Sorting and Statistical Discrimination in Schools

Abstract

The rigorous economic analysis of peer group formation is a burgeoning subject. Much has been written about how peers influence an individual’s behavior, and these effects are quite prevalent. However, less has been written on how exactly these peer groups begin and the resulting consequences of their formation. A reason for the dearth of knowledge on peer group formation is the lack of quality data sets that clearly define one’s peers. To resolve this issue, this paper explores data which allows a peer group to be defined openly through self nominations. Using these nominations as well as characteristics of the students and their friends, it is possible to see on what dimensions these individuals are sorting into friendships. The data suggests that there is heavy sorting within race and academic ability. Additionally, tests for statistical discrimination on race and academics show that it is exhibited towards blacks and Hispanics. There is also weak evidence of statistical discrimination against whites. Empirical analysis also shows that the degree of statistical discrimination decreases for blacks and Hispanics over a year. however, there is little change for whites over the same period.

Introduction

While the analysis of peer group formation and peer effects is well established in sociology and psychology, it has only recently been broached using rigorous economic analysis. Generally, the effect of one’s peer group on one’s behavior is very strong and profound in many facets. Knowing how one’s peers actually come into being, however, is a subject that is not as well understood as what happens after the group is formed. Nevertheless, the process of peer group formation can be important in many ways.

Specifically, an understanding of sorting into peer groups is important whenever the distribution of characteristics on which individuals sort affects an outcome. Examples of such characteristics are race, academics, and attitudes (Clotfelter 2004). Two of the mechanisms that can affect sorting along these lines are homophily, or affiliation with others of similar characteristics, and statistical discrimination, or stereotyping on observable characteristics. These two different but related processes may affect, for example, how students who are redistributed into schools based on race are received by the original members of the school, how the original members are received by those redistributed, and if any economic returns can be gained by the distributional changes.

For example, Arcidiacono and Vigdor (2009) find that there are weak effects between racial diversity in college and post-graduation outcomes for white and Asian students. Perhaps the reason that the effects are not stronger are that white and Asian students remain entrenched in their racial groups due to preference (homophily) or that they only associate with members of other races of whom they perceive give a signal that is both different from a mean perceived signal from the other races and similar to their own characteristics. Both of the above characteristics occurring together are hallmarks of statistical discrimination. If, for example, the signal is on intelligence or academics, both homophily and statistical discrimination may dampen any sort of gains to diversity that are attempted to be exploited by administrators and policy makers.

Knowing if homophily and statistical discrimination exist and the magnitudes of such effects based on a change in distributions is an important part of designing any sort of redistribution policy, such as school redistricting and affirmative action.¹ It is also important to know if repeated contact with peers over time results in any behavioral change with regards to homophily and statistical discrimination. With repeated exposure to signals and characteristics of potential peers, homophily and statistical discrimination may change. For example, after a school redistribution program is first implemented, homophily and statistical discrimination may decrease in magnitude. This result may further the goals of administrators and policy makers with regards to the policy’s initial intentions of having more interracial contact. This may in turn allow for a better scholastic experience and economic outcomes outside of school. In order to address the above issues, this paper will determine patterns of sorting across racial, academic, and attitudinal lines using two waves of the National Longitudinal Study of Adolescent Health (Add Health), estimate a model of homophily, and alter the model to estimate a model of statistical discrimination.

Literature Review

A large portion of the literature on peer groups focuses on their effects rather than their formation. Discerning how a peer group forms and on what dimensions they sort has not been attempted as much due to the lack of proper data on peer groups. However, the theory of group formation has been explored in detail, especially by psychologists. Raino (1966) and Tuma and Hallinan (1979) believe that similarity and status are two important precursors to friendship. Blau (1964) offers a model where an agent calculates the expected benefit and cost of forming a friendship before making a decision on the friend. Akerlof and Kranton (2002) form a theoretical framework of group formation amongst students. They suggest that students match their characteristics to a set of pre-existing social categories. Students receive greater utility by matching to a group that is most similar to their observed characteristics. After first choosing the group, they then choose how much effort they put into schooling (an example of a peer effect), which is conditional on group choice. However, the authors do not empirically test their premises.

Marmaros and Sacerdote (2006) suggest a model where the expected benefit of a friendship is dependent on information gathered and any shared experiences, while the cost is the time used to develop the friendship. They do not assume that the individual can predict with a reasonable degree of certainty who would be a good friend. Arcidiacono, Khan, and Vigdor (2011) develop a model of interracial contact where individuals want to match with a friend who is similar academically, but where the signal of academic quality is noisy. This results in individuals statistically discriminate over any potential friends.

