Do Well-off Families Compensate for Low Cognitive Ability? Evidence on Social Inequality in Early Schooling from a Twin Study

Abstract

This article bridges the literature on educational inequality between and within families to test whether high–socioeconomic status (SES) families compensate for low cognitive ability in the transition to secondary education in Germany. The German educational system of early-ability tracking (at age 10) represents a stringent setting for the compensatory hypothesis. Overall, previous literature offers inconclusive findings. Previous research between families suffers from the misspecification of parental SES and ability, while most within-family research did not stratify the analysis by SES or the ability distribution. To address these issues, I draw from the TwinLife study to implement a twin fixed-effects design that minimizes unobserved confounding. I report two main findings. First, highly educated families do not compensate for twins’ differences in cognitive ability at the bottom of the ability distribution. In the German system of early-ability tracking, advantaged families may have more difficulties to compensate than in countries where educational transitions are less dependent on ability. Second, holding parents’ and children’s cognitive ability constant, pupils from highly educated families are 27% more likely to attend the academic track. This result implies wastage of academic potential for disadvantaged families, challenging the role of cognitive ability as the leading criterion of merit for liberal theories of equal opportunity. These findings point to the importance of other factors that vary between families with different resources and explain educational success, such as noncognitive abilities, risk aversion to downward mobility, and teachers’ bias.

Keywords

educational inequalities cognitive ability tracking twins fixed effects compensation within-family inequality

Cognitive ability is one of the strongest predictors of learning and educational outcomes (Deary et al. 2007; Deary and Johnson 2010).¹ Yet cognitive ability does not necessarily lead to future educational achievement. Disadvantaged children with similar academic potential/ability as advantaged children have systematically fewer chances for educational success (Bukodi, Erikson, and Goldthorpe 2014; Jackson 2013; Papageorge and Thom 2018). Research on inequality between families argues that this gap is particularly large among children with low scholastic ability, because well-off parents tend to use compensatory strategies to offset the effect of low ability (Bernardi 2014; Esping-Andersen and Cimentada 2018).

Do similar compensation mechanisms also work within families? Building on the classic microeconomics literature on intrahousehold allocation of resources (Behrman, Pollak, and Taubman 1982), Conley (2008) hypothesizes that high–socioeconomic status (SES) families are more prone to compensate for siblings’ differences in endowments/traits. Thanks to their extensive pool of cultural and economic resources, siblings with lower ability in high-SES families can reach the same educational outcomes as their more gifted siblings.

Previous studies offer inconclusive and limited evidence on the compensatory hypothesis for four reasons. First, between-family models misspecify the total effect of social background (underestimation) and academic ability (overestimation) due to unobserved heterogeneity (Jæger 2011). Second, between-family models assume, by design, that siblings achieve the same educational outcomes, but this is not necessarily the case (Conley 2004). Third, within-family research has focused on the effect of birth weight on educational outcomes as a proxy of early ability, rather than using more direct measures of academic ability (Grätz and Torche 2016). Fourth, most previous studies using sibling/twin fixed-effects estimators do not stratify analyses by parental SES or across the absolute endowment distribution. Thus, whether high-SES families compensate for children’s low academic ability is an open empirical question.

To address these limitations of previous research, I use twin fixed effects to test whether high-SES parents compensate for children’s low cognitive ability in the transition to secondary education. Twins are born under the same parental circumstances and share at least 50 percent of their genetic makeup, thus ruling out most sources of confounding in between-family and sibling models. I also look at the heterogeneity of the effect of cognitive ability on track choice across parental SES and the absolute ability distribution. The compensatory hypothesis should be tested at the bottom of the ability distribution.

This article makes the twofold contribution of bridging the literature on between- and within-family inequality and answering two novel research questions: (1) How does parental SES moderate the effect of within-family differences in cognitive ability on track choice? (2) How do high-SES families compensate for within-family differences in cognitive ability at the bottom of the absolute ability distribution?

To answer these questions, I use the first wave of the TwinLife study carried out in 2014–15 (Hahn et al. 2016), a representative survey of the German population with a sample of same-sex 11-year-old twins at grades 5 and 6. The German educational system of early-ability tracking is an interesting scenario for testing the compensatory hypothesis. Because teachers recommend tracks on the basis of observed performance, parents may have less discretion to influence track decisions for their low-academic-ability children. Hence, the German case provides a stringent test of the compensatory hypothesis in comparison to educational systems without early tracking (Conley and Glauber 2008).

Results show that highly educated families do not compensate for children’s low academic ability at the bottom of the ability distribution. This may be due to the fact that, in the German educational system, tracking into secondary education is mainly dependent on early ability. Yet, highly educated families still have substantially larger transition rates to the academic track, even when controlling for parents’ and children’s cognitive ability. These findings point to the importance of other unobserved factors that vary between families and could explain educational success (e.g., noncognitive skills, risk aversion, and teachers’ bias). I carried out several robustness checks on reverse causality, confounding, attenuation and sample selection bias, and moderation and found consistent results.

Theoretical Background

Cognitive Ability and Educational Outcomes

Intelligence or general cognitive ability (g) is a theoretical construct and a highly valid and reliable measure (Nisbett et al. 2012). After adolescence, it is one of the most stable behavioral traits. It represents a latent factor of several subdimensions of analytic abilities, such as verbal, spatial, reasoning, perceptual speed, and working memory, that are highly and positively intercorrelated and less genetically influenced than the general construct (Knopik et al. 2017). Cognitive ability is not fixed at birth or genetically determined, but it is malleable and dependent on environmental quality (Farah et al. 2008; Gottschling et al. 2019; Guo and Stearns 2002; Kendler et al. 2015; Ritchie and Tucker-Drob 2018; Tucker-Drob, Briley, and Harden 2013).

