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Matching

Abstract and Keywords

This article examines matching processes, specifically two-sided matching contexts such as marriage and job markets, using an agent-based simulation approach. It begins with a conceptual discussion of matching processes, focusing on four key analytic features that define a matching process: the preferences actors have over characteristics (of alters or of pairings); the distribution of (relevant) characteristics in the population; the information structure that allows actors to know about potential matches and alternatives; and the operative rules or norms about matching. The article then considers formal models that describe matching processes before introducing an agent-based simulation model designed to shed light on labor-market segregation. This model takes into account the link between social networks and the dynamics of matching.

Keywords: matching, marriage, job market, preferences, information structure, norms, agent-based simulation model, labor-market segregation, social networks

What I have been describing is the problem of moving from a model of individual behavior to a theory of the behavior of a system composed of these individuals, taking social organization explicitly into account in making this transition, rather than assuming it away. This, I believe, is the central intellectual problem in the social sciences.

(James Coleman 1984: 86)

Introduction

Matching is a crucial yet often invisible process through which social structure is translated into the experiences of individuals and social organizations (Coleman 1991). By matching, we refer to the process by which social actors form mutually exclusive pairs from a pool of potential partners, or, as Mortensen describes it, ‘voluntary pairing under competitive conditions’ (1988: S216). Matching may be accomplished via a centralized decision maker, in which case the rules that govern allocation can be understood as an articulation of collective values, or through two-sided matching processes in which actors sort and sift through alternatives while seeking a mutually agreeable match. Some variant of matching is evident in a wide range of substantive domains, including the assignment of employees to (p. 366) postings within a firm, the college-application process, organ transplants, residential choice, and in modern monogamous marriage and job markets. Because matching processes frequently link individuals with social positions or opportunities, the institutions that rely on matching play a central role in stratification and intergroup relations (Gangl 2004). Understanding how actual individuals are matched in these arenas (rather than simply knowing the structure of association between traits) is therefore fundamental for sociological analysis of social organization (Solga and Konietzka 1999). Beyond this substantive import, models of matching offer an exemplary analytic example of how social organization is shaped by, and shapes, individual experience.

This chapter is organized as follows: we begin with a conceptual discussion of matching processes, introducing key features of matching problems and the range of empirical institutions that resolve them. We then turn to formal models designed to describe matching processes. Developed primarily in economics, matching models are equilibrium models that describe stable systems. Here we note that while economists have recognized the implications of information limits on matching solutions, to date the literature has not integrated insights from the field of social-network analysis into approaches to this problem. In the final section we describe an agent-based simulation model that remedies this problem. Our model, designed to shed light on labor-market segregation, incorporates social-network structure into an individual-level matching model.

16.1 A Conceptual Introduction to Matching Processes

In many social circumstances actors seek to form voluntary, mutually exclusive relationships with one another. Examples include marriage, of course, but also employment (Coleman 1991; Witte and Kalleberg 1995; Werum 2002), school placement (Elster 1993; Chen and Sonmez 2006), and, in some respects, housing decisions. The nature of these relations, in terms of their durability and the obligations and expectations associated with them, may vary by time and place, but in all matching problems actors seek pairings from a pool of alternatives, constrained by the fact that each must find a partner who is also willing to accept them. For instance, fifty years ago there were millions of men who would have been thrilled to marry Marilyn Monroe, but only a lucky few were able to pull off this feat, and even they had to wait their respective turns. Thus, while individual desires are a necessary condition for making a match, the fact that a match must be acceptable to both parties means an individual’s ability to meet her desires is ultimately limited by (p. 367) the structure of others’ desires, and the distribution of others in the population. Furthermore, before any match can be made, actors must have some means of learning about their potential partners, for one cannot marry someone that one is not aware of (even in arranged marriage systems there is an information path linking potential brides to potential grooms). Thus, matching processes are also highly dependent on the structure of information flow within a population.

Matching problems share some features with economic exchange in markets, most notably the idea of two actors among many agreeing to engage in a transaction. And certainly many matching problems have been analyzed in terms of economic exchange, largely by introducing the fiction of a price mechanism into the process (see e.g. Becker 1981). The idea here is that bundles of traits can be evaluated and valued, much as the quality of a good can be valued, and that exchanges occur when ‘buyers’ find ‘sellers’ who are willing to exchange equivalent values. However, as Coleman points out, matching problems are ‘very different from a neoclassical perfect market … [since] the role of “price” as an allocation mechanism is greatly altered; and the entities exchanged are not fungible—there is not a market in trading of wives’ (1984: 86). Another crucial distinction between matching processes and many economic exchanges is the stickiness of the pairing: quite often, there are significant costs or risks associated with changing partners, and these costs shape the temporal dynamics of matching.

At the macro level, the outcome of a constrained and competitive process of matchmaking is known as assortative mating, an aggregate phenomenon in which particular traits are more (or less) likely to pair with one another. Studies of assortative mating in marriage markets in the USA reveal a general tendency toward positive assortative mating with respect to race, and negative assortative mating with respect to age (Hayes and Jones 1991; Mare 1991; Kalmjin 1994; Blackwell and Lichter 2004). While many interpret such findings as revelatory of individual preferences, these findings are also consistent with clustered opportunity structures. In the end, all that analyses designed to assess the strength of assortative mating in US marriage markets show us is that whites are more likely to marry other whites.1 Without a model that takes into account individual behavior, such analyses, which fail to bridge the gap between individuals and social structure, are analytically inadequate.

