Adolescents’ Relative Position in School and Educational Attainment : The Mediating Role of Educational Expectations

Abstract

This study examines whether and how adolescents’ relative deprivation in school is associated with their years of education by incorporating the social comparison perspective into the Wisconsin status attainment model. Using Waves 1, 2, and 4 of the National Longitudinal Study of Adolescent to Adult Health (Add Health), this study finds that adolescents who are positioned at the bottom of the economic hierarchy in school are likely to have up to one less year of education, compared to their counterparts positioned at the top of the hierarchy, when holding other variables constant. Also, by using causal mediation analyses, I find that educational expectations account for more than 20% of the relationship between adolescents’ relative deprivation and educational attainment. The sensitivity analyses are conducted to examine how robust the main findings are to the violation of the assumption used in this study. These results provide evidence showing that adolescents’ educational outcomes do not only depend on their material resources but also on their relative standing in the economic hierarchy.

INTRODUCTION

Educational attainment is a key factor in shaping an individual’s life chances (Coleman 1961). Building on Blau and Duncan’s seminal work (1967), the Wisconsin status attainment model demonstrates that one’s social origins, such as family’s socioeconomic status (SES), determine his educational attainment, and that the relationship is mediated by his educational expectations (Sewell, Haller, and Ohlendorf 1970; Sewell and Hauser 1975). While the Wisconsin model emphasizes the socialization process, such as the role of significant others’ influences, critics argue that it does not pay enough attention to the constrained opportunity structure of society (Kerckhoff 1976; Morgan 2006). The structural differences in opportunity result in the experience of relative deprivation at the individual level (Festinger 1954; Merton and Kitt 1950; Runciman 1966).

Past research on the social comparison process demonstrates that individuals’ well-being depends not only on their absolute deprivation but also on their relative deprivation through the social comparison process (Marmot 2004; Wilkinson and Pickett 2009). For example, low SES adolescents are likely to feel higher levels of anger and subsequently become more involved with delinquency and violence in schools where deprivation is more of a rarity, as opposed to schools where deprivation is common (Bernburg, Thorlindsson, and Sigfusdottir 2009). Also, students attending more competitive schools are likely to show a lower academic self-concept and poorer achievement than those who attend less competitive schools (Crosnoe 2009; Davis 1966; Marsh 1987; Owens 2010). Despite the theoretical and empirical evidence that social comparison plays a role in determining life chances, the effects of adolescents’ relative deprivation in school on later educational outcomes, independent of absolute deprivation, have not been investigated.

By incorporating the social comparison perspective into the Wisconsin status attainment model, this study aims to (a) explicitly test whether adolescents’ relative deprivation in school is associated with their educational attainment and (b) demonstrate how adolescents’ educational expectations can play a role in the process. Waves 1, 2, and 4 of the National Longitudinal Study of Adolescent to Adult Health (Add Health) are used, and the relative deprivation in school is measured on the basis of family income. This study contributes to the social comparison literature by providing evidence on the educational consequences of relative deprivation in the school context and extends the Wisconsin status attainment model by illustrating the manner in which students perceive the economic hierarchy of society.

BACKGROUND

The Social Comparison Process: Focusing on Family Income

Previous research has investigated how family income plays an important role in adolescents’ futures. First of all, according to human capital theory (Becker and Tomes 1986), investments during adolescence are closely related to adolescents’ development. Since low-income families have fewer material resources, their adolescents are more likely to have poorer cognitive skills, lower educational attainment, and worse health outcomes, compared to their counterparts in middle- or high-income families (Brooks-Gunn and Duncan 1997; Guo and Harris 2000). Also, lower family income may have negative effects on adolescents because it increases the level of parental stress and the likelihood of parental depression resulting from constrained economic resources. Parents in low-income families tend to interact and socialize less with their adolescents, and thereby do not provide enough warmth and responsiveness (Duncan et al. 1998; Yeung, Linver, and Brooks–Gunn 2002). Regarding adolescents’ educational outcomes, for example, an additional $10,000 (in 1992 and 1993 dollars) in family income is roughly associated with between .10 and .20 years of schooling after controlling for other family background characteristics (Duncan et al. 1998; Mayer 2002).¹

In spite of the voluminous literature covering the consistent effects of family income on educational attainment, most previous works only focus on the absolute level of income without clarifying the role of the relative level of income. Research on the social comparison process, however, suggests that individuals’ well-being depends not only on their material resources but also on their relative standing in the economic hierarchy (Festinger 1954; McLeod, Lawler, and Schwalbe 2014; Merton and Kitt 1950; Runciman 1966). The rationale of the argument is that since people tend to compare themselves to others in order to evaluate their own status, unfavorable social comparison stemming from a low hierarchical position may lead to less happiness, stress-related illness, and unhealthy behaviors (Firebaugh and Schroeder 2009; Luttmer 2005; Marmot 2004; Wilkinson and Pickett 2009). For example, Townsend (1987) argues that children’s relative deprivation can be more important to their outcomes than the absolute level of parental income. He posits that when children cannot have the same material resources as other children in their school or neighborhood, they can feel relatively deprived, uncomfortable, and alienated (Townsend 1987). Yet, despite the importance of this perspective, the explicit effect of relative income on children’s outcomes has been rarely assessed in empirical studies (Mayer 2002).

The Wisconsin Status Attainment Model: The Role of Educational Expectations

The Wisconsin status attainment model elaborates on Blau and Duncan’s classical status attainment model (Haller and Portes 1973; Sewell and Hauser 1975). Blau and Duncan (1967) theorize that how an individual gains status is influenced by social origins including both achieved factors and ascribed factors. The Wisconsin model distinguishes itself from Blau-Duncan’s model by incorporating social-psychological processes, which include educational expectations as a key mediating variable linking social origins and status attainment (Sewell and Hauser 1975). It is argued that educational expectations are mainly shaped by students’ significant others’ influences and students’ academic performance, which are socialization processes in the family and in school (Bozick et al. 2010; Breen and Goldthorpe 2001; Haller 1982; Karlson 2015).

