiMaggio & Garip: Externalities, Homophily and Inequality ---13--likely to be restricted to elites. We suggest that, when returns to adoption are high, this tendency will reinforce inequality. To our knowledge, diffusion researchers have not considered the implications of homophily in diffusion processes for social inequality. A few scholars have addressed the relationship between homophily and inequality (especially the impact on educational or occupational attainment), but have not placed this relationship in the context of an explicit model of diffusion or behavioral change. Thus Buhai and van der Leij (2008) model occupational segregation as a result of social homophily combined with network effects on access to jobs. Quillian (2006) argues that friendship homophily reduces the academic achievement of high-achieving Black and Hispanic students relative to that of their equally able white peers. From the group perspective, homophily facilitates sustaining monopolies over scarce resources (Tilly 1999). From an individual perspective, however, it is precisely heterophilous ties (especially to persons higher status than oneself) that enhances mobility (Granovetter 1973; Lin, Ensel and Vaughn 1981). We apply these insights to the system level to contend that homophily, which facilitates collective action to sustain monopoly, increases intergroup inequality, whereas heterophily, which facilitates mobility, tends to reduce it. The systematic effects of homophily on inequality in a real social system are more complicated than individual-level models imply due to the fact that individuals have multiple identities (e.g., identities based on gender, race, age, religion, occupation, nationality, educational background, avocational interests, and so on). As Blau (1977) demonstrated, as long as these identity dimensions are only moderately correlated with one another (“intersecting” rather than “consolidated” in his terminology), and as long as homophily operates with respect to more than one identity dimension, an interaction DiMaggio & Garip: Externalities, Homophily and Inequality ---14--choice that is homophilous with respect to one dimension (for example, occupation) may introduce heterogeneity into a network with respect to another dimension (e.g., gender or religion). So a male Episcopalian banker who acquires a useful financial tip at a business lunch (homophily by occupation) or alumni gathering (homophily with respect to education) may spread it to shop owners and Catholics at a neighborhood poker game (homophily by residence and probably gender) and to women and Ph.D.s (or college dropouts) over Thanksgiving dinner (homophily by kin relation). Watts (1999; and Watts, Dodds and Newman 2002) develop this insight formally in the context of the small world problem, but it is likely to apply to network-generated inequality as well. Because we focus on inequality that induced by patterns of choice (rather than by collective action), we develop models in which homophily only induces inequality in the presence of network externalities -that is, when individual choices are interdependent. We argue that the interaction between network externalities and social homophily is a critical mechanism for the production and reproduction of social inequality in access to new goods and engagement in innovative practices. To the extent that adoption of new goods and practices characterized by such externalities contributes to individual life chances, this mechanism may also increase overall intergroup social inequality. In order to understanding the implications of research on externalities and homophily for macrolevel intergroup inequality, we must specify the mechanisms by which individual choices interact. The most useful instruments to this end are models of diffusion and contagion. Models of Diffusion There are innumerable models of diffusion (see Rogers 2003 for an exhaustive review). but we are interested only in those that rely on interdependence of choice between agents DiMaggio & Garip: Externalities, Homophily and Inequality ---15--and their network alters as a primary mechanism predicting adoption (and sometimes disadoption). These latter are ordinarily referred to as “contagion models” (Burt 1987), because they depict choices as spreading through a social network. We are particularly interested in contagion models that focus upon individual choice (as opposed to imitation or social learning). Many of these posit a distribution of adoption thresholds within the at-risk population, often as a function of individual attributes and network characteristics; and in some cases, with updating on the basis of changes in the behavior of network alters. Our own model is of this kind, but diverges from the existing literature by modeling differences in diffusion rates within stratified populations. We focus here on studies that influence or anticipated aspects of our approach. Although Gabriel Tarde (1903) may be considered the father of diffusion modeling, an early formal statement of ideas influencing the class of models in which we are interested was produced by Harvey Leibenstein (1950), in an essay on interdependence in consumer demand. Leinbenstein distinguished between positive and negative externalities in consumption, which he termed, respectively, “bandwagon” effects and “snob” effects. He also distinguished between the case in which ego’s demand was a function of aggregate consumption and the case in which ego was more influenced by the consumption decisions of some consumers than others. Leibenstein recognized that a major limitation of his analysis was its reliance upon comparative statics, the assumption that 5 We do not presume that choices are “rational” either phenomenologically or in effect. People may adopt courses of action unreflectively; or they may adopt them on the basis of poor information about costs, benefits, and risks. 