Marmaros and Sacerdote (2006) use a unique dataset from Dartmouth that measures the level of social interaction between any two individuals as the amount of e-mail sent between them. They find that the greatest dimensions of sorting are along racial lines and geographic boundaries by estimating Poisson regressions of the number of e-mails sent between any two people on various characteristics. Although e-mails may be a reasonable proxy for friendships, this paper aims to use the more concrete friendship nomination data in Add Health. Foster (2005) and Arcidiacono et al. (2011) also use datasets that list characteristics of respondents and how many friends they have across different lines.²

However, it is not possible to identify the actual friendship nominations using these sets of data. Therefore, apart from the line that is being matched, demographic data on friendship nominations is unavailable. Add Health has complete demographic data on friendship nominations within a particular school, so it is possible to observe matches across multiple lines. This feature of Add Health is exploited. This paper uses exact peer groups defined by friendship nominations where the characteristics of the friends are also known due to the fact that the friends are also surveyed, and all the information that is known about a survey respondent is also known for their friends. This wealth of information is generally not known in either the Marmaros and Sacerdote (2006) or the Arcidiacono et al. (2011) paper. In this way, any peer group reflection problems that may occur are avoided.³

Racial diversity is a very important topic that pertains to schools. Programs such as school desegregation and busing have been implemented with the intention of forming new peer groups and fostering better educational and cultural outcomes. One such outcome is the elimination of the black and white achievement gap. Bowen and Bok (2000) argue that learning across races takes place and is quite useful, while Clotfelter (2004) chronicles how important a topic such as school desegregation in America is to both whites and blacks alike, and shows how desegregation programs may have led to “white flight.” On the other hand, Bifulco and Ladd (2007) show that black students choose charter schools in North Carolina with a higher portion of black peers, despite poorer results than private schools. In essence, racial homogeneity is chosen over academic excellence. However, there is some dispute as to the importance of racial composition on academic outcomes. Rumberger and Palardy (2001) argue that the socioeconomic level of students’ schools as well as students’ own socioeconomic status have about the same impact on achievement growth for both advantaged and disadvantaged students as well as for both white and non-white students. These findings question whether integration policies have any impact at all.

It is also argued that integration policies may actually lead to more segregation if there is a small minority present. Moody (2001) argues that segregation through clubs and sports can result in the appearance of segregation based on race. The same process could happen if students are on academic “tracks,” such as honors classes. In these cases, racial sorting patterns and behaviors such as statistical discrimination can be confounded through other factors. However, Zeng and Xie (2008) model the selection of friendship based on “choice,” including dimensions such as race, and “opportunity,” which includes scholastic institutions that segregate, using a conditional logit framework. They find that race is the most important factor in choosing friendships. Regardless, this paper checks for robustness of results by controlling for these issues through a random effects framework with individuals as the group variable.

Data

The National Longitudinal Study of Adolescent Health (Add Health) is a nationally representative study that explores the causes of health-related behaviors of adolescents in grades seven through 12 and their outcomes into young adulthood (Udry 2003). It seeks to examine how social contexts such as families, friends, peers, schools, neighborhoods, and communities influence adolescents’ health and risk behaviors. There is an “In-School” component to the survey in which all students present on the survey date are administered questionnaires. There is also an “In-Home” component which takes a stratified and clustered sample of the In-School survey and follows them over multiple waves. This paper uses the In-Home portion of the survey.

The friendship nominations recorded in Add Health are exploited to form peer group characteristics. Of the 7,190 males in the In-Home portion of survey who are listed in both wave 1 and wave 2, 4,254 have at least one male friend listed, and of the 7,546 females listed in wave 1 and wave 2, 4,529 have at least one female friend listed. From the friendship nominations, a binary variable on whether an individual has a friend with a certain characteristic may be constructed. The analysis is limited to same-gender friends for simplicity and to avoid confounding factors such as romantic relationships.⁴

Sorting into friendships can potentially occur along many different dimensions. Race is often assumed to be a primary dimension, but others such as school performance and attitudes can affect friendship formation as well. Tables 1 and 2 describe the observations of only those in both wave 1 and wave 2 of the In-Home survey. The means reported in the tables are population weighted to reflect sampling procedures.