Despite the wide use of the Wisconsin model, the model has been criticized for its lack of consideration of the structural constraints of society (Gambetta 1987; Kerckhoff 1976). Based on the rational choice theories of educational decision making, Morgan (1998) claims that educational expectations are rationally calculated based on one’s likelihood of success in his circumstances. That is, while the Wisconsin status attainment model posits that what the individual attains is determined by what one chooses to do, the critics argue that it is determined by what one is permitted to do and that the individual tends to expect probable outcomes given the structure externally imposed (Horan 1978; Kerckhoff 1984; Sewell et al. 2003). Sewell and his colleagues (2003) advocate the parsimony of the Wisconsin status attainment model but also admit that better measures of social stratification will help to further develop the Wisconsin model.

The Importance of School Contexts

Stratification in school has mechanisms for sorting adolescents, especially representing the socioeconomic structures of the school, thus affecting adolescents’ educational expectations. School is essentially hierarchical in nature, and thereby social comparison processes are pervasive (Davis 1966; Huguet et al. 2009; Marsh 1987; West et al. 2010). Given that students not only interact with each other but also compare and compete with others to obtain finite resources (Crosnoe 2009; Owens 2010), relative standing in the economic hierarchy can play a key role in the school context. A notable approach regarding the contextual effects of school on adolescents’ outcomes is the frog-pond perspective or big-fish-little-pond-effect (BFLPE). It suggests that poor students evaluate themselves as worse in middle- or upper-class schools, compared to lower-class schools, because upward social comparison leads them to experience negative self-evaluation and poor performance (Crosnoe 2009; Marsh 1987; Roeser, Eccles, and Sameroff 2000).²

Nevertheless, little research has directly examined students’ relative economic standing in school and its effects on their educational outcomes because such data measuring the economic hierarchy are rarely available. While previous educational research has conventionally used absolute level of family income or parental education as indicators for understanding students’ socioeconomic backgrounds, school can provide specific contexts to students that amplify the mechanisms from family income to students’ educational outcomes. For example, low income students in a high SES school may be at more risk of stigmatization and thus face greater competition for academic credentials, compared to low income students in a lower SES school, because students tend to experience more stress when they are relatively low positioned in school. In this regard, students’ relative economic standing in school and subsequent effects on their educational outcomes need to be better understood.

The Present Study

Incorporating the social comparison perspective into the Wisconsin status attainment model, I hypothesize that students who have higher relative deprivation in school are likely to have lower educational attainment, and that adolescents’ pessimistic future expectations mediate this relationship, after controlling for other confounders. In order to correctly estimate the direct and indirect effects of adolescents’ relative position in school, causal mediation analysis will be used. This study may unveil the process by which relative position is associated with educational attainment.

Hypothesis 1: Adolescents’ relative position in school (relative deprivation in Wave 1) is associated with their educational attainment (years of education in Wave 4).

Hypothesis 2: Adolescents’ educational expectations (Wave 2) mediate the relationship between relative position in school and educational attainment in young adulthood.

DATA AND METHODS

Data

To test the hypotheses, this study uses the National Longitudinal Study of Adolescent to Adult Health (Add Health). The first wave of interviews of 20,745 students in grades 7 through 12 was conducted in 1994–1995. The Add Health cohort has been followed into young adulthood with multiple interview waves (Wave 2 in 1995–1996, Wave 3 in 2001–2002, and Wave 4 in 2007–2008), with the Wave 4 survey interviewing 15,701 respondents, aged 24–32. The Add Health data covers students’ sociodemographic, familial, behavioral, academic, and school characteristics. It also provides grand sampling weights to adequately represent the target population of US adolescents in 1994–1995 by accounting for oversampling, attrition, and clustered sampling in school (Chen and Chantala 2014). Further details pertaining to the study design of the Add Health are available on the Add Health website (http://www.cpc.unc.edu/projects/addhealth).

In the present study, I analyze data from Waves 1, 2, and 4 to investigate whether adolescents’ relative position in school in Wave 1 is associated with their eventual years of education as measured at Wave 4, with consideration of educational expectations in Wave 2. To address missing values for family income and other variables, I use multiple imputation, assuming a multivariate normal distribution (mi estimate command in Stata).³ Multiple imputation enables researchers to obtain consistent and efficient estimates by maximizing the use of information and minimizing the bias of estimates (Allison 2001; Enders 2010). This study excludes senior students who were not surveyed in Wave 2. The final analytic sample consists of 12,894 observations with Wave 4 survey weights and no missing values in the educational attainment outcome, which is 82.1% of the Wave 4 sample.

Variables

I use relative deprivation (Deaton index) as a treatment to measure students’ relative position in school, on the basis of family income (in $1,000). The Deaton index (RD) of a student i was calculated as:

$$R{D}_i=\frac{1}{\mu }\ast \frac{1}{N}\sum _u\left(y_u-y_i\right),\hspace{1em}\forall \hspace{0.17em}\hspace{0.17em}{y}_u>y_i,$$

where N is the total number of students within the reference group (i.e., school) and μ is the mean income of a school (Deaton 2001; Lhila and Simon 2010). y_i is the income of the student i, y_u is the income of a student u with a higher income than student i. A student will feel more deprived as the number of students above him in school increases. Deaton index ranges from 0 to 1, with 1 indicating the highest level of relative deprivation. Given that Deaton index accounts for both upward and downward comparisons (Adjaye-Gbewonyo and Kawachi 2012), it is considered to measure relative deprivation or relative advantage.

