How Do School Peers Influence Student Educational Outcomes? Theory and Evidence From Economics and Other Social Sciences

Conclusions: The evidence is not completely consistent with any single theory, though it is more supportive of some over others. A new hybrid theory—group-based contagion—is proposed that is more consistent with the evidence.

Social scientists have long been interested in how the behavior, beliefs, values, and educational outcomes of children are shaped by interactions with their peers in school activities. The reasons for interest in school social interactions are almost too numerous to list: Children spend as many hours in schools as they do interacting with their own parents,¹ and there is strong evidence, as shown in this article, that these school experiences have a significant influence on students as they move on to adulthood. In addition, there is good reason to believe that certain types of “beneficial” social interactions—those that are likely to result in better educational and life outcomes—are highly unequally distributed by student race and income and are becoming more unequal as minority and other disadvantaged students become increasingly concentrated in a small number of schools (Orfield, 2001). Given the importance of education for long-term well-being, this unequal and potentially worsening distribution of peers may reinforce racial inequality and the cycle of poverty.    

Although the evidence seems to suggest that peers are important, we know relatively little about how peers influence one another. That is, which theory or theories of peer influence are most consistent with the empirical evidence? This question is important because the correct policy response to peer influences depends on the nature of those influences. Desegregation by race is one possible policy response, though political support and legal options for pursuing this option have been dwindling (Harris, 2006; Parents Involved v. Seattle School District, 2007). Because of the legal constraints on using race, researchers and policy makers have recently shown interest in income-based desegregation. In addition, magnet schools and the federal No Child Left Behind Act indirectly redistribute students across schools based on their test scores, and students are further redistributed within schools through tracking (Gamoran, 1986; Mickelson, 2001; Oakes, 1985; Ogbu, 2003). The ultimate effects of such policies on student achievement depend on how peers influence one another and, particularly, on how race and initial achievement influence peer interaction.  

Yet, empirical research has been largely divorced from theories of peer influences. Jencks and Mayer (1990), in what is still one of the most extensive reviews of theory and evidence to date, wrote that “from an empirical viewpoint it is often difficult to choose among these . . . models [of peer influences]” (p. 115). Moreover, despite their extensive review of theory and research, they wrote that “the work we review throws little light on this controversy” (p. 115) about which theories and models are operative. Braddock and Eitle (2004) put the point even more strongly when they wrote that the “early studies [of the effects of desegregation] lacked any theoretical basis [and] this remains true for many recent studies as well” (p. 829)  The same can be said of economists. Manksi (2000), writing on the somewhat broader issue of social interactions, indicated that

empirical economists may borrow jargon from sociology and social psychology, and write that they are studying “peer influences,” “neighborhood effects,” “social capital,” or some other concept. Yet empirical analyses commonly fail to define these concepts with any precision, and often explain only obliquely how the reported findings shed light on the interactions being studied. (p. 117)

One goal of the present study is to draw a closer linkage between theory and evidence.

There are two obvious difficulties in understanding peer influences that plague this literature and that are addressed in the present study. First, given the likely complexity of peer influences, interdisciplinary research is probably necessary, but such research is difficult and rare. Second, even with a clear theory, there are inherent difficulties in identifying causal peer influences because of the nonrandom assignment of students to peers and school resources. A third challenge, highlighted by the present study, is that many of the multiple theories yield similar or ambiguous predictions about the observed patterns of student outcomes, making it difficult to test many theories.

The present study helps to address these theoretical and empirical problems in several ways. I start by summarizing and synthesizing a variety of social science theories regarding peer influences from anthropology (e.g., Ogbu, 2003), sociology (e.g., Jencks & Mayer, 1990), psychology (e.g., Gurin, Dey, Hurtado, & Gurin, 2002; Oyserman, Brickman, Bybee, & Celious, 2006), and economics (e.g., Austen-Smith & Fryer, 2005; Durlauf & Cohen-Cole, 2005; Hoxby & Weingarth, 2005).² I discuss the basic nature of the theories, including whether they hypothesize positive, neutral, or negative influences of more advantaged peers; whether the effects arise from peers influencing beliefs and values or serving as direct “instruments” to higher outcomes; and through what specific mechanisms the influences occur. I also identify the empirical predictions of each theory regarding the effects of peers on student achievement.

The focus on student achievement is justified for several reasons. First, it has been of considerable interest to researchers and policy makers. Second, achievement is the only outcome for which it is possible, across a range of settings, to convincingly address the significant methodological difficulties when trying to identify causal peer influences using quasi-experimental methods. Third, it would be impossible in a single article to discuss a wide range of theories, their implications, and evidence for more than one outcome given that other outcomes are likely to be the product of different types of social processes. Future research in this area might involve similar discussions for the many other student outcomes that are of interest (e.g., social cohesion, prejudice, racism).

I also draw tentative conclusions about which theories are most consistent with the most rigorous research. Experimental research has been reviewed extensively by others (e.g., Harris, 2007a; Linn & Welner, 2007); therefore, I focus on the recent innovative research by economists that appears to address key methodological issues. In short, this “peer effects” research tries to identify peer influences using detailed longitudinal data and value-added methods to test the roles of peer race and peer achievement, leveraging the fact that each individual student has different peer groups at different points in time. One strength of these studies is that, unlike the experimental studies, researchers have attempted to decompose peer effects in way that makes it possible to test the various theories. For this and other reasons, the economics-based peer effects research has the potential to address both the theoretical limitations of previous experimental research and the methodological (and theoretical) limitations of previous nonexperimental research. However, partly because they have focused on methodological issues, economists have not realized the potential of using these methods to learn about how peers influence one another. This in turn has created new methodological problems because the absence of theory has yielded empirical models that are often misspecified.

The evidence from the better specified statistical estimates from economists provides some support for several specific theories of peer influences, but none of the theories alone explains all the key empirical observations discussed. I therefore propose a new theory: group-based contagion. Although often considered outside the boundaries of peer effects, peers also appear to influence one another indirectly through changes in school resources.  

THEORIES OF PEER INFLUENCES

This section summarizes and synthesizes theoretical discussions of peer influences across disciplines. The discussion gives particular attention to economic theories because they are least well known and because this provides the necessary background for the later discussion of economics-based empirical evidence.

Following Jencks and Mayer (1990), I start with a discussion of the theories suggesting that having more advantaged peers is beneficial for disadvantaged students, and I proceed to theories suggesting that having more advantaged peers has a harmful effect or no effect. By “advantaged” students and peers, I mean those who typically have strong educational outcomes: White students and/or those who come from families with high levels of parental education and income. Further, an advantaged school is one that serves high percentages of advantaged students. The focus on the effects on disadvantaged students is justified because the basic presumption of desegregation efforts is that these are the students being harmed by the current state of affairs. The theory and evidence in this study suggest that the mentioned advantages, as well as peers, are among the many aspects of the broad social environment that create significant and persistent inequalities in outcomes and therefore deeply rooted social disadvantages for certain groups.  

I focus on school-related influences and therefore refer only to students and schools, not to preschool-age children or to the influence of school-age children that arises outside school (e.g., in neighborhoods), though most of the statements and arguments could be extended to all these categories and to the larger literature on neighborhood influences and other social interactions (e.g., Durlauf & Cohen-Cole, 2005). I therefore define a peer simply as another student with whom the individual student comes in contact in school-related activities, though an important point of this study is that some peers are likely to be more influential than others. A peer effect therefore occurs when the outcomes (in this case, academic achievement) of an individual student are influenced by the behaviors, attitudes, or other characteristics of other students with whom they interact during school activities. Some researchers implicitly use a narrower definition that excludes peer influences that operate in more indirect ways, especially through the allocation of resources (e.g., funding) and through the ways in which teachers form their expectations about students. The following discussion takes a broad view about potential peer influences partly because these indirect influences must be taken into account in empirical analyses that intend to isolate a narrower peer effect construct.

