The Pull of Popularity Explaining Conformity in Student Behaviors WORKING PAPER April 6, 2015 Nancy Haskell University of Dayton Dept. of Economics & Finance 300 College Park Dayton, OH 45469 [email protected] ABSTRACT: In contrast to most existing literature on social interactions, this paper posits a model with endogenously determined popularity that provides a novel, micro-founded mechanism for explaining conformity to group behavior. Model assumptions and predictions are tested with Add Health data using a multi-step estimation process. The empirical work combines a bivariate probit model of friendship formation with a two-stage least squares estimation of student behaviors. Results are consistent with a model in which students use behaviors to gain friendships, and the model allows for policy-relevant simulations to predict student behaviors in counterfactual school environments. This research uses data from Add Health, a program project designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris, and funded by a grant P01HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 17 other agencies. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Persons interested in obtaining Data Files from Add Health should contact Add Health, The University of North Carolina at Chapel Hill, Carolina Population Center, 206 W. Franklin Street, Chapel Hill, NC 27516-2524 (addhealth [email protected]). No direct support was received from grant P01-HD31921 for this analysis. 1 Introduction Almost every child in middle or high school has experienced a social situation in which they were torn between their preferred activity and the popular activity. These behaviors can range from the clothes students wear to the amount of time they spend studying or partying. A choice must be made as to how to act, and this decision will affect popularity differently depending on the school environment. As a result, a person’s social network position is not exogenous to her actions. Behaviors, to some extent, are a conscious choice with recognized consequences for an individual’s social status among a group of peers. This paper introduces the idea that people directly gain utility from being popular. The paper then explores how the desire to gain popularity affects the behavior of individuals relative to their peers. The assumption is consistent with literature from sociology and psychology that describes popularity as a measure of status and documents the time and effort that students spend trying to become more popular [Kiefer and Ryan (2008); Eder (1985)]. In contrast to the existing literature, popularity is endogenously determined within the model. This provides a novel mechanism for explaining why students conform to group behaviors. The model also provides a framework for determining how people choose their friends. Friendship between an individual and her peer is decided by two factors: (1) homophily, and (2) whether the peer perceives the individual’s behavior to be “cool.” The theory of homophily, the idea that people who are more similar to each other in behaviors and characteristics are more likely to be friends, has been well documented by sociologists and economists. In this model, being viewed as “cool” 1 by more of one’s peers is associated with an increase in the number of friends, thus greater popularity. The model, however, places no restrictions on the types of behaviors that are “cool.” Rather, data on the behaviors, characteristics, and reported friendships of students from a large number of high schools across the United States are used to estimate a unique, popularity-maximizing level of behavior. This theory of behaviors directed at achieving social acceptance differs from most existing work. Many studies by economists and sociologists use rich data on the structure of social networks to identify the extent to which people affect their close friends and their more distant acquaintances. These studies overwhelmingly estimate reduced form equations with little discussion of an underlying, micro-founded framework. Furthermore, existing literature largely ignores the paradigm described earlier in which students actively choose behaviors with the intent of altering their social standing. The model and empirical work introduced here allow behaviors to affect popularity, and use an instrumental variables approach to estimate the extent to which the desire to gain popularity drives a student’s observed behavior. The model developed in this paper predicts that each individual will choose an optimal behavior that is a convex combination of her popularity-maximizing behavior and the “innate” behavior that she would exhibit in the absence of any preference for popularity. Both the underlying assumptions and the model’s predictions are tested using data from the National Longitudinal Study of Adolescent Health (Add Health). The empirical analysis focuses on four indexes: (1) academic performance, studying, and effort in school as measured by a student’s grade point average (GPA), (2) an index of substance use composed of smoking and drinking behavior, (3) an index of unruliness as defined by skipping school, lying, fighting, and doing dangerous 2 things on dares, and (4) an index of interpersonal troubles with teachers and other students. In the data, good grades, substance use, and general unruliness, tend to be viewed as “cool” and have a positive influence on a student’s popularity, while interpersonal problems reduce popularity on average. Consistent with the theoretical predictions, the empirical results show that GPA, substance use, and unruliness are affected by the popular level of the behavior, with students putting the most emphasis on popularity-maximization with regard to their effort in school. The results suggest that altering the perceived “coolness” of certain behaviors can minimize risky behaviors or improve grades. While not a new idea, these findings provide an economic motivation for the many school programs and public service announcements that attempt to change perceptions of which behaviors are “cool” among youths. This paper further shows that the racial and socioeconomic composition of the school is a strong determinant of which behaviors are socially accepted because subgroups of the population tend to have different tolerances for the behaviors. Since homophily is a large part of the popularity process, changing the racial, ethnic, and socioeconomic composition has the potential to change the popularitymaximizing behaviors in a school, thereby altering the actual behavior of students. This could have implications for policy initiatives such as school-choice programs, which enable students to change their school and peer group. The next section discusses relevant literature. A detailed description of the model is provided in the third section. The fourth section presents data, while the fifth discusses the empirical methods and results. Finally, the sixth section concludes. 3 2 Literature A large literature exists on social interactions, but only a handful of studies focus on the relationship between an individual’s network position and her behavior. Two network positions, centrality and popularity, have received particular attention. Centrality describes how well-connected an individual is within a network. This measure includes the number of direct friends, as well as the number of indirect contacts (friends of friends) thereby capturing information about the local network structure. On the other hand, popularity is measured by the number of peers who nominate a particular student as a friend. The direction of friendship matters for defining popularity, meaning the distinction between nominee and nominator is important. Centrality and popularity are often correlated, and studies indicate that both measures of network position are strongly related to behavior. This result has been shown in theoretical models (Calvo-Armengol, Patacchini, and Zenou, 2009) and in empirical studies [Babcock (2008), Haynie (2001)] for a variety of data on academic achievement and delinquency. In all but one paper, however, these studies assume that centrality and popularity are given features of the network structure. Based on this assumption, they assess the effects of an individual’s position on her behavior, but fail to consider how behavior might influence her centrality or popularity. Rather than examining the causal effects of popularity on behavior, this paper explores how the desire to increase popularity affects a student’s behavior. If, as this paper posits, behaviors affect a student’s popularity, then endogeneity will lead to biased coefficient estimates in regressions of behaviors on popularity. The error terms in these regressions will be positively correlated with popularity for “cool” be4 haviors because higher levels of such behaviors lead to greater popularity, according to the model presented in this paper. The correlation between the error term and popularity suggests that the findings in prior literature, which assume popularity is exogenous, over-estimate the effects of popularity on “cool” behaviors. Recent literature on social interactions has attempted to address this possible endogeneity between friendships and behaviors. A common approach has been to exploit data on the random assignment of college roommates or military cadets in order to get a set of exogenous links between students. These papers find varying degrees of peer effects for college roommates on academic outcomes [Sarcedote (2001), Foster (2001), Zimmerman (2003), Stinebrickcer Stinkbrickner (2006), and Lyle (2007)]. However, these methods fail to account for differing effects based on the unique pattern of social interactions that develops endogenously even in randomly assigned peer groups (Carrell, Sarcerdote, and West, 2013). Foster (2001) further suggests that peer effects may be heterogeneous across different types of students, and so average effects may not be very informative. A model of endogenous friendship formation such as the one presented in this paper, allows for heterogeneous peer effects based on a student’s characteristics relative to the distribution of her classmates. This is not the first paper to attempt to simultaneously account for endogenous friendship formation and behavioral outcomes. Conti et. al. (2011) use a more sophisticated empirical model and estimation strategy to understand the relationship between popularity and labor market outcomes. While the authors show that popularity is largely determined by a student’s family environment, her personal characteristics relative to the school’s demographics, and the size of the school, they do not consider student behaviors as determinants of popularity. Similarly, Mihaly 5 (2009) estimates the effects of popularity on academic achievement, using a student’s race, gender, and background characteristics relative to the demographic composition of the grade as instrumental variables for popularity. Goldsmith-Pinkham and Imbens (2014) also estimate endogenous friendship formation as a function of individual characteristics. Weinberg (2006) models the endogenous selection of individuals into subgroups within a network. In his model, “peer pressure,” or a change in popularity, directly enters the utility function of his agents. Yet all of these papers posit that the relevant factor affecting behavior is the student’s actual popularity or friendships. The model and empirical findings presented in this paper suggest the relevant mechanism is not the level of popularity but rather the desire to increase popularity that drives student behaviors relative to their peers. By assuming popularity directly enters the utility function, students intentionally behave in a manner that will make them more popular. This paper is the first to explicitly model students’ desire to gain popularity through their behaviors, which endogenizes both the behavior and the network position. The model places no restrictions on the effects of behaviors on popularity. Rather, popularity-maximizing behaviors are determined from data. 3 Model This section describes a model of behavior and popularity in the presence of social interactions. In this paper, the model is applied to high schools so agents in the model will be referred to as students. Each student is defined by her “innate” behavior, y0 , which represents how she would behave in an environment without peer effects or concern for popularity. This “innate” behavior captures the non-social benefits and costs to engaging in various behaviors. The “innate” behavior is assumed to be a 6 function of an individual’s characteristics such as race, ethnicity, gender, age, and socioeconomic status. For example, students with well-educated parents are expected to have a higher “innate” level of academic achievement. The effects of parental education on a student’s academics could operate in part through a preference for learning passed on from her parents, or through lower costs to studying due to the student being smarter or having access to more resources at home. In the model, the students directly derive utility from being popular, but face a convex-utility cost of deviating from their “innate” behavior. Popularity is itself a function of an individual’s behavior relative to her peers, and the “coolness” associated with certain behaviors. In choosing an optimal behavior, y ∈ Y , a student must choose the extent to which she should follow her “innate” behavior and the extent to which she should act in a manner that will increase her popularity. This decision is formalized in the utility maximizing problem described below. In the model, popularity is defined as the probability of the student being nominated as a friend by a schoolmate, summed across all peers in the group of potential friends.1 maxy U (y, f (·); y0 , x, g(·), s) = αP (y, f (·); x, g(·), s) − β(y − y0 )2 P (y, f (·); x, g(·), s) = Z Z X Y p(x, x e, s) − θ(y − ye)2 + k(x, x e)y f (e y )de y g(e x)de x (1) (2) α, β, θ ∈ R+ 1 In this general model, the group of potential friends is defined as all other students in the individual’s school. 