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Party On: The Labor Market Returns to Social Networks in Adolescence
An individual's social capital (the number and quality of their connections) impacts many economic outcomes. Individuals' classroom and school peers impact their education (Sacerdote2001; Carrell2009), earnings (carrell2018disruptivepeers; Michelman2021) and health (Carrell2011). Whom one befriends from among these peers also influences important lifetime outcomes: Chetty2022 show that the number of high SES friendships and economic mobility in a neighborhood are positively associated. However, there is little evidence on whether the number of one's friends (not just the types they are exposed to) causally affect labor market outcomes.
Using data from the National Longitudinal Study of Adolescent to Adult Health (hereafter Add Health), which follows individuals from adolescence into adulthood, we study the labor market returns to adolescent friendships. During adolescence, individuals develop important cognitive and social skills, have key educational outcomes determined and form friendships heckmanmobility2014. Friendships are associated with better larbor market outcomes: Figure (ref) plots log annual earnings at ages 24--34 against the number of friends at ages 12--20, separately for males and females. The non-parametric lines show a striking positive association between adolescent friendships and young adult earnings for both sexes.\footnote{We detail later in the paper how we measure the number of friends.} OLS estimates of this association may be biased downward however: individuals with social skills may engage in activities excluded from regressions, like drinking and partying, that help them make friends but reduce their education and earnings. This “taste for partying” is unobserved and omitted from earnings regressions, and can cause the return to friendships to be downward biased. Conversely, social individuals may prefer productive social activities (working together), which improve their networks and yield higher earnings, biasing the return to friendships upward.\footnote{Social skills are associated with large and growing returns in the labor market (Weidmann2021; Deming2017).}
To estimate the causal returns to friendships, we construct an instrument for the number of friends that exploits the fact that homophily (similarity in traits) predicts friendship formation (Boucher2015; Jackson2014). Our instrument is the average absolute difference in age between a student and the peers in her school and grade, which we refer to as age distance. Because our baseline regression controls for own age and the average age of individuals in the school-grade, as well as grade and school fixed effects, age distance will vary across individuals because the distribution of ages varies across schools and grades. For example, a 13.5 year old with two peers aged 12.5 and 14.5 has an age distance of 1 while mean age is 13.5. If the same 13.5 year old were instead in a group with a 13 year old and a 14 year old, mean age would be the same, but age distance would be smaller (0.5), resulting in more friends. This variation is similar to what is used in Bifulco2011classmates and carrell2018disruptivepeers, who leverage variation across cohorts within schools to estimate the effects of peer characteristics on outcomes.\footnote{These papers typically investigate the direct (reduced form) relationship between peer traits and outcomes. Although we leverage similar (though not identical) variation, we use this variation in peer characteristics as an instrument for friendships -- we do not study the direct effect of peer similarity on outcomes.} In our setting, there is also variation in the instrument within school-grade because age distance depends both on the mean age in their group and the student's own age. Our identification strategy is most similar to Fletcher2020 who investigate the effect of friendships on education outcomes using similarity in race/ethnicity and socioeconomic status as instruments for friendships. We investigate the effect of friendships on earnings instead.
Education is also endogenous in these regressions because educational and social investments are determined jointly in adolescence. Studies with well-identified causal returns to education make use of large data sets and typically exploit state-level variation in compulsory schooling or the cost of schooling, such as distance to school (Mountjoy2022) or school openings (see card2001estimating for a review and Oreopolous2020 and Psacharopoulos2018 for more recent examples). In our data, these instruments are weak predictors of education.
We propose a novel approach to estimating the returns to friendships that does not require instruments for education. We rely on the findings from the previous literature and assume that the causal returns to a year of schooling range from 5 to 15% (Oreopolous2020; Psacharopoulos2018). Under this assumption, and making use of the homophily-based instrument for friendships, we derive bounds for the returns to friendships.\footnote{We are grateful to Larry Katz for suggesting this approach.}
We find that the returns to having one more friend during adolescence range between 7 and 14%, similar to the returns to one more year of schooling. Our identifying assumption is that age distance determines earnings only through its effects on education and friendships, conditional on own characteristics, mean peer characteristics, and grade and school fixed effects. The results are robust to a number of checks, including addressing the potential concern that parents sort into schools or grades based on relative age. These instrumented returns to friendships are larger than OLS estimates. Computations suggest that measurement error can explain the discrepancy, consistent with Griffith2021. The result is also consistent with downward omitted variable bias: the data show that preferences for activities like drinking are associated with more friendships but lower GPA and earnings.
We contribute to the well-established literature examining peer effects among adolescents and young adults (see the review by Jeon2015).\footnote{Identifying how the behaviors and characteristics of peers affect individuals was first discussed by Manski1993. A few early papers (BRAMOULLE2009identification) attempted to use friendship networks to instrument for peer outcomes and overcome the joint determination of outcomes (the reflection problem). These papers assume that a friendship network is exogenous or endogenous through unobserved group heterogeneity.} For example, having peers with good academic outcomes improves one's academic outcomes (Carrell2008,Carrell2009; SACERDOTE2011peer; Bifulco2011classmates; Denning2021). Peer effects in adolescence can also carry into adulthood. carrell2018disruptivepeers find that having disruptive peers in the classroom during adolescence has deleterious effects on individuals' labor market outcomes as adults, partly because disruptive peers lower test scores.