Intelligence can be divided into two components: analytic or fluid (nonverbal), and crystallized (i.e., store of knowledge, vocabulary, and arithmetic operations). Fluid or nonverbal intelligence tests (e.g., the Raven test) measure a person’s capacity to reason and solve novel problems, independent of previous knowledge. Fluid IQ tests are less influenced by sociocultural factors, but they cannot be considered completely context free. Fluid IQ tests do not directly measure creativity, knowledge, social sensitivity, or domain-specific cognitive competencies (reading, mathematics, or scientific literacy) that are the target of large-scale international assessment studies, such as the Programme for International Student Assessment (PISA), the Trends in International Mathematics and Science Study, and the Programme for International Assessment of Adult Competencies (Weinert et al. 2011).

Not surprisingly, IQ is a good predictor of educational performance and competencies (i.e., standardized tests: the American SAT, the British General Certificate of Secondary Education, or PISA), with correlations ranging from 0.4 to 0.7 (Deary et al. 2007; Erikson and Rudolphi 2010; Neisser et al. 1996; Rindermann 2007). This means up to 50 percent of the variance would be accounted for by intelligence, leaving ample room for other psychological or noncognitive characteristics to play a role, such as motivation and perseverance (Almlund et al. 2011; Poropat 2009).

Cognitive ability is less related to school- or teacher-assigned grades than to educational competencies, as grades are more influenced by noncognitive or behavioral factors (Duckworth, Quinn, and Tsukayama 2012). This investigation focuses on fluid IQ as a proxy for academic ability or potential (Erikson and Rudolphi 2010), which is less subject to sociocultural context and individual effort than are measures of academic performance (Bailey et al. 2017).

Between-family Inequality

Between-family models evaluate educational inequalities by drawing a random individual from each family, typically using formalized, rational action theories (Breen and Goldthorpe 1997). Rational action theories are built on the formal decomposition of the association between social background and educational attainment into two effects: primary and secondary (Boudon 1974). Primary effects denote the systematic association between parental SES and children’s academic performance, which is shaped by genetic, psychological, and cultural factors (Jackson 2013).² Secondary effects account for upper-class children’s advantage in transition rates to higher educational levels compared to their working-class counterparts when controlling for performance.

Goldthorpe (2007) points to three plausible reasons why working-class children with similar academic performance as more advantaged children would systematically follow less ambitious educational pathways or be more prone to dropout: (1) they are relatively risk averse, that is, lower educational outcomes suffice to avoid downward social mobility or demotion (a floor effect); (2) economic resources to afford the direct (e.g., tuition fees), indirect (e.g., living costs), and opportunity (e.g., forgone earnings) costs to keep studying are less available and less stable;³ and (3) they have lower actual and perceived chances of success due to poorer average performance along with underestimated or conservative perceived benefits of education.

The compensatory advantage mechanism

Most research following the rational action framework assumes that differences in transition rates between working-class and advantaged children remain constant across the academic-ability distribution (Jackson 2013). In other words, the lion’s share of differences in transition rates by social background would be found in the middle of the academic-ability distribution. The main rationale is that disadvantaged families have more difficulty evaluating the chances of success in the next educational level when their children are just below or above academic thresholds (Bernardi and Cebolla-Boado 2014).

Alternatively, some authors argue that social inequality in transition rates tends to concentrate among low-performing children from advantaged families, who enjoy larger transition rates to upper-secondary school (Bernardi and Triventi 2018). That is, upper-class families actively compensate for bad or mediocre academic performance to avoid intergenerational downward mobility (e.g., through private tutoring, parental involvement with homework, and expectations). Thus, the central point of the compensatory advantage mechanism is that the life-course trajectories of students from privileged backgrounds are less dependent on prior negative outcomes or disadvantageous traits (Bernardi 2014; Erola and Kilpi-Jakonen 2017).

Previous findings

Half a century ago, Sewell and Shah (1968) showed that 58 percent of U.S. children with low IQ and highly educated parents attended college, whereas only 9.3 percent of children with low IQ from low-educated families did the same. These differences were relatively constant across the middle (78.9 and 22.9 percent, respectively) and top (91.1 and 40.1 percent, respectively) IQ tertiles. To my knowledge, Bukodi and colleagues (Bukodi et al. 2014; Bukodi, Bourne, and Betthäuser 2017) provide the only recent evidence on the interaction between cognitive ability and parental background in the transition to upper-secondary education in Britain and Sweden. They did not find a clear moderation effect of parental background in Sweden; in England, they found inequalities concentrated among pupils in the top cognitive quintile.

Within-family Inequality

Compared to between-family models, studying inequality dynamics within families can account for a larger array of characteristics shared by siblings (i.e., neighborhood, school, genes, and parental environment; Conley et al. 2015; McGue, Osler, and Christensen 2010). That is, by drawing random individuals from different families, we cannot control for factors that siblings share or do not share (Turkheimer and Harden 2014). The environmental factors siblings share contribute to their overall social background (Sieben and de Graaf 2003), but several factors can vary between siblings in the same family: (1) parental circumstances may affect siblings in diverse ways (mother’s age, birth spacing and order, and shocks, such as divorce or employment loss; Grätz 2018; Härkönen 2014), and (2) there may be extrinsic (e.g., luck, random events) and intrinsic (e.g., unique personality traits) elements that are specific to each sibling.

Siblings share only about 50 percent of their genetic makeup, on average, and they have unique environmental experiences (e.g., teachers, friends) that are associated with personality traits (e.g., active self-selection). Accordingly, some authors claim that about 65 percent of the variation in early academic performance (reading and mathematics), and around half of the variation in educational attainment, is observed within families in the United States (Conley 2008; Conley, Pfeiffer, and Velez 2007) and Germany (Grätz 2018). These unique endowments and personality traits may also evoke different parental treatment or response (Tucker-Drob et al. 2013). That is, parents may consciously or unconsciously behave in a neutral way, compensate for, or reinforce siblings’ initial differences in traits associated with early educational outcomes.