SOCIAL SCIENCE THEORIES OUTSIDE OF ECONOMICS

This section starts with a discussion of anthropological, psychological, and sociological theories of peer influences, proceeding from those theories that suggest that having more advantaged peers is beneficial for disadvantaged students. This initial discussion also incorporates the names of theories given by the economists Hoxby and Weingarth (2005), who provided arguably the only other comprehensive attempt to outline theories across disciplines.³ Their theories are not rooted in economics, and their discussion of economics is more anecdotal than theoretical. For these reasons, and because their theories largely overlap the more academic and theoretical discussion of the noneconomics literature in the following section, I only mention the names they gave to these theories. A discussion of economic theories follows.

Potential benefits of advantaged peers for disadvantaged students. Jencks and Mayer (1990) defined the epidemic or contagion theory of peer influence in which children emulate the behavior of their peers, perhaps on the basis of peer group norms. Further, because more advantaged peers, by definition, are more likely to engage in academically oriented behaviors (e.g., paying attention in class and doing homework), other students in their presence are more likely to follow the advantaged students’ lead, engage in these behaviors themselves, and therefore obtain high test scores.  Hoxby and Weingarth (2005) apparently referred to this same theory as the bad apple and shining light. As the names imply, a bad apple is a disadvantaged student who pulls down the achievement of all others in the group, whereas the shining light is an advantaged student who pulls others up.

An implicit assumption in the epidemic theory is that each school “has a single dominant set of norms, to which every child . . . tries to conform” (Jencks & Mayer, 1990, p. 114). There are two senses in which this is likely not to be the case.  First, as Jencks and Mayer subsequently pointed out, some students may be less “susceptible” (p. 115) to imitative behavior than others, perhaps because they have stronger senses of individual identity and therefore rely less on groups as a source of identity. Second, students may be more likely to associate with, and emulate the behavior of, certain subgroups. Race and gender are two characteristics that affect each individual’s group affiliation and identification. Thus, in contrast to the epidemic theory, it may not be the characteristics of the overall group that matter, but the characteristics of the respective racial, gender, and other subgroups. I return to this issue in the later discussion of oppositional cultures and “acting White.”  

Gurin et al. (2002) also consider the importance of individual identity but from a psychological and cognitive perspective. They argued that interaction with diverse groups (those with whom students do not identify) induces people to seek out new information “in order to make sense of the new situation” (p. 335). Further, referring to Bargh (1997), they wrote that when people interact with “others,” they cannot rely on “automatic thinking” and must instead engage in “effortful and mindful” modes of thought (Gurin et al. p. 337), which they argued contributes to cognitive development.⁴ They argued further that the benefits of effortful and mindful thinking are most likely to occur in late adolescence and early adulthood, including the high school years. I refer to this as the “cognitive development theory.” Hoxby and Weingarth (2005) call this the “rainbow” theory.

Although the mentioned theories focus on the direct influences that students have on one another, Jencks and Mayer (1990) described other indirect forms of influence. The institutional theory highlights the fact that schools that serve more advantaged students are likely to have more resources than other schools because of the way that political and funding institutions operate. Heavy reliance in the United States on local property tax funding for education, for example, results in less funding per pupil for schools in low-wealth districts. Further, housing tends to be highly segregated by income and wealth so that some districts end up spending much more than others. Although low-poverty districts still spend more than high-poverty districts, state school finance litigation has led to changes in school finance that have significantly equalized spending across family income categories.⁵ Even if financial resources were exactly equal for advantaged and disadvantaged students, however, there is strong evidence that the teachers are less willing to teach in locations that serve disadvantaged students. Hanushek, Kain, and Rivkin (2001) found that student race is the strongest predictor of teacher departures. There is also some evidence that teachers with stronger academic credentials are less willing to teach in schools with disadvantaged students (Lankford, Loeb, & Wyckoff, 2002).⁶ These nonfinancial pressures also influence the overall distribution of teachers, and this is significant given the central role that teachers appear to play in the educational process (Rivkin, Hanushek, & Kain, 2005; Sanders & Horn, 1998).

The unequal distribution of resources is not only across districts. Within districts, especially large districts, housing is also segregated by race and income; more advantaged families tend to vote in school board elections in larger numbers and put more pressure on school boards to direct resources to the schools that their children attend. There is also evidence that the mentioned nonfinancial aspects that affect teacher departures influence the distribution of teachers within school districts as individual schools compete for the best local talent (e.g., Harris, Rutledge, Ingle, & Thompson, 2006). I refer to this as the institutional-resource theory because it highlights the close connection between peers and institutional resources. A second type of institutional theory, which I call institutional-expectations, refers to the idea that teachers’ instructional practices may be altered by the characteristics of students in the classroom, a result of teachers having lower expectations for disadvantaged students. For example, Ogbu (2003) found that teachers of students in lower track courses assign less homework and focus their instruction more on basic comprehension and memorization of facts than on critical thinking. These differences may in turn be due to differences in teachers’ expectations about what students are capable of. This theory of low expectations is implicitly used, at least rhetorically, by advocates of school accountability, such as President Bush and Education Trust (Harris, 2007b). In this case, it is not that the teachers are less skilled, as suggested by the institutional-resources theory, but that they do not put their skills to use for the maximum benefit of the students. Even if this is true, it is important to note that teachers’ expectations are intricately intertwined with those of the students, and instruction in the classroom can be viewed as a collective negotiation between teachers and students (Sedlack, Wheeler, Pullin, & Cusick, 1986). This is also why the institutional expectations experienced by each individual student depend on peers.

Harm from advantaged peers for disadvantaged students. There are also theories suggesting that advantaged peers may be harmful to the academic outcomes of disadvantaged students. According to Jencks and Mayer’s (1990) relative deprivation theory, children may simply become more frustrated and put forth less effort in the presence of advantaged peers because their relative social position is lower. One reason this might arise is that teachers often grade on a curve so that the grades of disadvantaged students would decline and reduce students’ perceived success. Hoxby and Weingarth (2005) referred  to this as the invidious comparison theory.

A variation on the relative deprivation model, called “oppositional culture” (Ogbu, 2004) or “cultural conflict” (Jencks and Mayer, 1990), posits that students who are low in the perceived social hierarchy choose to disassociate from the dominant group and form alternative peer groups that reject the dominant group’s preferences and behaviors.⁷ Ogbu (2004) wrote that oppositional culture is a mechanism for coping with the pressure to “act White” and takes form in students rejecting the behaviors and attitudes of Whites.

For Blacks in the United States, this pressure to act White, as well as the oppositional response, is rooted in the nation’s history of slavery and racism.⁸ This history leads to the perception among Blacks that they were—and still are—treated poorly by Whites in the form of low schooling resources and fewer job opportunities. Because of this discrimination, Blacks have a psychological need to develop coping mechanisms, including the formation of a clear and distinctive Black identity and group norms that deliberately conflict with the dominant White culture. Thus, existing inequalities in academic behaviors and outcomes become reinforced as the inequalities become ingrained as (subgroup) cultural norms. For other interpretations of Ogbu’s theory and research, see, for example, Foster (2005).⁹

Hoxby and Weingarth (2005) offer a somewhat different perspective on the role of race and social groups. Their subculture hypothesis is that the majority group in any classroom/school will accept minority members (where minority is apparently broadly defined to include, but go beyond, race), so long as the number of students in each minority group is very small and therefore does not “threaten the environment” of the majority (p. 7). This is similar to the oppositional culture theory except that it focuses on the behavior of the dominant group and its desire to band together rather than the responses to the dominant group by the minority group. But Hoxby and Weingarth’s version differs, importantly, in that the opposition is more localized to the classroom and school rather than, as in the oppositional culture theory, the broader historical and societal contexts in which the schools and students are situated.     

Potential noninfluence of peers on disadvantaged students. There are several ways in which the mentioned potential benefits and harms of advantaged peers may be attenuated so that peers essentially have no influence on one another. The most obvious is that other factors may simply dominate peer influences. The most notable example dates to Coleman (1966) and the idea that student outcomes are determined largely by home influences (also see Oreopoulos, 2003).