Our paper suggests a new mechanism by which peer characteristics might operate: friendship formation. A few papers investigate the effects of friendship networks on educational outcomes using data on friendship nominations (Babcock2008; LavySand2019; Fletcher2020). However, friendships may also matter for labor market outcomes, separately from their effects on education attainment. Previous work documents that the size and connectedness of an individual's social network in adulthood can improve wages and job match quality (granovetter1973strength; montgomery1991social; calvo2004effects; Cappellari2015; Dustmann2015). In addition to the number of friends, the types of friends one is associated with may also impact labor market outcomes (Chetty2022). Although our results on this are only suggestive (we do not have powerful instruments for different types of friendships), we find that almost all types of friendships have returns in the labor market, including friends from low SES backgrounds and with weak connections. This suggests that the overall number of friendships -- not just their type -- is a relevant factor in determining earnings.
There are no papers we are aware of that estimate the causal returns to the number of friendships on labor market outcomes -- this is the main contribution of this paper. The closest paper to ours is by conti2013popularity, who estimate returns to high school friendships on wages using data from the Wisconsin Longitudinal Survey. Their estimation strategy corrects for non-classical measurement error in the number of friendships due to under-sampling, but they do not account for endogeneity in both education and friendships which this paper addresses.
Our second contribution is methodological. A strand of econometric literature considers models with endogenous networks (goldsmith2013social; Hsieh2015network; Badev2021; johnsson2021peer; Auerbach2022; Griffith2022; Sheng2023). But these papers do not consider the joint determination of education and friendships. As a result, they do not address how the endogeneity in education complicates the identification of causal labor market returns to friendships.
Our identification approach is motivated by the econometric literature on partial identification, which is widely used as a remedy for identification failure in various applications such as interval data Manski2002, missing data Manski2003, auctions Haile2003, and games with multiple equilibria Tamer2003. We exploit the idea of partial identification to resolve a new challenge where we lack a good instrument for one of the endogenous regressors, but the coefficient of that regressor is not of primary interest and can be bounded. To our knowledge, this is the first paper that proposes a partial identification approach to avoiding instrumenting for a secondary endogenous regressor.
We start by summarizing a basic model of education and friendship formation (Appendix (ref)) and describe its implications for the empirical analysis.\footnote{All figures and tables designated with a letter (e.g., \textquotedblleft A\textquotedblright , “B”) are shown in the Online Appendix.}
During adolescence, individuals decide how to allocate their time between studying, socializing, and leisure. Studying increases educational attainment, and socializing increases one's number of friends, both of which have positive returns in the labor market. In deciding how to allocate their time, individuals consider the returns to each activity, which depend on their innate intelligence and social skills (Proposition (ref)).
Because time spent investing in education and friends is determined at the same time, both education and friendships are potentially endogenous in a Mincer earnings equation and thus OLS estimates of their returns may be biased. However, the sign of the bias in friendship returns is not clear ex-ante (Proposition (ref)). On the one hand, social skills may determine the number of friendships and have an independent effect on earnings, causing an upwards bias in the returns to friendships. On the other hand, partying and drinking may increase friendships but negatively affect skill accumulation and labor market outcomes, causing a downward bias in the returns to friendships.
To account for the endogeneity of friendships, we will exploit the fact that an individual's accumulated social capital also depends on the traits and decisions of their school-grade peers because the production of friendships requires coordination with others -- you cannot “party alone”. Conditional on time spent socializing, individuals that are more similar to each other are more likely to become friends.\footnote{In equilibrium this may not hold (see Proposition (ref)).}
We use the restricted-use National Longitudinal Study of Adolescent to Adult Health (Add Health). The in-school sample is a complete census of all students enrolled in a given school during the 1994--95 school year. The in-school sample data include basic demographics as well as friendship nominations. A random sample of the students interviewed in school was selected for in-home interviews in Wave 1 during the 1994--95 school year (ages 12--20 years) and tracked over in subsequent survey waves. In Wave 4 (which was conducted in 2008--09), respondents were age 24 to 34, on average 29 years old. For this in-home sample, we observe measures of endowments, investments, and cognitive and social outcomes.
Our estimation sample is constructed from the in-home sample, but we use information from the in-school sample to construct friendship and homophily measures. We include 10,605 individuals with complete data for gender, age, and race. Summary statistics for the estimation sample are presented in Table (ref).
Outcomes. The main outcome of interest is total earnings from wages or salary in the last year. If a respondent replied \textquotedblleft do not know\textquotedblright to the earnings question, they were prompted with twelve categories of earnings. We use the midpoint of the selected range for these respondents (approximately 2% of the sample). We drop individuals who reported zero earnings (\textasciitilde 6%), which means they were unemployed the entire year. Individuals in our sample made roughly \$38,000 in the previous year.
Intermediate outcomes: friendships and education. Our primary measure of the number of friendships is a person's grade in-degree. For a given student, grade in-degree is the number of people within the same school and grade who nominate them as one of their friends in Wave 1.\footnote{Individuals could list up to five nominations of each gender. } In-degree has been widely used in the social network literature as an objective measure of an individual's number of friendships because it does not rely on self-reporting conti2013popularity. Importantly, we observe all nominations sent to students in the in-home sample because the network data is derived from the in-school sample. Unlike Add Health's measure of in-degree, we exclude nominations from students in different grades: the majority of nominations (77%) occur within the same grade (on average, school in-degree is 4.4, whereas grade in-degree is only 3.4 (Table (ref))).
Education is measured by years of schooling. On average, individuals in our data obtain almost 15 years of schooling. We also observe GPA, a measure of how much students learned in school.