As an outcome, respondents’ years of education in Wave 4 is used. Educational attainment is a key component of life chance, which is affected by early life conditions, such as family and school contexts, and influences the rest of life from wages and marriage, to health status and longevity (Adler et al. 1994; Morgan 2005). In Wave 4, respondents were aged 24 to 32 years old, and the range of years of education is 8 to 26 years, with the mean of 14.63 and the standard deviation of 2.65.⁴ As a mediator, respondents’ educational expectations are used. Educational expectations represent “realistic appraisals rather than idealistic goals” (Morgan 2006:1529) and are considered a key factor linking family SES and children’s educational attainment (Johnson and Reynolds 2013). Adolescents in the Add Health data in Wave 2 were asked to rate their educational expectations in the future, “ On a scale of 1 to 5, where 1 is low and 5 is high, how likely is it that you will go to college?”.

This study controls for adolescents’ individual, familial, and contextual covariates that may be associated with educational expectations and educational attainment. They include respondents’ absolute family income at Wave 1, age, sex, race/ethnicity, immigration status, parental education, family structure, and Add Health Picture Vocabulary Test (PVT) standardized score. Absolute family income (in $1,000) is measured in the parent survey in Wave 1, and is divided by the square root of the number of individuals in the household, as outlined in the Luxembourg Income Study Scale approach (Harling et al. 2014).⁵ I also control for health status and unhealthy behaviors at Wave 1, including body mass index (BMI), poor self-rated health, depressive symptoms, the number of days smoking during the past 30 days, the number of days binge drinking over the past 12 months, and the frequency of marijuana smoking during the past 30 days. In addition, I adjust for school characteristics, including type of school (0= public school; 1= private school), whether it is a public magnet school, schools’ region, urbanicity, average income, proportion of college-educated parents, the range of family income, and the number of students in school.

Analysis Plan

This study employs the conventional ordinary least-squares (OLS) models and causal mediation analysis. The causal mediation approach permits causal interpretation from the counterfactual perspective, which is also referred to as the potential outcomes framework (Rubin 1974; Winship and Morgan 2007). When two alternative states are considered, potential outcomes are the values of a unit’s outcomes under treatment and under control. From the counterfactual perspective, it is assumed that each unit has a potential outcome under each state, even though each unit is observed in only one state at any given time (Morgan and Winship 2014). The unobserved and hypothetical potential outcome is defined as the “counterfactual” outcome.

That is, in the counterfactual framework, causal estimands are considered “comparisons of the potential outcomes that would have been observed under different exposures of units to treatments” (Little and Rubin 2000:122). However, it is impossible to observe both potential outcomes at once because one of the potential outcomes is always missing in real data. Each unit receives only one of the states, under treatment or under control, and therefore the unit level causal effect cannot be estimated. This is referred to as the fundamental problem of causal inference (Holland 1986). Instead of estimating the unit level causal effect, the counterfactual framework estimates the average causal effect among all units in the population by evaluating the mean value of the outcomes in both states.

The causal mediation approach with the counterfactual framework focuses on the potential mediator and outcomes (Imai et al. 2011; Imai, Keele, and Tingley 2010; VanderWeele 2015). First, the indirect effect or causal mediation effect for each unit i can be defined as:

$${\delta }_i\left(t\right)\equiv Y_i\left(t,M_i\left(1\right)\right)-Y_i\left(t,M_i\left(0\right)\right),$$

for each treatment status t = 0, 1. This quantity equals the change in the outcome variable corresponding to a change in the mediator from the value, M_i(0), to the value, M_i(1), holding the treatment status at t. In detail, M_i(0) is the value that would be realized under the control condition, and M_i(1) is the value that would be observed under the treatment condition. If the treatment does not have any influence on the mediator, the effect of causal mediation is zero.

Second, direct effect of the treatment can be defined as:

$${\zeta }_i\left(t\right)\equiv Y_i\left(1,M_i\left(t\right)\right)-Y_i\left(0,M_i\left(t\right)\right),$$

for each treatment status t = 0, 1. The direct effect of causal mediation analysis is considered as the change in the outcome variable corresponding to a change in the treatment status (i.e., t = 0 vs. t = 1) while holding the mediator constant at M_i(t). The direct effect indicates all other mechanisms from the treatment to the outcome, except the one through the specific mediator, M_i. Since we cannot observe the actual outcome and counterfactual outcome at the same time in an observational study, as discussed above, the average causal mediation effect (ACME) $\overline{\delta }\left(t\right)$ and the average direct effect (ADE) $\overline{\zeta }\left(t\right)$ are estimated, which are the population average of these causal mediation (indirect) and direct effect as follows (Tingley et al. 2014).

$$\begin{gathered} \text{ACME}:\hspace{0.17em}\overline{\delta }\left(t\right)\equiv E\left(Y_i\left(t,M_i\left(1\right)\right)-Y_i\left(t,M_i\left(0\right)\right)\right), \\ \text{ADE}:\hspace{0.17em}\overline{\zeta }\left(t\right)\equiv E\left(Y_i\left(1,M_i\left(t\right)\right)-Y_i\left(0,M_i\left(t\right)\right)\right). \end{gathered}$$

Figure 1 highlights both the ACME and ADE, both of which are useful when direct/indirect effects and the proportion of mediated effects are of primary interest to the research. In Figure 1, adolescents’ relative deprivation (Deaton index) in Wave 1 is denoted as treatment (T), educational expectations in Wave 2 as a mediator (M), and years of education as an outcome of interest (Y). The ACME of adolescents’ relative deprivation represents the effect mediated through educational expectations on years of education (represented by path 2*3). All other causal mechanisms are eliminated by holding the treatment status at t and changing only the mediator. The ADE of relative deprivation on years of education is not mediated through educational expectations (represented by path 1).

Figure 1.

Causal Diagram of the Conceptual Model in This Study

Note: Dotted lines (path 2*3) indicate the average causal mediation effect (ACME) and a solid line (path 1) represents the average direct effect (ADE) of relative deprivation.

Since the treatment in this study, relative deprivation, is a continuous variable, it is best to use two values that are the most typical or substantively meaningful (Imai et al. 2011; Tingley et al. 2014). As the two values for relative deprivation, this study uses 0 and 1 given that the relative deprivation index can range from 0 to 1. This makes the greatest possible contrast between students who are positioned at the top of the economic hierarchy and students who are positioned at the bottom of the hierarchy (Pais 2017). I use the medeff command in Stata to estimate the ACMEs and ADEs.