Table 1 Sample statistics by race for the representative population, in-home survey

Table 2 Sample statistics by GPA and race for the representative population, in-home survey

In order to see if individuals in the sample are sorting across racial, academic, and attitudinal lines, it is important to compare the friendships that are actually formed with a random assignment of friendships in each school, where the friendship nominations in the sample originate. For example, group A may not have much interaction with group B due to the fact that they are not often in the same setting, so the probability that they form a random friendship is remote. However, if the probability that an individual from group A actually forms a friendship with an individual from group B, derived from the friendship nominations in the survey, is different from the probability of a random friendship conditional on the setting and characteristics, it may signal a sorting pattern. Sorting into a certain category is implied by a higher actual probability of friendship formation comparing ratios between the groups. Perhaps the small sample size of high-achieving blacks who actually have legitimate friends for analysis (61 in wave 1, 46 in wave 2) may be skewing results.⁵

Tables 3 and 4 list the actual and chance probabilities for respondents in the sample, divided on various lines, having listed same-gender friends along those same lines. The actual probabilities of friendship are calculated straight from the sample conditional on the individual’s characteristics in the table. The random friendship probabilities are calculated by taking the mean of the relevant characteristic by school (since all friendships are contained within the school in the sample), conditional on an individual’s characteristics in the table. The ratio of the actual probability to the random probability is reported. Any difference in the number of observations between the actual and random probabilities comes from individuals who are in the school population who do not list any valid friends.

Table 3 Sorting along racial and academic lines (Wave 1)

Table 4 Sorting along racial and academic lines (Wave 2)

Same-gender friends are categorized by their race and their achievement based on grade point average (GPA) together.⁶ There is sorting within an individual’s own category. For whites and blacks, high achievers tend to self-segregate themselves at a higher rate than low black and white achievers in both wave 1 and wave 2. In fact, the degree of self-segregation that occurs for high achieving blacks is almost triple that of the degree of self-segregation for low-achieving blacks, as measured by comparing ratios between the groups. Perhaps the small sample size of high-achieving blacks who actually have legitimate friends for analysis (61 in wave 1, 46 in wave 2) may be skewing results.⁷ High-achieving Hispanics who have actual legitimate friendships also have a sample size problem here, as there are instances where there are no friends who are high-achieving Hispanics. However, when comparing similar statistics with the In-School survey, it is true that it is very unlikely, for example, for a low-achieving white to have a high-achieving Hispanic as a friend.

The same is true regarding other cells that are empty in the In-Home waves, i.e. high-achieving whites and low-achieving Hispanics are very unlikely to actually have a high-achieving black friend. Therefore, the sample size problem does not affect how actual and random probabilities are compared. Finally, when looking across waves, it seems that high-achieving whites are integrating more with other racial or academic groups (actual probability of 52.69 % of self-segregation in wave 1 compared to 44.26 % in wave 2). The opposite is happening for high-achieving blacks (actual probability of 28.68 % of self-segregation in wave 1 compared to 44.22 % in wave 2), although this result may be driven by small sample sizes. There is not much change in low achievers across all racial groups with regards to self-segregation over time. Overall, descriptive statistics lend credence to the fact that homophily actually does exist and that it transcends both race and academics.

Homophily

According to Table 2, it is apparent that whites on average have stronger GPAs than their black and Hispanic counterparts. Tables 3 and 4 show that there are heavy interactions within race and academic achievement. Assume that there is a large influx of one race into another school, for example. Will the subsequent changing of the distribution of academic achievement within the school, in addition to the change in racial composition, cause changes in friendship formation within a school?

Let the probability of an individual in a certain school that has a same-gender friend of a certain racial group (Prob(Y _ijk )) be represented by the following equation, where i represents an individual, j represents a school, and k represents the relevant racial group of friends:

$$ Prob\left({Y}_{ijk}\right)={\alpha}_0+{X}_i{\alpha}_1+ SHAR{E}_{jk}{\alpha}_2+{\left( SHAR{E}_{jk}\right)}^2{\alpha}_3+\varepsilon $$

(1)

X _i is a vector of personal characteristics like gender and attitudinal data on life in high school, and SHARE _jk is the share of the relevant racial group in a school.