Endowments. We use self-reported extroversion, collected in Wave 2, as the main measure of the social endowment of individuals. Extroversion is one of the “Big Five” psychological traits. About 65% of individuals report being extroverted.\footnote{The survey question is “You are shy?”, and the the choices are “strongly agree / agree / neither agree nor disagree / disagree / strongly disagree”. Individuals choosing last three categories are defined as extrovert. Due to the survey design this measure is missing for 26% of individuals in the data. To maximize sample size, we impute this measure and include a dummy for whether it is missing.} Consistent with existing evidence (lenton2014personality), extroverts have larger earnings, and perhaps not surprisingly, more friends (Columns 2 and 3 of Table (ref)). Most interestingly, they also have more years of schooling.
The Add Health Picture Vocabulary Test (AHPVT) score is our main measure for cognitive endowments. This test, administered in Wave 1, is an abbreviated version of the widely used Peabody Picture Vocabulary test and measures verbal ability. While it is not an overall measure of intellectual ability, it has a high correlation with other intelligence tests (Hodapp1999; Dunn2007). For simplicity, we refer to it as IQ. As expected, individuals with above median IQs have greater earnings and education (more years of education and higher GPA). Perhaps surprisingly, they also have more friends (Columns 4 and 5 of Table (ref)).
We now turn our attention to estimating the labor market returns to friendships. We follow the previous literature and estimate the following earnings equation (conditional on employment): \[ Y_{i}=r_{e}E_{i}+r_{f}F_{i}+\beta'X_{i}+\gamma'\bar{X}_{gs}+\alpha_{g}+\lambda_{s}+\epsilon_{i}, \] where the outcome of interest is the log annual earnings $Y_{i}$ in Wave 4 for a given individual $i$ (observed in grade $g$ and school $s$ during Wave 1), $E_{i}$ stands for years of schooling, and $F_{i}$ is a measure of $i$'s number of friends (such as in-degree). We control for $i's$ characteristics $X_{i}$ (age in Wave 1, sex, race, IQ, and extroversion) and mean characteristics in $i's$ school-grade $\bar{X}_{gs}$ (mean age, fraction female, fraction white, mean IQ and fraction extrovert). We control for grade fixed effects ($\alpha_{g}$) to account for differences across grades within a school. We include school fixed effects ($\lambda_{s}$) to control for unobserved school-level characteristics that could be correlated with labor market outcomes and potentially sort individuals into schools. Standard errors are clustered at the school level.
The object of interest is the coefficient $r_{f}$, measuring the returns to having one more friend. Proposition (ref) shows that OLS estimates of $r_{f}$ are biased because education and friendships are jointly determined. We take an instrumental variable approach to overcome the endogeneity issue, which will also address classical measurement error in number of friends.
We use homophily measures as instruments for friendships, following the evidence that individuals that resemble each other are more likely to become friends Jackson2008. Unfortunately, the instruments for education used in the literature (quarter of birth, distance to school) are weak in our data. Instead, we propose a novel approach to estimating the returns to friendships that does not require an instrument for education.\footnote{The education literature shows that relative age within a classroom also affects educational attainment (e.g., black2011too). However, we experimented using homophily measures for education as well as for in-degree and found that homophily instruments fail the weak IV tests if we use them to predict both education and friendships.}
There is a substantial literature estimating the (causal) returns to schooling in the United States using various approaches. While estimates differ across studies and populations, causal estimates of $r_{e}$ typically lie between 5 and 15% card2001estimating,Psacharopoulos2018,Oreopolous2020. Instead of estimating $r_{e}$, we assume that $r_{e}$, while unknown, lies in this range. Then by instrumenting for friendships only, we derive upper and lower bounds for the (causal) returns to friendships.
Let $\theta=(r_{f},\beta',\gamma',\alpha',\lambda')'$ denote the vector of parameters, where $\alpha=(\alpha_{g},\forall g)'$ is the vector of grade fixed effects, and $\lambda=(\lambda_{s},\forall s)'$ is the vector of school fixed effects. Let $\tilde{X}_{i}$ denote the vector of friendships $F_{i}$ and other covariates (individual characteristics $X_{i}$, school-grade mean characteristics $\bar{X}_{gs}$, and grade and school dummies), and $Z_{i}$ the vector that consists of the instruments for $F_{i}$ (homophily measures) and the covariates. Ideal instruments for friendships satisfy two conditions: (i) they predict friendships $F_{i}$ ($\mathbb{E}[Z_{i}\tilde{X}'_{i}]$ has full column rank); and (ii) they are excluded from the earnings equation ($\mathbb{E}[Z_{i}\epsilon_{i}]=0$). Instruments for friendships can also predict education. The exclusion restriction is satisfied if the instruments do not affect earnings except through friendships and education. This exclusion restriction implies the moment condition
Suppose that $W$ is a positive definite weighting matrix. If the education return $r_{e}$ were known, the parameter $\theta$ would satisfy $\theta=\mathbb{E}[Q_{i}(Y_{i}-r_{e}E_{i})]$, where $Q_{i}$ denotes the vector $(\mathbb{E}[\tilde{X}_{i}Z'_{i}]W\mathbb{E}[Z_{i}\tilde{X}'_{i}])^{-1}\mathbb{E}[\tilde{X}_{i}Z'_{i}]WZ_{i}$. Because the true value of $r_{e}$ lies between $r_{e}^{l}=0.05$ and $r_{e}^{u}=0.15$, the parameter $\theta$ is bounded between $\mathbb{E}[Q_{i}(Y_{i}-r_{e}^{l}E_{i})]$ and $\mathbb{E}[Q_{i}(Y_{i}-r_{e}^{u}E_{i})]$.