6 Leibenstein credits the insight that his paper develops to Oskar Morgenstern (1948). Morgenstern, one of the developers of game theory, contended that the interactive character of demand called for the replacement of dominant approaches in economics with models derived from game theory – a point on which Leibenstein declared himself agnostic. . 7 Leinbenstein also described “Veblen effects” – cases in which a high price makes the good or service especially attractive because of its prestige value – but these need not detain us here. DiMaggio & Garip: Externalities, Homophily and Inequality ---16--“the order of events is of no significance” (ibid.: 187). Subsequent progress would come in relaxing this condition and taking account of time. A step in this direction was taken in 1957, when Coleman, Katz and Menzel introduced diffusion models based on network-driven interdependence in their study of the adoption of tetracycline by physicians in four Midwestern cities. The authors reported that the rate of adoption was brisker and penetration after 17 months more complete among physicians with three or more friendship ties to other doctors than among less connected practitioners. This difference, they argued, represented interdependence of choices among the well-connected, which led to a “snowball” or “chain-reaction” pattern as use of the new drug spread. Mark Granovetter’s (1978) paper, “Threshold Models of Collective Behavior,” represented a significant advance towards the class of models employed here. The models that Granovetter developed apply to situations in which (a) agents are required to make a binary choice and can do so over a number of successive time points; (b) “The costs and benefits to the actor ... depend in part on how many others make which choice” (1422) (i.e. that there are network externalities); (c) each agent has a threshold (understood as a tradeoff of costs and benefits) at which she or he will choose to act; (d) agents may respond more directly to the actions of their friends and associates than to those of strangers; and (e) outcomes (the proportion of agents choosing to act and, especially, whether this proportion reaches the critical mass necessary to sustain some collective behavior) are dependent upon the distribution of thresholds and not just the mean. Granovetter describes this model’s applicability to a range of cases that have 8 Granovetter credits Schelling’s model of residential segregation (1971) as source of the notion of threshold. DiMaggio & Garip: Externalities, Homophily and Inequality ---17--choice and externalities in common: the adoption of birth control, the spread of rumors, the epidemiology of disease, strikes, riots, voting behavior, college attendance, and migration. Granovetter essentially assembled all the parts necessary for the models developed in this paper, with two exceptions: thresholds are exogenous and actors are homogeneous (except with respect to thresholds and network position). Granovetter and Soong (1988) extended this model to cases of heterogeneous populations whose members respond differently to the number of adopters from different groups. In a series of papers, Abrahamson and Rosenkopf (1993; 1997; Rosenkopf and Abrahamson 1999) extend the models to organizational behavior and build in heterogeneity with respect both to network position and adopter reputation. Bruch and Mare (2006) compare threshold to other forms of diffusion models and argue that the special properties of threshold decision-making generate high and stable levels of residential racial segregation. Note that different mechanisms may account for similar form of diffusion (Van den Bulte and Lilien 2001). Even when decisions to adopt reflect perceived self-interest influenced by the actions of members of each potential adopter’s network, any mechanism that increases the benefit, reduces the cost, or reduces the perceived risk of a practice is likely to increase it. Such changes can reflect tangible benefits (e.g., in our cases below, the size of the network to which an adopter has access, or the ability of high-quality information to increase returns); information about the rewards of the innovative practice from trusted or high-reputation sources (as in Rosenkopf and 9 Processes that are entirely driven by factors external to the system can be distinguished from those driven by internal dynamics by the shape of the diffusion curve (Rossman, Chiu and Mol 2006); those driven by normally distributed heterogeneous propensities to adopt (Van den Bulte and Stremersch 2004), or those characterized by general externalities can be distinguished from those driven by alter-specific ones on the basis of whether individual choices are responsive to those of network alters, specific population subgroups (as in snob effects), total numbers of adopters (as in pure bandwagon effects), or none of the above. Van den Bulte and Stremersch (ibid.) and Rossman, Chiu and Mol (2006) introduce innovative ways to use information on multiple innovations to distinguish among varying mechanisms. DiMaggio & Garip: Externalities, Homophily and Inequality ---18--Abrahamson 1999); or (with some modification of existing models) information cascades based on local (network-specific) imitation (Bikhchandani, Hirshleifer and Welch 1992). Distinguishing among explanations at this level ordinarily requires qualitative information about the phenomenology of decision-making within the at-risk population. We draw on the research we have reviewed, but diverge from many models by treating externalities as specific (i.e. decisions are driven only by members of one’s social network and not by the number of adopters in general) and innovate