The Influence of Classmates on Adolescent Criminal Activities in the United States

Abstract

This article examines the effect of delinquent peers on an individual's criminal activity by leveraging quasi-experimental variation in exposure to peers, separating confounding and causal effects. In particular, we examine the role of wider peer networks (i.e., classmates) as a critical source of influence on adolescents' delinquent behavior. Using a combined instrumental variables/fixed effects methodology, we address important methodological challenges in estimating peer effects. Results suggest that increasing the proportion of peers who engage in criminal activities by 5 percent will increase the likelihood an individual engages in criminal activities by 3 percentage points.

Introduction

Adolescent criminal activities and delinquency have received substantial recognition as a pressing social problem since they are known to have short- and long-term consequences at the individual level (Moffitt et al. 2002; Nilsson and Estrada 2011) as well as widespread social and monetary burden for society (Welsh et al. 2008). At the individual level, in particular, adolescent delinquency is known to be negatively associated with human capital accumulation, such as lower academic achievement, school dropout, and fewer years of schooling completed (Hirschfield 2009; Hjalmarsson 2008; Kirk and Sampson 2013; Monk-Turner 1989; Nilsson and Estrada 2011; Ou et al. 2007; Webbink et al. 2013). These early exits from school and lower educational attainment are, in turn, closely linked with a range of long-term detrimental effects, including poor health status, recidivism, and lower occupational attainment (Baert and Verhofstadt 2015; Moffitt et al. 2002; Monk-Turner 1989; Sewell and Hauser 1975).

A large and growing literature in the social sciences has suggested that peers play a significant role in determining adolescent risky behaviors and outcomes (Ali and Dwyer 2009, 2011; Clark and Lohéac 2007; Fletcher 2010, 2012; Gaviria and Raphael 2001; Lundborg 2006; Yuksek and Solakoglu 2016). Given that one of the most important features of crime and delinquency is its status as a group phenomenon (Erickson and Jensen 1977; Felson 2003; Warr 2002), an increasing number of research have also documented the role of peers in delinquency and criminal activities among adolescents (Baerveldt, Völker, and Van Rossem 2008; Burk, Steglich, and Snijders 2007; Haynie 2001, 2002; Haynie and Osgood 2005; Haynie, Steffensmeier, and Bell 2007; Knecht 2008; McGee 1992; Vogel and Keith 2015). Despite a large body of evidence on the association between engaging in delinquency and having delinquent friends, there has been the broad scholarly consensus that both selection and socialization effects seem to exist in the peer-delinquency link, and it is challenging to empirically separate socialization effects from selection effects.

In this study, we aim to obtain more credible causal estimates of the influence of peer groups in juvenile delinquency by separating selection and confounding effects from influence effects using a quasi-experimental empirical framework novel to this literature. In particular, we focus on a wider peer group (i.e., classmates) as a relevant peer context for several reasons. First, a wider peer group has long been ignored in the crime and delinquency literature, although it is a critical source of social norms for adolescents. Second, determining the effect of exposure to this peer group could be more policy-relevant since policymakers have more control over this group of adolescents. Third, using this particular peer group allows us to remove selection effects through novel strategies that leverage across-cohort, within school variation in peers.

Background

Peer networks and delinquency

The idea that peers play a critical role in influencing adolescents' delinquent behavior is based primarily on social learning theory. Integrating Sutherland's differential association theory (Sutherland 1947) with the behavioral and cognitive learning theory in psychology, social learning theory posits that individuals learn criminal behavior in both social and non-social situations through combinations of definitions transmitted from interactions, direct and vicarious reinforcement, and general observation/imitation (Akers 1973; Bandura 1977). In general, these perspectives emphasize that peer influence depends on the frequency, proximity, duration, and intensity of peer relationship, suggesting the importance of the role of close friendship.

Over the past decade, combining social learning theory and friendship network data, several studies have consistently documented that the association between peer and individual delinquency is one of the most robust findings in crime and delinquency research (Baerveldt et al. 2008; Burk et al. 2007; Haynie 2001, 2002; Haynie and Osgood 2005; Haynie et al. 2007; Knecht 2008; McGloin and O'Neill Shermer 2008; Meldrum, Young, and Weerman 2009; Worthen 2012). Research has also attempted to unpack the mechanisms by which delinquency is socially transmitted. Warr and Stafford (1991) suggest that delinquency is a consequence of other social learning mechanisms such as imitation, reinforcement, or peer pressure, rather than attitudes acquired from peers. In contrast, using social network data, a more recent study has rather found that peer attitudes play a more important role in the social transmission of delinquency than behavior of peers (Megens and Weerman 2012). Drawing upon the opportunity perspective (Briar and Piliavin 1965), other studies demonstrate that increased exposure to peers (e.g., spending time with peers in unstructured activities) is associated with delinquency, independent of the behavior of peers (Haynie and Osgood 2005; Osgood et al. 1996).

Despite existing evidence on the existence and strength of the peer influence in crime and delinquency, the observed relationship may not be causal. That is, the peer-delinquency association may be a spurious result of selection process (Glueck and Glueck 1950; Matsueda and Anderson 1998; Warr 2002). Specifically, many prior studies fail to account for the selection of individual's peer network, by making the assumption that one's network is randomly formed, which does not reflect reality. Although efforts have been made to distinguish social influence effects from selection effects by controlling for prior delinquency or modeling the co-evolution of friendship networks and behavior change, these results are still potentially contaminated by latent homophily (Shalizi and Thomas 2011). Thus, more rigorous evidence, particularly the use of experimental or quasi-experimental research designs, is required to allow for greater confidence in the estimates of the influence of peer groups.