Sensitivity analysis of causal mediation analyses

In addition to the advantage that the causal mediation approach allows for causal interpretation from the counterfactual perspective, another benefit of the approach over conventional OLS models is that it enables researchers to conduct sensitivity analyses in order to check the robustness of results. The estimates of the causal mediation analyses, ACME and ADE, are based on the sequential ignorability assumption, which represents two “no omitted variables” assumptions: one for the relationship between the treatment and the outcome, and another for the relationship between the mediator and the outcome. Since these assumptions are seldom met in observational studies, and thus the estimates of the causal mediation analyses might be biased, sensitivity analyses should be conducted to examine how robust the estimates of direct/indirect effects are to the violation of the assumption (Hicks and Tingley 2012; Imai et al. 2011).

To be more specific, when both the mediator and outcome variables are continuous, two linear regression lines can be fitted (Hicks and Tingley 2011).

$$M_i={\alpha }_2+{\beta }_2{T}_i+{\delta }_2^T{X}_i+{\epsilon }_{i2}$$

$$Y_i={\alpha }_3+{\beta }_3{T}_i+\gamma M_i+{\delta }_3^T{X}_i+{\epsilon }_{i3}$$

, where T_i represents a binary treatment indicator, M_i represents the mediator, and Y_i is the outcome variable. The sequential ignorability assumption implies that the sensitivity parameter (ρ), which is the correlation between the error for the mediator model (ε_i2) and the error for the outcome model (ε_i3), equals zero.

$$\rho \equiv Corr\left({\epsilon }_{i2},{\epsilon }_{i3}\right)$$

, where −1 < ρ < 1 (Imai, Keele, and Yamamoto 2010). If there are unobserved variables that affect both the mediator and the outcome, the sensitivity parameter (ρ) will not equal zero because the unobserved variables are part of the two error terms (Imai, Keele, and Tingley 2010). This condition can introduce bias into the results of mediation analyses, which is likely to happen in observational studies. To present how sensitive the original findings are to the violation of the sequential ignorability assumption, I draw figures for both causal direct and mediation effects (ADEs and ACMEs) in the Results section, with the use of the medsens commansd in the statistical software package, R.

In practice, I first use OLS regression to investigate whether one’s relative deprivation in school in Wave 1 is related to his educational expectations in Wave 2, which is the key mediator in this study. Second, I employ OLS regression to determine whether relative deprivation during adolescence is associated with later educational attainment, and whether the hypothesized mediator, educational expectations, does in fact mediate the relationship. Third, I estimate the average causal direct and average causal mediation effects (ADEs and ACMEs). Causal mediation analysis allows me to calculate the proportion of the total effect mediated by decomposing the total effects of relative deprivation into direct and indirect effects. Fourth, I conduct sensitivity analyses of the causal mediation approach to see how robust the ADEs and ACMEs are to violations of the sequential ignorability assumption. Fifth, by conducting two separate causal mediation analyses, I examine two alternative mediators --students’ GPA and having trouble with school in Wave 2-- that may link relative deprivation to educational attainment as auxiliary analyses. This part of the analysis will contribute to a better understanding of how students’ relative deprivation is transmitted to their educational attainment.

RESULTS

Descriptive Statistics

Table 1 provides the means and standard deviations of the variables used in this study (N= 12,894). It reveals that the mean years of education in Wave 4 is 14.63 (standard deviation is 2.65) and the mean of adolescents’ educational expectations in Wave 2 is 4.10 (standard deviation is 1.22). Mean of relative deprivation (Deaton index) at Wave 1 is .37 (standard deviation is .26). The mean of family income (number of family members adjusted) is $22.00 (standard deviation is $25.45, in thousands). The correlation matrix indicates that adolescents’ educational expectations are closely associated with both absolute and relative economic standings, as well as their later educational attainment (not shown but available upon request). The proportion of college-educated parent is .33, and parental educational expectations in Wave 1 are 2.30 (standard deviation is .71). Regarding school characteristics, the mean of average family income for the school is $45.99 (in thousands) and the mean of the proportion of college-educated parents is .32. The results of the VIF (variance inflation factor) test in Stata suggest that multicollinearity is less of a concern, based on the conventional threshold VIF of 10.

Table 1.

Descriptive statistics, National Longitudinal Study of Adolescent to Adult Health (Add Health), Wave 1 (W1), Wave 2 (W2), and Wave 4 (W4)

Variables	Wave	Mean or Proportion	Standard deviation
Exposure
Relative deprivation (Deaton index) (range: 0 – 1)	1	.37	.26
Mediator
Educational expectations (range: 1 – 5 highest)	2	4.10	1.22
Outcome
Years of education (range: 8 – 26 years)	4	14.63	2.65
Individual and familial confounders
Family income (# of family member adjusted) (in thousand $)	1	22.00	25.45
Age	1	15.34	1.60
Female	1	.53	-
Race and ethnicity
Non-Hispanic White	1	.55	-
Non-Hispanic Black	1	.22	-
Hispanic	1	.15	-
Others	1	.07	-
Immigrant (1= non-US born)	1	.06	-
Family structure
Two biological parents	1	.52	-
Two parents	1	.19	-
Single parents	1	.24	-
Other family	1	.05	-
Parental educational expectations (range: 1 – 3 highest)	1	2.30	.71
Parental education (1= college completion or more)	1	.33	-
Add Health Picture Vocabulary Test standardized score	1	100.51	15.42
Body mass index (BMI)	1	22.51	4.51
Poor self-rated health	1	.07	-
Depressive symptoms (range: 1 – 30 highest)	1	6.81	4.74
# of days of smoking during past 30 days	1	4.05	9.31
# of days of binge drinking over the past 12 months	1	1.11	2.10
Frequency of marijuana smoking during the past 30 days	1	1.79	17.81
School confounders
Private school	1	.07	-
Public magnet school	1	.12	-
Region of school
West	1	.23	-
Midwest	1	.26	-
South	1	.38	-
Northeast	1	.13	-
Urbanicity of school
Urban	1	.30	-
Suburban	1	.53	-
Rural	1	.17	-
Average family income (range: $12.3 – $176, in thousand $)	1	45.99	21.89
Proportion of college-educated parents (range: 0 – 1)	1	.32	-
Range of family income	1	182.56	109.50
Number of students in school	1	328.14	448.48
Number of Sample After 30 Multiple Imputation		12,894