Parental response to children’s endowments

Most theoretical contributions and findings on within-family inequality come from microeconomic models on intrahousehold resource allocation (e.g., child-specific monetary/time investment in human capital) as a function of children’s endowments (Becker and Tomes 1976).

The family wealth model (Becker and Tomes 1976) posits that, under the assumption of no capital constraints, parents try to maximize returns on human capital investment by either investing equally/neutrally in both children (over time, initial ability differences will unfold, thus generating reinforcement patterns) or investing more in the higher-ability child, thus reinforcing sibling differences in endowments. Alternatively, the separable earnings-transfer model (Behrman et al. 1982), based on parental preferences and (within-family) inequality aversion, hypothesizes that parents tend to compensate for sibling differences in endowments by investing more in the lower-ability child to maximize their children’s human capital and earnings. Overall, patterns of reinforcement for early endowments are commonly found for educational investments in comparison to health investments (Almond and Mazumder 2013; Yi et al. 2015).

Within-family (in)equality by parental SES: Compensation or reinforcement?

The literature discussed so far offers limited and mixed findings due to different research designs and measures of early ability or developmental potential (e.g., most research focuses on birth weight). Furthermore, these analyses do not stratify by parental SES, because within-family (in)equalities may depend on families’ pool of resources (Lynch and Brooks 2013).

Conley (2008) builds on the microeconomics literature to theorize about different patterns of within-family inequality by parental SES. In a similar vein as the compensatory advantage mechanism, he suggests that well-off families, thanks to their reliance on a large pool of cultural and economic resources, tend to compensate for within-family differences in endowments. In such cases, children with less academic ability will achieve the same results as their more endowed siblings, generating within-family equality. By contrast, disadvantaged families, due to scarcity of resources, tend to behave more efficiently by “betting” on the sibling with more academic potential, thus reinforcing within-family inequality.

An alternative hypothesis (Becker and Tomes 1986) posits that in the event of capital constraints, disadvantaged families “may not be able to optimally invest in their children’s human capital. Such underinvestment may lead to higher degrees of sibling resemblance at lower incomes since high ability children from poor families may receive the same low level of education as a sibling with lower academic ability” (cited in Conley and Glauber 2008:300).

Previous findings

Table 1 summarizes current research on within-family inequalities in cognitive ability and educational outcomes. To my knowledge, only five investigations directly assess the association between sibling/twin differences in cognitive ability and educational outcomes in the United States (Grätz and Torche 2016; Griliches 1979), Ethiopia (Ayalew 2005), Mexico (Hussain 2010), and Burkina Faso (Akresh et al. 2012). Only Grätz and Torche (2016) and Hussain (2010) stratify the analyses by parental SES.

Table 1.

Literature Review on Within-family (In)equalities in Cognitive Ability and Educational Outcomes.

Study	Country	Endowment → outcome	Parental response	Outcome(s)	Average result	SES	Parental SES measure	Design
Griliches (1979)	United States	IQ	Indirectly measured	Educational attainment (years of education)	Reinforcement	No	No	Fixed effects (siblings/twins)
Ayalew (2005)	Ethiopia	IQ (Raven test)	Indirectly measured	Attending school	Reinforcement	No	No	Fixed effects (siblings)
Conley, Pfeiffer, and Velez (2007)	United States	No	Indirectly measured	Cognitive outcomes (literacy, numeracy, reading comprehension, problem-solving skills): Woodcock-Johnson Revised Test of Achievement	High SES: <ICC (reinforcement) Low SES: >ICC (compensation)	Yes	Mother’s years of education (<13/>13) Race (black/white)	ICC (siblings)
Conley and Glauber (2008)	United States	No	Indirectly measured	Years of formal schooling completed	High SES: >ICC (compensation) Low SES: <ICC (reinforcement)	Yes	Mother’s years of education (<13/>13)	ICC (siblings)
Conley (2008)	United States	No	Indirectly measured	Educational attainment	No ICC differences by parental SES	Yes	Mother’s high school degree Race (black/white)	ICC (siblings)
Hussain (2010)	Mexico	IQ (Raven’s Progressive Matrices test)	Indirectly measured	Grade attainment Grade retention Age at enrollment Age quit school Secondary school	High SES: compensation Low SES: reinforcement	Yes	Parental education	Fixed effects (siblings)
Akresh et al. (2012)	Burkina Faso	IQ (Raven’s Colored Progressive Matrices and Wechsler Intelligence Scales Digit Span)	Indirectly measured	Current enrollment in primary school Ever enrolled Grade progression On-time start	Reinforcement	No	No	Fixed effects (siblings)
Grätz and Torche (2016)	United States	Bailey Scales of Infant Development at age 10 months (motor and cognitive) Early child development at age 10 months (crawling, sitting, walking, standing)	Directly measured: Parental cognitive stimulation at two years old (Two-bags test)	Cognitive performance (math and reading tests) at four years old	Cognitive t₀→ stimulation t₊₁ High SES: reinforcement Low SES: neutrality Stimulation t₊₁→ cognitive t₊₂ High SES: neutrality Low SES: neutrality Cognitive t₀→ cognitive t₊₂ High SES: reinforcement Low SES: reinforcement	Yes	Parental education Household income- Family SES (high/low)	Fixed effects (twins)
Grätz (2018)	Germany	No	Indirectly measured	Cognitive performance Grade point average Upper-track attendance	No ICC differences by parental SES	Yes	Parental education and class Parental ISEI (high/low) Migration background	ICC (siblings)

Note: ICC = intraclass correlation; ISEI = International Socio-economic Index; SES = socioeconomic status.