7 The utility function parameters, α and β, are assumed to be positive constants. A student’s cost of deviating from her “innate” behavior is quadratic, thus the student experiences greater disutility the further she moves from her “innate” behavior. Students are assumed to know their “innate” behaviors, and the distribution of these behaviors is exogenous (i.e. the model does not consider any selection into schools). Popularity, P (y, f (·); x, g(·), s), enters the utility function linearly, where ye represents the behavior of an individual’s peer. In the model, an individual’s popularity is both a function of her behavior relative to her peers, as well as her innate characteristics. Characteristics such as race, gender, or socioeconomic status may make a student very popular or very unpopular, irrespective of how she behaves. It is assumed that students cannot reasonably change their characteristics such as gender or race.2 Thus, students are assumed to start with some baseline level of popularity, p(x, x e, s), and become more or less popular as a result of their behaviors relative to other students in the school. Here, p(x, x e, s) is a function of the student’s characteristics (x) such as race, gender, and socioeconomic status, the peer’s characteristics (e x), and school-specific factors (s) such as the size of the student body. Popularity is also determined in part by a quadratic loss function in the distance 2 Since students report their own race in the data, it may be more appropriate to think of this term as “racial identification.” A student could alter her racial identification, particularly if she is multiracial, depending on her environment. In addition, students could self-identify with a race other than their true one. The first, selective racial identification based on peers, presents a potential problem for this paper. However, the empirical work controls for students being multiracial, and these are the ones most likely to successfully select their racial identification based on their peer group. The second issue of racial identification being different from a student’s true race is less of an issue if the relevant factor for friendship formation is racial identification and not genetic lineage. However, given that racial identification is a choice but genetic heritage is exogenous, this could lead to problems with the identification strategy in this paper. Using data on the small portion of the sample with interviewer-reported racial identification, it might be possible to estimate the extent to which self-reported race differs from the perceptions of an outside observer. 8 between a student’s behavior (y) and the behavior of her peers (e y ).3 The model assumes that greater distance between behaviors reduces the probability of receiving a friendship nomination by θ, where θ is assumed to be a positive constant. This functional form assumption is made primarily for analytical convenience, and is not rejected by empirical evidence.4 This portion of the popularity function is also consistent with the concept of homophily, meaning that people prefer friends who are similar to themselves. The “coolness” factor, k(x, x e), of behaviors is assumed to enter linearly into the popularity function.5 However, the perception of “coolness” for any given behavior is allowed to differ based on the gender, race, and socioeconomic status of both the student and her peer. This allows the tolerance for various behaviors to differ across racial, ethnic, and socioeconomic groups. For instance, drinking may be viewed as “cool” on average, but specific racial or ethnic subgroups of the population may view drinking negatively.6 In this framework, the desire to gain popularity draws students away from their “innate” behaviors and toward the popularity-maximizing behavior. The extent to which a student deviates from her “innate” behavior is characterized by the optimal decision rule derived from the utility-maximization problem. The purely popularity3 The probability density function, f (·), denotes the distribution of peers’ behaviors, ye. Results from a bivariate probit estimation of the probability of two students being friends, as reported in Table 11, show the distance between the two students’ behaviors, as measured by the difference between their behaviors squared, decreases the likelihood of them being friends. 5 The function k(x, x e) is itself assumed to be linear, so integrating over the distribution of student characteristics (denoted by g(·)), will yield a linear function of the average demographic characteristics in the school k(x, E(e x)). 6 A negative value of k(x, x e) indicates that the behavior is “uncool”. 4 9 maximizing behavior is found by solving ∂P ∂y ∗ = E(e y) + ypop = 0, which yields k(x, E(e x)) . 2θ (3) Taking and solving the first-order condition from the utility-maximization problem generates the following relationship. αθ k(x, E(e x)) β y= E(e y) + + y0 αθ + β 2θ αθ + β (4) Substituting equation (3) into equation (4), we are left with ∗ y ∗ = γypop + (1 − γ)y0 , where γ = (5) αθ . αθ + β Each student’s best response to the behavior of her peers is to choose a convex combination of her “innate” behavior and the popularity-maximizing behavior.7 Assuming that the utility gains from being popular (α) are constant, students will put more weight on behaviors for which θ is larger, meaning that friendship nominations are more affected by homophily in those behaviors. Students will put less weight on popularity-maximization for behaviors in which deviating from one’s “innate” behavior is particularly costly, a larger β in the model. These effects will be visible in ∗ the empirical results in the size of γ, the coefficient estimate on ypop . 7 The following simplifying assumptions serve as sufficient conditions for the existence of equilibrium: (1) behaviors and characteristics are independently distributed, (2) the “coolness” factor, k, is constant, and (3) popularity is only a function of in-degree nominations and no weight is placed on the connectedness of the nominator. The second simplifying assumption is relaxed in the empirical work. Proof available upon request. 10 The formulation in equation (4) departs only slightly from a standard Manskimodel in which behavior is a linear function of the group average, E(y). Specifically, the interaction between individual and group characteristics, k(x, E(e x)), affects behaviors in this model, unlike in a Manski-model where there is no interaction between the individual and correlated effects.8 More notably, this model provides a novel, micro-founded mechanism in which popularity is endogenously determined through utility-maximizing behavior that can generate a linear-in-means behavioral equation. The underlying assumption of the model, that popularity increases utility, is consistent with the data. The empirical findings are also consistent with the primary mechanism of the model; students modify their behaviors to increase popularity. 4 Data Both the underlying assumptions and the predictions of the model are tested empirically using data from the first wave of Add Health. This study uses the In-School portion of the survey, which was administered to a nationally representative sample of more than 90,000 students in grades 7-12 across 132 schools during the 1994-1995 academic year. In this paper, the sample is restricted to only include high school students, grades 9-12. This study omits schools with available data on fewer than ten students because of the focus on popularity and friendship networks. After cleaning the data, and eliminating observations with missing values, 35,490 students across 88 schools remain in the regression sample.9 8 Correlated effects is the term Manski uses to refer to the influence that average group characteristics have on individual behaviors. 9 About one-third of the reduction in sample size is the result of dropping middle school students in grades 7-8. The remainder of the loss of observations is the result of missing data for characteristics and the behavioral outcomes of interest. 11 The Add Health data set includes a wealth of information on student behaviors, health outcomes, and interpersonal relationships. In this study, popularity, academic grades, substance use (drinking and smoking), and general unruliness or delinquency, are the primary variables of interest. Characteristics such as age, gender, race and ethnicity, the presence of a father, and the education of the mother are considered innate and serve as exogenous controls in the regression equations. Table 1 provides summary statistics for the variables. The sample is evenly split between male and female students. In the sample, 14% of students are Hispanic. Approximately 70% of the sample are white, 15% are black, and 7% are Asian. The racial categories are not, however, mutually exclusive. The data show 6% of the regression sample reporting multiple races. Three-quarters of the students in the sample live with their fathers. The mother’s education is coded to correspond to the average number of years she has spent in school. On average, the mothers’ of these students have completed 13 years of schooling, meaning they graduated from high school but do not have a college degree. However, many of these demographic characteristics vary substantially by school. 4.1 Popularity The Add Health survey asks students to list their five closest male and five closest female friends. Popularity is defined as the number of in-degree nominations a student receives, meaning the number of times a student is listed as a friend by others. Since the survey questionnaire asks for only a student’s top five friends in each gender, the number of in-degree nominations may be biased downward. A student could be considered a friend, but she will not receive a nomination unless she is among the top 12 five friends in that gender. While this raises a concern that the measure of popularity could be biased downward, there is reason to believe that the bias is relatively small. The majority of students list no more than three close friends of each gender, so the limit of five friends is rarely binding and it is unlikely to affect the results.10 The distribution of popularity is heavily right-skewed. The majority of students receive between one and four in-degree nominations, with only a small handful of students receiving a substantially larger number of nominations. The average number of indegree nominations is approximately four. Only 5% of students receive more than ten nominations, and only 1% of students receive 17 or more nominations. However, the most popular students in the sample receive as many as 30 nominations. 4.2 Behaviors Study habits and academic achievement are measured using the grade point average (GPA) from the student’s reported grades in English, Mathematics, Science, and History.11 The distribution of GPA is mostly consistent across schools, with a mean of 2.9 and a median of 3.0 on a 4.0 scale. Grades are approximately normally distributed around the mean. The bottom ten percent of students have a cumulative GPA that is lower than a C-average, while the top ten percent of students maintain an A-average. Data exist on a variety of substance use and other delinquent behaviors. However, many of these behaviors are highly correlated. The degree of collinearity makes it very difficult to separately identify the relationship between the behaviors and friendship nominations when trying to control for all of the relevant behaviors si10 The effort of reporting additional friends might still create some downward bias. If a student does not report grades for all four subjects, the GPA is calculated using only the subset of classes for which grades are reported. 