In addition, a large number of research studies show that students are tracked within schools (Gamoran, 1986; Mickelson, 2001; Oakes, 1985). If disadvantaged students are going to be grouped with other disadvantaged students no matter what school they attend, then the school peer population may have only a modest influence in one direction or the other. At one level, tracking is less a theory than a description of how schools work. However, the term tracking is usually used to refer to the idea that tracking is harmful and that, with respect to peer effects, any benefits of being in a school with more advantaged peers are offset by the tracking of peers (and resources) within schools. It is not clear from theory alone whether the hypothesized effects attenuate or whether they actually reverse. For example, suppose that the institutional-resource theory mainly explains the nature of peer influences. It is unclear whether a disadvantaged student who moves from a disadvantaged school to an advantaged one still benefits at all. This would depend on whether the resources in the disadvantaged school are lower than the resources in the lowest tracks of the advantaged school. Similar issues arise with the other theories, and theory alone cannot resolve them.

Hoxby and Weingarth (2005), in their focus and boutique theories, offer a quite different view of tracking. Their logic is that students may do better in homogeneous (tracked) classrooms because teachers are better able to tailor instruction to the group’s individual needs. As we will see in the next section, they also found some evidence to support this.  

ECONOMICS-BASED THEORIES

Although this study is deliberately and extensively interdisciplinary, economics plays a somewhat distinctive role. Although most of this contribution is to the empirical methods (discussed later), much of the theoretical work by economists on this topic is quite new and not well known among noneconomists. Economists also approach social science research in somewhat different ways, making different assumptions about human nature and behavior, as compared with other disciplines.

Jencks and Mayer (1990) wrote that “strong individualists—especially economists—often assume that neighbors [peers] have no direct effect on an individual’s behavior” (p. 117). This characterization does not quite get to the heart of the economic theory, however. Economists are indeed “strong individualists” in the sense that they treat the individual as the unit of analysis and assume that individuals are rational¹⁰ and self-interested—that is, individuals maximize their well-being, or “utility.” Nevertheless, individuals in this framework can and do influence one another. Manski (2000) argued that there are two primary types of interactions that fit with economic theory: interactions in constraints (a resource one that chooses to use cannot be used by others) and expectations (educational decisions are based on expectations formed from information that not all agents have).¹¹ With the context of peer influences, the discussion of disruption in the next section provides an example of an interaction in constraints, and the subsequent discussion of signaling provides an example of an interaction in expectations.

Although interactions in constraints and expectations are not necessarily less “direct” than those proposed by other social scientists, as Jencks and Mayer (1990) argued, they are certainly of a different nature. The main implication of these mentioned assumptions is that peers are important, not because they change the beliefs and values of individuals—as the epidemic, relative deprivation and oppositional culture theories assume—but because peers can provide valuable services to the individual; that is, they are “instrumental” to academic skills.¹² In empirical studies, these services are generally unspecified, however, and this underspecification turns out to be a significant limitation of both economic theory related to peers and economic evidence on the topic. With regard to theory, the assumptions of rationality and self-interestedness might be reasonable starting points for explaining some types of behavior among adults. But it is questionable whether these same assumptions—as well as the assumption of fixed utility, beliefs, and values—are even roughly correct regarding the behavior and interactions among children as young as 5 years old. Although all economic theories of peer influences make these assumptions, the economic theories discussed next have some interesting and important features.

Classroom and school disruption. By its very nature, schooling involves a group of students interacting with a teacher in an enclosed space. Further, a substantial portion of instruction involves the teacher interacting with one or more students together as a group, such as when a teacher is lecturing an entire class. Therefore, any disruption in the class that prevents the teacher from engaging with other students in group instruction reduces the amount of instruction that each student receives. I refer to this as the disruption theory.

While I place this within the economics category, economists are certainly not the only ones to discuss it. For example, Ogbu (2003) wrote that “almost every study of Black students’ relationships with school personnel and among themselves has found that lack of discipline or disruptive behavior is a major obstacle to teaching and learning” (p. 133). Ogbu referred to several studies in support of this contention including, most recently, Fordham (1996).

An economics-based signaling theory. Austen-Smith and Fryer (2005) also approached the topic of peer influences from an economic perspective, though in a way that more explicitly combines standard economics with other social science approaches. Based on their sophisticated analysis, they concluded that the oppositional culture of Blacks arises not as a coping mechanism in response to pressure to “act White,” but because social groups have imperfect information about potential group members. Individuals choose their education partly to send a signal about their value to the group. Further, the result of these choices is that different social groups make very different decisions about their school behavior and education. They call this the two-audience signaling quandary.

The authors drew their conclusions from an elaborate mathematical model of (hypothetical) individuals who make educational choices in order to maximize their utility and who vary in their social status and economic ability. Social status is defined as anything that makes the individual more valuable to the group. Economic ability reflects the characteristics typically associated with high income—work ethic, intelligence, and so on. Each individual’s social status and economic ability are unchangeable (that is, they are given at birth), though an individual’s income can be changed as a result of the choice of education; that is, someone with low economic ability might still earn a good income as a result of investments in education.

Consistent with these theories from other disciplines, “all social types strictly prefer to be accepted rather than rejected by their peer group” (Austen-Smith & Fryer, 2005, p. 3). Social status and economic ability are also uncorrelated, so an individual of low social status is just as likely as a high-social-status individual to have high economic ability. Based on these social and economic statuses, people choose their education levels when they are young in order to maximize a combination of their short-term and long-term financial well-being.  

The other actors in the model—the “two audiences” referred to previously—are employers and a single peer group. It is assumed that employers pay each worker based solely on productivity, which in turn depends only on the individuals’ education level and economic ability. This means that employers do not care about the individual’s social status; that is, employers do not engage in racial or other forms of discrimination.¹³ An implication of these assumptions is that individuals of different social status would, on average, choose exactly the same level of education if it were not valuable to belong to the group.

In contrast, the peer group prefers individuals who are of high social status or, as Austen-Smith and Fryer (2005) wrote,

Peer groups, however, only want to accept members who are socially compatible group members in that they can be depended upon to support the group in difficult times. Examples are not hard to find; they range from gang members who can be trusted not to betray other members when subjected to police investigation, to residents of a community who can be relied upon to invest the time and effort to help their neighbors.¹⁴ (p. 4)

All these examples point to a particular notion of the value of group affiliation: that the group provides a form of “protective service” to group members. Because this part of the model focuses on nonfinancial group activities and because of the explicit role of social status, the overall model can be characterized as a true hybrid of sociological and economics thinking.

Although social status is important to the group, the authors assume that the individual’s social status cannot be observed by the group. Because of this imperfect information, individuals “signal” their value to the group through their behavior—specifically through their educational decisions. The authors assume that high-status individuals benefit more from being in the group than do low-status individuals; high-status individuals also benefit less from obtaining more education. As a result, individuals who choose less education are more likely to be of high social status. Further, because the group benefits more from having high-status members, the group is more likely to choose applicants who have less education.

How does all this help to explain relations among students of different racial groups? Based on the preceding examples given by the authors, we can think of the peer group as a gang. High-social-status individuals are those inherently more likely to be loyal to the gang. Students who are devoted to their schoolwork, by showing that they have other objectives, signal to the gang that they are unlikely to be loyal and help the group in hard times. The academically oriented student has less time to devote to group activities because she spends more time on schoolwork, and she has more to lose by helping the gang because one of the outcomes of group membership, getting arrested, would undermine the value of her academic effort^.15

The main prediction of Austen-Smith and Fryer’s (2005) model then is that “racial differences in the relationship between peer group acceptance and academic achievement will exist and these differences will be exacerbated in arenas that foster more interracial contact or increased [economic] mobility” (p. 5). Regarding the first part of this conclusion, more interracial contact increases the value of group membership because the need for protection (presumably protection from “others”), and therefore the need for loyalty, becomes more important.¹⁶ In making educational choices, it will therefore be more important to individuals who lack economic ability to signal to the group that they will be loyal; they therefore choose less education. This creates inequality that is exacerbated by more interracial contact because an increase in labor market benefits from education means that individuals who were barely in the peer group previously now choose more education, thus pulling down the average education of those who are accepted in the group. The predictions of the oppositional culture theory are somewhat more vague. Indeed, whatever the underlying differences in explaining why the opposition arises, the predictions of the Austen-Smith and Fryer formulation are easier to put to formal statistical tests. This is an advantage of the mathematical approach more generally.