Thus, following in the tradition of matching models, we treat matching as a process that must begin at the individual level, and build from there. From this perspective it is possible to identify four key analytic features that define a matching process: the preferences actors have over characteristics (of alters or of pairings), the distribution of (relevant) characteristics in the population, the information structure that allows actors to know about potential matches and alternatives, and the operative rules or norms about matching. Variation in these features—especially in preferences and information—affect the role sequencing and timing play in which matches are made.

(p. 368) 16.1.1 Preferences over characteristics

Lay explanations for outcomes often begin with individual preferences: Why did I marry this person? I fell in love with him. Why do I live in this neighborhood? I want my children to go to good schools. In everyday life, actors often express preferences over sets of alternatives, and though they may exaggerate preferences’ role in accounting for outcomes, this does not mean that preferences are purely fictive. Frequently, preferences are expressed in terms of characteristics of the possible outcomes: an employer may prefer to hire a college graduate, a landlord may prefer tenants with good credit records, parents may prefer brides with a large dowry, and a worker might prefer to work part-time. Within a given matching arena, particular characteristics may organize the preferences of most participants; for those looking for housing, relevant features might include location, age, quality, or size of dwelling, racial profile of neighborhood, rating of nearby schools, price, etc., as well as, typically, some idiosyncratic preferences (e.g. a preference for yellow houses). Individual buyers will have different preferences across these basic features, which enables them to evaluate houses.

Beyond the features of potential matches, however, actors may have preferences for characteristics of the search process (they prefer it to be short, or exhaustive), or the match itself (in courtship, some may simply prefer the one who adores them). It goes without saying that in two-sidedmatching arenas, agents on each side may have preferences over characteristics of agents on the other side.

One specific type of preference plays a key role in understanding matching processes: the reservation point. Borrowed from labor economics, a reservation point is defined as the boundary below which a potential match is deemed so unattractive that the actor would prefer to remain unmatched than accept a match with this feature. For instance, a worker laid off from a job paying twenty dollars an hour might prefer to stay out of the labor market rather than take a job paying ten dollars. The existence of reservation points contributes to the idea that matchings are voluntary rather than coerced. Even economists recognize that an individual’s reservation points may change: when young, a woman might be picky when choosing dates, though as she ages she might be willing to take a chance with a less desirable partner. Reservation points are important for individuals because they provide a mechanism for quickly screening alternatives; in the aggregate, they define classes of unacceptable matches.

Debates about the origins and durability of preferences divide disciplines; for theoretical and practical reasons, economists assume fixed preferences (at least in the short run), while many sociologists recognize (1) that preferences themselves may be formed through interaction, and (2) that persons may develop preferences to align with their opportunities. These sociological insights are nicely revealed in the social dynamics of matching, for one commonly observed outcome of the matching process is a shift in preferences (e.g. Solga and Diewald 2001). For our (p. 369) purposes, because preferences can be articulated at the individual level—even if they are socially produced—they ground our discussion of matching processes with a plausible microfoundation.

The concept of preferences advances our understanding of matching processes for several reasons. Preferences can be conceptualized as weights on possibly observed characteristics, and thus can be combined to produce an evaluation (and ranking) of the overall desirability of particular potential matches. In simple commodity-allocation problems, the preferences of actors, combined with constraints on availability of goods, is sufficient to describe allocation. Matching is more complex, however, because both sides have preferences and the matching process is contingent upon both sides accepting a pairing. Yet because the structure of observed matches is rarely consistent with a unique preference structure (and, in any case, preferences are notoriously difficult to discern empirically), variation in the structure of preferences is insufficient to describe variation in matching outcomes across contexts.

16.1.2 Distribution of characteristics in the population

Matching is pairing under competitive conditions, which focuses our analytic gaze on the pools from which matches are made. The empirical pool of potential partners constrains the ability of actors to realize their preferences. In most research, pools are described in terms of the distribution of key features that organize actors’ preferences. In some matching arenas—such as romance, or housing—a number of characteristics are invoked as relevant while in others only a few features structure the matching process. To follow the example of housing markets, the stock of housing in a specific metropolitan area could be described in terms of its age, its size, the quality/condition of dwellings, etc., and the relationship between this empirical distribution and buyers’ desires allows us to predict price and duration on the market.

Actual matches are in part determined by the composition of the pool. Agents with preferences for characteristics that are very rare will face stiff competition—in the sense that the other sides’ preferences for their characteristics will come to dominate the matching process. A young school child might enjoy the company of a child from a different ethnic background, but if she attends an all-white school, her friends will be white (or she will be isolated). This example rests on simple availability: actors are unable to realize their preferences if they prefer things that do not exist in their choice set. But in matching models the duality of choice introduces a second level of complexity: if all whites prefer cross-race friends, but there are only a few blacks in the population, only those whites who are desirable to these particular blacks will be able to realize their preference for cross-race friendships. This symmetry constraint, which is at the heart of Rytina and Morgan’s simple (p. 370) yet elegant work on the mathematics of social relations (1982), implies a strong matching process. The consequence of matching in this example is a network of friendships in which most whites have largely white peer groups, while blacks have more integrated networks. This same insight serves as the basis of the paradox recognized by Raymond Boudon (1973) in his analysis of the value of a college degree: as more and more people with college degrees enter the labor market, this credential is no longer sufficient to differentiate a candidate and make her a top choice for many jobs.