11 13 multaneously. Instead, indexes are used to represent “types” of behaviors. The substance-use index is a summation of the number of times in the last month a student smoked, drank alcohol, and got drunk. The substance-use index is extremely right-skewed, as are the distributions of smoking and drinking. The median student in the sample smokes, drinks alcohol, or gets drunk once per month. The bottom 25% of high school students report no use of any of these substances. However, a substantial number of students drink or smoke heavily. A mean of 7 implies that on average students engage in substance use a little less than twice per week. The top ten percent of students report smoking, drinking, or getting drunk every day. The remaining behaviors of interest include fighting, doing dangerous activities on dares, skipping school, lying, having trouble with teachers, and having trouble with other students. An exploratory factor analysis provides information on which of these activities belong in the same grouping or index. The analysis shows two underlying latent variables. The first latent variable corresponds to general unruliness. It is primarily defined by fighting, doing dangerous activities on dares, skipping school, and lying. The second latent variable describes interpersonal problems and is defined by getting into trouble with teachers and other students. Given the results from this exploratory factor analysis, two behavioral indexes are created to correspond with the underlying latent variables. The index of unruliness is a summation of the number of times per month a student did something dangerous on a dare, skipped school, or lied, and the number of times in the last year that the student got into a physical fight. As with substance use, the unruliness index is very right-skewed. The median student only engages in two or three of these activities. The bottom ten percent only participate in one of these activities once or twice per month (or once or twice per year in the case of fighting). The top ten percent of students, however, engage 14 in three or four of these activities every week. The mean is around 7.5 suggesting almost two incidences of unruly behavior per week. The final index describing interpersonal problems is a summation of how many times per month a student gets in trouble with teachers or other students. The median student has some sort of interpersonal altercation once a week. A mean of 11 indicates that, on average, students have interpersonal problems every few days. While the bottom ten percent of students report having no problems with teachers or other students, the top ten percent of students report having trouble getting along with teachers and other students more than once a day (40 or more times per month). Having trouble getting along with peers and teachers is likely the least relevant of the four behavioral measures for friendship nominations. If anything, one might expect it to negatively impact a student’s popularity. The regression analysis still includes this index to minimize potential omitted variable bias. As discussed in the next section, having interpersonal problems does not increase popularity, and thus the remainder of the paper focuses primarily on the first three behavioral measures: academic achievement, substance use, and general unruly behavior. 5 Empirical Methods and Results The empirical strategy and results described in this section provide evidence that students engage in some behaviors in order to gain popularity. The theoretical model is based on the assumption that students gain utility from being popular, and that a student’s popularity is a function of her behavior, particularly her behavior relative to her peers. The decision rule derived from the model implies that students will choose an optimal behavior that is a convex combination of their innate behavior 15 and their popularity-maximizing behavior. The empirical work can be divided into a pre-stage estimation of popularity, followed by a standard two-stage least squares (2SLS) estimation of the behavioral equation. The pre-stage estimation determines how behaviors influence popularity, and uses these results to predict a popularitymaximizing behavior for every student. The first stage of the 2SLS estimation uses a student’s socioeconomic and racial characteristics relative to the demographic characteristics of her schoolmates as instrumental variables for her popularity-maximizing behavior. This removes endogeneity between the popularity-maximizing behavior and the student’s observed behavior. The second stage of the 2SLS estimation determines the relative weight that students place on popularity-maximization when choosing their optimal behavior. The coefficient estimate from this last step corresponds directly with the parameter γ from equation (5). 5.1 Popularity In the data, popularity is determined by the number of in-degree nominations a student receives.12 For the purposes of estimation, predicted popularity is defined as the sum of the predicted probability of receiving an in-degree nomination across all other students in the school.13 The probability that two students nominate one another is assumed to follow a bivariate probit model, which controls for unobserved correlation in the likelihood of each student nominating the other. 14 The theoretical model directly informs the specification of the bivariate probit. 12 “In-degree” refers specifically to a student being listed as a friend by another student. A school is the boundary for friendship nominations because the data record friendship nominations made between students in the same school. 14 For instance, two students may name each other as friends, irrespective of characteristics or behaviors, because they happen to be next door neighbors. 13 16 The probability of receiving a friendship nomination depends on the distance between the nominee and nominator’s behavior, thereby capturing the effects of homophily in behaviors. The functional form allows for additional flexibility in the effect of similarity in behaviors on the likelihood of a friendship by also including an interaction term between the nominee’s and nominator’s behavior. The probability of a nomination is also dependent on the perceived “coolness” of the potential nominee’s behavior, which is given a flexible functional form. “Coolness” enters the equation as a quadratic to account for homophily, and perceptions of “cool” behaviors are allowed to differ by demographic group through interactions between the nominator’s characteristics and the nominee’s behaviors. The probability of a friendship forming is also a function of the nominee’s characteristics, the distance between the nominee and the nominator’s characteristics, and school fixed effects. The bivariate probit model takes the following functional form: Pr(nomij = 1, nomji = 1) = Φ2 (Zij β, Zji β, ρ) Zij β = b0 + L X 2 [b1l yjl + b2l yjl + b3l (yil − yjl )2 + b4l yil yjl ] |l=1 + M X {z } behaviors 2 [b5m zjm + b6m zjm + b7m (zim − zjm )2 + b8m zim zjm ] |m=1 + (6) {z } characteristics M1 X L X [b9ml zim yjl + b10ml zim zjm yjl ] + m=1 l=1 | {z perceptions of “cool” behaviors } sij. |{z} school fixed effects (7) 17 In the equations above, ρ refers to the correlation between the probability that person “i” and person “j” in a pair nominate each other. The vector Zij is composed of the vectors Zi , Zi0 Zi , Zj , Zj0 Zj , and Zi0 Zj . The vector Zj includes the set of innate characteristics, zjm , and behaviors, yjl , exhibited by the nominee “j.” The vector Zi includes linear terms for the characteristics and behaviors of the nominator “i” (zim and yil ). The term sij is an indicator for the school attended by the pair of students. The characteristics indexed by m include age, number of years attending the school, grade, gender, mother’s education, presence of a father, and indicator variables for being white, black, Asian, Indian, another race, and Hispanic.15 The behaviors y, indexed by l, refer to the four behavioral indexes described in the data section: GPA, substance use, unruliness, and trouble getting along with others. The interactions between characteristics and behaviors allow the perceptions of the relative “coolness” of a behavior to differ across types of students. The index M1 is a subset of M that refers only to gender, indicators for being white, black, Asian, Indian, another race, and Hispanic, the mother’s education, and the presence of a father. The vector Zji follows the same formulation as Zij . It is random whether a given student is indexed as an “i” or a “j” in the pair, so behaviors and characteristics are restricted to have the same effect on the probability of a nomination for both bivariate probit equations. In order to estimate the bivariate probit, each student is paired with every other student in his or her school and it is recorded whether one, both, or neither student in the pair nominates the other, as well as the direction of the nomination (i.e. which student is the nominator and which student is the nominee). The vast majority of student pairs in a school show neither student nominating the other as a friend. A 15 Of these characteristics, quadratic terms are only included for age, the number of years at school, and the mother’s education, because the other characteristics are binary. 18 random 5% sample of these pairs with no nominations in either direction are retained using choice-based sampling.16 The bivariate probit is estimated using more than 69,000 student pairs across the 88 schools. The results show that the probability of receiving a nomination is heavily driven by similarity in characteristics between students who are in the same grade.17 In contrast, the marginal effects of behaviors on the probability of a nomination are relatively small. Table 2 provides the marginal effects of each of the four behaviors on the probability of receiving a friendship nomination for students of different genders and races, with an average level of maternal education and a father present. These marginal effects are calculated assuming that the student’s peers are representative of the sample averages for all of the behaviors and characteristics.18 Specifically, from equation (7), at the mean the marginal effect of behavior l on the unconditional probability of receiving a friendship nomination for a student with a given race, ethnicity, gender, and socioeconomic status is defined as " # M1 X ∂Pr(nomij = 1) b9ml z m + b10ml z m zjm . = φ(Z ij β) b1l + 2b2l y l + 2b3l (yil − yjl ) + b4l y l + ∂yjl m=1 The first column and row of Table 2 indicates that the marginal effect of GPA on the probability of receiving a friendship nomination for a white male whose mother has the sample-average level of education, and who lives with his father, is equal to 16 Creating every possible student pair in the school, for every school in the sample, increases the sample size exponentially, and most of these pairs have no friendship nominations in either direction. To increase statistical efficiency and focus on understanding the process of friendship formation, choice-based sampling is used on these pairs without nominations. 17 These findings are consistent with Foster (2005), who estimates the probability of college students choosing to live together. 18 A full set of coefficient estimates from the bivariate probit are reported in the appendix. 