Association between Relative Deprivation and Educational Expectations during Adolescence

Table 2 presents the estimates of relative deprivation on educational expectations. The expectations observed in Wave 2 are a mediator in this research linking the relative deprivation and the outcome, which is the years of education. Model 1 in Table 2 reports a bivariate relationship between relative deprivation (Deaton index) and educational expectations during adolescence without adjusting for any variables. In Model 1, a one standard deviation increase in the Deaton index (.26) is associated with a .26 point drop in educational expectation, relative to a mean of 4.10 and a standard deviation of 1.22 (−.26= .26*(−.980)). In Model 2 in Table 2, a one standard deviation increase in the Deaton index is associated with a .15 point drop in educational expectation. Approximately 42% of the total effect of the Deaton Index is accounted for by confounders. These results suggest that adolescents’ higher relative deprivation (Deaton index) in school is significantly associated with lower educational expectations even after adjusting for individual, familial, and school factors. Appendix Table 1 provides the coefficients of all variables.

Table 2.

Ordinary Least Squares (OLS) Estimates of the Effects of Relative Deprivation (Deaton Index) on Educational Expectations during Adolescence

	Educational Expectations (W2)
Variables	Model 1	Model 2
Exposure (W1)
Relative Deprivation (Deaton index)	−.980*** (.065)	−.573*** (.087)
Including confounders (W1)	No	Yes
Observations	12,894	12,894

Note: Add Health (W1 and W2). Robust standard errors in parentheses *** p< .001 (two-tailed test). Thirty multiple imputed data sets are used.

Association between Relative Deprivation during Adolescence and Educational Attainment in Young Adulthood

Table 3 presents the estimates of the effects of relative deprivation on years of education after adjusting for all confounders in Wave 1. Model 1 reports the estimate of relative deprivation, controlling for the confounders, which indicates that a one standard deviation increase in the Deaton index (.26) is associated with .29 fewer years of education (−.29= .26*(−1.097)), relative to a mean of 14.63 and a standard deviation of 2.65. In Model 2 in Table 3, when including the mediator, educational expectations in Wave 2, the estimate of relative deprivation is decreased to −.836 but is still statistically significant. A one standard deviation increase in the Deaton index is associated with decreases of .22 years of education (−.22= .26*(−.836)). Model 2 also shows that a one standard deviation increase in educational expectations in Wave 2 (1.22) is related to .56 more years of education. Table 3 shows that adolescents’ higher relative deprivation in school is negatively associated with their educational attainment, even after adjusting for other confounders (Hypothesis 1). Appendix Table 2 provides the coefficients of all variables.

Table 3.

Ordinary Least Squares (OLS) Estimates of the Effects of the Relative Deprivation (Deaton Index) during Adolescence on Years of Education in Young Adulthood

	Years of Education (W4)
	Model 1	Model 2
Exposure (W1)
Relative deprivation (Deaton index)	−1.097*** (.172)	−.836*** (.160)
Mediator (W2)
Educational expectations (W2)	-	.461*** (.025)
Including confounders (W1)	Yes	Yes
Observations	12,894	12,894

Note: Add Health (W1, W2, and W4). Robust standard errors in parentheses *** p< .001 (two-tailed test). Thirty multiple imputed data sets are used.

Estimation of the Causal Mediation Models: Average Direct and Average Causal Mediation Effects (ADEs and ACMEs)

Drawing on the causal mediation models, Table 4 presents the estimated average causal direct effect (ADE, $\overline{\zeta }\left(t\right)$) and average causal mediation effect (ACME, $\overline{\delta }\left(t\right)$) of relative deprivation on years of education. The mediator is adolescents’ educational expectations measured in Wave 2, which is considered to link the treatment (relative deprivation during adolescence) and the outcome (years of education in young adulthood). Since the medeff command in Stata is not compatible with multiple imputed data sets, I manually conducted the same analyses 30 times in order to obtain estimates of 30 imputed data sets. Thus, ADE, ACME, and total effect in Table 4 are averages of the 30 estimates of imputed data.

Table 4.

Estimated Causal Effects (ADEs and ACMEs) of Relative Deprivation during Adolescence on the Years of Education in Young Adulthood

Effect	Mean	[95% Confidence Interval]
Average Direct Effect, $\overline{\zeta }\left(t\right)$, ADE	−.806	−1.078	−.550
Average Causal Mediation Effect, $\overline{\delta }\left(t\right)$, ACME	−.254	−.331	−.178
Total Effect	−1.060	−1.318	−.810
% of Total Effect Mediated	24.0%	18.2%	30.4%

Note: Add Health (N= 12,894). ADE, ACME, and Total effect are average estimates of 30 multiple-imputed data sets. The mediator represents adolescents’ educational expectations in Wave 2. All confounders in Wave 1 are included in the model.