Significance of wider peer networks

Recent literature has exclusively focused on best friends or close friendship (i.e., friendship dyads) as a relevant reference group that may affect adolescent delinquent behavior, often ignoring the role of a wider group of peers. Although a few studies find that delinquent behavior among relatively distant peers have also influence on individuals' delinquency, these peers are those who are still directly or loosely connected to the adolescents (e.g., Payne and Cornwell 2007; Rees and Pogarsky 2011). However, there is mounting evidence that a wider group of peers such as classmates and schoolmates is also an important part of social groups among adolescents that may affect adolescents' attitudes and behavior (Bearman and Brückner 1999; Coleman 1961; Frank et al. 2008; Giordano 1995, 2003).

Beyond close and intimate friendships, a wider peer group provides a more comprehensive picture of adolescents' social world, in which adolescent behaviors are governed and sanctioned based on specific norms of a group (Bearman and Brückner 1999; Brechwald and Prinstein 2011; Coleman et al. 1966; Furstenberg et al. 1987; Kemper 1968; Legewie and DiPrete 2012). There are several ways in which the normative context of a wider group influences adolescents' attitudes and behavior. A wider peer group such as schoolmates and classmates can serve as an important source of descriptive norms (i.e., existing patterns of behavior in a group) (e.g., Cialdini, Reno, and Kallgren 1990). Descriptive norms provide evidence to individuals of the behaviors that other people approve (or disapprove), and they could use this information to justify their own behavior or conform to new behaviors (e.g., Meier 2007). Research also suggests that descriptive norms affect injunctive norms (i.e., rules and beliefs that are socially enforced) because a sense of oughtness attaches to what is commonly done by most others (Opp 1982). Therefore, in the case of crime and delinquency, social stigma and social sanctions associated with delinquent behavior would be reduced as the number (or proportion) of delinquent peers rises.

In addition, as an effort to gain more popularity or simply avoid being ostracized, adolescents' behaviors may adopt attitudes and behaviors of peers in wider peer networks who are important sources of potential future friends (Frank, Muller, and Mueller 2013; Matsueda and Anderson 1998). For example, to build new friendship ties, adolescents often decide whether to maintain preexisting similarities with highly desired potential friends or change their dissimilar behaviors (Epstein 1989). Moreover, given the fact that friends in a wider peer group are less generous in punishing norm violators than close friends (e.g., Giordano 2003), adolescents' behaviors may be more strongly constrained by attitudes and behaviors of the wider peer network. In this sense, peers in a wider social network whom adolescents do not have any direct relationship or contact still could be considerably influential.

Indeed, the question remains which peer group could better serve as a source of norms. Although, as shown above, a large literature has argued that close friends influence an individual's delinquency, the mechanism of influence within the friendship network is believed to be primarily through direct and close interactions, rather than norm enforcement. In fact, a close friendship group might not be stable enough to establish and maintain group norms. Adolescents' friendship network is known to be considerably unstable and fluid: adolescents aged between 11 and 15 maintain less than 65% of their friendships across a school year and tend to lose more old friends than they form new ones (Berndt and Hoyle 1985; Chan and Poulin 2007; Neckerman 1996; Poulin and Chan 2010).

Members of a wider peer network, such as schoolmates and classmates, tend to be more stable (Schneider and Stevenson 1999; Urberg et al. 1995), thus providing a more consistent normative environment where adolescents may make sense of their own and peers' attitudes and behavior. However, there seems to be no clear theoretical predictions or empirical evidence on whether schoolmates or classmates provide a more powerful normative context for adolescents. Group norms between schoolmates and classmates, although possibly similar, do not necessarily overlap. Although schoolmates, especially older peers, are also an important source of influence on delinquent behavior, in this study, we focus on identifying the causal effects of classmates on delinquency, net of schoolmates and shared neighborhood normative climate.

Last but not least, determining the effect of a wider peer group such as classmates and schoolmates is especially policy relevant because it suggests that (1) the compositions of peer groups are important determinants of adolescent criminal behavior and (2) interventions that decrease the propensities of individuals' involvement in crimes will decrease those of their peers. Indeed, unlike friendship dyads, wider group composition is subject to direct policy influence (such as busing, school redistricting, voucher programs, etc.), suggesting the importance of understanding peer influences at this level (e.g., Billings, Deming, and Rockoff 2014; Cook and Ludwig 2006). Therefore, a better understanding of whether and how an individual's criminal activity is influenced by a wider peer context may be helpful for policymakers.

Conceptualizing peer effects

Manski (1993, 2000) distinguishes among the following two types of social effects: endogenous effects and contextual effects. Endogenous effects occur when the propensity of an individual to behave in some way varies with the behavior of the reference group (e.g., Thornberry 1987). Contextual effects (or exogenous effects) occur when the propensity of an individual to behave in some way varies with the exogenous characteristics of the reference group. Contrary to these two social effects that are created by social interactions, there could be “correlated” effects (Manski 1993): individuals in the same group tend to behave similarly because they have similar individual characteristics or face similar institutional environments.

Consider the case of adolescent delinquency. Endogenous effects can occur if an individual is more likely to engage in delinquent behavior if his peers behave delinquently—that is, if their decisions are interdependent. The majority of prior studies using friendship network data have focused on endogenous peer effects (e.g., Haynie 2001). On the other hand, contextual effects can occur if an individual is more likely to participate in delinquent behavior if he or she is surrounded by peers with similar backgrounds, say female-headed households. A number of studies in the economics literature has examined the role of various peer group characteristics in affecting adolescents' delinquent behavior and substance use (Bifulco, Fletcher, and Ross 2011; Billings et al. 2014; Black, Devereux, and Salvanes 2013; Carrell and Hoekstra 2010). Lastly, correlated effects, which are often not social in nature, can occur if individuals in the same school choose to engage in delinquency because they face low levels of punishment (i.e., relatively permissive school policies for delinquency punishment) (e.g., Damm and Dustmann 2014).