19 133x10−6 . This implies that a one standard deviation increase in GPA for such a student will increase his probability of a friendship nomination by 0.01 percentage points (0.0001 points, or approximately 0.0013 standard deviations). As noted in the data section, predicted popularity is defined as the predicted probability of receiving a friendship nomination from another student, summed over all other students in the school. With an average school size of approximately 1,000 students, this marginal effect corresponds to a 0.10 point (0.03 standard deviation) increase in a student’s predicted popularity. The results are similar for the other student types and behaviors. Although the magnitudes are small, the positive effects of GPA and substance use on popularity are statistically significant. Unruliness has a positive effect while interpersonal trouble has a negative marginal effect on popularity, but the effects are generally statistically insignificant for both behaviors. The coefficient estimates from the bivariate probit are used to predicted the probability that a student receives a friendship nomination from any other student. Summing these predicted probabilities across all other students in the school yields a predicted level of popularity for the student.19 However, the goal is to find the popularity-maximizing level of behavior, which is likely not the same as the actual level of behavior exhibited by the student. In order to find this popularitymaximizing level of behavior, the parameters of the bivariate probit are used to calculate the predicted popularity for a student across a grid of possible behavior levels. Specifically, holding all else constant for the student pair, the probability of receiving a nomination is calculated while varying one of the potential nominee’s behaviors. At each possible grid value of the behavior, the unconditional probability of receiv19 Results show the model predicts a slightly lower average popularity than found in the data. 20 ing a friendship nomination from every other student in the school is calculated.20 These predicted probabilities are summed to get a predicted popularity at each grid value. Searching across the grid, the behavior that yields the highest popularity is the popularity-maximizing behavior. For the three behaviors, GPA, substance use, and unruliness, that have on average a positive but diminishing marginal effect on popularity, an interior solution for the local popularity-maximizing level of behavior can be expected for most students. The same assumption does not hold for the index of interpersonal trouble, which has a negative effect on popularity for most students. Table 3 reports descriptive statistics for the popularity-maximizing levels of each behavior, which are larger on average than the observed levels of the behaviors. Substance use shows the greatest difference, with the average popularity-maximizing level being around 29 (smoking, drinking, or getting drunk almost every day). This is in contrast to the average level of 7 for observed behaviors, indicating substance use two or three times per week. Unruly behavior shows a similar discrepancy, with the average popularity-maximizing level being around 23, in contrast to an average of 7.5 for actual unruliness. For interpersonal problems and GPA, the average popularity-maximizing levels are only about 15% and 30% larger, respectively, than the averages for the observed behaviors. The large differences between observed and popularity-maximizing behaviors are not necessarily unreasonable. The popularitymaximizing behaviors represent how students would act absent any costs to engaging in these various activities. These costs will reduce actual behaviors relative to the popularity-maximizing levels, and are captured in students’ “innate” behaviors. 20 The predicted probability of a nomination is unconditional on whether the nomination is reciprocated because it is impossible to know whether the nomination would have been reciprocated at any grid value other than the observed behavior. 21 Consistent with equation (3) in the theoretical model, the popularity-maximizing behavior is closely related to the average behavior in the school for all but unruliness. The correlation coefficient between the average behavior in the school and the popularity-maximizing behaviors of each student is highest for GPA (approximately 0.93), lowest for unruly behavior (approximately 0.46), and equal to 0.75 and 0.77 for substance use and interpersonal trouble, respectively. The relationship between the school average and the popularity-maximizing behavior is driven largely by the importance of homophily in determining popularity. These results suggest that students are more concerned with a similarity in substance use, GPA, and interpersonal trouble, and less concerned with matching levels of unruliness when forming friendships. The correlation coefficients between popularity-maximizing and actual behaviors at the individual level are lower, ranging from 0.25 for GPA to 0.04 for interpersonal troubles, and approximately equal to 0.10 for substance use and unruliness. These lower correlation coefficients are the function of more noise and other unobserved factors at the individual level. While popularity-maximizing behaviors are heavily a function of students’ peers, costs are determined at the individual level as a function of characteristics, which also helps to explain the lower individual-level correlation between observed and popularity-maximizing behaviors. The underlying assumption of the model is that students derive utility from being popular. Table 4 provides suggestive evidence that this assumption holds true in the data. A student’s reported mental state is regressed on her predicted popularity, controlling for her characteristics, all possible interactions between her individual characteristics and average characteristics in the school, and school effects. The predicted popularity from the bivariate probit is positively associated with a student 22 “feeling happy at school” and negatively related to a student feeling depressed.21 While these regression results show no causal relationship, data are consistent with the theory that popularity increases a student’s utility, or happiness. Understanding the effects of various behaviors on the probability of receiving a friendship nomination is interesting in and of itself. However, the coefficient estimates from this bivariate probit are only a first step toward understanding the behavior of students relative to their peers. Moreover, the results from the bivariate probit should be interpreted with care. Endogeneity exists between popularity (the probability of receiving a friendship nomination) and behaviors. Much of the literature assumes the friendship link is exogenous and estimates the effects of friendship on behavior, but fails to control for the effects of behaviors on friendships. The bivariate probit estimation here does the opposite. The effects of behavior on popularity are estimated without controlling for the influence that friendship nominations could have on behavior. This omission would be of greater concern if the coefficient estimates from the bivariate probit were meant to be interpreted as a final results. Instead, the purpose of the bivariate probit in this paper is merely to provide a framework that can be used to search for the popularity-maximizing level of behavior. The use of an instrumental variables approach in estimating the behavioral equation helps to remove remaining endogeneity between the popularity-maximizing behavior and the observed behavior, which may have resulted from biased coefficient estimates in the 21 The Add Health survey asks students how often they felt “blue” or depressed in the past year. Their answers are reported on a scale of 0 to 4, where 0 corresponds to “never” feeling depressed, and 4 corresponds to “feeling down every day.” Data are coded such that 1 corresponds to an answer of “rarely”, 2 corresponds to “occasionally,” and 3 corresponds to “often” feeling depressed. Happiness is measured by students’ responses to the statement “I am happy to be at this school.” Responses have been coded with values ranging from 0 for an answer of “strongly disagree” to 4 for students who “strongly agree” with feeling happy at school. 23 bivariate probit as the result of endogeneity between popularity and behaviors. 5.2 Behavioral Equations The behavioral equation from the theoretical model predicts that students should choose a convex combination of their “innate” behavior and the popularity-maximizing behavior. In order to test this result, the observed behavior is regressed on the predicted popularity-maximizing behavior and the student’s characteristics, controlling for school fixed effects. For any student “i” in grade “g” and school “s”, the main behavioral equation takes the form pop yigs = γyigs + Xigs δ + λg + ηs + igs . (8) pop Here, yigs refers to the popularity-maximizing behavior for individual i in school s and grade g that was calculated from the bivariate probit results using the search algorithm described in the previous subsection. The coefficient γ refers to the weight that students place on the popularity-maximizing behavior relative to their “innate” behavior, and corresponds to the same parameter in equation (5). The vector of characteristics, Xigs , includes a constant, the student’s age, gender, and years at the school, indicators for the student being white, black, Asian, Indian, another race, or Hispanic, the mother’s education, and whether the father is present. The regressions also control for a set of grade fixed effects, λg , and school fixed effects, ηs .22 Finally, the equation includes a random error term, igs . 22 Robustness checks have considered specifications that also control for school-grade fixed effects. However, the school-grade effects soak up most of the variation in the instrumental-variables in the first stage of the 2SLS procedure. Weak first stage results then make it very difficult to precisely estimate coefficient estimates for equation (8) in the second stage. 24 Due to concerns over endogeneity between the observed behavior and the popularitymaximizing behavior, as discussed above, the behavioral equations are estimated using a two-stage least squares (2SLS) procedure.23 Different racial, ethnic, and socioeconomic groups tend to have different views of certain behaviors. For example, substance use, particularly drinking, is viewed as “cool” by most students. However, Asians on average are much less likely to choose friends who exhibit heavy substance use. The different preferences for behaviors across racial, ethnic, and socioeconomic groups provide an exogenous source of variation in the popularity-maximizing level of behavior across students and schools. This paper makes use of two sets of instrumental variables. A student’s racial, ethnic, and socioeconomic status interacted with the average racial, ethnic, and socioeconomic composition of the student’s school serve as the first set of instrumental variables. Under the assumptions of the model presented earlier, these interactions between student characteristics and average school characteristics directly affect the popularity-maximizing behavior, but do not directly affect a student’s observed behavior. Specifically, the first stage equation for the 2SLS estimation takes the following form, pop 0 = Xigs yigs X s π + Xigs θ + ψg + φs + νigs . (9) The vector of characteristics, Xigs , refers to the same set of characteristics as in 0 equation (8). The excluded instruments in equation (9), Xigs X s , are composed of student characteristics interacted with the average composition of the student’s school. Specifically, the set of racial and ethnic variables used as instruments include 23 The following assumptions are sufficient to guarantee that the 2SLS estimator is consistent: pop (1) the instrumental variables are valid, and (2) any bias in the measurement of yi,g,s from the bivariate probit procedure is linear and uncorrelated with the instrumental variables. This second assumption is admittedly very strong and difficult to justify. Proof available upon request. 25 indicators for the student being white, black, Asian, or Hispanic, interacted with the average level of the same racial or ethnic group in the school.24 Whether the student’s father is present interacted with the average share of students in the school who have a father present, and the mother’s education interacted with the average level of maternal education in the school serve as the instrumental variables that control for different perceptions of “cool” behaviors across socioeconomic groups. The second set of instrumental variables used in this paper is composed of a student’s racial, ethnic, and socioeconomic status interacted with the average racial, ethnic, and socioeconomic composition of the student’s grade within the school. The first stage equation under these instrumental variables takes the form, pop 0 0 = Xigs yigs X gs π e + Xigs θe + Xigs X −gs ξ + ψeg + φes + νeigs . (10) These grade-level instrumental variables require less stringent assumptions to justify their exogeneity, as they exploit variation in the demographic composition across grades within a school. Even if students select into schools based on unobserved parental traits that are also correlated with a student’s “innate” behavior, it is unlikely that this selection would occur at the grade level.25 However, these instrumental variables come at a cost. There is less variation in student characteristics relative to grade-specific demographics within a school, which weakens the first-stage results. 