An important implication of this signaling theory, and a key point of departure from the oppositional culture theory, is that the peer group (gang) has no inherent value or preference regarding “whether a potential member works hard at school, is employed or wealthy” (Austen-Smith & Fryer, 2005, p. 3). In contrast, the oppositional culture theory suggests that racial groups do have such preferences, which arise from perceived current and historical poor treatment by Whites and the psychological need to differentiate themselves. Thus, Austen-Smith and Fryer acknowledged that an oppositional culture exists in some sense but that the underlying source of the opposition has less to do with the perceived poor treatment by Whites and more to do with the need to address potential threats to safety.

As interesting as this conclusion might be, the underlying assumptions of the two-audience signaling quandary are less than compelling.¹⁷ Austen-Smith and Fryer (2005) made the standard economic assumptions that student beliefs and values are fixed and that children understand the relationship between education and long-term well-being. In addition, like the epidemic theory, the two-audience signaling quandary involves only one peer group that all members might try to join. Although this might seem like a useful simplification, the group dynamics could conceivably be quite different in a more realistic model in which the multiple purposes of groups were considered and in which, as a result, multiple groups would emerge. These groups would also interact and compete with one another, greatly complicating the analysis and potentially changing the implications of the theory.  

These questionable assumptions do not necessarily invalidate the model. As the authors (Austen-Smith & Fryer, 2005) argued, the predictions obtained from their model are consistent with a variety of empirical observations.¹⁸ However, the assumptions do suggest the possibility that the congruence of the model with empirical observations may be more of a coincidence than a validation of the model. I return to the issue of empirical support in later sections.

SUMMARY AND FRAMEWORK FOR PEER INFLUENCES

This section introduced a variety of theories about how peers influence one another. Those that predict that disadvantaged students will benefit from being in schools and classrooms with advantaged students are: epidemic, cognitive, institutional-resources, institutional-expectations, and disruption. In contrast, the relative deprivation, oppositional culture, signaling, and focus-boutique theories suggest that disadvantaged students lose out from having advantaged peers. All these effects may be attenuated by home influence, or institutional practice of tracking that limits the experiences that disadvantaged students have with more advantaged students even when they technically attend the same schools. (As Hoxby and Weingarth, 2005, noted in their focus-boutique hypothesis, tracking could be beneficial for disadvantaged students under certain circumstances.)

Most of the mentioned theories work in reverse in terms of the effects of disadvantaged peers on advantaged students. For example, the epidemic theory suggests that disadvantaged students benefit from having more advantaged peers because they will be imitating more academically beneficial behavior; the epidemic theory also suggests that the reverse would be true for advantaged students, who would more frequently imitate disadvantaged students. Whether these countervailing forces offset one another is a topic I return to later, in the discussion of evidence.

In addition to the direction of the effects, the theories also vary regarding the nature, or underlying causes, of peer influence. In the case of the epidemic, cognitive, relative deprivation, and oppositional culture theories, peers shape the beliefs and values (or, in economics language, the utility function) of the individual. In contrast, in the institutional-resource, institutional-expectations, focus-boutique, and signaling theories, peers are only “instruments” for the individual to improve her well-being, where well-being is determined by the individual’s fixed notion of utility, beliefs, and values.

The discussion of these theories is summarized in Table 1. Each theory is characterized according to its disciplinary perspective, the direction of peer effect for disadvantaged students (beneficial, no influence, and harmful), and the nature of the influence (beliefs/values, instrumental). As the table indicates, all the economic theories view peers as instrumental to individual well-being, whereas most of the other theories hypothesize that peers influence the beliefs and values of individuals.  

Table 1. Summary of Theories and Implications

These theories are not necessarily mutually exclusive, nor are theories within similar categories necessarily the same. For example, many of the theories are instrumental but assume different types of individual objectives and different ways in which the groups influence individuals. The economic theories focus on peer groups as instruments or providers of services, such as, in the case of the economics signaling theory, the service of protection. The disruption theory suggests that groups are instruments to individual well-being because the groups change the amount of instruction that individuals receive (interaction in constraints). The cognitive theory also suggests that groups are instruments to short-term well-being but because diversity stimulates students’ need to better understand their more complex environments.

This discussion of economics theory is important because it corrects some misperceptions about it; it suggests ways that peers influence one another—namely, by providing educational “services” to one another—that other social sciences give less attention to; and it shows how theories that are not rooted in economics might be expressed in terms of economics models. An advantage of these economics models is that they can be translated directly into testable implications more so than other theories; note, for example, that the testable implications of the Austen-Smith and Fryer (2005) model. On the other hand, economics models make simplifying assumptions that are at best counterintuitive and less substantively incorrect. The integration of abstract social science theory with the mathematical formalization of economics, therefore, is a potentially important avenue for future research. As I show in the following section, this formalization has the potential to provide important empirical contributions as well.   

EMPIRICAL IMPLICATIONS OF THE THEORIES

All the theories in Table 1 have at least some evidence suggesting that they might be important. The more difficult task is determining which theories are most important in explaining student outcomes. Next, I propose a single approach that tests many, though not all, of the theories simultaneously.  

Consider the following formal model of peer influences:

(1)

where y_it is student achievement of individual i at time t, x_it are the characteristics of the individual, x_-it are the average characteristics of the individual’s peers (i.e., everyone in the school or classroom other than the individual, hence the notation -i), and ε_it1 is an error term with the usual properties. Because of the linear relationship between student outcomes and mean peer characteristics, this is often called the linear-in-means model.

There are considerable methodological problems involved in estimating Equation 1 (Manksi, 1993, 1995). The goal, presumably, is to identify the effect of the group on the individual, but, if there is such an effect, then the individual simultaneously affects the group. This is sometimes called the reflection problem. Another issue is the usual one of nonrandom assignment of students to peers, which can be framed either as selection bias or omitted variables bias. The focus of attention in the present study is not on these methodological issues, as important as they are, but on the issue of the relationship between theory and evidence. Therefore, I simply assume, for the sake of argument, that the researcher has been able to address the reflection and selection bias problems.

Two important peer characteristics frequently incorporated into theories and empirical research are: peer racial composition (e.g., percent Black) and peer mean achievement. Peer race is consistently associated with student achievement for individuals (e.g.., Coleman, 1966) and is the basis for policies such as racial desegregation. Assuming that there are three racial/ethnic¹⁹ groups in all (typically, White, Black, and Hispanic), this yields the following slight variation of Equation 1:

(2)

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where y_-it represents average peer achievement, and Black_-it and Hisp_-it represent the percent of each individual’s peers who are in each respective racial/ethnic group. Whites represent the reference group.²⁰

The most obvious difference between the theories discussed in the previous section is that some theories imply that having advantaged peers is beneficial. whereas others imply that this is harmful. If having more advantaged peers is beneficial to disadvantaged individuals, then the coefficients φ₂ should be positive, and φ₃ and φ₄ should be negative. The evidence that follows suggests fairly consistently that having more advantaged peers is beneficial for disadvantaged students. It is therefore worth focusing on the theories that are most consistent with this result: the epidemic, cognitive, institutional-resource, institutional-expectations, and disruption theories.  

One implication of the epidemic theory is that the effects of peer race and peer achievement should be statistically indistinguishable for students across all racial groups.²¹ To test this, it is necessary to estimate Equation 2 separately for each group. That is, we would estimate the following set of equations:

(3a)

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(3b)

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(3c)

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where the superscripts on the dependent variable indicate that the model is estimated only for students of the respective racial group,  refers to the mean peer achievement of individual i’s peers who are Black, and so on for the other peer achievement variables.²² If the epidemic model holds, then we would expect that η_j=λ_j=κ_j for each j and that η₁=η₂=η₃ and η₄=η₅ for Blacks in Equation 3a, and so on for the other two racial groups in Equations 3b and 3c. This is just a mathematical way of saying that in the absence of a theoretical prediction to the contrary, each racial group should influence each other group in the same way (positively or negatively). As we will see next, this implication is not supported by the existing evidence.  