It is important to empirically separate these social effects (i.e., endogenous, contextual, and correlated effects) for both conceptual and policy reasons. Policy interventions aimed at taking advantage of endogenous effects are likely to produce a social multiplier (see Glaeser, Sacerdote, and Scheinkman 1996, 2003; Manski 1993). For instance, if adolescent criminal behavior in schools is subject to endogenous social effects, a policy that decreases the propensity of an individual or group of individuals to engage in crimes will affect other individuals who were not directly targeted by the policy—the effect of the policy is multiplied through social interactions (e.g., Cook and Ludwig 2006). On the other hand, policies designed to make contextual changes may not produce the same multiplier effect responses to a policy change. For instance, adding high-income students to a low-income school would benefit the students in the receiving school, but the students at the sending school would be worse off. Thus, the gains to the former school could offset the losses from the latter school so that there would be no predicted aggregate multiplier effect. In this study, we focus particularly on identifying endogenous peer effects that entail potential social multiplier effects (or spillover effects).

While empirically isolating endogenous peer effects from contextual and correlated effects is crucial for obtaining credible estimates of peer influence, there are several critical challenges. First, peer groups (assumed to be classmates in this paper) can be endogenously determined by parental choices (e.g. residential choices, private school enrollment), such that estimated peer effects may be attributable to the similarity among individuals rather than peer influences. Second, potential unobserved environmental characteristics that influence individual and peer group choices simultaneously (i.e., correlated effects) may confound the peer effect. Thus, failing to adequately control for these shared unobserved factors can lead to spurious conclusions about the importance of social influences on individual choices. A third empirical challenge is in separately examining bi-directional effects in social relationships. Since peer behavior affects individual-level behavior and vice versa (e.g., Thornberry 1987; Thornberry et al. 2003), a standard linear empirical model of peer influence may not be able to separate the two directions of effects (termed the “reflection problem” by Manski (1993)).

Present study

In order to quantify endogenous peer effects (i.e., whether individual behavior is influenced by group behavior) and address the methodological challenges described above, this paper uses the Add Health data and an instrumental variables/fixed effects methodology. To combat the potential for self-selection of peers, we use school level fixed effects (school-specific intercepts) in our empirical models. Since our measure of peers in our analysis is “classmates”, we are assuming that self-selection may operate to determine which school a student attends, but there are no remaining self-selection forces in choosing the grade-level in a school. We believe our assumption is consistent with an environment where “good” and “bad” schools can be observed by parents but the attributes of specific cohorts in a school are more difficult to observe. Our school-level fixed effects capture “good” vs. “bad” school environments and rely on across-grade (within school) differences in exposure to the criminal behaviors of grade-mate peers to provide quasi-experimental variation for the analysis. A growing literature has used a similar strategy to separate confounding and influence effects of peer behaviors, but no papers have focused on criminality peer influences using the approach (Hanushek et al. 2003; Hoxby 2000; McEwan 2003). A second advantage of the use of school level fixed effects is our ability to control for confounding at the school-level. For example, school policies related to the severity of punishment for delinquency (and all other school-level characteristics) are absorbed in our school-level indicators to further separate confounding from peer influence.

A remaining empirical challenge in the peer effects literature is separating the bi-directional effects in social relationships (the aforementioned “reflection problem”). In order to separate these effects, a common strategy in the economics literature is to locate an individual-level variable that influences the individual's behavior but has no additional effect on the peers' behaviors (i.e. using instrumental variable analysis). We follow this strategy by assuming that a student's exposure to criminality in his family (i.e. having an incarcerated father) affects his own criminal behavior but only affects his peers' criminal behaviors through peer influence. In addition to its conceptual plausibility as an instrumental variable, we also perform additional statistical tests to assess the robustness of our specifications by testing whether our instruments are plausibly quasi-random across cohorts, within schools (i.e. balancing tests). Moreover, in order to test the sensitivity of the instrumental variable estimates to deviations from the exclusion restriction, we apply the procedure suggested by Conley and colleagues (2012) to draw inferences that are valid if the instrumental variable does not perfectly satisfy the exclusion restriction assumption.

Data and methods

Data

The data in this study come from the restricted version of the National Longitudinal Study of Adolescent to Adult Health (Add Health). Add Health is a school-based, longitudinal study of the health-related behaviors of adolescents and their outcomes in young adulthood. Beginning with an in-school questionnaire administered to a nationally representative sample of students in grades 7 through 12 in 1994–1995, the study follows up with a series of in-home interviews of students approximately 1 and then 6 years later. Other sources of data include questionnaires for parents, siblings, fellow students, and school administrators. By design, the Add Health survey included a sample stratified by region, urbanicity, school type, ethnic mix, and size.

Of the 20,745 individuals who completed the Wave 1 survey, 18,772 have cross-sectional weights, valid school identification codes, and reported whether they were involved in criminal/delinquent activities in Wave 1 of the survey. Since the data represent a sample of the population of students within schools, the measures of classmates' characteristics will contain measurement error. Since the sampling scheme was random within grades and by gender, the measures should be correct on average, though. In order to limit measurement error in the peer (i.e. grade-level) variables, we drop those students who are in a school-grade-level where the number of sampled individuals was fewer than 20, leaving 18,206 students. Non-response to some of the family, individual, or school-level characteristics leaves an analysis sample of 16,912¹. We found no evidence that the key independent variable of the study (i.e., percent of classmates reporting “any crime”) is associated with the probability of being in the sample (Table S1 in supplementary material). Unweighted summary statistics are presented in Table 1.

Table 1. Summary statistics: Add Health data wave 1.