Griliches (1979) found patterns of slight reinforcement for the effect of a one-standard-deviation IQ difference on years of schooling achieved (0.4 to 0.9 years) in the United States. Similarly, Ayalew (2005) in Ethiopia and Akresh and colleagues (2012) in Burkina Faso reported reinforcement trends for children’s chances of attending school (probability difference of 0.09 and 16.4, respectively). In Mexico, Hussain (2010) also found (slight) reinforcement for the overall sample in the chances of attending secondary school (probability difference of 0.03). For families with high secondary education, he found compensating/neutral parental response (–0.02); for noneducated (0.05) and primary-educated (0.02) families, he found slight reinforcement. Grätz and Torche (2016) found that highly educated parents provide more cognitive stimulation to children with higher early ability (reinforcement), although this differential response does not explain later cognitive development or school readiness. In turn, early cognitive and motor development at age 10 months has a direct positive impact on cognitive performance at four years for low- and high-SES families alike (reinforcement of early ability), net of parental stimulation at two years old.

The overall picture from previous research points to the reinforcement of cognitive endowments on educational outcomes. Nevertheless, none of these investigations looked at the heterogeneity of this association across the absolute ability distribution, and only two stratified analyses by SES.

The German Educational System

The design of educational systems may attenuate or reinforce early inequalities generated within families (Landes and Nielsen 2012; Skopek and Passaretta 2018). Educational systems with early-ability tracking reinforce the magnitude of early academic ability on educational inequality (primary effects), whereas comprehensive systems reinforce the role of decisions (secondary effects), as all pupils follow similar tracks during lower-secondary education, and transitions to upper secondary are generally less dependent on previous performance (Blossfeld et al. 2016; Jackson 2013). Early tracking systems seem to lead to larger overall socioeconomic inequalities (Bol and Werfhorst 2013).

The German educational system is decentralized by federal states (länders), but early-ability tracking generally starts at the last grade of joint primary education, at age 10 (grade 4) or 12 (grade 6 at orientation-level schools). At this point, teachers recommend to parents a track choice for their children. Legislation between länders differs greatly regarding the existence or level of binding of the recommendation, but recent research shows that the effect of social background on children’s chances of accessing the academic track remains fairly stable across different levels of binding recommendations (Roth and Siegert 2016).

After primary grade 4, most pupils have access to three track-specific types of secondary schools: lower secondary (hauptschule), middle secondary (realschule), or upper secondary (gymnasium). Hauptschule and realschule lead to vocational training education, whereas gymnasiums offer the most academically oriented education. The vast majority of gymnasium students enter university after passing the abitur exam (Schneider 2008).⁴ Some states have other types of schools; for example, comprehensive schools (gesamtschule) were created in the 1960s by the Social Democratic Party to integrate the three-track system into one school with three tracks. However, in practice, comprehensive schools are considered lower rank and have not replaced the three-tier system. Even though Germany has relaxed the regional legislation in tracking age and the binding of track recommendations, and has allowed more horizontal movement between tracks (Blossfeld et al. 2016), the initial tracking allocation is a bottleneck that makes it very difficult to change one’s educational pathway (Fishkin 2014; Schneider 2008).

Because sizeable academic-ability differences by parental background exist before track sorting (primary effects; Blossfeld et al. 2017), early-ability tracking fosters “ability or meritocratic selection” (Esser 2016), whereas the comprehensive system leaves more leeway for parental choice. Because teachers recommend track allocation on the basis of observed academic performance (math, German, and classroom behavior), parents of children with low academic performance or ability may have less room to influence track decisions. Thus, the German case is a stringent test for the compensatory advantage hypothesis, compared to previous research on educational systems without early tracking.

Given that the transition to secondary education in Germany mainly sorts on observed academic performance, in the event of low-performing children in high-SES families, compensatory patterns could essentially work through parental pressure for a positive recommendation, directly ignoring grades or teachers’ positive bias (Schneider 2008). Teachers’ recommendations are subject to bias (Boone et al. 2018) by, for instance, misconceiving cultural capital as academic brilliance (Jæger and Møllegaard 2017) or assessing more favorably children with fewer behavioral problems (Møllegaard 2016). Additionally, Jürges and Schneider (2007) claim that low-SES parents are more likely to send their children to vocational tracks even if they have a recommendation for the academic track, whereas the opposite occurs in high-SES families. They argue that this difference may be explained by high-SES parents’ higher levels of educational aspirations.

By using cognitive ability as a measure of academic potential, which is less tightly associated with recommendations or track choice than are teacher-assigned grades, compensatory patterns may also work through active parental involvement with the lower-ability twin to improve academic performance (e.g., help with homework and school curriculum, motivation). These are the mechanisms I attempt to isolate by testing the compensatory advantage hypothesis at the bottom of the academic-ability distribution in Germany.

Data, Variables, and Sample Selection

Data

To answer the aforementioned research questions, I use the first wave of the TwinLife–Genetic and Social Causes of Life Chances study carried out in 2014–15 (Diewald et al. 2018), a representative survey of the German population with a sample of same-sex 11-year-old monozygotic (MZ) and dizygotic (DZ) twins at grades 5 and 6 (N = 2,012 twins/1,006 families) born in 2003 and 2004. This study identified twins in local registration offices from large municipalities and rural areas. Technical reports of the TwinLife study compared distributions of the key sociodemographic variables of the survey with the German microcensus and concluded that the twin-sample is representative, covering the full distributions for the parental SES variables (Lang and Kottwitz 2017).