The implications of the epidemic theory, as reflected in Equations 3a–3c, would appear to be identical for the disruption theory. There is no reason to believe that the disruptions would take away from the instruction of one group more than another or that disruptions created by one group would be more influential than disruptions by any other group.²³

With the cognitive theory, we would expect that individual educational outcomes would be positively associated with the percent of students in other groups regardless of whether they are minorities. Thus, in Equation 3a, it should be the case that η₄ < 0 and η₅ > 0, and so on for the other racial groups. It may also be the case that diversity in terms of achievement would be beneficial in this way, though the cognitive development theory is less clear about whether differences between the individual and the group in terms of achievement have the same effect as differences in race. It may be that peer achievement is less important because it is not directly observed by students and therefore may not stimulate students to engage in more “effortful” thought. On the other hand, achievement may just be a proxy for academically oriented behaviors, and these behaviors are observed by students. Gurin et al. (2002) did not discuss this issue in their study of the theory.

The institutional theories have quite different implications. In the case of the institutional-resource theory, if the researcher has good measures of classroom/school quality and these are included as control variables in the regression, then it should be the case that peer race and peer achievement are unrelated to individual learning, or η_j=λ_j=κ_j=0 for all j. The institutional-expectations theory, in contrast, is arguably impossible to test in this framework because expectations are rarely observed. If expectations are formed slowly based on race and achievement, then in the absence of valid observations on teacher expectations, this theory would be difficult to test because the influence of the expectations of teachers would be confounded with the direct effects of peers on one another. This, of course, also complicates tests of the more direct theories.

In short, the cognitive development theory and institutional-resource theories appear to have unique testable implications in the framework outlined previously in this article. The other theories also have testable implications, but these are not unique (i.e., not clearly distinguishable from other theories); this is especially true of the institutional-expectations theory. Nevertheless, this is a promising approach for learning about the nature of peer influences because multiple theories can be tested while still addressing some of the key methodological issues. To distinguish it from the simple linear-in-means model shown in Equation 1, which is rejected by some of the evidence presented next (most explicitly by Hoxby & Weingarth, 2005), I refer to the preceding approach, and its formalization in Equations 3a–3c, as the multiple equations linear-in-subgroup means framework.

FROM IMPLICATIONS TO EVIDENCE

The purpose of this section is to discuss whether one or more of the theoretical implications discussed previously are supported by empirical evidence regarding peer influences on student achievement. For reasons discussed next, this section focuses on recent quasi-experimental research conducted by economists.

A BRIEF DISCUSSION OF RANDOMIZED TRIALS

Considerable methodological issues arise in trying to estimate peer effects, as noted earlier. One of the central problems—selection bias—can be generally addressed by randomly assigning students to classrooms and schools. Indeed, many researchers used this method to study the effects of school desegregation during the 1960s and 1970s. More recently, studies have considered the effects of the Moving to Opportunity Housing experiment that, although focused on housing, also indirectly involved changes in schools. I discuss these only briefly because, unlike the economics studies, they have been reviewed elsewhere. In addition, as I will show, these studies are of limited usefulness for understanding the complexities of peer influences.  

In 1984, the National Institute of Education (NIE) commissioned seven extensive reviews of the topic (Armor, 1984; Cook, 1984; Crain, 1984; Miller & Carlson, 1984; Stephan, 1984; Walberg, 1984; Wortman, 1984). These NIE reviews were subsequently reviewed by Jencks and Mayer (1990), Schofield (1995) and, most recently, Harris (2007a) and Linn and Welner (2007). Although there is not universal agreement about the interpretation of these studies, even among the authors of the NIE studies, the subsequent reviews (Harris, 2007a; Linn & Welner; Schofield), which incorporate both the NIE reviews and other more recent evidence, are relatively consistent in concluding that having advantaged peers does appear to be beneficial for disadvantaged students.

In the Moving to Opportunity (MTO) experiment, more than 9,227 families in Baltimore, Boston, Chicago, Los Angeles, and New York were randomly assigned to receive housing voucher.²⁴ As discussed by Harris (2007a), two studies have examined the effects of the MTO program on student academic achievement. Ludwig, Ladd, and Duncan (2001) found that,

compared with the control group, treatment group students who entered the program before age 12 were 17.8 percent more likely to pass the state standardized test and scored 7 percentile points higher (equivalent to 0.17 standard deviations) on a district test. No effects on state test scores emerged for those students entering the program after age 12. (Harris, 2007a, p. 554)

In a second study of the MTO in all five cities, Sanbonmatsu, Kling, Duncan, and Brooks-Gunn (2006) found that there were no achievement effects for students in any age group, in contrast to the Baltimore study.

Harris (2007a) discussed two possible explanations that could account for the different results. First, because the test used by Sanbonmatsu et al. (2006) was not aligned with state standards or accountability, it may not have measured whether students were learning the curriculum taught in schools.²⁵ Second, the data in Sanbonmatsu et al. show that the movement of families under the MTO resulted in only small changes in the characteristics of the students’ classmates. The differences in the percentages of students who were racial minorities or who were eligible for free or reduced price lunches declined by only 3–6 percentage points, and the mean percentile test score rank increased by only 4 points. This relatively small change in school circumstances might be insufficient to generate significant differences in student learning.

A more general limitation of these randomized experiments, for the purposes here, is that they can only provide evidence about whether there was an effect, and they do not provide evidence about why the effects might have arisen or failed to arise. For example, they give little consideration to the variation in school resources, making it impossible to disentangle the direct effects of peers from the indirect effects of school resources. In addition, the studies based on experimental data give little consideration to the effects for separate racial subgroups or other characteristics, such as mean peer achievement.²⁶

For this reason, and because this literature has already been extensively reviewed elsewhere, I do not discuss the experimental research further. This is not to say that experiments could not or should not be used to learn about the nature of peer influences, only that they have not been used this way. It is therefore useful to consider other approaches, both to assess the current state of knowledge and to facilitate the design of future experiments on the topics.

INTRODUCTION TO VALUE-ADDED

Researchers have also tried to address nonrandom selection using quasi-experimental methods, often called value-added modeling, which address both key forms of nonrandom selection: that students are nonrandomly assigned to peers and nonrandomly assigned to resources, especially teachers. In effect, value-added models attempt to address the two forms of nonrandom selection by using each student as his or her own control group. The data used in value-added modeling allow researchers to track individual achievement over time and therefore observe student achievement under different conditions—including different peers and school resources. For each student, the researcher estimates an average growth trajectory and then uses the deviations from this trajectory to identify the effects of peers and other factors such as school resources. For example, if student achievement gains tend to be larger than average in classrooms with more advantaged peers, this might suggest that advantaged peers are beneficial. Drawing such causal conclusions from these models obviously requires addressing the reflection problem and omitted variables problems discussed earlier.  

The value-added approach also accounts for the effects of school resources. Research increasingly suggests that the teacher is the most important school resource (e.g., Sanders & Horn, 1998), and it is therefore worth considering how value-added models measure teacher quality. Just as the researcher can estimate each student’s expected achievement growth based on past performance, it is possible to estimate each teacher’s contribution to student achievement by comparing students’ expected growth with what actually occurs. As we will see next, this makes it possible to test the institutional-resource theory in relation to other “beneficial” theories. This approach is also superior to accounting for teacher and other school resources solely by measuring specific characteristics such as teacher education and class size, which are only weakly related to student achievement (Hanushek, 1996; Harris & Sass, 2007).

RESULTS FROM VALUE-ADDED STUDIES

Despite using data in different states and somewhat different value-added approaches, there were at least three consistent findings across studies.²⁷  The first consistent finding from the value-added peer effect studies, and one that is consistent with the mentioned experimental results, was that having more advantaged peers generally results in better outcomes for minority students. This result was found in each of the four studies that estimated peer effects by race (i.e., the multiple equation model similar to Equations 3a–3c): the two studies that used statewide data from North Carolina (Cooley, 2006; Hoxby & Weingarth, 2005) and two that used similar Texas data (Hanushek, Kain, & Rivkin, 2002, 2008; Hoxby, 2000).²⁸ Because of the consistency of this finding across the various types of evidence, I focus next on the more nuanced findings that relate to the specific theoretical implications.