16.1.3 Information

To find a spouse or to get a job—or to conclude any other kind of match—one must have information about potential spouses or jobs, and be able to evaluate this information. Potential spouses and jobs that are not known about might as well not exist, while sometimes it is difficult to assess, a priori, the merits of a potential match. As some wise parents of children choosing among highly selective colleges recognize, perhaps the biggest consequence of choosing one school over another is that college defines the pool from which lifelong friends and romantic partners are most often drawn. Information is equally important in other matching arenas, and demand for scarce and high-quality information frequently drives the market for matchmakers and other brokers. Information matters for matching processes for two reasons: some high-quality matches may not be made, simply because the potential partners are unaware of each other, while other matches turn out differently than expected because signals are noisy and hard to read.

This latter insight is developed most fully in Stiglitz’s and Spence’s work on screening and signaling (Stiglitz 1975; Spence 1973, 1974). Screening is particularly important when the matching arena is flooded with too much information (as in a very large number of applicants for a single low-skill position), or because it is difficult to predict the future from the past (such as with promising Ph.D.s who flame out at prestigious universities). Under these conditions, actors may weigh information from known sources more heavily than information from unknown sources. As we show below, the consequences of such responses to information overload have implications at the macro level: if actors rely on networks for reliable information, and these networks are biased with respect to some attribute, the resulting matching can reproduce clustering across domains and maintain segregation.

Signaling models incorporate the insight that actors are rarely able to pick and choose from a set of offers without first making their quality and availability known to potential partners. So somehow participants in matching arenas need to simultaneously gather information about alternatives and convey information about their (p. 371) own value as matches (Spence 1973, 1974). Severe information asymmetries concerning the reliability of these signals may create a classic ‘lemon’ market (Akerlof 1970); avoiding this trap involves investing extensively in screening, hiring, training, and evaluating prospects (Spence 1973, 1974).

In matching arenas, the consequences of information overload, costs of screening signals, or simple constraints on the information available about alternatives can limit individuals’ opportunities. These constraints effectively shrink the pool of competitors—and may shift its composition as well—and therefore will benefit the remaining individuals, at the expense of those unknown. When matches are sticky, the consequences of information asymmetries are particularly significant: those who are able to match early may face systematically better (or worse) opportunities later—because of additional experience they gain, or because they are trapped. Thus, it is in matching arenas when decoupling is difficult (marriages, some jobs) that economists most often lament the prevalence of ‘mismatch.’

The basic neoclassical model of exchange recognizes the importance of information: full and perfect information is typically considered a condition for the proper functioning of markets. Deviations from perfect information may result in suboptimal sorting of sellers and buyers (for an empirical example, see Fountain 2005). Yet while many economic models presume perfect information, in most real settings information is noisy and flows through a variety of socially structured channels, including educational institutions, organizations and secondary associations, newspapers, websites, headhunters, and word-of-mouth. Each of these channels constrains access to information—in terms of both the number of persons who might hear about available options, and which particular persons hear about them. One additional channel through which a great deal of information flows is personal contacts, or social networks.

If networks were socially equivalent to other information sources, they would not merit further discussion here. And yet there is ample evidence to suggest that networks are, in some fundamental ways, distinct from more generalized information channels. Consider job searching: If an individual’s personal-contact network is disproportionately composed of others who share a particular trait, then this individual may disproportionately hear about jobs held by (or known about by) other workers with the same trait (Fernandez and Fernandez-Mateo 2006). From the employer’s perspective, this creates a pool of potential employees that mirrors the contact network of current employees; selection from this pool will amplify the level of segregation in employment. Further, using networks to find and evaluate possible matches creates ‘bilateral asymmetries’ in information (Granovetter 2005) which can amplify the fragility of the matching process. Thus, in and of itself, a constraint on the flow of information—combined with a segregated network structure—could produce and maintain segregation within jobs or neighborhoods, without any discriminatory action on the part of individual employers (ibid.). Similar effects can occur in housing and marriage markets when information (p. 372) about neighborhoods or potential spouses diffuses through religiously or ethnically structured networks. Surprisingly, very little research has explicitly connected the structure of communication networks with formal matching processes, though Granovetter and others have argued for the theoretical import of this connection.

16.1.4 Rules or norms about matching

The final analytic feature of matching is the set of rules or norms governing the process. These rules or norms can be understood as encoded values: they reflect and produce priorities about fairness and control. In empirical contexts, the informal rules governing matching processes describe how interaction between actors is coordinated; different kinds of rules place different pressure on preferences and information structures. There are two major families of matching regimes: centralized and decentralized systems. Centralized regimes are typically introduced either to maintain authority of a decision maker (patronage systems) or to improve efficiency (e.g. assignment of organs to donors; Healy 2006). We consider them briefly, and then turn to decentralized matching.

In centralized matching systems some central agent assigns partnerships. The classic example here is a matchmaker in a marriage market, whose role is to arrange partnerships between people or families (Dissanayake 1982; Ahuvia and Adelman 1992; Bloch and Ryder 2000). The main analytic feature of centralized matching systems is that after entering the arena one or both sides gives up the right to refuse a match. Centralized matching is most commonly found either when information constraints are particularly acute (e.g. quality is particularly difficult to discern) or when power is highly centralized (as in traditional Indian marriage markets, or Soviet labor markets).

An interesting empirical case of centralized matching rules is the matching of organs to donors, which is a formalized brokerage situation in the sense that there is an intermediary who resolves information asymmetries and coordinates transfer. Although families of donors might have preferences about who their loved ones’ organs go to, this possibility is eliminated in centralized organ-donation systems. (Once the decision to donate is made, the family has no say in who receives it.) Rather, characteristics of recipients are identified (e.g. general health, age, stage of disease, geographic location), and when organs become available they are assigned to patients based on an established protocol (Elster 1993; Healy 2006). In this case, patients in need of an organ have a relatively low reservation point: by joining a waiting list they are agreeing to accept an offered organ—though the agency that administers the list implicitly promises to certify the quality of the offered organs. The actual rules of allocation are often a stratified first-come, first-served model (or a lottery), within equivalency classes. Centralized allocation regimes emerge in contexts like organ donation in part because of signaling problems (p. 373) (it is very difficult for patients to discern the quality of the organs in a timely fashion), and distributional asymmetries (demand for organs is massive relative to supply). Finally, in many western countries there are ethical concerns about using a price-based bargaining process to allocate organs because it creates incentives for the poor to sell their body parts.