In practice, we can estimate the bounds by setting $r_{e}$ at $r_{e}^{l}$ and $r_{e}^{u}$ and estimating a GMM regression of $Y_{i}-r_{e}E_{i}$ on friendships $F_{i}$ and other covariates, using $Z_{i}$ as the instrument. For example, if we set $r_{e}=r_{e}^{l}$ and regard $Y_{i}-r_{e}^{l}E_{i}$ as the dependent variable, then the GMM estimator yields an estimator for the bound $\mathbb{E}[Q_{i}(Y_{i}-r_{e}^{l}E_{i})]$. The bound $\mathbb{E}[Q_{i}(Y_{i}-r_{e}^{u}E_{i})]$ can be estimated similarly.\footnote{To ensure that the upper and lower bounds are estimated using the same weighting matrix, we use the GMM estimator that assumes homogeneous errors, that is, we set $W=\mathbb{E}[Z_{i}Z'_{i}]^{-1}$. This estimator is equivalent to 2SLS.} For each component of $\theta$, we then obtain a consistent estimator for the upper (lower) bound by taking the maximum (minimum) of the two estimates of the component.\footnote{Whether the upper or lower bound of a component of $\theta$ is achieved at $r_{e}^{l}$ or $r_{e}^{u}$ depends on the sign of the corresponding component of $\mathbb{E}[Q_{i}E_{i}]$. For example, let $Q_{i,1}$ denote the first component of $Q_{i}$. Then $r_{f}$ has the upper bound $\mathbb{E}[Q_{i,1}(Y_{i}-r_{e}^{l}E_{i})]$ if $\mathbb{E}[Q_{i,1}E_{i}]\geq0$ and $\mathbb{E}[Q_{i,1}(Y_{i}-r_{e}^{u}E_{i})]$ if $\mathbb{E}[Q_{i,1}E_{i}]<0$. The lower bound of $r_{f}$ can be derived by swapping $r_{e}^{l}$ and $r_{e}^{u}$. In practice, the components of $\mathbb{E}[Q_{i}E_{i}]$ can be recovered by regressing education $E_{i}$ on friendships $F_{i}$ and other covariates, using $Z_{i}$ as the instrument. The sign of the coefficient on friendships determines whether the upper bound of $r_{f}$ is achieved when $r_{e}$ is high or low. A positive friendship coefficient implies that the upper (lower) bound of $r_{f}$ is achieved at low (high) $r_{e}$.}
Inference. We follow Imbens2004 to construct a confidence interval for any true value of $\theta$ that lies between the bounds. These confidence intervals are asymptotically valid regardless of whether $\theta$ is point identified or partially identified. If a component of $\mathbb{E}[Q_{i}E_{i}]$ is $0$, the upper and lower bounds for the corresponding component of $\theta$ coincide, and this component of $\theta$ is point identified. In general, the components of $\mathbb{E}[Q_{i}E_{i}]$ are not equal to $0$, the bounds do not coincide, and $\theta$ is only partially identified.
We can assess whether $r_{f}$ is point identified or not by regressing education $E_{i}$ on friendships $F_{i}$ and other covariates, using $Z_{i}$ as the instrument, as noted in footnote (ref). If the coefficient of friendships is not significantly different from zero, then we cannot reject the null that $r_{f}$ is point identified -- the exact returns to education are not important because $F_{i}$ and $E_{i}$ are not correlated. In this case, we would not need to instrument for education in order to obtain an unbiased estimate of $r_{f}$. In our data, the coefficient on friendships is significant from zero -- we can reject the null that $r_{f}$ is point identified.\footnote{This also ensures that the estimated upper and lower bounds are jointly asymptotically normal, as required by Imbens2004.}
To be specific about the confidence intervals, denote the upper and lower bounds of $\theta$ by $\theta_{u}$ and $\theta_{l}$. Let $\hat{\theta}_{u}$ and $\hat{\theta}_{l}$ be the estimators for $\theta_{u}$ and $\theta_{l}$ and $se(\hat{\theta}_{u})$ and $se(\hat{\theta}_{l})$ the standard errors of the estimators.\footnote{In Section (ref) we also consider an instrument constructed using estimates from a pairwise regression. In general, standard errors in two-step estimators should account for the presence of first-step estimators. However, we are in a special case where the moment condition in equation ((ref)) has a zero derivative with respect to the first-step parameters (coefficients in the pairwise regression). Therefore, the first-step estimation has no impact on the standard errors in the second step and standard calculation of standard errors is valid NEWEY1994.} Imbens2004 proposed a $(1-\alpha)$ confidence interval for the true value of $\theta$ that takes the form of $[\hat{\theta}_{l}-c\cdot se(\hat{\theta}_{l}),\hat{\theta}_{u}+c\cdot se(\hat{\theta}_{u})]$, where the critical value $c$ satisfies $\Phi(c+\frac{\hat{\theta}_{u}-\hat{\theta}_{l}}{\max\{se(\hat{\theta}_{u}),se(\hat{\theta}_{l})\}})-\Phi(-c)=1-\alpha$, with $\Phi(\cdot)$ being the cdf of the standard normal distribution.\footnote{The confidence intervals proposed by Imbens2004 require a superefficient estimator of the length of an identified set (Assumption 1(iii) in their paper). Nevertheless, Stoye2009 provides a simple sufficient condition for the superefficiency to hold: the estimated upper and lower bounds are almost surely ordered. Our estimated bounds are ordered because we take the maximum/minimum of the two estimates. Therefore, by Stoye2009 the confidence intervals in Imbens2004 are appropriate.} In practice, each component of $\theta$ has a critical value $c$, and we need to solve for it numerically. Using the critical values for each component of $\theta$, we can construct confidence intervals for each component of $\theta$.\footnote{The STATA code for the bound estimates and confidence intervals can be found in Appendix (ref).}
Advantage of bounding. Provided that the true return to education is between 5 and 15%, our approach provides consistent bound estimates and valid confidence intervals for the returns to friendships. This approach is preferable to a simple calibration that assumes the return to education is known and equal to a particular value (e.g., $r_{e}=10\%$), which yields a biased estimator if the true return to education is different from the presumed value and provides no confidence intervals.