There could potentially be nonlinear, most likely decreasing, returns to having more of a particular group at a school, which can be measured by including the squared term on the group shares at a school variable. So, it is expected that α ₂ should be positive, while α ₃ should be negative in order to confirm the decreasing returns hypothesis. In order to test whether academics matter when sorting into friendship groups, the following addition can be made to the above equation:

$$ Prob\left({Y}_{ijk}\right)={\alpha}_0+{X}_i{\alpha}_1+ SHAR{E}_{jk}{\alpha}_2+{\left( SHAR{E}_{jk}\right)}^2{\alpha}_3+\left(GP{A}_i-{\overline{GPA}}_j\right){\alpha}_4+\varepsilon $$

(2)

$GP{A}_i-{\overline{GPA}}_j$ is a measure of academic achievement for the individual relative to the school. It can measure if the student is above or below average relative to the school in which the individual is enrolled. If this measure does affect friendship formation, α ₄ should be significantly different from zero. If α ₄ is positive, than higher-achieving students are sorting into the friendship group of the race in question (k). If α ₄ is negative, then higher-achieving students are sorting away from the friendship group of the race in question. If α ₄ is zero, then homophily along academic achievement lines is insignificant in facilitating cross-race relationships.

Tables 5 and 6 provide probit estimates of the above equation in waves 1 and 2, respectively. The dependent variable is an indicator of whether an individual in a racial group that is not the race in question (−k) has a same-gender friend of the race in question (k), and that race in question is white, black, or Hispanic.⁸ X _i is represented in this case by gender, race, and attitudinal variables such as how the individual views his prospects for college and to what degree the individual is happy with experiences at school. The academic metric analyzed here is the individual’s GPA. The coefficient on group shares (α ₂) is positive and significant on all groups in both waves, which is expected. The coefficient on the square of group shares (α ₃) is not significant for any groups across the two waves, so there is no evidence in these samples that there are decreasing returns. The individual characteristic (X _i ) attitudinal variables are insignificant. In both waves, blacks have a negative and significant coefficient compared to other races on the probability of having a white friend. In wave 1, blacks have a positive, although insignificant, coefficient compared to other races on the probability of having a Hispanic friend. However, this coefficient is negative in wave 2. This lends some credence to the fact that blacks are self-segregating more in wave 2 than wave 1, and the difference can be weakly attributed to the switching of Hispanic friends to black friends. The coefficient on relative GPA also follows expected patterns regarding signs. It is positive and significant for those who have white friends in wave 1. Therefore, if a student is above average relative to schoolmates academically, this student is more likely to have a same-gender friend who is white.

Table 5 Estimates on having friends from various groups, homophily (Wave 1)

Table 6 Estimates on having friends from various groups, homophily (Wave 2)

The opposite effect is true when analyzing the coefficient on relative grades when the relevant friendship racial group is black or Hispanic. The coefficients are negative, meaning that if a student is above average relative to schoolmates academically, then the student is less likely to have a same-gender friend who is black or Hispanic. The individuals in these regressions exclude the racial group of the friends in question, and through racial dummy variables that take away any sorting effects across races, homophily based on GPA can be isolated. So, on average, increasing the relative GPA of non-white students in a school has a positive effect on the probability of having a white friend, while increasing the relative GPA of non-black or non-Hispanic students in a school has a weakly negative effect on the probability of having a black or Hispanic friend respectively. Since whites in general have higher GPAs amongst these races, followed by Hispanics and blacks, it seems like sorting along GPA lines can facilitate cross-race friendships. All coefficients in wave 2 are not significant, but do have the expected signs. This result may be attributable to the GPA noise and carryover that is mentioned previously. A robustness check using a random effects probit with the group variable being the individual shows that coefficients on relative GPA follow the expected patterns. This method eliminates any factors that the individuals and schools may have that affect sorting over the two waves, such as any sort of academic tracking (most plausibly) and other institutions such as clubs (less plausibly).

These tables, along with the above descriptive tables with the actual and random probabilities, all suggest that similarities in characteristics associated with academic achievement (as well as attitudes to a lesser extent) seem to at least have a weak effect on friendships within and across races. It is also acknowledged that the SHARE variables and some attitudinal characteristics may have an endogeneity issue. For example, they may be correlated with unobservables such as attitudes towards interracial friendships regardless of academic ability. A robustness check using individual fixed effects, which would control for unobservables constant over time, was used that yielded results similar to both homophily regressions in waves 1 and 2.