Variables

Track attendance

The dependent variable on track attendance is measured with a dummy on the type of secondary school currently attended: 0 = hauptschule and realshule (vocational training tracks comprising lower- and intermediate-secondary schools, integrated secondary schools, and comprehensive schools) and 1 = gymnasium (academic track: upper-secondary schools). I dropped pupils still attending primary education and orientation-level schools, which usually delay tracking decisions until 12 years old. I conducted sensitivity checks by dropping observations of students attending comprehensive schools, and results are robust.

Cognitive ability

I measure cognitive ability with the Culture Fair Test, a widely used and well-validated cognitive test battery that captures nonverbal (fluid) intelligence as a proxy for general cognitive ability, as the general factor of intelligence also includes verbal ability (Schulz et al. 2017). This test is designed to minimize the influence of sociocultural and environmental factors; however, it still reflects them. The test was administered via computer, resulting in a sum of all correctly answered items in a battery of four subtests on figural reasoning (15 items), classification (15 items), matrices (15 items), and reasoning (topology) (11 items). I applied a latent factor approach on the four subtests (Gottschling 2017). The factor analysis (principal components) indicates that the four subtests load strongly on a single component with the following factor loadings by subtest: figural reasoning (0.7424), classification (0.7597), matrices (0.7969), and reasoning (0.5922). I constructed a standardized general cognitive ability score from these four items with a satisfactory Cronbach’s alpha at 0.86.

The test was administered when respondents were in grade 5 or 6. Thus, cognitive ability was measured at least one grade after tracking (grade 4). Given that education is causally associated with gains in cognitive ability (Carlsson et al. 2015), I carried out a robustness check (see below) and concluded that overestimation bias is not compromising the results.

Parental background

I measure parental background with a dummy for the highest education level (International Standard Classification of Education [ISCED]) achieved by either the father or the mother; 0 = ISCED 1 to 5B (≤ upper secondary) and 1 = ISCED 5A to 6 (university and PhD). I codify this variable in such a reduced way to maximize sample size to split the analysis by parental background, and to compare the children of university graduates versus everyone else. I carried out sensitivity analyses with an alternative measure of parental background, using the highest parental SES (according to the International Socio-economic Index), and results hold.

Covariates

I control for a set of key variables that may confound the main associations under study, both within families—z birth-weight deviation from pair mean—and between families—twin-pair zygosity (MZ = 0; DZ = 1), twin-pair gender (male = 0; female = 1), z birth-weight pair mean, and mean parental cognitive ability (as measured by the Culture Fair Test).

Sample selection

Table 2 describes the cases missing and excluded from the overall sample for this study’s variables of interest. The majority of missing cases come from the dependent variable on track attendance (23 percent). Within the missing cases on track attendance, the majority (47 percent) were students still attending primary education due to grade retention or orientation-level schools delaying tracking until age 12. The incidence of missing cases on the outcome variable is slightly higher for lower-/medium-educated families (+6.3 percent), due in part to a larger prevalence of grade retention. Cognitive ability and birth weight each account for 8.9 percent of missing cases. After applying listwise deletion on the variables of interest, 36.6 percent of cases are excluded, with a larger incidence for lower-/medium-educated families (40 percent) than for highly educated ones (34 percent). In Appendix A, I discuss in more detail the possible sample selection bias and conclude that inequalities may be underestimated due to the positive selection of the analytic sample.

Table 2.

Sample Selection.

Variable	All sample (N = 2,082)^a		Lower/medium educated (n = 1,104)^b		Highly educated (n = 996)^c
Variable	n missing	% missing	n missing	% missing	n missing	% missing
Academic track	478	22.96	282	25.54%	192	19.28%
Zygosity	0	0	0	0	0	0
Gender	0	0	0	0	0	0
z birth weight^d	186	8.93	102	9.24	82	8.23
z cognitive ability^d	186	8.93	108	9.78	78	7.83
z parental cognitive ability	50	2.40	34	3.08	16	1.61
Highest parental education	12	0.58

Excluded cases, n = 762 (36.60%); analytic sample, n = 1,320 (63.40%).

Excluded cases, n = 442 (40.04%); analytic sample, n = 662 (59.96%).

Excluded cases, n = 338 (33.94%); analytic sample, n = 658 (66.06%).

Including nonmissing cases within unbalanced twin pairs.

Empirical Strategy

Identification Strategy: Twins as a Natural Experiment

An ideal test of the compensatory advantage hypothesis would compare siblings who differ in nothing but their (observable) academic potential.⁵ Nature provides an experimental setting with the incidence of twins (Knopik et al. 2017). Twins are a quasirandom phenomenon, being born into the same family on the same day and sharing at least 50 percent of their genetic makeup. Hence, twin fixed-effects models rule out most sources of variation within families that might confound the association between cognitive ability and educational outcomes. Twin pairs discordant in exposure can be thought of as a natural counterfactual in which the co-twins can be used as their own control/experimental group (McGue et al. 2010).

This design allows me to control for more unobserved confounding than most previous research that uses between-family estimates and sibling fixed effects (Jæger 2011), but within-family variation in cognitive ability might not be randomly assigned. Three potential sources of variation might confound the associations of interest: prenatal (e.g., birth weight), genetic (DZ twins), and unique environmental (DZ and MZ twins) (Knopik et al. 2017). In Appendix B, I discuss these sources of confounding and how I address them; I conclude that they do not seriously compromise the identification strategy.