Decentralized matching dominates empirical matching arenas. Here actors navigate the terrain of possible alternatives more or less on their own, guided by their preferences, what they know about what is available, and their understanding of the rules of the game. Matching rules are institutionalized to the extent that actors reproduce them through their own action. Within informal (decentralized) matching systems, key features of the rules involve (1) whether one side dominates the choice process; (2) whether it is possible to simultaneously hold multiple offers; and (3) the expected durability of matches once made (their ‘stickiness’).2

In some matching arenas it is conventional for one side to initiate the matching process. The classic example here is monogamous courtship and marriage: in most western societies, men (or their agents) take the lead on making a proposal to a particular woman. While women can signal interest, they have traditionally been forced to wait for a man to ask for their hand. This asymmetry reflects an underlying power difference; though women can refuse a particular proposal, under these norms they cannot express their own preferences or use the matching arena to learn their value. The consequence of this rule is particularly detrimental to women (at least with respect to their ability to realize preferences for particular types of partners) because they cannot collect and hold multiple offers simultaneously. Two sides of the same coin, the norm for male-led courtship often coincides with weak female economic power, which means that women may have a low reservation point for husbands (e.g. they prefer marriage to an undesirable spouse over remaining single), thus if they wish to find a mate, they must choose quickly from a restricted set of possible offers. Empirically, a macro-level consequence of the male-dominated matching norm is substantial asymmetry in status within marriages—and a larger pool of unmatched higher-status women (Rose 2005).

Contrast this market for wives with a typical job or residential-housing market. As in the marriage market, one side monopolizes the offer stage (employers or buyers) but there is no normative prohibition against recipients simultaneously holding multiple offers. Instead, desirable candidates (or sellers) may collect and compare offers, gaining valuable information about characteristics of potential matches and about their own bargaining position. Employers or sellers may try to regain the upper hand by imposing a time limit on the offer (analogous to an engagement period), but high-demand candidates are frequently able to string employers along while they evaluate their alternatives (or wait for even better offers). Note that, as in many matching arenas, the relative power of each side in the match is in part a function of demand and supply; if many workers are chasing few jobs, employers can put candidates on short leashes. One important consequence of such (p. 374) tight markets is a shift in the reservation point, a change that can have long-term consequences when matches are sticky.

The final important feature of matching rules is the extent to which matches are durable. Here we observe great variation across empirical contexts: some matches are expected to be short (rental housing) while others have longer-term implications (some jobs, marriage). In general, the longer matches are expected to last, the more individuals are willing to invest in search (in order to avoid a bad, lasting match). One way to accomplish this is to be choosy—i.e. to have a high initial reservation point. And yet because these durable partnerships are often the means by which collateral social resources or position are allocated (status, wages), remaining unmatched may ultimately drive down an individual’s private reservation point. Thus, individuals’ preferences are likely to be more sensitive to waiting time when matches are sticky, with reservation points coming in to play much more frequently. Sticky matches also shape the population distribution, since early matches take desirable players out of the matching arena. Thus, new entrants may perceive that ‘all the good ones are already gone,’ and, in a sense, they may be right.

16.2 Formal Matching Models

Formal models of matching processes come mainly from economics, where equilibrium solutions dominate. While some (e.g. Becker) study matching with market models, a better economic model of matching processes is a queueing model, proposed by Thurow (1975) in the context of labor markets. The idea here is that rather than workers and employers negotiating over price, workers compete for jobs with fixed characteristics. Workers queue up for jobs in order of desirability (in the eyes of employers), and are selected based on their position in the queue. Once selected, workers receive the rewards associated with the position. Because employers in large organizations can rarely evaluate workers effectively, Thurow argues that position in the queue is based on employers’ assessment of the ‘typical’ productivity of workers of a particular type. The result, according to Thurow, is ‘statistical discrimination’ against certain types of workers, particularly low-skilled blacks. The basic queueing model was used to explain labor market experiences of women by Reskin and Roos (1990) and has more recently been applied to local labor markets (e.g. Bluestone and Stevenson 1999).

Extending from a basic queueing model, Sørensen (1977) and Sørensen and Kalleberg (1981) develop a model that focuses on the implications of queues combined with contracts between employers and workers. As in the basic queueing model, wages are a function of holding a particular job (rather than marginally (p. 375) related to productivity), and workers compete for access to vacancies in the labor market (see also Baron 1984). Here the ‘stickiness’ of the match distinguishes such a vacancy-competition model from a spot market for labor. In this respect, the analytic features of Sørensen’s queueing and contract model more closely mirror empirical features of many matching arenas, including marriage and housing, than do traditional market models.