Statistical Discrimination

A test of statistical discrimination can be constructed as follows (Arcidiacono et al. 2011). Consider the share and share-squared variables in Eq. 1. The share includes everyone in group k (the race in question). These individuals in k can be split into those who have a better measure of achievement than individual i, those who have a similar measure of achievement to individual i, and those who have a worse measure of achievement than individual i.

$$ SHAR{E}_{jk}{\alpha}_2= SHAR{E}_{jkB}{\alpha}_{2B} + SHAR{E}_{jkS}{\alpha}_{2S}+ SHAR{E}_{jkW}{\alpha}_{2W} $$

(3)

SHARE _jkB is the share of students in school j and group k who have a better academic achievement metric than individual i, SHARE _jkS is share of students in school j and group k who have a similar academic achievement metric than individual i, and SHARE _jkW is the share of students in school j and group k who have a worse academic achievement metric than individual i.

Equation 3 is simply splitting the SHARE _jk α ₂ variable and coefficient into three tiers of academic achievement relative to the individual. The share is still relative to the entire population of the school, not just of the race in question. If the coefficients α _2B , α _2S , and α _2W are carried into the squared term as well, Eq. 1 becomes the following:

$$ Prob\left({Y}_{ijk}\right)={\alpha}_0+{X}_i{\alpha}_1+ SHAR{E}_{jkB}{\alpha}_{2B} + SHAR{E}_{jkS}{\alpha}_{2S}+ SHAR{E}_{jkW}{\alpha}_{2W}+{\left( SHAR{E}_{jkB}{\alpha}_{2B} + SHAR{E}_{jkS}{\alpha}_{2S}+ SHAR{E}_{jkW}{\alpha}_{2W}\right)}^2{\alpha}_3+\varepsilon $$

(4)

The reason that the linear share coefficients enter into the squared term is to make sure that tiers with minimal first order effects (linear term) on the probability of having a friend in group k will also have minimal second order effects on the same probability. For example, if a certain tier does not have a large effect on the probability of having a friend in k, then an increase in the share of that tier should also be ensured not to have any effect on any second order effects, which is now purely measured by α ₃.

If the tiering based on academic achievement is not important, then the coefficients on all three share variables should be the same. If the coefficient on the share of students in k who are better than the individual is higher than the coefficient on the share of students in k who are worse than the individual, and k has a measure of achievement that is lower than other races not in k, then the following is clear. Those individuals not in k are much more likely to have a friend in k if they are surrounded by high achieving members of k. In essence, individuals not in the group in question (−k) happen to project the academic characteristics of k in their school (j) onto those students who could be potential friends. In this case, those individuals who are not in k are statistically discriminating on the basis of academic achievement against group k.

Now, if the coefficient on the share of students in k who are worse than the individual is higher than the coefficient on the share of students in k who are better than the individual, and the measure of academic achievement for those not in k is lower than those in k, the opposite effect happens than mentioned above. However, once again, individuals not in the group in question (−k) project characteristics of the k’s in their school (j) onto potential friends. This phenomenon also is an example of statistical discrimination against k by those not in k. Finally, the coefficient on the share of k that is similar in academic achievement to i can be used to measure the degree of sorting on academic achievement, since a projection of similar achievement to those not in k is placed on potential friends who happen to be in k. In summary, the estimation results of Eq. 4 can lead to the following. If α _2B   > α _2W , and ${\overline{GRADE}}_{-k}>{\overline{GRADE}}_k$ , this implies statistical discrimination. If α _2W   > α _2B , and ${\overline{GRADE}}_k>{\overline{GRADE}}_{-k}$ , this also implies statistical discrimination. The coefficient α _2S is a measure of homophily.

Tables 7 and 8 provide estimates for waves 1 and 2 of Eq. 4 and the marginal effects of a change in one standard deviation of the individual share variables of racial group k on the probability of having a same-gender friend in k, if the respondents are not in k.8 As shown in Table 2, blacks and Hispanics have lower GPAs in general than the population average, and whites have higher GPAs in general than the population average. Table 7 shows that there does exist statistical discrimination against blacks and Hispanics by non-blacks and non-Hispanics respectively in wave 1. A one standard deviation increase in the share of high-achieving blacks will result in an increase in the probability of having a black friend by 1.95 % for non-blacks, while the corresponding probability increase that results from a one standard deviation increase in low-achieving blacks is 0.97 %. In regards to having a Hispanic friend, the probability increases by 3.63 % with a one standard deviation increase in the share of high-achieving Hispanics. The probability increases by 1.04 % with a one standard deviation increase in the share of low-achieving Hispanics, but the estimate is insignificant. There is no evidence of statistical discrimination against whites, as the coefficients on the share of high-achieving whites and low-achieving whites are about the same, and the probabilities of having a white friend for non-whites change between 7 and 9 %. In wave 1, there are decreasing returns to scale on the probabilities of having a Hispanic or white friend, but the coefficient on the share-squared coefficient is insignificant for blacks.