Hybrid Multilevel Models: Between-within Estimators

Given the paired structure of the data, I implement multilevel models comprising two twins (level 1) clustered in families (level 2), keeping only balanced pairs at level 1. As I am interested in estimating and comparing both between- and within-family parameters, I use hybrid multilevel models (also known as between-within models; Carlin et al. 2005; McGue et al. 2010; Turkheimer and Harden 2014). These models include the twin-pair average ( $β_{2} (\bar{X_{j}}) = \frac{X_{i 1 j} + X_{i 2 j}}{2}$ ), and the deviation from the twin-pair average ( $β_{1} (X_{ij} - \bar{X_{j}})$ ), for each twin for the variables that vary within families (birth weight and cognitive ability). The former parameter is largely equivalent to a naive or pooled ordinary least squares (OLS) regression in which twins are treated as individual observations; the latter is equivalent to a standard twin fixed-effects model that accounts just for variation within families, controlling for family-constant factors. Finally, because cross-level interactions are estimated for the deviation of cognitive ability and the pair-mean cognitive ability, all models include random slopes for the level 1 variable interacted (deviation of cognitive ability; Heisig and Schaeffer 2019). I estimate linear probability models (LPM) in all specifications for the sake of comparability and interpretation.

\begin{array}{l} y_{i j} = α + β_{1} (X_{i j} - \bar{X_{j}}) + β_{2} (\bar{X_{j}}) \\ + β_{3} (Z_{i j} + Z_{j}) + μ_{0 j} + e_{i j} + e (X_{i j} - \bar{X_{j}}) \end{array}

(1)

Equation (1) shows the baseline hybrid multilevel model in which y_ij measures type of track attendance for twin i in family j, α represents the intercept or grand-mean probability of accessing the academic track across families, β₁ stands for the main coefficient of interest on the (fixed) effect of twin ij’s cognitive ability deviation from the pair-mean cognitive ability in family j within discordant twin pairs, β₂ stands for the effect of pair-mean cognitive ability in family j, and β₃ represents a vector of covariates between and within families. On the right-hand side of the equation, the random-effects parameters represent the error term decomposed in a between- and within-family component: μ_0j is the pair-level error of prediction, or unaccounted variance between families; e_ij stands for the individual/within-family error of prediction, or the individual unaccounted share of the variance; and $e (X_{ij} - \bar{X_{j}})$ expresses the random slopes’ parameter for the cognitive-ability deviation. This parameter represents to what extent the effect of cognitive-ability deviation varies across families.

I estimate four different models. Model 1, as expressed in equation (1), estimates the effect of within- and between-family differences in cognitive ability and parental background on the probability of attending the academic track. To answer research question 1, I estimate the model expressed in equation (1) independently for lower-/medium-educated (Model 2a) and highly educated (Model 2b) families.

To answer research question 2, equation (2) includes β₄, which represents the cross-level interaction between cognitive-ability deviation from pair-mean and pair-mean cognitive ability. That is, to test the compensatory advantage hypothesis within families, we must assess whether the fixed effect of twin differences in cognitive ability on track choice (β₁) is heterogeneous across the cognitive-ability distribution (β₂), being compensated (β₁≤ 0) at the bottom. I estimate two subspecifications of equation (2) independently for lower-/medium-educated (Model 3a) and highly educated (Model 3b) families.

y_{ij} = α + β_{1} (X_{ij} - \bar{X_{j}}) + β_{2} (\bar{X_{j}}) + β_{3} (Z_{ij} + Z_{j}) + β_{4} (\bar{X_{j}} * (X_{ij} - \bar{X_{j}})) + μ_{0 j} + e_{ij} + e (X_{ij} - \bar{X_{j}})

(2)

All models are estimated with maximum-likelihood, unstructured covariance to allow the within- and between-family residual variance to be correlated, random slopes for β₁ to allow its effect to vary across families, and robust standard errors to better account for non-normally distributed residuals at the family level. Finally, to estimate the share of variance between families, I rely on the intraclass correlation (ICC; ρ), as expressed in equation (3), in which σμ_0j accounts for between-family variance and σe_ij for within-family variance.

ρ = \frac{σ μ_{0 j}}{σ μ_{0 j} + σ e_{ij}} = Intraclass correlation (ICC)

(3)

Within-family (In)equality: Compensation and Reinforcement

As shown in Table 1, previous literature has tested within-family (in)equalities directly and indirectly. Following the former approach, one can measure early endowments at t₀, parental response at t+1, and educational outcomes at t+2. This empirical strategy is ideal but rare, given that high-quality panel data with rich information on endowments and parental behavior are needed from birth to the first important educational crossroad (Grätz and Torche 2016).

Regarding the latter approach, most previous research measures within-family (in)equality indirectly in two ways. First, some investigations evaluate the degree of siblings’ resemblance (ICC) in a given socioeconomic outcome and its potential stratification by parental SES (Conley 2008). Second, other studies assess the effect of sibling differences in a given endowment on later educational outcomes (Ayalew 2005). I apply this second indirect strategy by defining two intrafamily patterns in the slope of twins’ fixed-effect cognitive ability on track attendance (β₁): equality or compensation if β₁ ≤ 0 and inequality or reinforcement if β₁ > 0.

Descriptive Analysis

Table 3 shows the descriptive statistics for all variables of the analyses, stratified by parental education. On average, 54 percent of pupils attend the academic track. There are large differences by parental education. Just 36 percent of students from low-/medium-educated families attend an academic track, compared to 73 percent of students from highly educated families. Previous research on full siblings shows that within-family variance accounts for 50 percent of total variance in track placement in Germany (Grätz 2018); I find an estimate of 12.3 percent (see Table 3).⁶ In contrast to some previous findings that siblings from high-SES families have greater resemblance in educational attainment (Conley 2008), the share of total educational attainment variance explained within families does not vary considerably by parental background. Table 3 shows an average ICC in cognitive ability at 0.64, with virtually no variation by parental background. Figure 1 illustrates the distribution of (within-family) absolute twin differences in cognitive ability (left-hand side) and deviations from pair-average cognitive ability (right-hand side). This is the main source of within-family variation that I exploit in this investigation. On average, absolute twin differences in cognitive ability stand at 0.77, with standard deviation of 0.6, with slight variation by SES (see Table 3).