24 As mentioned previously, the data on racial and ethnic group are not mutually exclusive. A student can report being both black and white, thus there is no need to omit a category. Indian and other race are not used as instrumental variables because the share of students in these categories is extremely small, leading to weak instruments. 25 To remove any selection effects, the first-stage regression controls for school fixed effects, as well as for interactions between student characteristics and the average characteristics of students from other grades in the school. 26 5.2.1 First Stage Results Table 5 shows coefficient estimates from the first stage of the 2SLS procedure for all four behaviors using the first set of instrumental variables. The coefficient estimates on the excluded instruments are sensible. As mentioned before, Asians tend to view delinquent behaviors least favorably. Asians in schools with a greater Asian population have much lower levels of popularity-maximizing substance use and unruliness. In general, a good GPA is viewed more favorably by every racial/ethnic group when that group comprises a larger share of the school. The popularity-maximizing levels of unruliness are lower among students of high socioeconomic status (better educated mothers and a father present) who attend schools with an overall higher socioeconomic status. Although white students tend to have higher popularity-maximizing levels of substance use, these levels decrease when whites make up a greater share of the student body. Similarly, blacks tend to have lower levels of substance use, but these increase among blacks in more heavily black schools. Overall, the excluded instruments are strong. The joint F-statistics for the six excluded instruments 26 range from 26 to 1,000 and are always statistically significant at the 5% -level. Table 6 provides coefficient estimates from the first stage of the 2SLS procedure using the second set of instrumental variables. The coefficient estimates on the excluded instruments are similar to those from the first IV strategy, but a few differences exist. A student’s socioeconomic status relative to the average socioeconomic status of her grade has stronger effects on the popularity-maximizing level of behaviors than previously estimated. Students with better educated mothers in grades with a 26 The instruments are indicators for whether the student is white, black, Hispanic, Asian, interacted with the average share of the racial/ethnic group in the school, as well as the mom’s education and whether the father is present interacted with the school average of each, respectively. 27 higher average level of mothers’ education have a higher popularity-maximizing level of GPA, and a lower popularity-maximizing level of substance use, unruliness, and interpersonal trouble. The same pattern holds for students whose father is present in grades with more students living with their fathers in this second IV strategy. Some of these coefficient estimates have the reverse sign or are statistically insignificant in the first IV strategy. The coefficient estimates for a student’s race and ethnicity interacted with the average race and ethnicity in the grade generally have a smaller magnitude and are less statistically significant in the second IV strategy relative to the first. The joint F-statistics range from about 7 for substance use to 86 for unruliness, and are less than 30 for both GPA and interpersonal troubles. Overall, these joint F-statistics on the excluded instruments indicate that this second set of instrumental variables is weaker than the first. 5.2.2 Second Stage Results Results for the behavioral equations can be found in Tables 7-10. The first and second columns of each table show the results from ordinary least squares (OLS) estimation of the behavioral equation with and without school fixed effects, respectively. The third column of each table reports coefficient estimates for the 2SLS estimation of equation (8), which controls for potential endogeneity of the popularity-maximizing behavior using interactions between student characteristics and average characteristics in the school. The fourth column of the tables reports coefficient estimates for the 2SLS estimation using the second set of instrumental variables, which rely on interactions between student characteristics and school-grade averages. For three of the four behaviors, in all specifications, the coefficient estimate on popularitymaximizing behaviors (γ) falls between zero and one as predicted by the model. 28 Column 1 of Table 7 shows a coefficient estimate of 0.26 in the OLS specification, which indicates that a one point increase (approximately 2 standard deviations) in the popularity-maximizing GPA will increase a student’s studying and academic achievement, as measured by a 0.26 point (approximately one-third of a standard deviation) increase in her GPA. Interestingly, the coefficient estimate in column 2, controlling for school-fixed effects but not endogeneity, is only 0.09. This suggests that among students within the same school, the popularity-maximizing behavior explains only a small portion of the actual GPA students achieve. The substantial reduction in the coefficient estimate after controlling for school-fixed effects could be explained if teachers grade on a curve. Within a school, even if everyone tries to get good grades because academic achievement is popular, some students will still receive lower marks on the grading scale. Thus, a student’s ability to modify her GPA in an attempt to gain popularity is more limited when looking only at variation in academic outcomes among students in the same school. The instrumental variables procedure breaks this relationship between good grades by other students making academic achievement more “cool,” and it being more difficult for a student to attain a high GPA since her classmates are studying hard too. Controlling for school effects and using the first set of instrumental variables to eliminate endogeneity yields a coefficient estimate of 0.21 on the popularitymaximizing level of GPA, as reported in column 3. This suggests that the OLS estimate in column (1) is slightly biased upward. To put the result in perspective, a one standard deviation increase in the popularity-maximizing GPA yields the same increase in academic achievement, on average, as the student’s mother having 5 additional years (two standard deviations) of educational achievement. 29 The results are similar for substance use and unruliness in Tables 8 and 9, respectively. Overall, popularity-maximization plays a smaller role in determining these behavior levels. The coefficient estimates indicate that a one unit increase in the popularity-maximizing level of substance use or unruliness leads to an 0.5-0.10 point increase in the actual behavior.27 While these coefficient estimates appear small, a one standard deviation increase in the popularity-maximizing level is associated with the same magnitude increase in substance use, on average, as the mother having 2.5 (one standard deviation) fewer years of education. Table 10 provides results for the index of personal problems with teachers and other students. While the OLS and fixed effects results are similar in magnitude to the other behaviors, the 2SLS results using interactions between individual characteristics and average school characteristics as instrumental variables show that the popularity-maximizing behavior has a negative effect on actual behaviors. This runs contrary to the theoretical model, which predicts that true behaviors will be a convex combination of “innate” and popularity-maximizing behaviors. These results are not entirely surprising given that interpersonal trouble has a negative marginal effect on popularity for many students. It is natural to think that an inability to get along well with others is unlikely to have a substantial, positive impact on popularity.28 27 Although the IV estimate in column 3 of 8 for smoking is a bit larger than the OLS estimate in column 1, the standard error bands are such that the two coefficient estimates are not statistically different from each other. 28 It remains important to include the index of interpersonal problems at least in the initial bivariate probit in order to minimize any omitted variable bias from entering coefficient estimates on other behaviors, particularly substance use and lack of good grades, that are correlated with getting in trouble with students and teachers. The results are, however, robust to dropping interpersonal troubles from the bivariate probit. In particular, the second-stage coefficient estimates have very similar magnitudes but slightly larger standard errors. 30 The results from the 2SLS estimation of behavioral equations with the second set of instrumental variables that use interactions between individual characteristics and school-grade averages are reported in column 5 of all the tables. These results are similar to those reported in column 4. For GPA and unruliness, the coefficient estimates are slightly larger but not statistically different from those found with the first set of instrumental variables. The coefficient estimates on the popularity-maximizing level of behavior for substance use and interpersonal troubles are substantially larger using the second instrumental variables strategy. For substance use, the difference in second-stage results is likely the result of a very weak first-stage. The coefficient estimate on the popularity-maximizing level of interpersonal troubles reverses sign, but remains statistically insignificant. While this change in the magnitude of the coefficient estimate is difficult to explain, the effect is imprecisely estimated and interpersonal troubles already have an unclear relationship with popularity. Disregarding the behavioral results for interpersonal trouble, the empirical results match the theoretical predictions well. For GPA, substance use, and general unruliness, students place some positive weight on the popularity-maximizing level of behavior when choosing their optimal behavior. It is not necessarily surprising that popularity-maximization accounts for about 20% of students’ decisions regarding academic success but only accounts for 5-10% of their decision to engage in delinquent behaviors such as smoking, drinking, skipping school, lying, fighting, or taking dangerous dares. The most compelling explanation for these results is that a student’s grade point average is a proxy for behaviors such as time spent studying relative to hanging out with friends, and participation in extracurricular activities. It seems natural that the allocation of time between studying and other activities is 31 sensitive to the time-use of one’s peers, as well as to the extent to which studying and academic achievement is perceived favorably in the school environment.29 5.3 Policy Simulation The model and empirical results provide a framework for understanding the behavior of students not just within their own school, but also for predicting the behavior of these students if placed in different environments. To illustrate, this paper considers three hypothetical students in the 10th grade.30 The first archetypical student is a white female with high socioeconomic status. The student’s father is present in the household, and her mother holds a master’s degree or higher, placing her in the top 5% for education among white mothers. The second representative student is a white male with average socioeconomic status.31 The third student type is a black male who also has average socioeconomic status.32 Results from the empirical work are used to predict how these students would behave in different schools in the sample. 29 An alternative explanation posits that time use is an intensive margin response, and thus may be easier for students to alter in order to gain popularity. Engaging in substance use or unruly behavior in order to gain popularity first requires an extensive margin change for many students. Almost 50% of students report no substance use or unruly behavior. For the majority of students, the popularity-returns to substance use or unruly behavior may not be large enough to meet the threshold needed to start smoking, drinking, or fighting. Furthermore, the utility cost (β in the theoretical model) of initially engaging in substance use or delinquent behavior may be much higher than the utility cost of spending more or less time in the library relative to the amount of time you would have spent studying absent any concerns over popularity. This could explain why, on average, students place less weight on popularity-maximizing levels of substance use and unruly behavior than grades. However, re-estimating the results using an indicator for whether students engage in substance use and unruly behaviors, and using a linear probability model for behaviors, shows no increase in the coefficient estimates on the popularity-maximizing levels of these behaviors. 