By far the most well-known and commonly used formal model of two-sided matching was introduced by Gale and Shapley (1962). It shares many analytic features with queueing and contract models, including a fixed set of positions with defined rewards (i.e. it is not a bargaining model). The basic logic of Gale–Shapley is a deferred-acceptance model, with one side proposing and the other accepting. Given a rank ordering of all actors in the system for actors of the other type, one proposer is randomly selected to propose a match to her most preferred match. This recipient provisionally accepts the match, as long as it is in his ranked set (e.g. is above his reservation point). Then another proposer is randomly selected to make an offer to her most preferred match. Again, the offer is provisionally accepted, contingent on the proposer being in the recipient’s ranked set. However, if the recipient has already provisionally accepted a match, but the new offer comes from a preferred partner, the new offer is provisionally accepted and the first proposer returns to the pool of unmatched proposers. The matching proceeds in this fashion until all proposers have made offers to all the potential partners they prefer over remaining unmatched. Some recipients may receive no offers, and some proposers may remain unmatched.

It has been shown that given a fixed set of preferences, the conventional Gale–Shapley matching algorithm produces a stable, optimal (but not necessarily unique) match (see Roth and Vande Vate 1990). The Gale–Shapley procedure has been frequently used in two-sided matching models—including to match medical students to residencies (Roth 1990)—and its properties are fairly well understood. Extensions of this and other matching models (Becker 1973; Jovanovic 1979) have been developed in economics that allow for time and search costs (see e.g. Shimer and Smith 2000; Rogerson, Shimer, and Wright 2005; Atakan 2006; Hoppe, Moldovanu, and Sela, 2006; Smith 2006) and uncertainty in quality (Mortensen and Pissarides 1994; Mortensen 1998; Moscarini 2005).

Our review shows that many features of the matching process are well described in the analytic and empirical literature. The largest gap, however, concerns one of the more sociological aspects of matching, the structures over which information flows. Given the significance of information for altering the outcomes of matching processes, it is somewhat surprising that the vast literature on social networks and information diffusion (e.g. Granovetter 1995; Watts 1999) has not been explicitly integrated into social-scientific matching models (see Calvo-Armengol and Zenou 2005). Studies of networks reveal a great deal of local homogeneity in networks (McPherson, Smith-Lovin, and Cook 2001), which could result in highly clustered (p. 376) opportunities for matching (Granovetter 2005). In the remainder of this chapter we describe an agent-based matching model that demonstrates the utility of combining models of network structure with matching models.

16.3 An Illustration: Social Networks and Labor-Market Segregation

While those who study matching processes have become increasingly interested in modeling the consequences of limited information, very little research integrates a sophisticated sense of social networks into matching models. This is unfortunate, since, like matching models, the study of social networks is explicitly oriented toward building models of social structure from actual social behavior—in this case, networks of relations. We address this lacuna with a model that focuses explicitly on the link between social networks and the dynamics of matching; this exercise reveals that fundamentally different macro-level conditions are produced by varying preferences or information structure. The model we describe here is motivated by questions about the persistence of segregation in the labor market, but the basic finding extends to other two-sided matching arenas with fixed positions. Simulated results based on this model reveal how network homophily can result in acute segregation, even when employers do not have discriminatory preferences and workers are equally qualified. The key insight is that information flows are frequently socially structured (in some cases as the result of previous matching), and that the nature of these information flows can profoundly affect the macro-level patterns generated by the matching process.

16.3.1 Model overview

Our basic strategy is to build a very simple artificial world populated by workers who want to find jobs and managers who want to staff jobs. Empirical evidence reveals that labor markets are often highly segregated with respect to the ascribed attributes of workers. Many occupations are sex-typed, while in heterogeneous societies certain fields are often dominated by specific ethnic groups. Various explanations have been proposed to account for segregation in labor markets. On balance, most of these explanations can be classified as essentially supply-side arguments, emphasizing differences in human-capital distributions between groups, or demand-side accounts, based on employer preferences. Yet labor-market (p. 377) stratification is actually produced via a matching process where outcomes are a function of preferences, distributions, rules, and information structure.

While real labor markets are multidimensional and complex, our goal in designing the artificial world is to capture (and vary) core features of theoretical interest. Thus, our workers are heterogeneous with respect to only two characteristics: a binary attribute (e.g sex or race) and a quantitative measure that captures variation in qualification (e.g education or skill). Managers’ preferences about potential workers are reflected in utility equations that operationalize various employer-based decision rules. The primary source of information about job vacancies is a social network that links workers and managers. Within each iteration of the model, workers become aware of a set of job openings, and managers select among their pool of available candidates. Workers are assigned to a job or are left unmatched via the basic Gale–Shapley matching algorithm, labor-market features are adjusted in response to the new conditions, and the process begins again. We use this basic simulation framework to conduct experiments contrasting different labor-market conditions. We vary three families of parameters: employer preferences; characteristics of populations; and the information regime.

Employer preferences

Employer preferences for—or against—certain classes of workers are often identified as an important source of labor-market segregation. We compare employers who are indifferent to workers’ characteristics to two distinct types of employer preferences: a preference for more skilled workers, and a discriminatory preference. These preferences are controlled in a utility calculation: in the most general form, an employer i’s utility for a worker j is a linear function of characteristics of the worker, the employer, and the current labor market conditions.3

(1)

U ij =α X ij +βL M t + ε j

In this conceptualization, Xij includes a variety of worker and job characteristics, LMt contains current labor-market conditions, and εj is a small employer-specific noise term. The sets of parameters α and β can be thought of as preferences for characteristics: a higher relative value of a parameter means a stronger employer preference for this characteristic.

In the first preference condition, all workers are fully equivalent in the eyes of employers and selection among candidates is essentially random.4 In practice, this means that the αs associated with workers’ skill and attributes are set to zero.

The second condition is designed to capture employers’ preferences for more skilled workers. Here we set the α associated with workers’ skill to a value >0, while keeping the α associated with workers’ attributes equal to zero. This means that ceteris paribus, workers who present with higher skills will be preferred over workers who present with lower skills.