	Obs	Mean	SD	Min	Max
Individual-level characteristics
Any crime	16912	0.149	0.356	0.0	1.0
Steal	16907	0.055	0.227	0.0	1.0
Break in	16905	0.052	0.222	0.0	1.0
Armed robbery	16904	0.042	0.201	0.0	1.0
Sell drug	16889	0.076	0.265	0.0	1.0
Grade 7	16912	0.130	0.336	0.0	1.0
Grade 8	16912	0.129	0.336	0.0	1.0
Grade 9	16912	0.174	0.379	0.0	1.0
Grade 10	16912	0.200	0.400	0.0	1.0
Grade 11	16912	0.197	0.397	0.0	1.0
Grade 12	16912	0.170	0.376	0.0	1.0
Age	16912	16.159	1.698	12.0	21.0
Male	16912	0.488	0.500	0.0	1.0
White	16912	0.523	0.500	0.0	1.0
Black	16912	0.217	0.412	0.0	1.0
Hispanic	16912	0.172	0.378	0.0	1.0
Other race	16912	0.088	0.283	0.0	1.0
PVT score (Std)	16912	0.045	0.961	-5.7	2.6
Religiosity	16912	1.756	1.213	0.0	4.0
Number of older siblings	16912	0.845	1.212	0.0	13.0
Maternal education	16912	13.155	2.297	8.0	17.0
Family income	16912	0.347	0.213	-0.3	2.4
Both biological parents	16912	0.527	0.460	0.0	1.0
Own parental incarceration	16912	0.078	0.269	0.0	1.0
Missing parental information	16912	0.332	0.471	0.0	1.0
Rural	16912	0.243	0.429	0.0	1.0
Classmate-level characteristics
% Any crime	16912	0.149	0.074	0.0	0.4
% Steal	16912	0.055	0.042	0.0	0.2
% Break in	16912	0.052	0.040	0.0	0.3
% Armed robbery	16912	0.042	0.035	0.0	0.2
% Sell drug	16912	0.076	0.054	0.0	0.3
% Parental incarceration	16912	0.076	0.051	0.0	0.4
% Both biological parents	16912	0.522	0.118	0.1	1.0
% Black	16912	0.219	0.260	0.0	1.0
% Hispanic	16912	0.170	0.228	0.0	0.9
% Other race	16912	0.090	0.134	0.0	0.8
Mean religiosity	16912	1.752	0.267	1.0	2.9
Mean number of older siblings	16912	0.848	0.255	0.2	2.1
Mean maternal education	16912	13.139	0.927	10.2	16.2
Mean family income	16912	0.345	0.097	0.1	0.8
% Missing parental information	16912	0.342	0.132	0.0	0.7

Note: Family income and maternal education contain imputed values and the missing parental information indicator reflects this missingness.

Dependent variable

Add Health includes a number of questions regarding delinquent behavior. We use four criminal activities: stealing something worth $50 or more, selling drugs, burglarizing, and using or threatening to use a weapon in a robbery. As presented in Table 1, 5.5 percent of the sample reports stealing something worth $50 or more in the previous year, 7.6 percent of the sample reports selling drugs in the last year, 5.2 percent reports committing burglary (“break in”) in the past 12 months, and 4.2 percent committed a robbery in the past twelve months. Fifteen percent of the sample reports at least one of these outcomes, which is labeled as “any crime.”

Independent and control variables

We use the percentage of classmates (excluding the respondent) who reported any of the four juvenile crimes described above as the independent variable of interest (endogenous peer effect). We include individual-, family-, and school-level variables in the empirical models. For individual- and family-level variables, we include gender, grade level, age, race, an academic ability proxy (Peabody Picture Vocabulary Test score), religious attendance, number of older siblings, mother's educational attainment, family income, co-residence of both biological parents, own parental incarceration, a dummy of missing parent information, and rural status. Peer-level characteristics include percent Black, percent Hispanic, percent other race, mean religious attendance, mean number of older siblings, mean maternal education, mean family income, and percent missing parental information.

In order to capture parental incarceration information, we use retrospective reports from Wave 4 (when the respondents were 30 years old on average) that measure whether their biological father or mother had ever spent time in jail or prison. In particular, we use information from “How old were you when your biological mother/father went to jail or prison (the first time)?” (These are two separate questions). If the respondent retrospectively reports that his or her parent was incarcerated when they were younger than age 18, they are considered to be “exposed” to parental incarceration for the purposes of this study². Individuals not followed in Wave 4 are imputed a value of zero for each of the parental incarceration variables³. In our sample, two percent of respondents reported having incarcerated mothers and 7 percent reported having incarcerated fathers prior to age 18.

Analytic strategy

The primary empirical specification of this paper is the linear-in-means model of social interactions (Case and Katz 1991; Manski 1993):

$$Y_{\mathit{\text{igs}}}=X_{\mathit{\text{igs}}}B+{\overline{X}}_{-\mathit{\text{igs}}}\delta +W_s\theta +\alpha {\overline{Y}}_{-\mathit{\text{igs}}}+{\epsilon }_{\mathit{\text{igs}}}$$ (1)

where Y_igs is the criminal activity of individual i in grade g in school s, individual and family characteristics are contained in a vector X, and classmate characteristics are measured as grade-level averages of the X vector excluding the individual, labeled X̄_−igsδ In all results the random error terms of ε_igs are allowed to be clustered at the school level, and cross-sectional sample weights are used in all estimation models. W_s is a vector of school dummies that controls for unobserved school-level characteristics or confounding factors shared by all individuals within the same school. These school-level fixed effects could capture some important measures of environmental factors that may influence both peers' and individuals' criminal activity (e.g., local crime rates). Finally, Ȳ_–igsδ is the grade-level average outcome excluding the individual (i.e., the proportion of individuals in the same grade and school who report engaging in any criminal activity). The main coefficient of interest is the endogenous effect, α, which demonstrates the extent to which individuals are influenced by their peers' choices to engage in criminal activities. If α is estimated to be positive, interventions that change the criminal behavior of individuals (or subsets of individuals) within a reference group would be predicted to affect non-treated individuals in the same reference group.