30 The students are 15 years of age and have attended the school for 2 years. These represent the median age and years of attendance among 10th grade students in the sample. 31 His father is present, and his mother holds a high school degree but only attended a vocational school or some college, which represents the median education level among white mothers. 32 His father is present in the household and his mother completed high school but only attended a vocational school or some college. As with the other hypothetical students, both of these qualities represent the median among parents of black students in the sample. 32 The first step to predicting behaviors requires finding the popularity-maximizing level of all four behaviors. Each archetypical student is paired with every student in the data for a given school. For a set of behaviors,33 the coefficient estimates from the bivariate probit are used to predict the probability of the hypothetical student being nominated as a friend by every student in the school. The sum of these predicted probabilities of receiving a nomination is the hypothetical student’s predicted popularity in the school. Searching over a 4-dimensional grid representing all possible combinations of the different levels of each behavior yields the set of behaviors that would maximize the student’s popularity in a given school in the sample. Once the popularity-maximizing behaviors have been found, the coefficient estimates from the second-stage of the 2SLS estimation of the behavioral equations are used to predict behaviors for the hypothetical students. The set of estimates used for this simulation exercise come from the first instrumental variables strategy, which relies on variation in a student’s characteristics relative to the demographic composition of the school.34 Figures 1-3 show the results of the simulation exercise for the three hypothetical students described above when placed in three very distinct school environments. The first figure illustrates the results for academic performance, the second for substance use, and third for unruly behavior.35 The student types and school charac33 The behaviors are academic performance (GPA), substance use, unruliness, and having interpersonal trouble with teachers and other students. 34 The results are not drastically different when using the coefficient estimates from the second IV strategy that relies on variation in a student’s characteristics relative to the demographic composition of the grade. However, the first stage regressions from the first IV strategy are stronger, and the behavioral equation results from the first IV strategy relying on school-composition are the focus of most of the discussion in this paper. 35 A figure for interpersonal troubles is not reported here since that behavior has an unusual relationship with popularity and the coefficient estimates from the behavioral equation are inconsistent with the theoretical model. 33 teristics are listed along the horizontal axis. The first panel of each graph represents an urban school located in the southern United States. The school is composed of 93% black students and 3% white students, and the students have average socioeconomic characteristics. The average mother in the school completed high school but not college, and fathers are present in 60% of the students’ households. The second panel represents a suburban Midwestern school in which 95% of the students are white and 3% of the students are black. The school has above average socioeconomic status, with the median mother completing college and 90% of fathers living in the students’ homes. Finally, the third panel shows predicted behaviors in a racially diverse, urban, Midwestern school with average socioeconomic characteristics. In this school, 33% of students are black and 62% of students are white. On average, the mothers have completed high school but have no additional education, and 64% of students live with their fathers. In the figures, diamonds represent the predicted behavior for each student type. The small circles illustrate the actual behaviors observed for students in the data attending the given school who have identical characteristics to the hypothetical student. By the nature of the in-sample simulation, the predicted behaviors fall near the average of observed behaviors across student types and schools. For some combinations of student type and school, however, the data have no observations matching the student description in attendance at the school. In such cases, the model developed in this paper can predict how a specific type of student is likely to behave when placed in a demographic environment that is very different from the type of school in which she is usually found in the data. Across all of the schools, the white female with high socioeconomic status earns 34 better grades and engages in less substance use and unruliness than the other two student types. In each of the schools, black students engage in less substance use than white students from similar socioeconomic backgrounds. Furthermore, in Figure 1 it is clear that academic achievement for the three student types is highest in the suburban school in which the students come from families with high socioeconomic status. The effects of average school characteristics on all student types is consistent with the correlated effects in a standard Manski-model. Students of all types exhibit better academic performance when placed among peers with higher socioeconomic characteristics. However, the results differ from the standard Manski-result in that the effects of the group demographics on student behavior differ by student type. Specifically, the popularity-maximizing and thus the actual behavior depend on interactions between student characteristics and average-group characteristics. Academic performance (Figure 1), shows some differences in the effects of average group characteristics on each type of student. Socioeconomic status plays a relatively larger role than race in determining the “coolness” of academic achievement. The male students with average socioeconomic status attain similar GPAs in the heavily black and the racially diverse schools that have average socioeconomic characteristics. However, both of these student types exhibit higher academic achievement in the suburban school with high socioeconomic characteristics. Between the two, the white student experiences a larger increase in academic achievement than the black student when they move from the diverse school to the heavily white school. This result stems from the fact that both white and black students view academic achievement more favorably when forming friendships with peers of the same race.36 36 See the panel for “Varying Perceptions of “Coolness” for Behaviors by Characteristics of the Nominator - GPA” in the appendix. Similar interactions between student characteristics and the 35 In Figure 2, substance use is lowest in the heavily black school and highest in the racially diverse school among all three student types. Substance use by these representative students more than doubles when the students move from a heavily black school to a school with more racial diversity but similar socioeconomic characteristics. These findings can be explained by the fact that white students view substance use more favorably than black students when nominating friends. However, the predicted behaviors in the suburban school show that increasing the socioeconomic status of the peer group while also increasing the share of white students in the school will decrease substance use by more for the white students than for the black student. This effect is derived from the fact that substance use is viewed as less “cool” by white students when they are nominating a friend of the same race as a opposed to when they are nominating a friend of a different race. The varying effects of group characteristics on students of different types is also visible in Figure 3. Unruly behavior is lowest among all three types of students in the heavily black, urban school. However, the black student engages in the highest level of unruliness in the heavily white, high socioeconomic school, while both white students engage in the most unruly behavior in the third, racially diverse school. The different effects on the white and black students between these schools can be explained by the finding that unruliness is viewed least favorably by students considering whether to nominate a peer who has similar racial and socioeconomic characteristics. In contrast, unruly behavior does not reduce the probability of a friendship nomination by as much when the nominee has a different race and socioeconomic background from the nominator. other behaviors can be found in the other panels of the bivariate probit results. 36 A simulation of this nature illustrates the possible uses of the model and empirical results for predicting the behavior of students when placed in a variety of different environments. While group characteristics increase achievement and reduce delinquency for all students in the expected manner, the magnitude of these effects differs depending on the characteristics of each student. For instance, moving a black student with average socioeconomic characteristics into a heavily white school with high socioeconomic status does not always lead to beneficial outcomes on all dimensions. Although the move is predicted to increase the academic achievement, it also leads to slightly more substance use and substantially more unruliness such as fighting, lying, and skipping school. Furthermore, the increase in academic achievement is not as large as it could be if the student were moved to a school with equally high socioeconomic status as well as greater racial diversity. These comparisons across schools and student types have implications for policies that allow students to move to alternative schools through programs such as public school choice. The results suggest that moving students from a low-performing school to the opposite extreme may not generate the largest possible gains in all behavioral outcomes. 6 Conclusion The paper presents a novel mechanism for explaining conformity in student behavior. Prior literature generally takes a student’s position in a network of friends as exogenous and uses the information to understand how her network position affects behaviors. This paper focuses on a specific network position, popularity, and endogenizes it within the model. The model provides a micro-foundation for a linear-in-means behavioral equation. Empirical results show the assumptions and implications of the 37 model are consistent with data. Students are found to consider the popularity implications of their actions when deciding how to act in different school environments. High school students derive utility from being well-liked by their peers, and strive to gain this popularity through behaving appropriately. The empirical findings from estimating the probability of a friendship nomination using a bivariate probit model show that popularity is a function of students’ behaviors and characteristics relative to their peers (homophily), as well as the general “coolness” associated with certain actions and types of students. A unique popularity-maximizing level of behavior for each student is predicted using coefficient estimates from the bivariate probit. Two instrumental variables approaches are then used to estimate the effect of these popularity-maximizing levels on actual behaviors. The coefficient estimates show that students place some positive consideration on the popularity-maximizing level of GPA, substance use, and unruliness, although perhaps unsurprisingly the results do not hold for the index of interpersonal trouble with teachers and students. Studying the endogenous formation of subgroups, as well as popularity or social acceptance within those groups, is an important extension of this work. It may be the case that the desire to be accepted by a specific subgroup (clique) of students drives behaviors much more than any concern over the total number of nominations.37 A richer model in which students are only concerned with popularity in endogenously determined subgroups of peers also generates important differences from the linearin-means Manski-model. Most notably, the weight placed on the average group be37 However, Goldsmith-Pinkham and Imbens (2013) find that both direct and peers who are a number of links removed have a substantial effect on student behaviors, which suggests students care about social acceptance among a wider group of peers than their immediate clique. 