McPherson2001 report the results of various studies documenting that in many settings (including schools) individuals of the same age are much more likely to be friends. Based on this evidence, we compute age distance for each pair of individuals as the absolute difference between their ages to use as an instrument.
The distance between individuals $i$ and $j$ is defined at the pair level -- that is, between two students of the same school and grade. To construct an instrumental variable for in-degree at the individual level, we average the pairwise distances over all $j$ that are in $i$'s school-grade. We call this measure “age distance”. In Appendix (ref) we consider another aggregating approach. We run a Probit regression of friendships among pairs of students on the pairwise age distance and basic controls. We then use the predicted in-degree, calculated by the sum of the predicted friendships, as an instrument for in-degree.
To be valid our instrument must operate only through friendships and education (the two endogenous variables). Although age distance also potentially affects educational attainment (black2011too), the returns to friendships are still (partially) identified because we estimate the returns to friendships after subtracting off the impact of education from log earnings. The instrument satisfies the exclusion restriction so long as it is uncorrelated with the remaining unobservables.
We use a similar set of controls and identifying variation as Murphy2020 who study the effects of academic rank on academic outcomes, and Cicala2017 who show that where an individual ranks within a given social distribution determines their choice of friends, behaviors, and outcomes. Given that we control for cohort-mean age and own age, this leaves variation in age distance among students with the same age and cohort-mean age for identification.
Table (ref) illustrates this variation for a simple example. In the first cohort, students are aged 13, 13.5, and 14 (mean age 13.5). The second cohort has three students aged 13.2, 13.5, and 13.8 (same mean age of 13.5). In both cohorts, there is a student aged 13.5. However, the age distance for this student is smaller in cohort 2 (0.3 years) compared to cohort 1 (0.5 years). In the absence of coordination effects, our model predicts that the student in cohort 2 will have more friends than the student in cohort 1 because they are closer in age to their peers. The greater variance in the distribution of ages in cohort 1 compared to cohort 2 results in a greater age distance in cohort 1 (0.67) than cohort 2 (0.4).
Following Bifulco2011classmates, we document in Table (ref) that there is sufficient variation of this kind in our data after accounting for the basic set of controls. The variation in age distance, measured by the standard deviation (s.d. 0.435), is about halved by the inclusion of individual age (s.d. 0.2). But 45% of the original variation (s.d. 0.2) remains after including the full set of controls, regardless of whether we control for grade FE or mean age in the cohort. This residual variation in age distance is significant, and larger than the residual variation in Bifulco2011classmates.
A key identifying assumption is that conditional on our basic controls, age distance does not predict earnings except through its effects on education and friendships (exclusion restriction). Because the identifying variation in age distance is generated from differences in the age distribution across cohorts, we must assume that individuals do not sort into schools and grades based on the variance in age -- that is, parents do not care or know about age distance and do not sort using this criterion.
Our identification assumption is not violated if parents want to place their child in a cohort where the child is older relative to their classmates (the practice sometimes referred to as red-shirting). In our previous example, both cohorts have the same mean age, which means that parents would be indifferent between the two cohorts because the child\textquoteright s age relative to the cohort mean will be identical in both cohorts. However, age distance will be on average smaller in cohort 2. Alternatively, parents may care about their child\textquoteright s age rank within a cohort. In our example, a 13.7 year old child would still be indifferent between the two cohorts, because they would be the second oldest in both cohorts. But this student would be closer in age to their peers in cohort 2, and we expect they would have more friends.
While we cannot test the exclusion restriction directly, we conduct a series of placebo tests using observable pre-determined characteristics (parental education, parental and own nativity, religion, birthweight and breastfeeding, height, disabilities, etc.): age distance should not predict these variables conditional on our basic controls. We select the variables using two criteria. First, they are mostly determined early in life, before adolescent friendships are formed. Second, the prior literature and our data suggest they determine earnings.\footnote{We check that these variables predict earnings by regressing log earnings with and without the predetermined variables, conditional on the basic covariates (Columns 1 and 2 of Table (ref)). We reject the null that these variables do not jointly predict earnings (p-value < 0.001). The $R^{2}$ increases from 0.059 to 0.066 (a 12% increase) with the addition of these variables, confirming that they predict earnings.} Table (ref) shows that age distance does not predict any of the 14 variables we consider, conditional on basic controls: the coefficients on age distance are statistically insignificant in all regressions. Moreover, if we regress age distance on all of these variables (Column 3 of Table (ref)), we cannot reject the null that they do not predict age distance, conditional on the basic controls (the p-value of the joint F-test is 0.56).
These placebo tests show that many important pre-determined characteristics that predict earnings are not statistically associated with age distance, providing support for the exclusion restriction.