As noted above, due to the “reflection problem,” α cannot be uncovered without using instrumental variables or other methods (Brock and Durlauf 2001; Manski 1993). Thus, to identify endogenous peer effects, we use a combined instrumental variables/fixed effects approach. The instrument variables used in the present study include (1) classmates' reports of parental incarceration and (2) classmates' co-residence with both biological parents. In order to be compelling instruments, these variables must meet two criteria: (1) be strongly correlated with classmates' criminal activities and (2) not affect the individual's own criminal activities except through peer influences (exclusion restriction). The first criterion is testable, through an F-test of the statistical association between the instruments and peer criminal behaviors. We show below that our instruments meet this criterion. The second criterion is untestable, though the intuition for the exclusion restriction is that classmates' parental incarceration is assumed to affect the individual's criminal activities only through its effect on classmate criminal activities. Similarly, we assume that classmates living with both biological parents have only indirect effects on the individual's criminal activities by affecting classmate criminal activities. Additionally, in using these instrumental variables, we implicitly make an assumption that peer delinquency does not cause the likelihood of living with both biological parents and parental incarceration. Thus, the endogenous variable does not have reverse causality issues with these instruments.

We believe our use of school-fixed effects makes our assumptions more likely to be satisfied because the distribution of classmates with incarcerated parents (or living with both biological parents) is quasi-random across grades within schools. This means that for some schools, the 9th grade cohort may have a high proportion of parental incarceration while in other schools, the 12th grade cohort may have a high proportion. Without controlling for school fixed effects, it is possible that students whose father or mother has ever been incarcerated attend different schools than students whose father or mother who has never been incarcerated, which would likely invalidate this approach because the instrument would be correlated with school-level characteristics. However, the use of school fixed effects should eliminate this concern since identification relies on variation in classmates' parental incarceration within the same school.

In Panel A of Table 2, balancing tests provide evidence against the validity of the instrument without school fixed effects. For example, the instruments are shown to be strongly related to parental socioeconomic status (i.e., maternal education, family income, and rural status), suggesting that the instrument might be related to unmeasured family characteristics that might also be related to the outcome. On the other hand, we show in Paenl B of Table 2 that after controlling for school fixed effects the instruments are not correlated with important individual-level characteristics. This balancing test provides suggestive evidence that the proportion of parental incarceration and the proportion of classmates living with both biological parents can be treated as plausibly exogenous (or quasi-random) within schools; in other words, parents are not systematically changing student's schools based on these cohort characteristics (Bifulco et al. 2011; Lavy and Schlosser 2011). In addition, the results from over-identification tests where the joint null hypothesis is that the excluded instruments are valid instruments support the validity of our instruments.

Table 2. Balancing tests for the association between the cohort-level instruments and individual characteristics.

	(1) Male	(2) Black	(3) Hispanic	(4) Other race	(5) PVT score (Std)	(6) Religiosity	(7) Number of older siblings	(8) Maternal education	(9) Family income	(10) Both biological parents	(11) Rural
A. % Parental incarceration	-0.016 (0.093)	0.665** (0.334)	0.049 (0.229)	0.007 (0.142)	-2.140*** (0.519)	-0.584* (0.349)	0.115 (0.331)	-4.821*** (1.057)	-0.692*** (0.111)	-0.952*** (0.160)	0.666* (0.346)
F-test	0.030	3.964	0.046	0.002	17.002	2.800	0.121	20.803	38.866	35.403	3.705
F-test p-value	0.8601	0.0488	0.8323	0.9628	0.0001	0.0972	0.7279	0.000	0.000	0.000	0.0563
B. % Parental incarceration	-0.167 (0.118)	-0.106 (0.076)	0.012 (0.065)	0.042 (0.052)	0.151 (0.253)	0.197 (0.446)	-0.170 (0.294)	0.466 (0.549)	0.069 (0.059)	-0.009 (0.141)	0.142 (0.112)
F-test	2.003	1.945	0.034	0.652	0.356	0.195	0.334	0.720	1.368	0.004	1.607
F-test p-value	0.1606	0.1667	0.8523	0.4181	0.5506	0.6587	0.5651	0.3969	0.2453	0.9511	0.2059
N	17893	17893	17893	17893	17042	17867	17893	17893	17893	17893	17893
	(1) Male	(2) Black	(3) Hispanic	(4) Other race	(5) PVT score (Std)	(6) Religiosity	(7) Number of older siblings	(8) Maternal education	(9) Family income	(10) Own parental incarceration	(11) Rural
A. % Both biological parents	0.011 (0.050)	-1.013*** (0.143)	-0.070 (0.095)	0.010 (0.055)	1.489*** (0.213)	0.285** (0.140)	-0.024 (0.140)	2.536*** (0.480)	0.387*** (0.053)	-0.178*** (0.028)	0.187 (0.164)
F-test	0.048	50.182	0.543	0.033	48.869	4.144	0.029	27.914	53.318	40.413	1.300
F-test p-value	0.8247	0.000	0.4611	0.8522	0.000	0.0434	0.8647	0.000	0.000	0.000	0.2547
B. % Both biological parents	0.052 (0.073)	0.016 (0.037)	0.041 (0.041)	0.014 (0.030)	-0.464*** (0.140)	0.215 (0.181)	-0.041 (0.228)	0.389 (0.342)	-0.040 (0.028)	-0.045 (0.038)	0.034 (0.064)
F-test	0.507	0.187	1.000	0.218	10.984	1.411	0.032	1.294	2.041	1.402	0.282
F-test p-value	0.4791	0.6642	0.3178	0.6511	0.0012	0.2365	0.8563	0.2578	0.1533	0.2386	0.5917
N	17893	17893	17893	17893	17042	17867	17893	17893	17893	17893	17893

Note: Additional controls for Panel A include a complete set of grade dummies. Additional controls for Panel B include a complete set of grade dummies and school dummies. Cross-sectional weights are used. Robust standard errors are clustered at school-level. The F-statistics is for the effect of cohort level parental incarceration or cohort level prevalence of co-residence of both biological parents.