38 havior differs with the student’s location in the distribution of group behaviors and characteristics. If a student is very dissimilar from her peers, the popularity-returns to conforming will be too small to substantially change the student’s behavior. From a policy perspective, the results in this paper suggest that the desire to gain popularity may have a substantial effect on improving a student’s grades if she were moved to a school in which academic success was viewed favorably by peers. Similar effects hold to a lesser extent for substance use and unruliness. However, the school environments that are best for some types of students will not be optimal for other types of students. For instance, academic achievement leads to greater popularity among students of higher socioeconomic status, and also among peers with the same racial characteristics. The benefits of moving a student to a school with higher socioeconomic status can be mitigated by racial differences between the student and her peers. Additionally, in schools with a greater share of white students there is a greater incentive to engage in substance use, particularly for non-white students. These effects, as discussed in the previous section, can be seen in Figures 1-3. Since the perception of behaviors varies by race, ethnicity, and socioeconomic status, public programs that alter the demographic composition of schools may have substantial effects on student behavior by changing the returns to popularity of certain actions. 39 Table 1: Summary Statistics Variable Mean Standard Deviation Popularity 4.20 3.74 GPA 2.87 0.77 Substance Use 7.10 14.04 Unruliness 7.54 12.82 Interpersonal Trouble 11.50 16.80 Age 15.72 1.20 Male 0.47 0.50 Hispanic 0.14 0.34 White 0.69 0.46 Black 0.15 0.35 Asian 0.07 0.25 American Indian 0.04 0.20 Other Race 0.07 0.26 Years at School 2.56 1.41 Lives with Dad 0.81 0.39 Mom’s Education 13.68 2.48 N. Observations 35,490 Median 3 3 1 2.5 4 16 0 0 1 0 0 0 0 2 1 14 a) Summary statistics are reported for the behavioral equation regression sample. The bivariate probit regression uses the same set of students, but by pairing each student with every schoolmate the sample size increases exponentially. 40 Table 2: Marginal Effects of Behaviors on Popularity by Gender & Race/Ethnicity GPA White Black Hispanic Asian Substance Use White Black Hispanic Asian Unruliness White Black Hispanic Asian Interpersonal Trouble White Black Hispanic Asian Male 133*** (9.75) 135*** (16.3) 124*** (16.5) 105*** (16.7) Male 4.87*** (0.77) 7.49*** (1.16) 6.61*** (1.16) 6.02*** (1.16) Male 0.427 (0.80) 1.15 (1.12) 1.10 (1.14) 1.39 (1.15) Male 0.34 (0.63) -1.08 (0.81) -0.75 (0.82) -1.02 (0.83) Female 157*** (10.2) 158*** (16.4) 148*** (16.7) 129*** (16.9) Female 4.46*** (0.78) 7.08*** (7.08) 6.20*** (1.15) 5.61*** (1.15) Female 0.70 (0.83) 1.42 (1.12) 1.38 (1.14) 1.67 (1.15) Female 0.67 (0.64) -0.75 (0.82) -0.41 (0.83) -0.68 (0.84) a) Marginal effects are calculated for students with the average level of each behavior whose mothers have the sample average level of education and who live with their father, in schools that exhibit the sample average level of all behaviors and demographic characteristics, as reported in Table 1. Standard errors are reported in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and 1-percent level, respectively. Coefficient estimates and standard errors reported here have been scaled by a factor of 106 . 41 Table 3: Summary Statistics for Popularity-Maximizing Behaviors Popularity-Maximizing Behaviors Mean Observed Behaviors Mean (s.d.) (s.d.) GPAp 3.64 (0.48) GPA 2.87 (0.77) Substance Usep 28.73 (24.82) Substance Use 7.10 (14.04) Unrulinessp 23.41 (25.55) Unruliness 7.54 (12.82) Interpersonal Troublep 13.17 (8.28) Interpersonal Trouble 11.50 (16.80) Observations 35490 Observations 35490 a) A superscript p indicates the predicted, popularity-maximizing level of each behavior. b) Standard deviations are reported in parentheses beside the means for each popularitymaximizing and observed behavior. c) For comparison, the summary statistics for observed behaviors are repeated in this table. 42 Table 4: Relating Utility and Popularity Variable Happy at School Depressed 0.04*** (0.01) -0.05*** (0.01) 0.16*** (0.02) 0.01 (0.03) 0.07* (0.04) -0.22*** (0.05) -0.05 (0.04) -0.15*** (0.04) -0.04* (0.02) 0.02* (0.01) 0.02*** (0.004) 0.08*** (0.02) 0.02 35,167 88 -0.03*** (0.01) 0.02* (0.01) -0.58*** (0.02) 0.04 (0.03) 0.11*** (0.02) -0.12*** (0.03) 0.11*** (0.03) 0.22*** (0.03) 0.08*** (0.03) -0.000 (0.01) -0.001 (0.003) -0.12*** (0.02) 0.07 35,357 88 Predicted Popularity Age Male Hispanic White Black Asian Indian Other Race Years at School Mother’s Education Lives with Dad R-squared N. Observations N. Schools a) The regressions also control for school and grade fixed effects, as well as all possible interactions between individual characteristics and the average characteristics in the school. Standard errors are listed in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and 1-percent level, respectively. b) The table reports bootstrap standard errors 43 Table 5: First Stage Results From 2SLS Estimation of Behavioral Equations (First IV Strategy: School-Composition) White*W hite Black*Black Hispanic*Hispanic Asian*Asian Mom’s Edu*M om0 sEdu With Dad*W ithDad Age Male Hispanic White Black Asian Indian Other Race Years at School Mother’s Education Lives with Dad Constant R-squared N. Observations N. Schools F-statistic on Excluded IV’s F(6, 35382) GPAp Substance Usep Unrulinessp Interpersonal Troublep 0.12*** (0.02) 0.34*** (0.03) 0.20*** (0.03) 0.02 (0.05) -0.003*** (0.001) 0.03 (0.05) -0.02*** (0.003) -0.07*** (0.004) -0.04*** (0.01) -0.01 (0.02) -0.08*** (0.01) -0.001 (0.01) 0.02** (0.01) -0.01 (0.01) -0.001 (0.002) 0.04*** (0.01) -0.05 (0.04) 3.88*** (0.06) 0.03 35,490 88 44.66*** -14.04*** (1.48) 14.10*** (2.13) 4.47** (2.11) -17.56*** (3.17) -0.01 (0.06) -5.10 (3.40) 0.84*** (0.20) 2.54*** (0.24) 2.05*** (0.65) 5.01*** (1.05) -2.77*** (0.80) -3.93*** (0.84) -1.60*** (0.59) -1.24** (0.53) -0.14 (0.13) 0.43 (0.81) 1.10 (2.70) 17.49*** (3.72) 0.03 35,490 88 26.34*** -42.14*** (0.98) -28.67*** (1.42) -55.21*** (1.40) -19.76*** (2.11) -1.01*** (0.04) -53.04*** (2.26) 0.29** (0.14) -2.88*** (0.16) -1.43*** (0.43) 9.26*** (0.70) -15.67*** (0.53) 0.16 (0.56) 4.86*** (0.39) -5.88*** (0.35) 0.05 (0.09) 6.63*** (0.54) 27.25*** (1.79) 155.62*** (2.47) 0.65 35,490 88 1271.30** 10.76*** (0.39) -4.72*** (0.56) 11.28*** (0.56) -15.93*** (0.84) 0.06*** (0.02) 0.79 (0.90) 0.19*** (0.05) -2.83*** (0.06) -0.23 (0.17) -0.19 (0.28) 4.73*** (0.21) -1.53*** (0.22) -5.00*** (0.16) 3.45*** (0.14) -0.05 (0.04) 0.15 (0.21) 0.26 (0.71) -10.34*** (0.98) 0.34 35,490 88 262.78*** a) Behaviors are estimated, popularity-maximizing levels for each student. Excluded IV’s are interactions between the student’s own characteristic and the school average, denoted with a bar over them. Regressions control for school and grade fixed effects (12th grade is excluded). Standard errors are listed in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and 1-percent level, respectively. 44 Table 6: First Stage Results From 2SLS Estimation of Behavioral Equations (Second IV Strategy: Grade-Composition) White*W hitegs Black*Blackgs Hispanic*Hispanicgs Asian*Asiangs Mom’s Edu*M om0 sEdugs With Dad*W ithDadgs Age Male Hispanic White Black Asian Indian Other Race Years at School Mother’s Education Lives with Dad White*W hite−gs Black*Black−gs Hispanic*Hispanic−gs Asian*Asian−gs Mom’s Edu*M om0 sEdu−gs With Dad*W ithDad−gs Constant Observations R-squared Number of Schools F-statistic on Excluded IV’s, F(6, 35382) GPAp Substance Usep Unrulinessp Interpersonal Troublep -0.05 (0.05) 0.47*** (0.07) -0.02 (0.10) 0.05 (0.12) 0.004*** (0.001) 0.14*** (0.05) -0.02*** (0.003) -0.07*** (0.004) -0.04*** (0.01) -0.01 (0.02) -0.09*** (0.01) -0.002 (0.01) 0.02** (0.01) -0.01 (0.01) -0.0004 (0.002) 0.05*** (0.01) -0.07 (0.04) 0.17*** (0.05) -0.13* (0.07) 0.21** (0.10) -0.04 (0.12) -0.01*** (0.001) -0.09 (0.06) 3.87*** (0.06) 35,490 0.04 88 17.74*** 2.06 (2.90) -11.85*** (4.48) -3.73 (6.15) -9.61 (7.56) -0.20*** (0.04) -5.25* (3.11) 0.82*** (0.20) 2.52*** (0.24) 2.20*** (0.65) 4.68*** (1.05) -2.09*** (0.79) -3.80*** (0.85) -1.53*** (0.59) -1.22** (0.53) -0.15 (0.13) 0.62 (0.80) 0.27 (2.70) -15.45*** (2.95) 23.69*** (4.39) 7.72 (6.09) -7.95 (7.90) 0.17*** (0.05) 1.23 (3.79) 17.68*** (3.71) 35,490 0.03 88 7.55*** -19.80*** (1.92) -23.00*** (2.98) -41.08*** (4.08) -14.42*** (5.02) -0.21*** (0.02) -19.35*** (2.07) 0.30** (0.14) -2.87*** (0.16) -1.23*** (0.43) 9.03*** (0.70) -14.98*** (0.53) 0.32 (0.56) 4.91*** (0.39) -5.85*** (0.35) 0.04 (0.09) 6.76*** (0.53) 25.58*** (1.79) -21.66*** (1.96) -7.90*** (2.91) -13.84*** (4.05) -5.42 (5.25) -0.81*** (0.04) -31.51*** (2.52) 155.48*** (2.47) 35,490 0.65 88 86.51*** 4.15*** (0.76) 2.55** (1.18) 5.06*** (1.62) -6.57*** (1.99) -0.10*** (0.01) -1.78** (0.82) 0.19*** (0.05) -2.83*** (0.06) -0.23 (0.17) -0.14 (0.28) 4.53*** (0.21) -1.55*** (0.22) -5.02*** (0.16) 3.44*** (0.14) -0.05 (0.04) 0.21 (0.21) 0.77 (0.71) 6.50*** (0.78) -6.42*** (1.15) 6.24*** (1.60) -9.18*** (2.08) 0.16*** (0.01) 1.94* (1.00) -10.42*** (0.98) 35,490 0.34 88 29.11*** a) The behaviors are the estimated, popularity-maximizing levels for each student. The excluded IV’s are interactions between the student’s own characteristic and the school-grade average characteristic, denoted here with a bar over them. A subscript of “-g” indicates an average taken over all other grades in the school. The regressions also control for school fixed effects and grade fixed effects (12th grade is the excluded category). Standard errors are listed in parentheses. One, two, and three asterisks indicate statistical significance at the 10-, 5-, and 1-percent level, respectively. 45 Table 7: Behavioral Results – GPA GPA GPAp Age Male Hispanic White Black Asian Indian Other Race Years at School Mom’s Education Lives with Dad Constant R-squared N. Observations N. Schools OLS School FE 0.26*** (0.01) -0.15*** (0.01) -0.10*** (0.01) -0.12*** (0.01) 0.02* (0.02) -0.20*** (0.02) 0.21*** (0.02) -0.10*** (0.02) -0.04*** (0.02) 0.02*** (0.003) 0.05*** (0.002) 0.15*** (0.01) 3.78*** (0.12) 0.15 35,490 88 0.09*** (0.01) -0.15*** (0.01) -0.13*** (0.01) -0.10*** (0.02) 0.04*** (0.02) -0.20*** (0.02) 0.26*** (0.02) -0.11*** (0.02) -0.04** (0.02) 0.01 (0.004) 0.05*** (0.002) 0.14*** (0.01) 4.36*** (0.13) 0.09 35,490 88 2SLS (IV-Strategy 1) 2SLS (IV-Strategy 2) 0.21* (0.12) -0.15*** (0.01) -0.12*** (0.01) -0.10*** (0.02) 0.03** (0.02) -0.20*** (0.02) 0.26*** (0.02) -0.11*** (0.02) -0.04** (0.02) 0.01 (0.004) 0.05*** (0.002) 0.14*** (0.01) 3.88*** (0.50) 0.34* (0.20) -0.014*** ( 0.01) -0.12*** (0.02) -0.13*** (0.02) -0.01 (0.03) -0.13*** (0.03) 0.30*** (0.03) -0.11*** (0.02) -0.04** (0.02) 0.01 (0.004) 0.03 (0.03) -0.18** (0.08) 3.37*** (0.78) 35,490 88 35,490 88 a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p denotes the popularity-maximizing level of the behavior. b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification. 46 Table 8: Behavioral Results – Substance Use Substance Use OLS Substance Usep 0.05*** (0.003) Age 1.78*** (0.12) Male 1.07** (0.15) Hispanic -1.13*** (0.27) White 2.27*** (0.29) Black -2.98*** (0.33) Asian -0.44 (0.37) Indian 3.13*** (0.37) Other Race 1.04*** (0.33) Years at School 0.02 (0.06) Mom’s Education -0.21*** (0.03) Lives with Dad -2.14*** (0.19) Constant -21.10*** (2.24) R-squared 0.04 N. Observations 35,490 N. Schools 88 2SLS School FE 0.03*** (0.003) 1.81*** (0.13) 1.04*** (0.15) 0.35 (0.30) 2.01*** (0.29) -3.28*** (0.35) -0.27 (0.38) 3.13*** (0.37) 1.17*** (0.33) -0.004 (0.08) -0.21*** (0.03) -2.29*** (0.19) -20.93*** (2.32) 0.03 35,490 88 2SLS (IV-strategy 1) (IV-strategy 2) 0.11** (0.05) 1.74*** (0.13) 0.83*** (0.20) 0.07 (0.34) 2.33*** (0.35) -3.35*** (0.36) 0.33 (0.53) 3.23*** (0.37) 1.26*** (0.34) 0.01 (0.09) -0.24*** (0.04) -2.04*** (0.25) -22.33*** (2.48) 0.28*** (0.10) 1.60*** (0.16) 0.39 (0.30) 1.29*** (0.48) 2.76*** (0.85) -3.45*** (0.58) -0.29 (0.69) 3.39*** (0.42) 1.50*** (0.37) 0.04 (0.09) 0.23 (0.50) 3.22* (1.72) -24.38*** (3.06) 35,490 88 35,490 88 a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p denotes the popularity-maximizing level of the behavior. b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification. 