Table 3.

Analytic Sample Summary Statistics.

	All sample					Lower-/medium parental education (ISCED 1–5B)					High parental education (ISCED 5A–6)
Variable	M	SD	Min.	Max.	ICC^a	M	SD	Min.	Max.	ICC^a	M	SD	Min.	Max.	ICC^a
Academic track	0.542		0	1	0.877	0.358		0	1	0.870	0.728		0	1	0.835
Dizygotic twin pairs	0.603		0	1		0.556		0	1		0.650		0	1
Female twin pairs	0.521		0	1		0.547		0	1		0.495		0	1
z birth weight	0.058	0.982	−3.143	3.487	0.874	−0.001	1.017	−3.050	3.339	0.893	0.119	0.941	−3.143	3.487	0.850
z birth weight pair mean	0.058	0.925	−3.119	3.311		−0.001	0.967	−3.022	3.311		0.119	0.877	−3.119	2.191
z birth weight deviation	0.000	0.329	−1.667	1.667		0.000	0.317	−1.218	1.218		0.000	0.340	−1.667	1.667
z birth weight absolute difference	0.481	0.449	0.000	3.333		0.475	0.420	0.000	2.435		0.486	0.476	0.000	3.333
z cognitive ability	0.115	0.946	−3.508	2.576	0.639	−0.061	0.988	−3.508	2.576	0.628	0.291	0.867	−2.854	2.327	0.613
z cognitive ability pair mean	0.115	0.811	−2.520	2.321		−0.061	0.844	−2.520	2.321		0.291	0.736	−1.568	1.995
z cognitive ability deviation	0.000	0.488	−1.760	1.760		0.000	0.515	−1.760	1.760		0.000	0.459	−1.505	1.505
z cognitive ability absolute difference	0.766	0.604	0.001	3.519		0.805	0.642	0.001	3.519		0.726	0.560	0.001	3.011
z parental cognitive ability	0.071	0.911	−3.420	2.033		−0.291	0.969	−3.420	1.575		0.434	0.676	−2.752	2.033
High parental education	0.498		0	1
n twins	1,320					662					658
n families	660					331					329

Note: ICC = intraclass correlation from one-way random effects; ISCED = International Standard Classification of Education.

Coefficients statistically significant at p < .001.

Figure 1.

Distribution of twin differences and deviations from pair average in cognitive ability.

Results

Table 4 summarizes the main findings of this investigation. Model 1 sheds light on between- and within-family dynamics. Net of child and parental differences in cognitive ability, twins from highly educated backgrounds are 27 percent more likely to attend the academic track compared to their least advantaged counterparts. The effect of parental education (coefficient at 0.36 before controls for cognitive ability) on track allocation is mainly exerted (74.2 percent) net of parents’ and children’s cognitive ability. This suggests that other unobserved factors, net of cognitive ability, that vary between families with different socioeconomic resources (e.g., risk aversion to downward mobility, noncognitive abilities) and mediate the association between parental education and track attendance (e.g., via grades, teachers’ recommendation, or bias) may account for these observed inequalities. Cognitive ability account for only around 14 percent of the variance in track allocation, so there is ample room for other factors explaining early educational success.

Table 4.

Hybrid Multilevel Linear Probability Model with Maximum Likelihood, Random Slopes, and Unstructured Covariance.

Outcome: Academic track	Model 1	Model 2a	Model 2b	Model 3a	Model 3b
Independent variable	All sample	Lower/medium education	High education	Lower/medium education	High education
z cognitive-ability deviation	.0625*** (.0153)	.0622** (.0208)	.0625** (.0227)	.0756*** (.0221)	.0719** (.0237)
z cognitive-ability pair mean	.175*** (.0214)	.168*** (.0300)	.175*** (.0311)	.168*** (.0300)	.178*** (.0312)
Parental z cognitive ability	.0454* (.0207)	.0635* (.0257)	.0149 (.0381)	.0639* (.0258)	.0147 (.0381)
z cognitive-ability deviation ×z cognitive-ability pair mean				.0643* (.0253)	−.0618* (.0259)
High parental education	.268*** (.0361)
Constant	.331*** (.0353)	.353*** (.0442)	.592*** (.0476)	.354*** (.0443)	.591*** (.0476)
ICC	.7882	.8199	.7572	.8185	.7549
R ² level 1 Snijders/Bosker	.2501	.1485	.1136	.1510	.1157
R ² level 2 Snijders/Bosker	.2763	.1630	.1257	.1630	.1257
R ² level 1 Bryk/Raudenbush^a	.0378	.0369	.0399	.0592	.0550
R ² level 2 Bryk/Raudenbush^a	.3099	.1818	.1427	.1785	.1397
AIC	1039.153	539.386	516.173	535.049	514.560
Observations	1,320	662	658	662	658
Number of families	660	331	329	331	329

Note: Controls for twin-pair gender, zygosity, and birth weight (pair mean and deviation). Robust standard errors are in parentheses.

Variance explained compared to the null model.

p < .05. **p < .01. ***p < .001.

Table 5.

Random-effects Parameters.

Random-effects parameter	Model 1		Model 2a		Model 2b		Model 3a		Model 3b
Random-effects parameter	Var	RSE	Var	RSE	Var	RSE	Var	RSE	Var	RSE
Var(within family)	0.0379	0.0071	0.0337	0.0108	0.0340	0.0105	0.0411	0.0096	0.0415	0.0096
Var(between family)	0.1410	0.0081	0.1534	0.0111	0.1533	0.0110	0.1280	0.0119	0.1278	0.0119
Var(z cognitive-ability deviation)	0.0316	0.0121	0.0352	0.0209	0.0317	0.0191	0.0304	0.0157	0.0272	0.0145
Cov(z cognitive-ability deviation between family)	−0.0037	0.0034	0.0005	0.0047	0.0028	0.0047	−0.0083	0.0054	−0.0080	0.0056

Note: Var = variance; Cov = covariance; RSE = robust standard error.