^*p< 0.1,

^**p< 0.05,

^***p< 0.01.

One may still be concerned about the violation of the exclusion restriction assumption: classmate's parental incarceration (and/or their co-residence of both biological parents) may influence an individual's own criminal activity through other channels than peers' engagement in criminal activity. In order to test the sensitivity of the instrumental variable estimates to deviations from the exclusion restriction, we apply the procedure suggested by Conley and colleagues (2012) that produces valid inferential statements without imposing the assumption that the instrument exactly satisfies the exclusion restriction requirement.

We implement the instrumental variable estimator through a two stage least square framework. In the first step of the analysis, peer-level (i.e. classmates) criminal activity is estimated as a function of the instruments and a set of control variables (i.e. sociodemographic characteristics) and school-level fixed effects. These estimates are then used to generate predicted values of peer criminal activity that are now separated from the bi-directional influences between individuals and their peers (the reflection problem). As a second step, we estimate the effects of (predicted) peer criminal activities on individual-level criminal activities (α in Equation 1), controlling for the same sociodemographic characteristics and school fixed effects.

Results

Table 3 presents baseline OLS regression results predicting “any” criminal activities for the individuals at Wave 1. The focus of this table is on describing the association between the outcome and socio-demographic characteristics of the respondents. Column 1 presents results for the full analysis sample. We find that 8th, 9th, and 10th graders are 4.7, 5.2, and 4.3 percentage points more likely to conduct criminal activities than 7th graders (the omitted category). Several family-level variables are highly associated with the probability of engaging in criminal activities. For example, students living with both biological parents are 7 percentage points less likely to report criminal activities, and students with either a father or mother who has ever been incarcerated are 6 percentage points more likely to conduct criminal activities. Students living in rural areas are 3 percentage point less likely to engage in crimes. Few contextual (school or grade-level) characteristics are found to be associated with an individual's criminal activities. Columns 2 and 3 in Table 3 stratify the baseline results by gender. Surprisingly, most associations at the individual level are similar for males and females, although the magnitude of the association slightly differs. Exceptions are age and rural status.

Table 3. OLS analysis of the associations between adolescent criminal activity and individual and grade-level characteristics, full sample and by gender.

	(1)	(2)	(3)
Dependent variable	Any crime	Any crime	Any crime
Specification	OLS	OLS	OLS
Sample	Full	Male	Female
Male	0.082*** (0.008)
Grade 8	0.047*** (0.014)	0.050** (0.022)	0.044*** (0.016)
Grade 9	0.052*** (0.018)	0.061** (0.025)	0.043** (0.021)
Grade 10	0.043* (0.023)	0.053 (0.034)	0.032 (0.027)
Grade 11	0.025 (0.029)	0.031 (0.042)	0.019 (0.034)
Grade 12	0.010 (0.035)	0.024 (0.051)	-0.004 (0.039)
Age	0.010 (0.006)	0.021** (0.009)	-0.002 (0.007)
Black	0.009 (0.013)	0.008 (0.019)	0.011 (0.018)
Hispanic	0.036** (0.017)	0.033 (0.025)	0.034 (0.022)
Other race	-0.010 (0.016)	-0.011 (0.029)	-0.004 (0.022)
PVT score (Std)	0.001 (0.005)	0.008 (0.008)	-0.006 (0.006)
Religiosity	0.003 (0.003)	0.005 (0.006)	0.003 (0.004)
Number of older siblings	0.009** (0.004)	0.011** (0.005)	0.007* (0.004)
Maternal education	-0.002 (0.002)	-0.002 (0.003)	-0.002 (0.002)
Family income	-0.003 (0.021)	-0.008 (0.035)	-0.003 (0.023)
Both biological parents	-0.068*** (0.009)	-0.092*** (0.015)	-0.042*** (0.010)
Own parental incarceration	0.061*** (0.018)	0.077*** (0.025)	0.046** (0.022)
Missing parental information	0.010 (0.010)	0.006 (0.015)	0.013 (0.011)
Rural	-0.029*** (0.009)	-0.045*** (0.014)	-0.011 (0.011)
% Black	-0.018 (0.025)	-0.002 (0.035)	-0.033 (0.028)
% Hispanic	-0.002 (0.035)	0.010 (0.053)	-0.013 (0.039)
% Other race	0.072 (0.046)	0.042 (0.065)	0.105* (0.054)
Mean religiosity	0.001 (0.018)	-0.015 (0.028)	0.019 (0.020)
Mean number of older siblings	-0.027* (0.016)	-0.044* (0.023)	-0.010 (0.020)
Mean maternal education	0.005 (0.010)	0.011 (0.015)	-0.001 (0.010)
Mean family income	0.057 (0.099)	-0.041 (0.146)	0.158 (0.101)
% Missing parental information	0.006 (0.041)	-0.040 (0.058)	0.056 (0.040)
Constant	-0.103 (0.134)	-0.180 (0.203)	0.070 (0.157)
N	16912	8251	8661
R-squared	0.037	0.037	0.020

Note: Cross-sectional weights are used. Robust standard errors are clustered at school-level.

^*p< 0.1,

^**p< 0.05,

^***p< 0.01.