(p. 378) The third condition introduces a discriminatory preference. The general thinking here is that employers may prefer to hire workers who are like them in salient ways: women managers prefer women employees, Irish foremen prefer Irish workers, and black business owners prefer black employees. We call this an in-group bias, and operationalize it by introducing a binary Xij term that indicates whether the worker and manager are in the same attribute category. When this preference is operative, the α assigned to this indicator variable is set to >0, so that managers will select same-group candidates over candidates who do not share the attribute.

Population structure

While employer preferences may be an important source of labor-market segregation, there is reason to believe that their significance is contingent on the structure and characteristics of the supply of labor that employers confront. At the most basic level, a highly skewed population distribution could make it very difficult for some employers to exercise a discriminatory preference, simply because workers matching their desired profile are scarce. Drawing from the logic of economists’ arguments concerning human capital, we compare scenarios where workers’ skills and attributes are correlated to scenarios where these two characteristics are independent of one another.

Information regimes

While employer preferences and the association between skill and attribute dominate discussions of labor-market segregation, the key contribution of this model is its focus on how access to information about vacancies and candidates affects labor-market processes. We have two aims here: first we model the effects of randomly restricting the amount of information available to all actors in the labor market. Second, and more importantly, we examine the relationship between the structure of networks through which information flows and labor-market outcomes.

As a baseline comparison, we evaluate the model under a condition of full information. Full information is an important assumption of neoclassical microeconomic models of markets, and, while it is empirically unrealistic, it offers a theoretical benchmark against which we can compare outcomes derived from models capturing key features of social processes that influence labor markets.

Once we move away from a full information regime, agents in the model have access to jobs primarily via a social network linking workers and managers.5 A substantial body of research shows that informal social networks are an important vector for the diffusion of information about jobs; here we concentrate directly on whether network homophily translates into labor-market segregation. By homophily we refer to the tendency of like to choose like as a relationship partner (McPherson, Smith-Lovin, and Cook 2001). The primary question we ask (p. 379)

Matching

Fig. 16.1 Representative simulated networks at varying levels of homophily

is: Are there levels of network homophily that can generate substantial segregation in employment, even absent explicitly discriminatory preferences on the part of employers?

We fix the network at the outset, and vary the level of homophily across trials. We control the level of homophily in the network with a simple function that governs the probability Pij of a tie between two actors i and j.

(2)

P ij =( 12p )( ( 1θ ) H ij +θ( 1 H ij ) )+p

The key parameter here is Ë, which controls the strength and direction of the network bias. Hij is a binary measure that indicates if i and j share an attribute, and p is a very small underlying probability of a tie. When θ = 0.5, the probabilities of in- and out-group ties are equal, and the graph approximates a Bernoulli random graph. As θ approaches zero, most ties will cross group boundaries, while as θ approaches 1, in-group ties will dominate. Figure 16.1 depicts networks generated with θ values of 0.5, 0.9, and 1.0. One nice feature of this expression is that in the case of equally sized groups θ can be interpreted as the proportion of all ties that are within the group.

In our network-restricted information scenarios, workers have access to information about any jobs controlled by managers they are tied to directly, as well as about those jobs controlled by managers connected to their network partners.

16.3.2 Outcomes

Our outcome is the level of segregation in the simulated labor market. Because we have implemented a simple two-group model, we use the familiar index of dissimilarity to measure segregation (Reardon and Firebaugh 2002), with the cluster of jobs controlled by a single manager as our unit of aggregation. Substantively, the index of dissimilarity measures the proportion of workers who would have to (p. 380) shift from one manager to another in order make the distribution across managers proportional to the distribution in the population. A value of zero means that workers are distributed in proportion to their representation in the population; higher values mean greater segregation.

16.3.3 Results

The experimental design varies three families of parameters: preferences, population, and information.6 To establish the baseline, we consider how employer-preference regimes interact with different population structures under conditions of full information. We then restrict information via social networks, and examine what happens when networks are more or less structured by our attribute variable. The results show that several combinations of parameters generate substantial levels of segregation in the artificial labor market, including scenarios in which employers are indifferent to workers’ characteristics.

16.3.4 Full-information regime

The first scenarios we examine give all actors full information about each other, but employer-preference regimes vary. This verifies the model, and reveals some preliminary comparisons about the mechanisms of interest.

Figure 16.2 plots results of 50 trials for each of 5 distinct employment-preference/population-structure scenarios. Each unique constellation of parameter values is arrayed along the x-axis, while the level of labor-market segregation from the resulting trials (measured with the dissimilarity index) is plotted on the y-axis. Variability within each scenario comes from the stochastic aspects of the model.

In the first employer-preference regime, managers are completely indifferent to all types of worker heterogeneity (skill and attribute). Further, they are aware of all workers. We consider this scenario a baseline; it produces a dissimilarity index centered about 25 percent, with very little variability. This is the minimum level of segregation possible in our model; what segregation remains is driven largely by small numbers and technical features of the model.

The second scenario adds in a taste for discrimination. In the absence of any other structure in the model, when managers prefer workers who share their attribute over workers who don’t, segregation becomes extremely high. In trials run under this scenario, close to 100 percent of workers are employed in fully segregated firms. Again variability is relatively low.

The third scenario is a variation on discrimination. In this case, rather than preferring to hire workers that are similar to themselves, all managers prefer to hire (p. 381)

Matching

Fig. 16.2 Employer-preference regimes and labor-market segregation under full information

one group over the other, regardless of their own attribute. In this case, the level of segregation is similar to that of the other type of discrimination.