Table (ref) documents that age distance has a negative and statistically significant effect on in-degree. If the average age distance between a student and the students in their school-grade increases by one year, the student has one less friend (Column 1). Increasing the age distance by one standard deviation (0.44) lowers the number of friends by about 0.44 friends, a 13% decline relative to the mean (3.4). The F-statistic is about 94, well above the standard thresholds required to rule out weak instruments and large enough for standard t-statistics in the second stage to be valid Lee2022. These results are similar if we estimate the first stage using the pairwise data where an observation is a potential link between two students in the same school-grade (22 million potential links). Using a Probit probability model, we show that pairwise age distance is a strong predictor of friendships between two individuals, even after controlling for the age of the nominated individual in the pair and the mean age in the cohort (Column 1 of Table (ref)).\footnote{We do not control for the age of the individual who nominates the friendship because otherwise there is no variation in the pairwise distance.}
In settings with heterogeneous treatment effects, IV estimates are interpretable only under monotonicity: the endogenous variable (number of friends) must be weakly monotonic in the instrument (age distance) for all individuals. From a theoretical standpoint, increasing an individual's homophily level has ambiguous predictions on socializing and the number of friends because of coordination effects (Proposition (ref)). For example, suppose that an adolescent is placed in a cohort with adolescents that are older instead of being of the same age. If older individuals socialize more than younger individuals, then the adolescent may socialize more and accumulate more friends in the older cohort because it is more productive to socialize in this group, despite the larger age difference.
Although monotonicity remains an untestable assumption, we empirically investigate whether it appears to be violated. Figure (ref) shows a bin-scatter plot of friendships and age distance, in the raw data (left plot) and with basic controls (right plot). The slope is negative. A non-parametric plot (Figure (ref)) further confirms that the relationship is weakly decreasing: age distance does not increase the number of friendships.\footnote{There is a small portion where this is not true but this occurs for very high values of age distance that are uncommon.} Column 2 of Table (ref) shows that age distance squared has a negative but insignificant effect on friendships. In the pairwise first stage, age distance squared is significant, so the relationship is not exactly linear (Column 2 of Table (ref)). However, the coefficients still imply a monotonic relationship: these negative coefficients imply that the curve is strictly decreasing and concave.
We also investigate whether the effect of age distance is symmetric. Column 3 of Table (ref) shows that it is not: it is more detrimental --- from the point of view of making friends --- to be young among older peers than it is to be older among young ones (this is also true in the pairwise estimation, see Column 3 of Table (ref)). However, age distance is still negatively correlated to friendships regardless of whether peers are older or younger.
Angrist1995 discuss what is needed for the monotonicity assumption to be met in the case of a continuous treatment. A testable implication of monotonicity is that the CDFs of the treatment (in-degree) at different levels of the instrument (age distance) should not cross. A visual representation of this test is given in Figure (ref). We plot the difference in the CDF of in-degree as age distance increases by one unit.\footnote{Let $X$ denote in-degree and $Z$ age distance. We estimate the CDF difference $\mathbb{E}[1\{X\leq x\}|Z=z']-\mathbb{E}[1\{X\leq x\}|Z=z]$ for all $x$ and $z'\geq z$ by regressing the indicator variable $1\{X\leq x\}$ on $Z$. The coefficient of $Z$ provides an estimate of the CDF difference by one unit increase in $Z$ Rose2021.} The CDF differences are non-negative throughout the support, whether we control for the basic covariates or not. A formal test of this no-crossing condition is provided by Barrett2003. We split the data evenly into high and low values of age distance. The null hypothesis is that the distribution of in-degree with high age distance is first-order stochastically dominated by the distribution of in-degree with low age distance.\footnote{Let $N_{H}$ and $N_{L}$ denote the number of individuals with age distance higher and lower than the median in the sample. Let $F_{H}(x)$ and $F_{L}(x)$ denote the CDFs of in-degree for the subgroups with high and low age distance. The null and alternative hypotheses are $H_{0}:F_{H}(x)\geq F_{L}(x)$ for all $x$ and $H_{1}:F_{H}(x)<F_{L}(x)$ for some $x$. Barrett2003 propose the test statistic $\hat{S}=\left(\frac{N_{H}N_{L}}{N_{H}+N_{L}}\right)^{1/2}\sup_{x}(\hat{F}_{L}(x)-\hat{F}_{H}(x))$, where $\hat{F}_{H}(\cdot)$ and $\hat{F}_{L}(\cdot)$ are estimators of $F_{H}(\cdot)$ and $F_{L}(\cdot)$. They suggest that the p-value can be computed by $\exp(-2(\hat{S})^{2})$.} The p-values for the raw and residual distributions are 0.927 and 0.993 respectively, suggesting that we cannot reject the null, further supporting the monotonicity assumption.
We now turn our attention to estimating the causal returns to friendships.
Figure (ref) shows the correlation between log earnings and age distance in a bin-scatter plot. Greater age distance is associated with lower earnings in the raw data (left plot), and with basic controls (right plot). Conditional on basic controls, individuals in cohorts with more dissimilar peers in terms of age have lower earnings as adults: increasing age distance by one standard deviation (0.44) lowers earnings by 7.5% (Column 1 of Table (ref)). This relationship is statistically significant.
Table (ref) reports the estimated bounds on the returns to adolescent friendships. The OLS estimates for in-degree are reported in Column 1 for reference, where the return to one more friend is 0.025. If in-degree is treated as endogenous but education is not, the estimate for in-degree increases to 0.12 (Column 2). If we take a calibration approach, where we assume the return to education is 10%, the returns to in-degree remain at 0.11 (Column 3).\footnote{This estimate is obtained by running a regression on in-degree, controlling for covariates and instrumenting for in-degree, where the dependent variable is given by log earnings minus 10% times years of schooling.}
Our main specification, which allows for the returns to education to vary anywhere from 5 to 15%, bounds the returns to friendships from 0.093 to 0.137 (Column 4). The confidence interval (CI) for the returns does not include zero -- these estimates are also statistically significant. The upper bound corresponds to the lower return to schooling, and vice versa. This is because the correlation between in-degree and schooling is positive (Figure (ref) and Table (ref)): if we regress education on in-degree, controlling for covariates and instrumenting for in-degree, the coefficient on in-degree is 0.44 and statistically significant. The significant coefficient also implies that the returns to friendships are not point identified.