The same four studies also found that the benefits of advantaged peers for Whites are smaller than the benefits for minorities. That is, in terms of Equations 3a–3c, κ₁, κ₂, and κ₃ are all smaller than the corresponding coefficients for Blacks (η₁, η₂, and η₃) and Hispanics (λ₁, λ₂, and λ₃). Likewise, κ₄ and κ₅ are generally larger (in absolute value) than the corresponding coefficients for racial minorities. If the results of these studies are accurate, then members of the dominant group (White) are less susceptible to peers, implying further that redistributing students based on race can increase both the equity and average level of achievement.  

Third, the value-added studies suggest that each racial group appears to be influenced most by peers of their own race. That is, η₁ is greater than η₂ and η_3; λ₂ is greater than λ₁ and λ₃; and κ₃ is greater than κ₁ and κ₂. Likewise, it should be the case that η₄>η₅ and λ₅>λ₄ (in absolute value). This is consistent with the idea that racial identity is an important factor that affects how individuals respond to their peers.

Several value-added studies have also explored whether and how peer influences depend on the individual student’s initial level of achievement, though the results here are somewhat less consistent. Burke and Sass (2006) found that the effects of peer achievement occurred for students throughout the distribution of test scores, and the effects were largest for students who were among the lowest 20% of the test score distribution and smaller for high-scoring students. Cooley (2006) found this same result for White students but found that the reverse was true for minorities: High-scoring minorities benefitted the most from more advantaged peers. Although Burke and Sass (2006) did not break out their results by racial subgroup, it is likely that their results were driven by White students (who represented the majority of their sample), which makes their results consistent with those of Cooley.

On the same general issue, Hoxby and Weingarth (2005) found that students in the top quintile on achievement were sharply and negatively influenced by classrooms with low average achievement (below the 45th percentile), though raising mean achievement above the 45th percentile appeared to yield no influence on these highest scoring students.²⁹ Their results suggest that low-scoring students do benefit from having higher scoring peers in some cases, so long as the higher scoring students are not too far ahead. Likewise, higher scoring students might not be harmed from lower scoring students so long as those students are not too far behind. In short, this research suggests that a balance of tracking and peer redistribution is likely to increase average achievement without increasing achievements gaps between groups.  

The mentioned studies do not generally control for classroom and school resources, however. It is therefore possible that these findings are being driven by nonrandom assignment of students to resources. This is suggested by Vigdor and Nechyba (2005), who found that the apparently positive effects of advantaged peers were eliminated when unobserved differences in teachers were taken into account. None of the other studies accounted for differences in teachers in this way, though the approach used by Hoxby (2000) and Hoxby and Weingarth (2005) should address the resource issue indirectly.³⁰ It is therefore unclear why the results of those two studies differ.  

This is not the only area of disagreement.³¹ Vigdor and Nechyba (2005) found that having more minority peers actually has a positive impact within racial subgroups (e.g., Blacks benefit from having more Blacks), after controlling for peer mean achievement. Perhaps the most important disagreement relates to whether peer achievement or peer race is the most important peer characteristic. This is an important issue because the basis for redistributing peers obviously depends on the characteristics of peers that are most important. If peer achievement is indeed more important, this may be a viable alternative given the steady stream of court decisions limiting the use of race. (Student income is the most frequently discussed alternative to student race as a basis for student assignment, but these studies rarely have good measures of income, and, even when they do, it is rarely the focus of attention in the research.)

Hanushek et al. (2002) found that peer influences are most closely related to peer race and are unrelated to peer achievement. In contrast, Cooley (2006) and Hoxby (2000) found that both peer percent minority and peer mean achievement are associated with individual achievement, whereas Hoxby and Weingarth (2005) found that peer achievement is much more important than peer race. Further, Hoxby and Weingarth concluded that, after controlling for peer achievement, most of the peer race and income variables are statistically insignificant, and those that are significant “are small relative to what would interest a policymaker” (p. 27). They even went so far as to begin the title of their article with the words, “Taking race out of the equation.”   

However, even if we ignore the differences in results across studies on this topic, this conclusion is unwarranted. First, the fact that a majority of the coefficients are insignificant simply reinforces their earlier finding that peer influences are race dependent and complex. Consistent with earlier studies, Hoxby and Weingarth (2005) found that own-race peers have the greatest effect on individuals, suggesting that race does in fact matter.  

Second, interpreting the size of the coefficients is more complicated than this or other studies acknowledge. Take Hoxby and Weingarth’s (2005) finding that “if a student who is himself black and poor experiences a ten percent increase in the share of his class that is black and poor, [then] his achievement falls by . . . 2.5 percent of a standard deviation” (p. 27). Although this effect is small compared with the usual Cohen effect size standards, these standards are not as useful for interpreting the policy relevance of empirical estimates as they might seem. To see why this is the case, consider that if these single-grade effects are cumulative across grades, then a 10% increase in Black and poor students could be 13 times this amount (reflecting each of the grades K–12), accounting for nearly half of the achievement gap between Whites and Blacks (Harris & Herrington, 2006). Given the large initial achievement gap between Whites and Blacks, this is hardly a small effect. It is also worth noting that a 10% increase in classmates who have a particular set of characteristics amounts to only two students in a typical classroom. Although this might be all that policy makers can do in the present legal and political context, it is still a rather small change in circumstances.³²

Finally, even if their finding is correct, it ignores the potentially larger long-term benefits that come from additional exposure of minority students to White peers. There is some evidence that income inequality is partly driven by geographical isolation, which in turn may be partly driven by race and a lack of experience with, and comfort in, dealing with more advantaged students. Rivkin (2000) found, for example, that minority students who attended schools with more White students earned larger incomes, other things being equal. Therefore, although it is reasonable to expect that peer achievement would be the more important peer factor when individual achievement is the outcome of interest, this might well not be the case for individual outcomes such as long-term earnings given the apparent importance for minorities of being able to interact in the workplaces with Whites who, on average, earn higher wages.³³

DISCUSSION: TOWARD A NEW THEORY

As with the school desegregation experimental results, the value-added studies suggest that having more advantaged peers is beneficial, though the value-added studies also suggest that peer influences are complex. Next, I discuss these findings in relation to the five theories suggesting that advantaged peers are beneficial—epidemic, cognitive, institutional-resource, institutional-expectations, and disruption—and propose a new theoretical framework as the basis for future theory development.  

Perhaps the most important finding, from a theoretical perspective, is that advantaged peers are most beneficial within groups (e.g., race). This finding is inconsistent with all five theories about why such benefits arise. In fact, the only one of the five theories that allows for any role for race is the cognitive development theory, but this theory suggests a different pattern: that diverse peers, rather than advantaged peers, are more beneficial. In this respect, the theories suggesting that more advantaged peers are harmful, even though they are inconsistent with the basic finding that advantaged peers are beneficial, have something useful to offer; the oppositional culture and two-audience signaling (and, arguably, relative deprivation) both place race at the center. Given the evidence of within-race effects, it does not appear justified to “take race out of the equation,” as Hoxby and Weingarth (2005) suggested.

I propose a new theory that peer effects are driven partly by group-based contagion in which students follow the leads of their classmates (as in the epidemic theory)—especially those classmates who belong to the same group. Group identity might be based on race or other factors. The reference to “group” in the theory name also suggests the possibility that that the groups themselves interact with one another. For example, as Hoxby and Weingarth (2005) pointed out, conflict may be most likely when there is a large minority group, one of nearly equal size to the majority that represents a potentially larger perceived threat. A small number of students in a class or school from another group pose little threat.