47 Table 9: Behavioral Results – Unruliness Unruliness OLS Unrulinessp 0.06*** (0.004) Age 0.34*** (0.11) Male 3.09*** (0.14) Hispanic 2.28*** (0.26) White 1.06*** (0.27) Black 1.68*** (0.32) Asian -0.28 (0.33) Indian 2.49*** (0.34) Other Race 1.13*** (0.30) Years at School -0.07 (0.06) Mom’s Education 0.25*** (0.04) Lives with Dad -0.27 (0.19) Constant -6.76*** (2.13) R-squared 0.03 N. Observations 35,490 N. Schools 88 School FE 0.06*** (0.004) 0.36*** (0.12) 3.18*** (0.14) 2.11*** (0.28) 1.29*** (0.28) 1.28*** (0.33) 0.17 (0.35) 2.38*** (0.34) 1.11*** (0.30) -0.002 (0.08) 0.28*** (0.04) -0.23 (0.19) -7.95*** (2.22) 0.03 35,490 88 2SLS (IV-strategy 1) 2SLS (IV-strategy 2) 0.06*** (0.01) 0.37*** (0.12) 3.17*** (0.14) 2.06*** (0.30) 1.22*** (0.31) 1.19*** (0.38) 0.17 (0.35) 2.41*** (0.35) 1.09*** (0.31) -0.002 (0.08) 0.25*** (0.08) -0.29 (0.23) -7.289*** (2.57) 0.08** (0.04) 0.36*** (0.12) 3.22*** (0.18) 2.39*** (0.38) 2.06*** (0.66) 0.42 (0.73) -0.43 (0.48) 2.31*** (0.39) 1.23*** (0.37) -0.002 (0.08) 0.70 (0.45) -0.362** (1.63) -10.08 (6.28) 35,490 88 a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p denotes the popularity-maximizing level of the behavior. b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and gradeschool specific averages for identification. 48 Table 10: Behavioral Results – Interpersonal Trouble Interpersonal Trouble Interpersonal Troublep Age Male Hispanic White Black Asian Indian Other Race Years at School Mom’s Education Lives with Dad Constant R-squared N. Observations N. Schools OLS School FE 0.13*** (0.01) 2.42*** (0.15) 2.52*** (0.18) 1.28*** (0.33) -3.01*** (0.35) 1.68*** (0.40) 2.05*** (0.44) 2.08*** (0.44) -0.05 (0.39) -0.03 (0.08) -0.59*** (0.04) -1.06*** (0.23) -24.63*** (2.67) 0.05 35,490 88 0.04*** (0.02) 2.39*** (0.15) 2.28*** (0.18) 1.13*** (0.36) -2.51*** (0.36) 2.23*** (0.42) 1.61*** (0.46) 1.64*** (0.44) 0.13 (0.40) 0.07 (0.10) -0.43*** (0.04) -0.79*** (0.23) -26.22*** (2.77) 0.03 35,490 88 2SLS (IV-strategy 1) 2SLS (IV-strategy 2) -0.28*** (0.07) 2.45*** (0.15) 1.36*** (0.27) 1.83*** (0.39) -0.43 (0.58) 3.22*** (0.48) -0.003 (0.58) -0.09 (0.58) 1.28*** (0.47) 0.06 (0.10) -0.12 (0.08) -0.48** (0.24) -28.87*** (2.84) 0.29 (0.22) 2.33*** (0.157) 2.96*** (0.63) 2.59*** (0.48) -2.50*** (0.77) 1.93* (1.13) 0.46 (0.73) 2.82** (1.17) -0.66 (0.84) 0.08 (0.10) -0.87 (0.56) 2.52 (1.91) -22.94*** (3.56) 35,490 88 35,490 88 a) Standard errors are listed in parentheses below the coefficient estimates. One, two, and three asterisks indicate statistical significance at the 10- , 5- , and 1-percent level, respectively. The 2SLS procedure controls for school fixed effects. All specifications also control for grade fixed effects. A superscript p denotes the popularitymaximizing level of the behavior. b) IV-strategy 1 uses interaction terms between individual characteristics and school averages as the excluded instruments. IV-strategy 2 uses interaction terms between individual characteristics and grade-school specific averages for identification. 49 Figure 1: Predicted & Actual Academic Grades Across Student Types & Schools a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds indicate the predicted behavior for the three types of students across the schools. Small circles represent observations in the data for students in the school who match the description of the hypothetical student. b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father present in the household. Median socioeconomic status refers to a having a mother who has completed high school but does not have a college degree, and having a father present. 50 Figure 2: Predicted and Actual Substance Use Across Student Types and Schools a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds indicate the predicted behavior for the three types of students across the schools. Small circles represent observations of behaviors in the data for students in the school who match the description of the hypothetical student. b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father present in the household. Median socioeconomic status refers to a having a mother who has completed high school but does not have a college degree, and having a father present. 51 Figure 3: Predicted and Actual Unruly Behavior Across Student Types and Schools a) The three panels, separated by the dotted lines, show behaviors for students in three different schools. Diamonds indicate the predicted behavior for the three types of students across the schools. Small circles represent observations of behaviors in the data for students in the school who match the description of the hypothetical student. b) All three hypothetical students are 15 years old, in 10th grade, and have been at the school for 2 years. The race, gender, and socioeconomic status of each hypothetical student are listed along the horizontal axis. High socioeconomic status corresponds with having a mother who holds at least a master’s degree and having a father present in the household. Median socioeconomic status refers to a having a mother who has completed high school but does not have a college degree, and having a father present. 52 7 Appendix: Bivariate Probit Results Table 11: Bivariate Probit Results Probability that Person j Nominates Person i General “Coolness” in Behaviors Behaviors (yi , yi2 ) GPA -0.14233211*** (0.017) 0.00354063*** (0.001) 0.00038622 (0.001) 0.00111946* (0.001) 0.01551107*** (0.002) 0.00000983* (0.000) 0.00000429 (0.000) -0.00000246 (0.000) Substance Use Unruliness Interpersonal Trouble GPA2 Substance Use2 Unruliness2 Interpersonal Trouble2 Homophily in Behaviors Distance in Behaviors ((yi − yj )2 ) GPA-distance -0.05503049*** (0.002) -0.00008118*** (0.000) -0.00001013*** (0.000) -0.00001517*** (0.000) Substance Use-distance Unruliness-distance Interpersonal Trouble-distance Interactions in Behaviors (yi ∗ yj ) GPA-interaction 0.01362604*** (0.001) 0.00013761*** (0.000) 0.00000732 (0.000) -0.00000146 (0.000) Substance Use-interaction Unruliness-interaction Interpersonal Trouble-interaction (CONTINUED) 53 Table 1.11 Continued: Bivariate Probit Results Probability that Person j Nominates Person i Characteristics of the Nominee Characteristics (xi , x2i ) Age 0.04870483 (0.031) 0.05380015*** (0.014) -0.04275485* (0.025) -0.07837962*** (0.027) -0.08066360** (0.037) 0.00856091 (0.037) -0.05710053* (0.030) -0.04606534* (0.027) 0.07843586*** (0.006) 0.03763856** (0.019) 0.00202729 (0.006) -0.00154896 (0.001) -0.00976036*** (0.001) 0.00056820*** (0.000) Male Hispanic White Black Asian Indian Other Race Years at School Lives With Dad Mother’s Education Age2 Years at School2 Mom’s Education2 (CONTINUED) 54 Table 1.11 Continued: Bivariate Probit Results Probability that Person j Nominates Person i Homophily in Characteristics Distance in Characteristics ((xi − xj )2 ) Grade-distance -0.04185820*** (0.002) -0.01648061*** (0.001) -0.13381297*** (0.015) 0.02085278 (0.026) -0.04073913 (0.028) -0.25858481*** (0.037) -0.10304419*** (0.037) 0.04920090* (0.029) 0.03929546 (0.027) -0.00673962*** (0.001) -0.03822054* (0.020) -0.00292635*** (0.000) Age-distance Male-distance Hispanic-distance White-distance Black-distance Asian-distance Indian-distance Other Race-distance Years at School-distance Lives with Dad-distance Mom’s Education-distance Interactions in Characteristics (xi ∗ xj ) Age-interaction -0.00075587*** (0.000) -0.07089025*** (0.023) 0.24070085*** (0.046) 0.14308518*** (0.048) 0.30389580*** (0.058) 0.35002329*** (0.070) 0.12764530 (0.116) 0.09444958 (0.065) 0.00547474*** (0.000) -0.01162758 (0.031) -0.00038033** (0.000) 0.76549501*** (0.008) 0.67152154*** (0.006) 0.60153644*** (0.006) 0.58258758*** (0.008) Male-interaction Hispanic-interaction White-interaction Black-interaction Asian-interaction Indian-interaction Other Race-interaction Years at School-interaction Lives with Dad-interaction Mom’s Education-interaction 9th Grade-interaction 10th Grade-interaction 11th Grade-interaction 12th Grade-interaction 55 (CONTINUED) Table 1.11 Continued: Bivariate Probit Results Probability that j Nominates i Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - GPA Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi ) Male-GPA 0.02295788*** (0.004) Hispanic-GPA -0.02015993** (0.008) White-GPA -0.02046619** (0.008) Black-GPA -0.03629561*** (0.011) Asian-GPA 0.00742348 (0.011) Indian-GPA -0.02007624** (0.009) Other Race-GPA -0.00523329 (0.008) Lives with Dad-GPA 0.01188473** (0.006) Mom’s Education-GPA 0.00456669*** (0.001) Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi ) Male-Male-GPA -0.01482142*** (0.005) Hispanic-Hispanic-GPA 0.02512044** (0.011) White-White-GPA 0.00891471 (0.006) Black-Black-GPA 0.04419077*** (0.011) Asian-Asian-GPA -0.03195628* (0.017) Indian-Indian-GPA 0.05809285* (0.035) Other Race-Other Race-GPA 0.00346160 (0.020) Lives with Dad-Lives with Dad-GPA -0.00370797 (0.005) Mom’s Education-Mom’s Education-GPA -0.00001416 (0.000) (CONTINUED) 56 Table 1.11 Continued: Bivariate Probit Results Probability that j Nominate i Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Substance Use Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi ) Male-Substance Use -0.00054331** (0.000) Hispanic-Substance Use -0.00020388 (0.001) White-Substance Use 0.00026357 (0.001) Black-Substance Use -0.00176891** (0.001) Asian-Substance Use -0.00165487** (0.001) Indian-Substance Use 0.00086756 (0.001) Other Race-Substance Use 0.00085307 (0.001) Lives with Dad-Substance Use -0.00005873 (0.000) Mom’s Education-Substance Use -0.00024887*** (0.000) Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi ) Male-Male-Substance Use 0.00025390 (0.000) Hispanic-Hispanic-Sustance Use 0.00096450 (0.001) White-White-Substance Use -0.00054887 (0.000) Black-Black-Substance Use 0.00268157*** (0.001) Asian-Asian-Substance Use -0.00063008 (0.001) Indian-Indian-Substance Use -0.00400246* (0.002) Other Race-Other Race-Substance Use -0.00112316 (0.001) Lives with Dad-Lives with Dad-Substance Use -0.00026279 (0.000) Mom’s Education-Mom’s Education-Substance Use 0.00000577* (0.000) (CONTINUED) 57 Table 1.11 Continued: Bivariate Probit Results Probability that j Nominates i Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Unruliness Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi ) Male-Unruliness 0.00033803 (0.000) Hispanic-Unruliness -0.00029864 (0.001) White-Unruliness -0.00031634 (0.001) Black-Unruliness -0.00072003 (0.001) Asian-Unruliness -0.00014430 (0.001) Indian-Unruliness -0.00062938 (0.001) Other Race-Unruliness -0.00040016 (0.001) Lives with Dad-Unruliness 0.00000532 (0.000) Mom’s Education-Unruliness 0.0015907** (0.000) Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi ) Male-Male-Unruliness -0.00017156 (0.000) Hispanic-Hispanic-Unruliness -0.00083765 (0.001) White-White-Unruliness -0.00045553 (0.000) Black-Black-Unruliness -0.00069326 (0.001) Asian-Asian-Unruliness -0.00045232 (0.001) Indian-Indian-Unruliness 0.00065168 (0.002) Other Race-Other Race-Unruliness -0.00093372 (0.001) Lives with Dad-Lives with Dad-Unruliness -0.00028295 (0.000) Mom’s Education-Mom’s Education-Unruliness -0.00000889*** (0.000) (CONTINUED) 58 Table 1.11 Continued: Bivariate Probit Results Probability that j Nominates i Varying Perceptions of “Cool” Behaviors by Characteristics of the Nominator - Trouble Interactions Between Nominator’s Characteristics & Nominee’s Behavior (xj ∗ yi ) Male-Interpersonal Trouble -0.00012521 (0.000) Hispanic-Interpersonal Trouble 0.00008857 (0.000) White-Interpersonal Trouble -0.00034147 (0.000) Black-Interpersonal Trouble 0.00073576 (0.001) Asian-Interpersonal Trouble 0.00013171 (0.001) Indian-Interpersonal Trouble 0.00093555** (0.000) Other Race-Interpersonal Trouble -0.00073496* (0.000) Lives with Dad-Interpersonal Trouble -0.00021189 (0.000) Mom’s Education-Interpersonal Trouble -0.00011108** (0.000) Interactions of Nominator’s & Nominee’s Characteristics, & Nominee’s Behavior (xj ∗ xi ∗ yi ) Male-Male-Interpersonal Trouble -0.00020825 (0.000) Hispanic-Hispanic-Interpersonal Trouble 0.00026008 (0.000) White-White-Interpersonal Trouble 0.00051352** (0.000) Black-Black-Interpersonal Trouble -0.00043573 (0.000) Asian-Asian-Interpersonal Trouble -0.00066907 (0.001) Indian-Indian-Interpersonal Trouble -0.00304771* (0.002) Other Race-Other Race-Interpersonal Trouble 0.00085060 (0.001) Lives with Dad-Lives with Dad-Interpersonal Trouble 0.00006204 (0.000) Mom’s Education-Mom’s Education-Interpersonal Trouble 0.00000331 (0.000) Constant -3.20359793*** (0.255) ρ Observations 0.82 643,293 a) Standard errors are listed in parenthesis below the coefficient estimates. 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