The total effect in Table 4, which is the average treatment effect of the highest relative deprivation on the outcome compared to the lowest relative deprivation, is −1.060. It suggests that, when holding others constant, students who experience the most relative deprivation are likely to have one less year (−1.060) of education, compared to those students who experience the least relative deprivation. The estimate of the ADE, $\overline{\zeta }\left(t\right)$, equals −.806, while the estimate of the ACME, $\overline{\delta }\left(t\right)$, through the educational expectations in Wave 2 equals −.254. This indicates that approximately 24.0 percent of the relative deprivation effects on years of education is mediated through educational expectations (Hypothesis 2).⁶

Sensitivity Analyses

Sensitivity analyses examine how robust the results are to violation of the sequential ignorability assumption, which is a unique advantage of the causal mediation model. Figure 2 presents the results of the sensitivity analysis with the sensitivity parameter (ρ) on the X-axis. The sensitivity parameter (ρ) is the correlation between error terms for the mediator and outcome models, which equals zero under the sequential ignorability assumption.⁷ The dashed horizontal lines represent the observed direct effect (the left panel) and the indirect effect (the right panel) of relative deprivation on educational attainment. The Y-axis represents the range of potential direct and indirect effects. The curvilinear line and the grey region (95% confidence intervals) in Figure 2 denote the results from the sensitivity analyses for each value of the sensitivity parameter (ρ). The left panel shows the average direct effect (ADE) as a function of ρ, and the right panel shows the average causal mediation effect (ACME) as a function of ρ.

Figure 2.

Average Causal Direct Effect (ADE) and Causal Mediation Effect (ACME) of Relative Deprivation (Deaton Index) on Years of Education as a Function of The Sensitivity Parameter (ρ)

Note: the grey region in the plot indicates the 95% confidence intervals for ρ, which is the correlation between the error for the mediator model and the error for the outcome model.

The results of the sensitivity analyses provide two important findings. First, when the sequential ignorability is assumed to hold (i.e., ρ = 0), both the ADE and ACME of relative deprivation on educational attainment are statistically significant and negative, which are consistent with the main results in Table 4. Nevertheless, it should be noted that the sequential ignorability assumption is seldom met in observational studies, and some omitted variables bias the ADE and ACME estimates.

Second, while the original finding about the negative ADE is relatively robust to the violation of the sequential ignorability assumption, that of the negative ACME is more sensitive to the violation. In the left panel of Figure 2, when ρ is lower than −0.4, the estimate of the ADE is non-significant; when ρ reaches −0.6, the estimate of the ADE becomes positive. In the right panel of Figure 2, ρ should be less than 0.2 to conclude that the true ACME of relative deprivation on years of education is negative and statistically significant like the estimated ACME in Table 4. Thus, the findings on ACME estimates require careful interpretation.

The true value of the sensitivity parameter (ρ) is unknown, and there is no absolute threshold of the parameter to conclude that the original finding is valid (Imai, Keele, and Tingley 2010). Nevertheless, if students’ unmeasured confounders lead them to have higher educational expectations and also to pursue more educational attainment, these confounders will be reflected as a positive correlation between the error terms for the mediator model and the outcome model (i.e., 0 < ρ < 1) (Imai et al. 2011). In sum, in the presence of omitted variables, while the ADE of relative deprivation on educational attainment is fairly robust, the ACME of relative deprivation mediated through educational expectations is more sensitive.

Auxiliary Analyses on the Mediator

In the previous section, I showed that adolescents’ educational expectations account for approximately 24 percent of the effects of relative deprivation as a mediator, as seen in Table 4. In this section, I further analyze the mediating effects of the two alternative mediators and compare them with those of educational expectations in order to better understand the mechanism from the relative position to educational attainment. Since the causal mediation approach allows researchers to analyze one mediator at a time, I estimate the effects of the alternative mediators in two separate models. Two mediators are students’ average GPA and having trouble with school in Wave 2. I replicate the analyses used in Table 4 with each mediator, respectively.

Both alternative mediators represent aspects of students’ lives in school, which might link students’ relative position and educational attainment. The average GPA variable is calculated by students’ grades in classes for which data is available, including English, mathematics, history, and science. The values range from one, lowest score, to four, highest score. Having trouble with school is operationalized by using four variables, such as “how often have you had trouble getting along with your teachers,” “paying attention in school,” “getting your homework done,” and “getting along with other students.” The values range from zero (never) to four (every day), and the average value of the four questions is used in the analyses.

Drawing from causal mediation analyses, Figure 3 presents the mediated percentages through the two alternative mediators, as well as that through the original mediator, educational expectations. In Figure 3, I note that the mediated percentage through educational expectations is 24.0%, as seen in Table 4, which indicates that more than one-fifth of the total effect of relative deprivation on educational attainment is mediated through educational expectations. Separate models using the alternative mediators report that the percentage mediated through average GPA is 9.5% and that concerning having trouble with school is 2.9%. Both alternative mediators are statistically significant (p< .001) although their magnitudes are noticeably smaller than those of educational expectations. Each model does not take into account other mediators but holds others constant. In sum, compared to alternative school-related variables, students’ educational expectations better explain the association between relative position and educational attainment.

Figure 3.

Mediated Percentages through Educational Expectations, Having Troubles in School, and Average GPA in Wave 2

Note: Total effect is the effect of relative deprivation on the years of education. Three separate causal mediation models were conducted with each mediator.

DISCUSSION

By incorporating the social comparison perspective into the Wisconsin status attainment model, I investigated whether adolescents’ relative position in the economic hierarchy in school is related to their eventual educational attainment. I also examined how that process plays out by highlighting the mediating role of adolescents’ educational expectations.

Based on the findings from the causal mediation analyses of Add Health data, I revisit the first hypothesis: adolescents’ relative position in school (relative deprivation in Wave 1) is associated with their educational attainment (years of education in Wave 4). The results of this study suggest that students who experience higher relative deprivation are likely to have lower years of education when holding other variables constant. That is, regardless of his actual family income and other characteristics, a student who is positioned at the bottom of the economic hierarchy in school tends to have one less year of education than his counterpart positioned at the top of the hierarchy. Additional stratified models by family income (i.e., low- and high-income groups) also found that students’ relative economic standing matters among both low- and high-income groups (not shown but available upon request). In sum, individuals’ educational attainment does not only depend on their absolute level of family income but also on their relative standing in the economic hierarchy.