In the fourth scenario, employers prefer higher-skilled workers and are indifferent to attribute. However, worker skill and attribute are independent of one another. This scenario represents what some would consider a labor market ideal, in the sense that employers are seeking the most competitive workers, but whatever process produces skill in the population is not associated with ascribed attribute. In our model, this scenario produces levels of segregation that are statistically indistinguishable from the baseline model.

The final scenario combines an employer preference for higher-skilled workers with an association between skill and attribute. This regime generates substantially higher levels of segregation than the baseline model, though there is a bit more variability than in the discriminatory regime. In this scenario, human capital is rewarded, but since it is unevenly distributed between the two groups, one group enjoys better labor-market outcomes. (p. 382)

Matching

Fig. 16.3 Levels of firm segregation across five experimental regimes

16.3.5 Network-information regimes

We now turn to scenarios in which information flows primarily through a social network that links workers and managers. Figure 16.3 displays the level of segregation resulting from the same experimental regimes shown in the previous figure, however here we connect workers and managers through social networks characterized by varying levels of homophily with respect to the binary attribute.

The baseline scenario, found in the top panel, contains boxplots for sets of 50 trials (at each parameter combination) when employers are indifferent to worker (p. 383) characteristics. While the index of dissimilarity is still plotted along the y-axis, the x-axis now arrays trials characterized by various levels of network homophily. On the far left the graphs are random with respect to attribute (θ = 0.5); as we move toward the right, networks’ in-group biases become more pronounced. This figure reflects the baseline association between network homophily and labor-market segregation in our network-restricted models. It is evident that when networks are integrated, the level of segregation is comparable to our full-information baseline. However, as networks become more homophilous (θ ≥ 0.7), the level of labor-market segregation begins to rise quite dramatically. When networks are largely segregated into two distinct clusters, the average level of segregation in the simulated data is almost four times greater than in the baseline model. The implication of this result is that high levels of segregation are possible even when employers are indifferent to any worker characteristics. The mechanism generating segregation when networks have a strong in-group bias is a selective pool: if job-relevant information flows through networks, and networks are disproportionately composed of those in the same attribute category, workers will predominantly hear about jobs controlled by in-group managers, and managers will be forced to choose from a pool that disproportionately reflects their own attribute identity.

The second row of Figure 16.3 shows analogous plots for trials when employers exhibit an active preference for workers who share their own attribute (left) or belong to a single sought-after category (right). For reference, we indicate the level of segregation for the full-information baseline as well as the segregation trajectory for the baseline model under varying network conditions. Results here are substantially different from the baseline: When networks are random, discriminatory preferences increase labor-market segregation substantially over baseline levels (D—the index of dissimilarity—is roughly three times higher than the baseline). However, the index of dissimilarity for these trials is not as high as in the full-information discrimination regime, because the restriction on information means that some employers are ‘forced’ to choose workers they don’t prefer, simply because there are no others in their randomly generated pool. As the network bias gets stronger, the level of labor-market segregation rises. However, even at the highest levels of in-group bias, segregation does not rise above the network-restricted baseline levels. This suggests that when networks are highly segregated (θ ≥ 0.9), the network itself is the cause of extremely high levels of labor-market segregation, rather than any existing employers’ discriminatory preferences. Interestingly, in the exclusionary regime employers are unable to segregate the firms to quite the same high level as in the in-group-discrimination regime.

The last row reports results of trials where employers prefer higher-skill workers, but skill and attribute are independent (left), as well as where there are skill differences between groups (right). When skill and attribute are independent, the pattern in the level of segregation is identical to our network-baseline model. While segregation does rise, it is purely as a result of changes in the level of in-group bias in (p. 384) the underlying network through which job-related information flows. In contrast, when groups differ in their average skill, the pattern is closer to that generated by the discriminatory-preference regime—though the level of segregation observed for low levels of θ is somewhat lower. As in the discriminatory case, when networks have a strong in-group bias, the level of labor-market segregation is substantially higher, though again the values do not rise above those generated in the baseline model.

When comparing the impact of employer preferences and population characteristics on segregation, the results from the network-restricted-information trials mimic the crude pattern observed in the full-information trials. Specifically, discriminatory preferences are extremely effective at generating segregated labor markets, while the combination of skill preferences and group differences in skill levels is almost as effective. However, the network-restricted scenarios reveal that these well-known mechanisms for creating segregation are not necessary conditions: When networks reveal strong in-group biases, these biased networks themselves are sufficient to segregate the artificial labor market. In fact, adding either of the segregating mechanisms to a homophilous network does not result in an increase in labor-market segregation above the level observed with the homophilous network alone.

Concluding Comments

The study of social life requires understanding how individuals form relations with one another, and how these relations structure access to positions and other resources. Neither individual preferences nor the structure of opportunities alone is sufficient to explain this complex process. Treating the link between person and position as a matching process, however, enables scholars to explicitly model the interplay between individuals and social positions and provides an analytic foundation for understanding the reproduction of institutionalized patterns of interaction. Substantively, this orientation sheds light on one of the major sources of segregation, since empirically both norms and information constraints effectively restrict individual choice in the matching processes. The result is local clustering, and the development of subsequent preferences and capacities that may reinforce this pattern.

In this chapter we have reviewed some of the core features of matching processes, discussed formal models describing matching regimes, and presented results from a simulation that brings a network model into the matching literature. We now offer some additional comments on various endogenous aspects of matching processes.