The inclusion of contagion in the title implies that this new theory is rooted in the older epidemic/contagion model described by Jencks and Mayer (1990), which implies further that peers influence one another’s beliefs and values more than they serve as service providers or instruments. The group-based contagion theory allows for multiple groups with which individuals identify and therefore serve as relevant peer groups. Some Whites listen to hip-hop and some Blacks are on the swim team, and membership in these groups might also serve as the basis for group identification and interaction. The absence of multiple group identifications is a limitation of the two-audience signaling model, though perhaps an understandable one given the other complexities of that model. But the presence of multiple groups also suggests a possible way to sort out the nature of peer effects. As suggested earlier, different theories might suggest that certain types of group identification are more important than others. This could be studied by comparing students who belong to one group but who differ in their other group identifications and interactions.

Further evidence on this topic might also come from better measurement of peer behaviors, akin to the vast literature on parenting practices (e.g., Jencks & Phillips, 1998). The difficulty with this approach is that peer behaviors may influence beliefs and provide services. For example, if a friend is willing to help with homework, this is a service, but the willingness of the friend to provide that help could also change student’s beliefs about the importance of education. Other behaviors, such as the frequency with which peers say that school is not “cool,” obviously provide no service but could change beliefs. Relating these different categories of behavior to individual student outcomes could help determine the central mechanism of peer influence and test the group-based contagion theory.

There are still some existing empirical observations that must be accounted for in any complete theory. Earlier, I presented evidence from Vigdor and Nechyba (2005), as well as more indirect evidence on teacher mobility (Hanushek et al., 2001; Lankford et al., 2002), that peer effects are driven by institutional resources. This is excluded from the group-based contagion theory because the indirect nature of the institutional resource effect is inconsistent with the more direct notion of peer effects that most scholars seem to consider. However, any complete theory of peer influences, broadly defined, needs to account for this, and any effort to identify more direct mechanisms of peer influence requires accounting for these indirect effects.³⁴

The new theory, and old ones, also fail to explain why (a) advantaged peers seem more beneficial for disadvantaged students than advantaged ones, (b) advantaged peers may not be beneficial if they are “too” advantaged, and (c) peers seem more influential in elementary school (Harris, 2006). One explanation for (a), suggested by Harris (2007c), is that school resources, including peers, display “diminishing returns”; in other words, having better peers might provide benefits, but these benefits become smaller and smaller as other resources (e.g., from parents and schools) become larger. Hoxby and Weingarth (2005) provided an explanation for (b) rooted in the fact that some aspects of instruction are applied to classrooms as a whole, and students may benefit from instruction targeted to their specific needs. Finding (c) might be explained by Ogbu’s (2003) observation that oppositional culture is strongest in high school. But the larger point is that the group-based contagion model, even if it does prove to explain a substantial share of student outcomes, will inevitably have to be combined and integrated with theories in order to explain all the relevant empirical observations.

CONCLUSION

As Braddock and Eitle (2004), Jencks and Mayer (1990), and Manski (2000) argued, past empirical research on peer influences have largely ignored theory. This study summarizes a variety of social science theories regarding the underlying reasons for peer influences, covering a variety of social science disciplines. I have also identified some potential empirical implications of the various theories, taking one step closer to being able to empirically test the theories and to better understanding the nature of peer influences.

Another step toward testing the theories comes from the expanded availability of student achievement data that has made it possible to estimate empirically sophisticated regression models that address issues of methodological issues and to allow researchers to isolate the various predicted peer influences from the theories. The results of these value-added studies tend to reinforce past school desegregation experiments, in that having more advantaged peers is beneficial, but they go beyond the results of past experiments in important ways.

Collectively, the theory and evidence point toward a new theory—group-based contagion—in which students benefit from advantaged peers mainly when those peers are in the same group. In addition, there is clear evidence that peers indirectly influence one another by affecting the school resources to which they have access, especially the qualifications of the teachers who teach them.

Although the basic elements of the proposed theoretical framework are in many ways persuasive, it would obviously be premature to draw any firm conclusions about the validity of either individual theories or the proposed new theory. These value-added studies are new, few in number, and, in some respects, inconsistent in their findings. In addition, none of the four value-added studies has been published in peer-reviewed journals. Additional value-added studies, as well as experimental studies, are necessary to confirm the empirical findings from these studies. in addition, other types of theoretical and empirical reviews of this type are warranted for outcomes beyond student achievement, such as criminal and sexual behavior, graduation from high school and college attendance, and long-term success in the labor market. The new theory proposed here may or may not be the correct one for these other outcomes because the basic social processes generating those outcomes may differ.

Despite the difficulties in doing so, understanding how and why peers influence one another is important. Because the theory and evidence suggest that minorities gain more than Whites lose from peer redistribution—and, contrary to how some have interpreted the evidence, these gains could be educationally substantial—it appears that such redistribution efforts would increase average achievement as well as equity. If this is true, then this may increase the political viability of desegregation of various types. By better understanding how peer influences work, we can also determine whether and how desegregation might be an educationally viable way to improve the nation’s educational system.

Acknowledgements

The author wishes to thank Kathryn Borman, Sara Goldrick-Rab, Michael Olneck, Roslyn Mickelson, and anonymous referees for their valuable comments.

Notes

1. Hofferth and Sandberg (2001) documented the way in which children spend their time using household survey data. They found that children aged 9–12 spend an average of 33.5 hours per week in school. They also measured “time with parents” and other variables where parents might be typically involved: household work, going to church, eating, visiting, doing art activities, having household conversations, and other passive leisure. The sum of these categories yields only 22.7 hours per week.

2. Gurin is a sociologist, but her research and that of her collaborators draw primarily on psychology, as indicated.

3. Hoxby and Weingarth (2005) are primarily interested in the topic of “nonlinearities” in peer influences. This is a central issue in court cases because nonlinearities in effects of peers imply that it might be possible to help some students without harming others. Oreopoulos (2003) also discussed different theories of peer influences, although his work is focused more on neighborhood effects.

4. Gurin et al. (2002) focused on how effortful thinking promotes “a clearer and stronger sense of individuality and a deeper understanding of the social world” (p. 337).

5. In 2003–2004, total expenditures per student were highest in low-poverty districts ($10,857), followed by high-poverty districts ($10,377). Districts with moderate poverty averaged just over $9,000 per pupil (U.S. Department of Education, 2008).

6. This evidence may be less significant than it seems at first glance because other evidence suggests that academic credentials are only weakly related to student learning (Harris & Sass, 2007) and that teachers who leave teaching have similar levels of “value-added” (Rivkin et al., 2005).

7. Ogbu (2004) argued that other researchers have misinterpreted his work—specifically, that they have translated “my cultural–ecological framework into a single-factor hypothesis of oppositional culture” (p. 2). He went on to argue that oppositional culture is just one of many coping mechanisms that Blacks use in response to the “burden of acting White.” In explaining the meaning of oppositional culture, he wrote that “oppressed minorities are bitter for being forced into minority status and subjected to oppression. They usually hold the dominant group responsible for their ‘troubles’ . . . . That is, their very attempts to solve their status problem lead them to develop a new sense of who they are, that is in opposition to their understanding of who the dominant group members are” (p. 5).

8. Further, these peer groups may involve a whole package of behaviors, such as “being in a gang, not finishing high school, having children in early adolescence, and leaving school to support family members” (Oyserman et al., 2006, p. 855).

9. One additional clarification worth noting here is that because oppositional theory is rooted in a history of involuntary slavery, Ogbu distinguished between the responses of Blacks and (voluntary) immigrants, for example, recent waves from Latin America. Nevertheless, similar patterns of behavior can be observed among second-generation immigrants (Kao & Tienda, 1998; Valenzuela, 1999).  

10. As Jencks and Mayer (1990) noted, “the ‘sociological’ views need not deny that most people are rational utility maximizers” (p.117).