Also, the findings of mediation analyses answer the second hypothesis: adolescents’ educational expectations (Wave 2) mediate the relationship between relative position in school and educational attainment in young adulthood. The results show that educational expectations explain approximately 24% of the effects of relative deprivation on eventual educational attainment, suggesting that the effect of relative deprivation is not only direct but also indirect through adolescents’ educational expectations. This indicates that adolescents’ relative position in school as a structural constraint is one of the determinants of educational expectations, which then affect educational attainment. By conducting the sensitivity analyses, which is a unique advantage of the causal mediation approach that conventional OLS models do not have, I demonstrate how robust the findings are to the potential violation of the sequential ignorability assumption used in the casual mediation approach. While ADEs are relatively robust to the omitted variables, ACMEs are more sensitive to the potential omissions. As auxiliary analyses, I also show that although students’ academic abilities (i.e., GPA) and their having troubles in school are both statistically significant mediators linking their relative deprivation and educational attainment, the magnitude of the mediated effects is, in both cases, notably smaller than that of educational expectations.

The current study contributes to the previous research in three ways. First, the findings lend support to the social comparison theory by showing that individuals’ educational attainment depends on their relative deprivation in the economic hierarchy, as well as on their absolute deprivation (Festinger 1954; Marmot 2004; Merton and Kitt 1950; Runciman 1966; Wilkinson and Pickett 2009). While existing research has thoroughly documented the relationship between the absolute level of income and adolescents’ educational attainment (Brooks-Gunn and Duncan 1997; Hill and Duncan 1987), this study provides evidence that adolescents’ relative deprivation in school is independently associated with their educational outcomes, even after accounting for their absolute level of income. The findings of this study have further implications for research on the frog-pond perspective or BFLPE (Crosnoe 2009; Marsh 1987), providing evidence that students’ low standing in the economic hierarchy is negatively associated with their educational expectations and attainment. That is, while higher SES schools provide a better quality of education to poor students, they may also create disadvantages that poor students in low SES schools do not experience (Crosnoe 2009).

Second, this study suggests that students’ educational expectations are influenced by their views of constrained opportunity structure, which have been underestimated in the Wisconsin status attainment model. As previous studies using the Wisconsin model have proven, interpersonal relationships with significant others, such as parents’ educational expectations, are important determinants of educational expectations (i.e., socialization process) (Bozick et al. 2010; Karlson 2015). However, it appears that adolescents also look around at their current circumstances and acquire a sense of their place in society, all of which contribute to their educational expectations. The relative positions of family income in school may allow adolescents to understand their relative standing in the hierarchy and their likelihood of future success. That is, relative position in the economic hierarchy is an important but neglected structural constraint that determines adolescents’ expectations for the future, as well as their educational attainment. These findings support economic inequality research suggesting that adolescents’ low economic position tends to heighten their feelings of economic marginalization, which makes their future expectations more pessimistic (Cherlin, Ribar, and Yasutake 2016; Lewis 1966; Wilson 1987).

Third, as an analytical contribution, this study appropriately defines students’ reference groups by relying on the institutional boundaries of schools. In previous research, measures of relative deprivation are usually unavailable or inappropriate because of the difficulty in defining reference groups (Deaton 2001). By operationalizing adolescents’ relative deprivation in school vis a vis family income, however, this study illuminates how students’ relative standing in a small unit – the school – is related to educational expectations and attainment. Since social comparisons are generally considered to occur in small units (Messner and Tardiff 1986; Runciman 1966), schools serve as a place where both favorable and unfavorable comparisons occur, and thus school is an ideal place for observing the social comparison process. In sum, examining the social comparison process in an institutional context (i.e., school) provides a novel research setting with respect to reference group.

A few limitations of this study should be acknowledged. First, drawing on social comparison theory, this study assumes that students in school compare themselves to each other. However, data that supports this assumption is not available. Add Health does not provide data on the degree to which students actually compare themselves to their fellow students in school and what their reference groups are. If students only compare themselves within their small friendship networks, they would be relatively more homogenous in economic status, which may decrease both favorable and unfavorable comparisons. Nevertheless, as Crosnoe (2009) and Owens (2010) found that low-SES students are more disadvantaged in high-SES schools, compared to low-SES students in low-SES schools, it might be reasonable to assume that students perceive their relative standing in their schools and react accordingly. Also, although school class is a more meaningful reference group for most students than the school as a whole, class data is not available within Add Health data.

Second, although this study takes parents’ and students’ educational expectations as well as other education-related variables into account, there might be unobserved confounders. For example, both educational expectations and attainment can be affected by guidance support in school, the number of college-educated people in students’ close networks, and students’ alternative career plans apart from going to college. Also, relative deprivation at earlier and later stages could impact individuals’ educational expectations in adolescence and educational attainment in adulthood, and students might graduate from other schools after the Wave 2 survey, which can bias the results. Moreover, this study is subject to the self-selection issue, in that parents may select the schools that best benefit their children (Sharkey and Elwert 2011). These factors are not considered in this study because of data limitations.

Third, the sensitivity analysis used in this study allows researchers to examine the sensitivity to the possible presence of omitted pre-treatment confounders, but not intermediate confounders, which confound the association between the mediator and the outcome (Imai et al. 2011). Although it is useful to quantify the degree of sensitivity to the omitted pre-treatment confounders, the intermediate confounders may also bias the results. Lastly, since the measure is empirically defined, the measure of relative deprivation (Deaton index) may be biased when the analytic sample does not represent the population due to sampling error.

Despite these limitations, this study provides new potential approaches to considering individuals’ relative standing in school that should be addressed in future research on educational attainment. From a policy perspective, this study advances our understanding of how adolescents differently perceive impoverishment or affluence depending on their standing. The findings of this study suggest that policy can be effectively implemented in the context of the school. For example, if students with low social standing tend to view themselves negatively and have low educational expectations, school-based mentoring programs could help them to enhance their feeling of self-esteem. Such interventions could especially help those who, while not living in poverty per se, are suffering from low relative standing. These interventions can have synergic effects with other socioeconomic policies, such as those relating to poverty, in improving adolescents’ life chances.