Table 7 Estimates on having friends from various groups, statistical discrimination (Wave 1)

Table 8 Estimates on having friends from various groups, statistical discrimination (Wave 2)

Table 8 shows similar patterns exhibited in wave 2 as in wave 1, but magnitudes of statistical discrimination have lessened somewhat against blacks and Hispanics. The range in the probability of having a black friend for non-blacks goes from a 1.69 % increase with a one standard deviation increase in high-achieving blacks to a 0.88 % increase with a one standard deviation change in low-achieving blacks. The range in the probability of having a Hispanic friend for non-Hispanics goes from a 3.09 % increase with a one standard deviation increase in high-achieving Hispanics to a 1.57 % increase with a one standard deviation increase in low-achieving Hispanics. For whites, there is a slight shift towards being weakly statistically discriminated against by non-whites. The probability of having a white friend for non-whites increases by 9.61 % with a one standard deviation increase in the share of low-achieving whites, while the probability increases by 8.37 % with a one standard deviation increase in the share of high-achieving whites. The difference is slight. Sorting across both waves 1 and 2 seem to be prevalent, since the coefficients on shares that are similar to the GPAs of individuals are significant.

However, the estimates of sorting here may be inflated due to the generally normal distribution of GPAs across the population.⁹ To once again control for factors such as academic tracking and clubs, a robustness check using a random effects probit model with the group variable as the individual supports shows that there exists statistical discrimination against blacks and Hispanics, but not against whites.¹⁰ The endogeneity issue explained in the homophily section also may appear here as well, but a robustness check using individual fixed effects was also performed here with similar results as the cross-sectional regressions.

Conclusion

It has been shown that sorting is very prevalent along racial lines and somewhat prevalent along academic lines. It has also been shown that statistical discrimination along academic lines exists against blacks and Hispanics by non-blacks and non-Hispanics. Both of these results concur with Arcidiacono et al. (2011) Finally, it has been shown that the degree of statistical discrimination is also decreasing between wave 1 and wave 2, suggesting that the signal that is sent out by potential friends regarding academic achievement is becoming clearer, and each individual who chooses a friend stereotypes less as this signal becomes clearer.

The major policies that involve redistribution along racial lines are school redistricting and affirmative action. In principle, these policies assume certain randomness in interracial contact based on the sheer number of students of a racial group in a certain institution. Therefore, any peer effect benefits that may be garnered from the interracial contact is often analyzed based on this often assumed randomness in peer group formation.

The results of this paper show how non-randomness in peer group formation can be explained, which in turn can influence any peer effects from these groups. For example, take a policy that redistricts high-achieving minorities (in this case, high-achieving black and Hispanic students) from poor school districts into better school districts with relatively few minorities.¹¹ The results above show that these minorities may experience statistical discrimination if the minorities who are already in the advantageous school district are low achievers. Therefore, the redistricted minority students may not integrate very well with the majority. The results, though, potentially show that the signal of achievement put forth by the new minority students can become clearer after some time, and the degree of statistical discrimination based on academic achievement can decrease. So an actionable policy measure suggested by the results of this paper would be to continue redistricting and school integration programs, but to be patient with the results of interracial contact.

While this analysis has a limitation in that it does not have a simulation of these policies using a structural model, the reduced form results suggest that policies such as redistricting and affirmative action may not achieve the desired level of interracial contact as intended. Future work would include structurally modeling these plans in a similar way such as Arcidiacono et al. (2011), but now having the advantage that actual friendship nominations are used to determine peer groups. The paper is also limited through the use of only two waves of data that occur while the respondents are in school. Using later Add Health waves, a connection could possibly be made to statistical discrimination and future health and employment outcomes.

Racial integration is both an end and a means to an end with regards to redistribution policies. This paper analyzes how redistribution affects peer group composition, but the group composition’s relation to the actual peer effects of the policy, such as future labor market outcomes or happiness due to the increase in diversity of these programs, is not analyzed. However, the composition of groups will certainly have an effect. This analysis shows that group composition forms in complex ways.