by including status homophily as a key variable and focusing on group-specific diffusion paths (and their implications for social inequality) rather than rates for the population as a whole. Summary In the analyses that follow, we combine insights from research on network effects, status homophily in social networks, and threshold models of diffusion to argue that diffusion processes of good and practices with strong and identity-specific network externalities under conditions of status homophily tend to exacerbate social inequality. To do so we present two cases. First, we develop a computational model to predict group-specific diffusion paths for Internet use, varying the extent of homophily and the strength of network effects to assess the importance of each. Second, we present an empirical analysis of variation in rates of rural-urban migration in Thailand, to test the hypothesis that variations among villages in status homophily combined with network externalities will generate heterogeneous migration patterns across villages over time. These cases are very different. The diffusion of Internet use is a conventional instance of new-product adoption where the network effects act directly on the value of the product for the agent, for whom the value of the network to which the technology DiMaggio & Garip: Externalities, Homophily and Inequality ---19--provides access is a function of the number of friends and associates accessible through it. Rural-urban migration is a longstanding practice in Thailand that became much more widespread in the 1980s; network effects are indirect, in the sense that connections to prior adopters are not the source of greater value in themselves, but rather are posited to provide information that increases the returns to and reduces the risks of migration. Nonetheless, the two cases share the requisite characteristics for the model to apply: network effects and interdependent choice; status homophily within networks; and sequential choice by large numbers of agents. Case 1: The Internet: Transitional Inequality or Permanent Divide? For the first of our two cases, intergroup inequality in access to and use of the Internet, we employ computational modeling as our strategy. We do so for two reasons. First, our theory directs us to network effects, but we lack suitable network data. Second, we began this inquiry when the Internet was at a relatively early stage of penetration and we were interested in projecting its trajectory forward. Our other case, rural-urban migration in Thailand, is directly empirical, because we have detailed individual-level data from twenty-two villages over a twenty-eight year time periods (1972-2000) that enables us to track the practice from takeoff through maturity. Computational models – also known as “intelligent-agent models” because they are based on simulated actors whose choices are guided by relatively simple rules – have become an increasingly important tool for theory development throughout the social sciences (Macy and Willer 2002; Watts 2003). Computational models enable the investigator to trim down the complexity of a case to the key mechanisms to facilitate theory development. In particular, computational modeling is useful for exploring DiMaggio & Garip: Externalities, Homophily and Inequality ---20--interactions among individual choices when the choices themselves are amenable to theory-based predictions but the interactions themselves are nonlinear and not easily apprehended through intuition. Such models indicate both the plausibility of the proposition that given mechanisms are operative (based on the fit between predicted and observed aggregate patterns) and the robustness of those mechanisms against different states of the world and ranges of key variables. Computational modeling entails a tension between realism and generalizability. We attempt to strike a balance by basing as many parameters as possible on available data, while varying two theoretically central variables as, in effect, experimental treatments. The Problem Although the results we report here are based on computational models, the models originated in efforts to solve a concrete empirical puzzle. At the dawn of the Internet era, some observers claimed that the technology would be equality enhancing, for two reasons: proficiency seemed associated with youth rather than socioeconomic status (Loges and Young 2001); and the technology dramatically reduced the cost to its users of acquiring many kinds of information, thus leveling the playing field (Cairncross 1997). By contrast, other observers cautioned that the rise of the Internet could simply reproduce or even exacerbate existing inequality. In this view, a variety of advantages might enable high-income, high-education persons were to take advantage of the Internet more extensively and more productively than their lower-status counterparts. If this were the case, then the Internet could actually exacerbate the “knowledge gap” (and a gap in the rewards that knowledge can bring) reported by researchers studying other media (Bonfadelli 2002; DiMaggio, Hargittai, Celeste and Shafer 2004). DiMaggio & Garip: Externalities, Homophily and Inequality ---21--Even after a decade or so of widespread commercial availability, use of the Internet was still considerably more common among Americans with lots of education and relatively high incomes than among the less educated and the poor. This led many observers to contend that such inequality – the so-called “digital divide” – was an enduring problem and an appropriate focus of public policy. Critics of this position pointed out that intergroup inequality in adoption rates are likely whenever groups start at different baselines or reach critical mass at different times (Leigh and Atkinson 2001).