Appendix

Appendix Table 1.

OLS Estimates of the Effects of Relative Deprivation (Deaton Index) on Educational Expectations during Adolescence, Add Health (W1 and W2)

	Educational Expectations (W2)
Variables	Model 1 in Table 2	Model 2 in Table 2
Exposure (W1)
Relative deprivation (Deaton index)	−.980*** (.065)	−.573*** (.087)
Confounders (W1)
Individual/familial Characteristics
Family income (# of family member adjusted) (in thousand $)		−.001 (.001)
Age		−.032** (.011)
Female (= 1)		.336*** (.029)
Race/Ethnicity (ref: NH-White)
NH-Black		.189*** (.053)
Hispanic		−.050 (.060)
Others		.189** (.063)
Immigrants (= 1)		.097 (.078)
Family Structure (ref: two biological parents)
Two parents		−.093* (.040)
Single parents		−.032 (.042)
Other family		−.256** (.081)
College educated parents (= 1)		.245*** (.035)
AH-PVT score		.011*** (.001)
Parental educational expectations		.305*** (.027)
Body mass index (BMI)		−.001 (.003)
Poor self-rated health (= 1)		−.232*** (.062)
Depressive symptoms		−.029*** (.004)
Number of days of smoking		−.016*** (.002)
Number of days of binge drinking		−.014 (.008)
Frequency of marijuana smoking		.001 (.001)
School Characteristics
Average family income (in thousand $)		.000 (.001)
Proportion of college-educated parents		.596*** (.139)
Private schools (= 1)		.172** (.053)
Public magnet school (= 1)		−.144* (.059)
Region of school (ref: West)
Midwest		.038 (.050)
South		.054 (.052)
Northeast		.052 (.055)
Urbanicity of school (ref: Urban)
Suburban		.083* (.037)
Rural		.088 (.049)
Number of students		.000 (.000)
Range of family income		.000* (.000)
Constant	4.408*** (.027)	2.565* (.234)
Observations	12,894	12,894

Note: Robust standard errors in parentheses *** p< .001, ** p< .01, * p< .05 (two-tailed test). Thirty multiple imputed data sets are used.

Appendix Table 2.

OLS Estimates of the Effects of Relative Deprivation on Years of Education, Add Health (W1, W2, and W4)

	Years of Education (W4)
Variables	Model 1 in Table 3	Model 2 in Table 3
Exposure (W1)
Relative deprivation (Deaton index)	−1.097*** (.172)	−.836*** (.160)
Mediator (W2)
Educational expectations		.461*** (.025)
Confounders (W1)
Individual/familial Characteristics
Family income (# of family member adjusted) (in thousand $)	.004 (.002)	.004* (.002)
Age	.070*** (.017)	.085*** (.017)
Female (= 1)	.739*** (.054)	.584*** (.054)
Race/Ethnicity (ref: NH-White)
NH-Black	.227** (.085)	.142 (.084)
Hispanic	.001 (.106)	.023 (.102)
Others	.192 (.132)	.105 (.133)
Immigrants (= 1)	.556*** (.147)	.510*** (.141)
Family Structure (ref: two bio parents)
Two parents	−.345*** (.072)	−.303*** (.070)
Single parents	−.103 (.074)	−.090 (.072)
Other family	−.532*** (.133)	−.415** (.132)
College educated parents (= 1)	.824*** (.074)	.711*** (.073)
AH-PVT score	.045*** (.002)	.040*** (.002)
Parental educational expectations	.428*** (.043)	.287*** (.046)
Body mass index (BMI)	−.010 (.006)	−.010 (.006)
Poor self-rated health (= 1)	−.283** (.106)	−.177 (.105)
Depressive symptoms	−.033*** (.003)	−.020** (.007)
Number of days of smoking	−.031*** (.003)	−.028*** (.003)
Number of days of binge drinking	−.011 (.014)	−.006 (.013)
Frequency of marijuana smoking	−.002* (.001)	−.003* (.001)
School Characteristics
Average family income (in thousand $)	.005 (.003)	.005 (.002)
Proportion of college-educated parents	1.648*** (.278)	1.374*** (.268)
Private school	.091 (.106)	.011 (.102)
Public magnet school	−.156 (.104)	−.091 (.102)
Region of school (ref: West)
Midwest	.040 (.090)	.022 (.086)
South	.121 (.085)	.095 (.082)
Northeast	.343** (.098)	.322** (.094)
Urbanicity of school (ref: Urban)
Suburban	.031 (.068)	−.009 (.067)
Rural	.034 (.086)	−.008 (.083)
Number of students	.000* (.000)	.000* (.000)
Range of family income	.001* (.000)	.000 (.000)
Constant	7.271*** (.421)	6.098*** (.414)
Observations	12,894	12,894

Note: Robust standard errors in parentheses *** p< .001, ** p< .01, * p< .05 (two-tailed test). Thirty multiple imputed data sets are used.

Appendix Table 3.

Comparison of the Actual Full Sample and Analytic Sample

	Mean or Proportion
Selected key variables	Actual full sample (non-imputed) a	Analytic sample (non-imputed) b
Years of education	14.67	14.71
Educational expectations	4.09	4.10
Relative deprivation (Deaton index)	.36	.36
Family income (family member adjusted)	22.30	22.50
Age in Wave 1	15.64	15.32
Female	0.53	0.53
NH-White	0.53	0.54
NH-Black	0.21	0.20
Immigrant (1= non-US born)	0.06	0.06
Family structure (1= two bio parents)	0.52	0.54
Parental educational expectation	2.30	2.30
Parental education	0.33	0.34
Add Health PVT score	100.59	100.79
Body mass index (BMI)	22.62	22.47
Poor self-rated health (1= poor health)	0.07	0.07

^aActual full sample: Respondents in Wave 4 (not restricted in any way; not imputed)

^bAnalytic sample: Respondents in Wave 4 that surveyed in both Wave 1 and Wave 2 with non-missing outcome and survey weight variables (not imputed)