Table 4 begins the examination of endogenous social effects for criminal behaviors. Two-stage least square and first stage results are presented. In these analyses, we use the instruments—classmates' parental incarceration and co-residence with both biological parents. As we argue above, the validity of exclusion restriction is based on the presumption that classmates' parental status measures including incarceration and marital status may not be well known by an individual high school student, and only affect the student through peer behaviors. To provide further confidence in the instruments, we present results from balancing tests in Table 2, showing that these instruments are essentially uncorrelated with individual- and family-level characteristics of the students (Bifulco et al. 2011; Lavy and Schlosser 2011). This is suggestive evidence that these instruments can be thought of as plausibly exogenous within school and that parents are not systematically changing students' schools based on these cohort characteristics.

Table 4. Analysis of peer effect in adolescent criminal activity, 2SLS and 2SLS/FE results.

	(1)	(2)	(3)	(4)
Dependent variable	Any crime	Any crime	Any crime	Any crime
Specification	2SLS	2SLS first stage	2SLS/FE	2SLS/FE first stage
Sample	Full	Full	Full	Full
% Any crime	0.775*** (0.096)		0.599*** (0.220)
Grade	-0.006 (0.006)	0.009*** (0.002)	-0.007 (0.007)	0.004 (0.003)
Age	0.009 (0.006)	0.002 (0.002)	0.010* (0.006)	0.002** (0.001)
Male	0.081*** (0.008)	0.001 (0.002)	0.080*** (0.008)	-0.001 (0.001)
Black	0.012 (0.014)	-0.001 (0.002)	0.013 (0.014)	-0.006** (0.002)
Hispanic	0.039** (0.017)	-0.002 (0.002)	0.043** (0.018)	-0.001 (0.003)
Other race	-0.016 (0.016)	0.007** (0.003)	-0.019 (0.016)	-0.007 (0.004)
PVT score (Std)	0.001 (0.005)	0.000 (0.001)	0.001 (0.005)	0.001 (0.001)
Religiosity	0.003 (0.004)	0.001 (0.001)	0.003 (0.004)	-0.000 (0.001)
Number of older siblings	0.010*** (0.004)	-0.000 (0.001)	0.010*** (0.004)	0.000 (0.001)
Maternal education	-0.002 (0.002)	-0.000 (0.000)	-0.002 (0.002)	-0.001** (0.000)
Family income	-0.008 (0.020)	0.007** (0.003)	-0.010 (0.020)	0.001 (0.004)
Both biological parents	-0.061*** (0.009)	-0.005*** (0.002)	-0.059*** (0.009)	-0.002 (0.001)
Own parental incarceration	0.056*** (0.017)	0.004 (0.003)	0.055*** (0.017)	0.004* (0.003)
Missing parental information	0.009 (0.010)	-0.000 (0.001)	0.010 (0.010)	0.000 (0.001)
Rural	-0.014* (0.007)	-0.013** (0.005)	-0.014 (0.009)	0.000 (0.001)
% Black	-0.034** (0.017)	-0.020 (0.023)	-0.065 (0.094)	-0.249*** (0.088)
% Hispanic	-0.011 (0.022)	0.026 (0.026)	-0.007 (0.061)	-0.039 (0.083)
% Other race	0.013 (0.027)	0.062* (0.034)	-0.128 (0.099)	-0.259** (0.127)
Mean religiosity	-0.016 (0.010)	0.016 (0.016)	-0.033* (0.019)	-0.020 (0.017)
Mean number of older siblings	-0.008 (0.009)	0.012 (0.016)	-0.011 (0.014)	0.012 (0.020)
Mean maternal education	0.009 (0.006)	-0.007 (0.008)	0.004 (0.011)	-0.022** (0.010)
Mean family income	0.029 (0.055)	0.265*** (0.083)	0.085 (0.112)	0.128 (0.127)
% Missing parental information	0.010 (0.023)	-0.060* (0.033)	0.023 (0.039)	-0.020 (0.043)
% Parental incarceration		0.172* (0.093)		0.212** (0.097)
% Both biological parents		-0.273*** (0.037)		-0.148*** (0.046)
Constant	-0.158** (0.076)	0.144 (0.092)
N	16912	16912	16912	16912
R-squared	0.033	0.214	0.014	0.573
F-statistic (First stage)		33.571		8.947
J-statistic p-value	0.27		0.12

Note: J-statistic p-value reflects the over-identification test results where the null is valid instruments. Cross-sectional weights are used. Robust standard errors are clustered at school-level.

^*p< 0.1,

^**p< 0.05,

^***p< 0.01.

The results in Column 1, Table 4 show that the endogenous effect of peer-level criminal activities on an individual's crimes appears to be large (b = 0.775). The results also suggest our analysis satisfies several statistical diagnostic tests related to instruments. The instruments are “strong” predictors in the first stage of the analysis (i.e., reported F-statistic is large (34)), and the over-identification test fails to reject the validity of the instruments (p = 0.27). However, we may be concerned that the instruments are correlated with individual-level characteristics that also predict selection into the school (and, mechanically, the peer measure), and are thus not validly excluded from the second-stage outcome. For example, children with divorced parents may be more likely to attend schools with higher crime than children with married parents. This process of selection could invalidate the instrumental variable strategy if the selection process is not accounted for in the models.

To account for school-level unobservables that influence individual and grade-level criminal activities simultaneously, as well as selection effects related to the chosen school, school fixed effects are controlled in the analysis. Before interpreting the results, we note that there is substantial within-school variation in the grade-level proportion any crime, proportion of parental incarceration, and proportion of co-residence of both biological parents while there is less variation in the grade-level racial composition, family income, and maternal education within a school (Table S2 in supplementary material). The main results and first-stage results from our preferred specifications (i.e., 2SLS/FE model) are presented in Columns 3 and 4, respectively. As we expect, in Column 4, the coefficient is reduced after controlling for school fixed effects by over 20%, from 0.775 to 0.599. This preferred estimate suggests that increasing the proportion of peers who engage in criminal activities by 5 percent (within-school variation in peer delinquency) will increase the probability of individual's own crimes by 3 percentage points (0.599 × 0.05). The results have a F-statistic of 9, which is quite close to the recommended cutoff of an F-statistic of 10 in Staiger and Stock (1997), and the over-identification test fails to reject the validity of the instruments (p = 0.12)⁴.