Robustness. If we use a Probit probability model to predict links using the pairwise data and then use the predicted in-degree as an instrument, the bounds are similar and range from 0.065 to 0.096 (Column 5), although the estimates are not significant.
The results are robust to using alternative measures of friendships (Table (ref)), including reciprocated friendships, which suggests that we are not simply capturing the returns to popularity.
We also check if the results are robust to the inclusion of additional controls (Table (ref)). Column 1 reproduces our preferred specification for reference and shows bounds of 0.093--0.137. Our estimates are similar (and the CI does not include 0) if we control for age rank (Column 2), predetermined individual-level controls (the ones we used for the placebo tests in Section (ref), Column 3), variables capturing current SES including parental income and living with parents (Column 4), or their respective cohort-level means (Column 5). The last two regressions are potentially problematic because income (or living with parents) is endogenous (it is not truly predetermined) but it is nevertheless reassuring that the results are similar.
Table (ref) investigates another potential violation of the exclusion restriction. Perhaps in settings where age distance is larger, there is greater bullying. Because bullying can affect mental health Arseneault2010 which in turn affects earnings, our instrument could affect earnings through this additional channel. We test this by controlling for measures of social cohesion in adolescence. These controls do not individually or jointly affect the estimated bounds.
Magnitudes. The magnitude of the returns to friendships ranges from 0.07 to 0.14 across specifications. Since recent estimates of the returns to schooling are on the larger side (more than 10%), the more likely bound for the returns to friendships is the lower bound, which hovers around 0.07--0.09. Thus an increase of one standard deviation in the number of friends (3.2) increases earnings by 22% -- a large and economically significant return. By comparison, a one standard deviation increase in years of schooling (2.1) would increase earnings by 21% so the effect size is similar.\footnote{The implied elasticity of earnings with respect to friendships is 0.24, whereas the elasticity of earnings with respect to education is 1.5, assuming the return to education is 10%.} While the return to in-degree seems large, it represents the returns to having a friend during adolescence -- we are not measuring the returns to one year of friendship but the returns to having a friend. These friendships likely last many years, potentially into adulthood (Section (ref)).
Our bounds are larger than the point estimates in conti2013popularity of around 2%. In addition to methodological differences (they do not account for the endogeneity of education and friendships), they study men who were seniors in high school in Wisconsin in 1957, whereas the Add Health data is nationally representative and surveys students in middle or high school in 1994--95, at a time when the returns to education and other individual traits in the labor market are much larger. They measure labor market outcomes 35 years later whereas we observe them 15 years later. The returns to friendships in adolescence may attenuate over time, yielding larger returns when respondents are surveyed earlier in their careers.
Our preferred bounds do not include the OLS estimate of 0.025.\footnote{However, the confidence interval for the returns to friendships {[}0.008, 0.224{]} includes the confidence interval for the OLS estimator {[}0.018, 0.031{]}, so we cannot reject the null that the IV and OLS estimates are the same.} We explore two reasons why the estimated bounds are larger than the OLS estimate: omitted variable bias and measurement error.\footnote{IV estimates might also exceed OLS estimates if treatment effects are heterogeneous. OLS estimates in Table (ref) suggest that while there is some heterogeneity in the returns to friendships across subpopulations, it is too small to explain the discrepancy between OLS and IV estimates.}
Omitted variable bias. Omitted variable biases in our model are in general ambiguous (Proposition (ref)). The sign of the OLS bias is determined by the correlation between in-degree and the error term $\epsilon_{i}$.\footnote{Strictly speaking, the bias is given by the covariance between in-degree and $\epsilon_{i}$, multiplied by the inverse of a matrix $X'X$, where $X$ consists of residualized education and in-degree. In our sample this inverse matrix has positive diagonal elements and relatively small off-diagonal elements (Table (ref)). Therefore, the sign of the bias is mostly determined by the correlation between in-degree and $\epsilon_{i}$.} A downward (upward) bias arises if in-degree is positively correlated with an unobserved factor that negatively (positively) affects earnings.
The data suggest possible omitted factors that could explain our findings: partying and drinking. Alcohol consumption among adolescents is largely motivated by its capacity to facilitate social interactions (feldman1999alcohol; kuntsche2005young), but it may have detrimental impacts on other outcomes. We find that drinking alcohol increases friendships but lowers GPA and the odds of working in cognitively demanding jobs (Table (ref)).\footnote{We use data from the O{*}NET to construct indices of the extent to which occupations require social or cognitive skills and match these scores to a person's occupation. See Appendix (ref) for details.} Drinking also increases depression and lowers self-reported health in adulthood. However, time spent with friends is associated with more friends and better health, lowers the odds of working in jobs with high cognitive demands, but it does not lower GPA. Thus certain social behaviors, like drinking, increase friendships but lower cognitive productivity and lower health, both of which likely affect wages.
Additional results suggest that OLS is downward biased. Table (ref) shows that the addition of covariates in OLS regressions of earnings on grade in-degree increases the estimated returns to friendships. We control for education only (Column 1), and then we progressively control endowments (IQ and extroversion - Column 2), personal demographics (age, gender, race - Column 3), mean characteristics of one's peers (Column 4), grade fixed effects (Column 5) and school fixed effects (Column 6). The model with all the controls yields the largest coefficient. This evidence suggests that individual characteristics and school fixed effects capture preferences and environments that cause OLS to be downward biased.