(p. 385) At some fundamental level matching is governed by preferences, and to the extent that we are willing to treat individual preferences as fixed and exogenous, matching may be relatively straightforward. However, sociologists recognize that this conceit is little more than an analytic convenience: it flies in the face of empirical investigations of behavior. Though this direction has not been well developed, there is ample reason to believe that studies of matching may contribute to our understanding of how some preferences are structured and constrained by local opportunities. The idea here rests on three important facets of matching processes: that matches are constrained by others’ preferences, the strength of local rules about the importance of being matched, and the costs of decoupling. Each of these factors may cause actors to come to prefer that which is available to them (Baron 1984; Solga and Konietzka 1999). Thus, matching arenas may best be understood as settings in which actors’ preferences are, at least in some respects, endogenously produced.

Matching processes may also play a role in structuring the production of actors with particular characteristics. Key here are the complex temporal dynamics that operate in matching arenas. Particular matches occur at a given moment in time, but the operative rules frequently have a longer life span. For any actors watching the process, ‘made matches’ (and failed matches) offer the best guide of what to expect. These later actors read the outcomes of those ahead of them and attempt to position themselves accordingly. Consider a labor market that rewards (or ignores) educational credentials. If this reward structure is stable over the medium term, actors who anticipate entering this labor market may invest in (or avoid) acquiring credentials in order to be more competitive in the matching arena. This proactive investment will alter then the subsequent distribution of potential employees over which employers choose, and may ultimately change the rewards to the credential—often to the detriment of those who thought they were acting in their own best interest (Boudon 1973; Stovel, Savage, and Bearman 1996). The general point here is that because matching systems have a large number of ‘moving parts,’ there are numerous possibilities for feedback loops. Frequently these are self-reinforcing, though they may also result in significant disruptions.

Our investigations into the interactions between network structures and matching processes point to another form of reinforcement that may occur as actors are matched to position. We have shown that homogeneous networks are sufficient to generate segregated workplaces. But what if segregated workplaces themselves increase the level of homophily of networks? This would clearly have implications for subsequent job-finding (Stovel and Fountain 2006), but it could also have implications for how persons navigate other matches as well. Consider the substantive domains in which matching plays a prominent role: marriage, school assignment, housing markets, finding a job. These are exactly the places where people’s networks are formed. Because networks can play such an important role in structuring the (p. 386) type and amount of information that individuals have access to, networks stitch these matching domains together, and changes in one domain may have significant implications for adjacent domains.

Obviously the feedback inherent in matching processes has implications for the individuals: as actors observe matching, they may prospectively adjust their behavior or attitudes, thus shaping their own prospects. Yet this feedback can also have consequences at the macro level, where these cumulative effects will often appear as more than a simple aggregation of individual changes. Rather, if actors fail to appreciate the two-sided nature of most matching processes, the combination of interdependence and uncertainty can trigger a cascade that profoundly alters the structural landscape. Consider a common finding in evolutionary game theory: When actors are randomly paired, exploitative strategies easily dominate, but if actors are paired via competitive matching, something interesting occurs. Initially, exploiters dominate, but over time they are surpassed by more cooperative players (Yamagishi, Hayashi, and Jin 1994; Skyrms and Pemantle 2000; Hauk and Nagel 2001; Chiang 2008). This result is a direct consequence of the two-sided nature of the matching process: exploiters benefit from playing with altruists, but altruists prefer other altruists over exploiters. Because matches must be mutually acceptable, the exploiters are unable to find altruists willing to play with them, and vanish as a consequence.

Pairings such as those described throughout this chapter are a basic building block of social structure, so understanding the matching processes that link us to one another as well as to opportunities and positions should be of central importance to sociologists. The primary social institutions in which we participate, including families, schools, the labor market, the economy, religious organizations, neighborhoods, and other social groupings, are all built in part from these processes. The advantage of the matching model is that it neglects neither choice nor constraint, while directing analytical focus on the interdependence of actors on the preferences, attributes, information, and actions of others in the matching arena. Matching models can provide a useful tool with which to describe and build theory about the complex, interdependent processes through which individuals’ choices create—and are constrained by—social structures.

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                                                                                                                                Notes:

                                                                                                                                (*) Research for this chapter was supported by the National Science Foundation (SES-351834).

                                                                                                                                (1.) John Logan’s two-sided matching model (Logan 1996; Logan, Hoff, and Newton 2008) is an attempt to incorporate the population marginals into the choice structure of individuals, and therefore is an improvement over existing log-linear models of net association. However, these models also confound individual preferences and the local choice set that individuals confront.

                                                                                                                                (2.) A fourth element of the rules of matching concerns whether actors regularly hire agents to represent them. Agents or brokers are most common when information asymmetries are acute and matches are relatively sticky; that is, when the costs of mismatch are high. When actors choose agents to represent them, matching can proceed as in other contexts though search times may decline (see Levitt 2005). Matching arenas in which brokers gain complete control may be indistinguishable from centralized matching.

                                                                                                                                (3.) We also calculate an analogous set of utilities from the workers’ perspectives. This allows us to use the two-sided matching algorithm.

                                                                                                                                (4.) In all trials reported here the model does include a slight preference for previous employees; this ‘stickiness’ is included to reduce the overall amount of turnover in the labor market and serves to crystallize observed patterns more quickly (Fountain and Stovel 2005).

                                                                                                                                (5.) We also distribute a small amount of random information, to simulate non-network recruitment strategies.

                                                                                                                                (6.) All trials are based on labor markets with 200 workers and jobs, and 20 managers, k = 5, 100 iterations per trial with 50 representatives in each θ by regime configuration. There is 0.005 random information (except with the perfect-information regime) and two equally sized worker categories with mean skill 70 and 30 (s.d. = 5) when relevant.