We confirm that the results do not differ when we estimate exactly identified IV models that use each instrumental variable separately, although the coefficient for the endogenous peer effects are larger when using peers' parental incarceration as an instrument (Table S3 in supplementary material). In addition, to test the sensitivity of the results by model specifications, we use IV-probit specification and present the marginal effects for IV-probit in Table S4 in supplementary material. The estimates are extremely similar to the 2SLS/FE estimates we present.

In order to further assess the robustness of the IV estimates, we adopt the bounds approach proposed by Conley et al. (2012) to draw inferences that are valid if the instrumental variable does not perfectly satisfy the exclusion restriction assumption⁵. For the sake of brevity, the results are reported for 90% confidence intervals and detailed descriptions of the procedure are discussed in supplementary material (see “B. Sensitivity Analysis of Instrumental Variable”). The results from this sensitivity check suggest that even if peers' parental incarceration and co-residence with both biological parents had a relatively large direct impact on an individual's criminal activity, the IV estimates of endogenous peer effects remain positive and statistically significant⁶. In sum, the IV estimates of endogenous peer effects are very robust, even to substantial departures from a perfect IV.

Conclusion and discussion

Juvenile criminal activities and delinquency have received substantial attention from scholars, the media and the public. A resurgence of research focusing on the effects of delinquent peers has surfaced recently. In this paper, we use a social interactions framework to examine whether adolescent criminal activities are influenced by classmates' criminal involvement, and to quantify more accurately how much peer delinquency causes adolescent's delinquency. We address several large empirical challenges in addressing this question, including the endogeneity of school (and thus classmates) through residential location choices, ‘third factors’ such as school-level confounding factors (i.e., correlated effects), and the “reflection problem.” In particular, we use a combined instrumental variables/fixed effects methodology that compares students in different grades within the same high school who face a different set of classmates and classmates' decisions.

Our attention to the empirical challenges of peer effects models is important. After controlling for observed and unobserved school-level characteristics, the effect of delinquent peers is reduced by about 23 percent, indicating that failing to account for selection into a certain peer context could overestimate peer effects. Our preferred specification (i.e., a combined instrumental variables/fixed effects approach) demonstrates that increasing the proportion of classmates who are involved in criminal activities by 5 percent (across-cohort, within school variation in peer delinquency) will increase individual adolescent's own crime by 3 percentage points (about 20% increase). The findings of this study suggest that a wider peer group is an important social group that influences adolescents' engagement in criminal activity.

This study contains several limitations. First, causal inference can be threatened when using the instrumental variables strategy if the instruments fail to satisfy the exclusion restriction assumption. Unfortunately, there is no way of directly testing this assumption. Indeed, there are some possible reasons that the exclusion restriction might be violated in our context. For example, the parents of one's peers may prevent his or her delinquency by providing supervision and thus preclude opportunities to be influenced by peers (Osgood et al. 1996). Although the procedure proposed by Conley and colleagues (2012) to check for the sensitivity of IV estimation results yields highly stable estimates for a wide range of relaxations of the exclusion restriction, this only reduces, and does not eliminate, the concern that the exclusion restriction assumption may be violated.

Second, there is the possibility of school-grade specific correlated effects that are not removed by school fixed effects, so that school-grade-level factors could still bias the results. For example, a particularly strict 9th grade teacher could reduce the delinquency of all students in the grade, which in our analysis would appear to be a peer effect. Third, there are restrictions on the generalizability of the results of this study because the IV estimates in this study should be interpreted as local average treatment effects (LATE) (Imbens and Angrist 1994). The results are generalizable largely to those who have classmates whose delinquency is influenced by parental incarceration and/or not living with both biological parents.

Despite these limitations, we make several important contributions to the literature. First, we provided causal evidence in the literature of peer influences in criminal activity during high school. Specifically, by using a quasi-experimental empirical framework, we were capable of addressing several methodological challenges in estimating peer effects, including self-selection of friends, the issue of unobserved environmental confounders, and the bi-directionality of peer effects. Second, our finding that delinquent behavior of classmates influences an adolescent's delinquency is novel because the role of wider peer networks has been largely ignored in the crime and delinquency literature. Further research is needed to better understand the mechanisms in which delinquent behaviors among members of wider peer networks shape adolescents' delinquency (e.g., Megens and Weerman 2012), and how this peer group interacts with close friendships to influence juvenile delinquency.

Our findings may be relevant for policy discussions about reducing juvenile delinquency. Among other social effects, endogenous peer effects can take advantage of social multiplier effects (or spillover effects) because an intervention on one individual is predicted to influence the untreated in the same reference group. Thus, establishing credible evidence of the endogenous social effects in criminal activity is crucial to understanding the potential multiplier effects of policies that can successfully reduce delinquency in subset of students, which can spillover over on other students in the peer group. It is also important to examine the effects of wider peer groups in these processes (i.e. schoolmates and classmates) because policymakers tend to have more control over the composition of these particular groups than on the composition of friendship networks and other smaller group processes that can hardly be sorted by outsiders.

For example, in many states, disruptive or delinquent adolescents are often retained in grades, placed in self-contained classrooms, or even assigned to alternative schools. In the juvenile justice system, delinquent adolescents are placed with similar peers in training schools, detention centers, and correctional facilities (Bayer, Hjalmarsson, and Pozen 2009; Sickmund 2010). In order to better understand the overall effectiveness and social costs of the assignment location, policymakers should understand how the assignment influences the behavior of not only delinquent youths but also all who are affected by the assignment. Our estimates of the effects of delinquent classmates on an individual's criminal activity may provide some guidance about harm-minimizing assignment strategies.