11. Manksi (2000) also mentioned interactions in “preferences,” giving examples such as “jealousy” and “conformism” (p. 120). Because these types of interactions are rarely (though increasingly) studied by economists and are the primary basis for theories of peer influences from other disciplines, I exclude it in the discussion of economic theories. Although not a theory per se, economists such as Durlauf and Cohen-Cole (2005) often make the assumption of “complementarity,” which means that students receive greater payoffs to effort if peers also display greater effort. What is the nature of these payoffs? Durlauf and Cohen-Cole did not give examples or an explanation, partly because their purpose was to outline a very general model of not only peer influences but also social interactions more generally. For example, if students work hard in school in order to earn the “payoff” of a higher income in the future, and if the effort of peers results in greater payoffs to effort for each individual, then a complementarity exists, and this is yet another case in which having advantaged peers would be beneficial. The reason that this theory is attractive and intuitive to economists is that there are ready examples in other forms of production. For example, we would expect that the productivity of a machine in a manufacturing process would be greater if the workers were better trained to use the equipment. However, it is unclear whether this theory is anything more than a conceptually and mathematically precise way of framing the other theories discussed previously. Unlike the manufacturing analogy, there is no economic theory suggesting how the behavior of peers changes the payoffs of the individual.

12. The term instrumental in this case should not be confused with the economic method of instrumental variables, which is used to address selection bias in peer influences.

13. Another way to put this is that the marginal product of workers depends only on their economic type and level of schooling.

14. Austen-Smith and Fryer (2005) went on to write that “an important characteristic of these and many other examples, one that defines what it is to be a member of a social group rather than a strictly economic market, is that the costs of membership are in terms of personal time and effort, not money per se” (p. 4).

15. Although I have accepted their premise to this point, it is not entirely evident that joining a gang actually increases protection. A considerable portion of deaths among young people involve gang members, which might be interpreted as either evidence of the need for gangs as protection, or as evidence that gangs create more danger.

16. This interpretation of the role of diversity in affecting acting White is the opposite of that proposed by Oyserman et al. (2006). They wrote that “the combination of a low-income context and racial segregation reduces the possible group memberships—if one does not fit with one’s racial-ethnic group, there are unlikely to be many alternative social identities to engage” (p. 855). In other words, segregation may be self-reinforcing by essentially forcing students to identify with groups that are disengaged from the activities that would give them some prospect of long-term social and economic success.

17. An additional assumption that might seem questionable is that well-being (the value of leisure time) is proportional to actual (unobserved) social status individuals—that is, Blacks gain more from membership the in Black club than do Whites; moreover, these additional benefits are proportional to the amount of leisure time available to individual, presumably because students who work hard in school will have less time to “hang out” with the group and participate in group activities.

18. They argued that their theory is consistent with the decline of the inner city that came along with the decline of legalized discrimination and with why middle-class Blacks continue to remain behind their lower income peers. Further, they argued that their results are consistent with other research findings, such as evaluations of the Moving to Opportunity, Job Corps, and A Better Chance programs. This research is beyond the cope of the present study.

19. For simplicity, I refer only to race and not ethnicity throughout the study, though I acknowledge the important difference between these two concepts.

20. These two variables, mean peer achievement and percent minority, differ in that the former reflects changes in the amount of advantage that students experience in the aggregate, whereas percent minority treats advantage as an inherent characteristic and relies on counting the number of peers with that characteristic. This can be framed as a measurement problem, in which race is a proxy for disadvantages that are correlated with it.

21. There is a broader literature on “heterogeneous treatment effects” in which differences in the effects of educational programs (we can think of peers as the “program” here) arise by racial group and initial achievement levels. This literature addresses the topic more in terms of the implications for statistical analysis than for the theoretical implications that are of primary interest here. The implicit assumption in the text here is that variation across racial groups must arise for a reason—one explained by a theory.

22. Note that x_it is deleted to simplify the subsequent discussion. The effects of individual characteristics are of interest here only in the sense that they may aid in accounting for selection bias.

23. Jencks and Mayer (1990) argued that an additional implication of the epidemic theory is that there would be nonlinearities in the relationship between student achievement and peer characteristics. Because students emulate one another, each instance of a behavior leads to more students engaging in the behavior, leading to more emulation, and so on. Nonlinearities are also proposed in the signaling theory. Austen-Smith and Fryer (2005) showed that in their model, pressures on Blacks against acting White is more likely to occur in diverse schools and is less likely when Blacks are either in heavily Black or heavily White schools. This suggests more of a U-shaped relationship between individual achievement and peer characteristics.

24. There were actually two different “treatments.” One treatment group was given Section 8 federal housing vouchers to be used wherever they could find suitable private-sector housing. The second treatment group was given the same vouchers, combined with counseling and a restriction that the vouchers only be used to move to neighborhoods where the poverty rate was lower than 10%. Participants in the Section-8-only treatment received no counseling and could move to private housing in any neighborhood. The two treatment groups together were 54% Black and 39% Hispanic and had household incomes averaging less than $10,000 per year.

25. There is evidence to support the argument that achievement tests are more likely than other tests to pick up intervention effects. For example, the Perry preschool project found long-term term sustained effects on achievement scores but not on tests of intelligence (Barnett, 1992). The appropriate measure depends partly on which outcome is of greatest interest.  

26. Most of the experimental studies are relatively old and focus only on Blacks and Whites. The experiments focus on the former because the experiments were intended to study the effects of desegregation for Blacks.

27. Some of the studies use value-added models, very similar to that described previously, that address selection bias by explicitly measuring differences in students and schools other than peers (Burke & Sass, 2006; Cooley, 2006; Hanushek et al., 2002), whereas others take advantage of “exogenous variation” in student peers (Hoxby, 2000; Hoxby & Weingarth, 2005).

28. A fourth study, by Burke and Sass (2006), found that more advantaged peers are beneficial, but this study did not estimate the effects by racial subgroup. In addition, this interpretation of the Hoxby and Weingarth (2005) study is different from the authors’ own interpretation. See later discussion.

29. In additional to their empirical findings regarding the different effects at different parts of the test score distribution, Hoxby and Weingarth (2005) discussed the general importance of this issue in their introductory remarks. Specifically, they wrote that “neither educational policy-makers nor economists would care much about peer effects . . . [if] society would have the same average level of outcomes” under redistributional policies (p. 2). This is a strong statement and gives relatively little value to educational equity. It is nevertheless true that if peer influences could improve both the equity and average level of outcomes, then redistributional policies would be much more tenable.

30. These studies vary in their modeling specifications. Burke and Sass (2006) included student, teacher, and school fixed effects. This means that their resulting estimates were identified from variations in student assignment to classrooms within schools and that possibly nonrandom selection of students to teachers was accounted for with the student and teacher effects. Cooley (2006), however, included only teacher fixed effects and excluded student and school fixed effects.   

31. Second, as Harris (2006) pointed out, some of the estimated peer effects are also implausibly large. For example, Hoxby’s estimates of peer effects imply that moving a Black student from a 100% Black school to a (slightly less than) 100% White school would raise individual achievement by an additional 0.7 standard deviations in a single year. To see why this is implausible, consider that the total achievement gap between Whites and Blacks is about 0.7–0.9 standard deviations. Hoxby’s results suggest that this could be eliminated in a single year simply by moving students to different schools. There is considerable evidence of substantial achievement gaps even in schools that are mainly White, as highlighted by the well-known Shaker Heights example (Ogbu, 2003). If Blacks really could catch up in majority-White settings, then these within-school gaps should be considerably smaller than they are. Nevertheless, given the consistency with which researchers find benefits of more advantaged peers, including through experiments, it seems likely that at least parts of these effects are causal.   

32. In addition, these effects ignore the fact that redistribution is, in an economic sense, nearly costless; that is, it suggests that large reductions in the achievement gap are possible through peer redistribution alone (Harris, 2006).

33. Findings from other studies of neighborhood effects, including the Moving to Opportunity program discussed earlier and a similar experiment in Canada, show more mixed results of neighborhood effects (Ludwig et al., 2001; Oreopoulos, 2003).

34. Some efforts to account for selection bias make it difficult to identify the effects of school resources. For example, as one anonymous reviewer noted, including school fixed effects in the multiple-equations linear-in-subgroup-means model eliminates any possible effect on peers of the types of teachers who teach in the school. This is not a problem so long as one is interested only in the direct effects.

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