Measurement error. Classical measurement error in friendships would attenuate the OLS coefficient. The direction and magnitude of the OLS bias depend on the ratio of the covariance between in-degree and the true measure, divided by the variance of in-degree: if the ratio is smaller than one then OLS is attenuated Bound2001. Suppose that high-engagement friendships are the “true” number of friends and grade in-degree is a poor proxy. What would the OLS bias be in this case? In our sample, the covariance between (residualized) grade in-degree and (residualized) high-engagement degree is 2.28. The (residualized) variance of grade in-degree is 8.67 (Table (ref)). Their ratio is about 0.26, which suggests that a consistent estimate could be 4 times larger than OLS, roughly 0.09, similar to our IV estimates.
Limitations. Measurement error may also come from the fact that individuals in the survey are only allowed to list up to five friends of each gender, generating censoring -- a non-classical form of measurement error. In this case our IV might be inconsistent -- an IV estimate is consistent only if the instrument is uncorrelated with measurement error Bound2001.
We end with an informal discussion of two important issues. First, do all friendships yield positive returns in the labor market? Second, what are the mechanisms by which adolescent friendships increase earnings? While we cannot fully answer these questions in a causal manner, we discuss some suggestive evidence.
Figure (ref) plots the non-parametric relationship between in-degree and earnings, for different measures of in-degree suggested by prior studies: same vs. opposite gender (McDougall2007; Hall2011), high vs. low engagement Gee2017strongties, high vs. low SES (LavySand2019; Fletcher2020; Chetty2022), and disruptive vs. non-disruptive peers carrell2018disruptivepeers. The friendships that are expected to have higher returns indeed appear to have higher returns: it pays off more to be friends with people of the same gender, to have more close friends, to have more friends who are not disruptive or come from higher SES families. However, all friendships (except for disruptive ones) appear to have positive returns, albeit smaller ones. Table (ref) confirms these descriptive patterns using OLS. Unfortunately, our instruments are not powerful enough to produce precise estimates of different types of friendships so further work is needed in this area.\footnote{Although all the first stages are strong (Table (ref)), we do not have sufficient variation to separately identify the effects of, e.g., male and female friendships.}
Why do friendships in adolescence matter for adult earnings? We do not have estimates of the causal effect of education on potential mediators, so we cannot estimate the ideal IV bounds. Instead, we summarize the suggestive evidence from OLS regressions. Friendships formed in adolescence are associated with higher likelihood of working (Column 1 of Table (ref)), consistent with the previous literature that friends help workers find jobs (Dustmann2015). Adolescent friendships are associated with a lower likelihood of working in repetitive occupations (Column 2) and a greater likelihood of working in supervisory roles (though this relationship is not statistically significant, Columns 3). Individuals with more friends are more likely to be employed in occupations that require greater social skills, which on average pay larger wages (Column 4). Individuals with more friends appear to have greater social and management skills and broader networks as adults. They have more friends in adulthood (Column 5) and are more likely to be married (Column 6). Controlling for extroversion in adolescence, those with more adolescent friends are more likely to be extroverted in adulthood (Column 7). Individuals with more friends also have greater GPAs (Columns 1 of Table (ref)), are less likely to get in trouble while they are in school (Columns 2 and 3), and ultimately are more likely to work in jobs that require higher cognitive skills (Column 4). They are also less depressed and healthier (Columns 5 and 6). Thus the returns to friendships in the labor force do not operate uniquely through social skills and networks -- friendships also help in the formation of other cognitive and non-cognitive skills that are rewarded in the labor market.
We show that individuals that have more friends in adolescence have higher earnings in adulthood, partly because they are employed in higher paying occupations that require higher social and cognitive skills, and partly because they turn into more socially connected adults that are also more extroverted.
Our results confirm recent findings emphasizing the importance of adolescence as a formative period for socio-emotional outcomes Jackson2020 and particularly for friendships Denworth2020. Our findings also suggest that when students are more similar to each other they are more likely to form friendships. Therefore, how students are allocated in groups in schools has important long-term consequences. Re-structuring classrooms to be more homogeneous in age would appear to benefit all students involved, from the point of view of friendships and adult earnings. An important direction for future research is to investigate which other contexts and student compositions are most conducive to the creation of friendships.
The importance of socialization during schooling years has further implications for higher education policy. Many colleges and universities face criticism for investing in infrastructure for non-academic, recreational facilities that are believed to contribute to increasing tuition Jacob2018college. These investments are more reasonable in the presence of high returns to socialization. Our results help rationalize why, for instance, Greek fraternities and sororities persist, despite the fact that they can detract from strictly academic endeavors. While partying may decrease education, particularly if it is associated with drinking, it does not necessarily decrease earnings. Overall if schools can promote productive social activities (like working together), it might be possible to improve both students' social connections and their educational attainment.
Like recent work (Xiang2019; Heckman2012), our findings suggest that paying excessive attention to traditional education measures like test scores might lower the long-term outcomes and well-being of individuals because they reduce investments in other important forms of human capital. They also suggest that educational interventions that are becoming common, such as remote learning, might deter from social capital formation and result in lost lifetime earnings. In contrast, interventions that target soft skills might have large returns, partly through their effects on network formation. Indeed an emerging literature shows that interventions targeting non-cognitive skills among young adults can have large returns (Katz2022, Heller2017). Our paper complements this research by documenting the importance of having friends, separately from social skills.
There are many unanswered questions that remain. For example, we don't know much about which environments best foster friendships while maintaining academic performance. We provide some evidence that not all friendships matter equally in the labor market but our evidence is only suggestive. Finally, we only track the impact of adolescent friendships -- not whether earlier friendships matter, how social networks evolve from adolescence onward and how adult networks affect labor markets. These important questions are left to future research.
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