In contrast to the compensatory advantage mechanism found in between-family models, the differences in transition rates by parental education remain constant across the (pair-mean) cognitive-ability distribution. The interaction term between parental education and average cognitive ability across families is neither substantial nor statistically significant, as formally tested in Table 6 and illustrated in Figure 2. However, the main contribution of this investigation is to complement this result by testing the compensatory advantage hypothesis within families with different socioeconomic resources.

Table 6.

Interaction Effects and Wald Tests.

Wald test for interactions	Coefficient (robust SE)	χ² (df)	p
z cognitive-ability deviation × parental education	.0004 (.0306)	0.00 (1)	.990
z cognitive-ability pair mean × parental education	−.0116 (.0402)	0.08 (1)	.772
z cognitive-ability pair mean ×z cognitive-ability deviation × parental education	−.1234** (.0362)	11.65 (1)	.001

p < .05. **p < .01. ***p < .001.

Figure 2.

Predicted probabilities at observed values of academic track attendance by pair-mean cognitive ability and parental education with 95% confidence intervals (see Table 4, Model 1).

Model 1 in Table 4 also shows that twin differences in cognitive ability are predictive of track attendance differences within families (fixed effect at 6.3 percentage points),⁷ although this effect is of less magnitude than between families (marginal effect at 17.5 percentage points). More substantially, this coefficient also tells us that intrafamily differences in cognitive ability tend to produce intrafamily inequalities in educational attainment. This result is in line with most previous findings that report reinforcement patterns (see Table 1).

Regarding research question 1 on the potential heterogeneity of within-family dynamics by parental background, I find that the effect of twin differences in cognitive ability on track placement is not stratified by parental education at average absolute levels of cognitive ability (see Table 4, Models 2a and 2b; formally tested in Table 6 with an interaction). Contrary to some previous theoretical predictions and findings (Conley and Glauber 2008; Hussain 2010), results suggest that twin differences in cognitive ability tend to produce within-family inequalities in educational outcomes among advantaged and disadvantaged families alike.⁸ That is, twins with greater cognitive ability show larger transition rates (+6 percent) to the academic track than do their co-twins with lesser academic potential.

The main drawback of previous investigations’ theories and findings is that within-family associations by parental SES may be contingent on children’s absolute level of endowments. Thus, the compensatory advantage hypothesis should be tested at the bottom of the absolute academic-ability distribution. To do so, Models 3a and 3b in Table 4 display the cross-level interaction between twin differences in cognitive ability (deviation) and pair-average cognitive ability (absolute distribution). In Models 3a (lower-/medium-educated parents) and 3b (highly educated parents), this interaction term is statistically significant and of similar substantial magnitude but of different sign (0.06 and −0.06, respectively). The difference between both interaction coefficients by SES is statistically significant, as formally tested in Table 6. This result means that within-family (in)equalities depend on twin pairs’ absolute level of cognitive ability.

Figure 3 displays the predicted probabilities at observed values for this interaction term. Overall, this figure shows a more fine-grained picture than do previous theories and findings. In both low-/medium- and highly educated families, twins’ differences in cognitive ability generate within-family equality (compensation) and inequality (reinforcement) patterns. As Figure 4 shows in the fixed-effects slopes across the (twin-pair) cognitive-ability distribution, in disadvantaged families, twin differences in cognitive ability lead to within-family equality at the bottom of the cognitive-ability distribution (β = 0.00), but they produce inequality at the middle (β = 0.07) and, especially, at the top (β = 0.14). Advantaged families show the opposite pattern. Twin differences in cognitive ability generate the largest within-family inequalities at the bottom of the cognitive-ability distribution (β = 0.14), more modest inequalities at the middle (β = 0.07), and equality at the top (β = 0.00).

Figure 3.

Predicted probabilities at observed values and random effects = 0 for the interaction between z cognitive-ability deviation (fixed effect) and pair-mean cognitive ability by parental education (see Table 4, Models 3a and 3b) with 95% confidence intervals.

Figure 4.

Interaction between z cognitive-ability deviation (average marginal effects or fixed effects) and pair-mean cognitive ability (absolute cognitive-ability distribution, moderator in x-axis) by parental education (see Table 4, Models 3a and 3b) with 95% confidence intervals.

These intrafamily patterns across the absolute cognitive-ability distribution point to the compensatory advantage mechanism going in the opposite direction in the German educational system. That is, it seems highly educated families are not able to compensate for children’s low academic ability, as lower-ability twins at the bottom of the cognitive-ability distribution show the largest differences in transition rates with respect to their relatively more gifted co-twins. One might think the absence of compensatory patterns in advantaged families is good news for equality of opportunity. Nonetheless, as we saw in Figure 2, children from highly educated families still have substantially larger transition rates to the academic track.

Rational action theories have mainly been developed and applied to studying educational inequalities between families, but I argue that the theorized mechanisms that differ between low-, medium-, and highly educated families (resources and risk aversion to downward mobility) may help us understand these opposite patterns of within-family (in)equalities. In the German educational system, and others like it, in which the recommendation or transition to secondary education is mainly dependent on early academic ability, highly educated parents may have difficulty compensating for twins’ ability differences at the bottom of the ability distribution. The risk of downward mobility might be at a maximum at this threshold; hence, ability differences may be magnified so that at least the higher-ability twin makes it to the academic track.

In contrast, for lower- and medium-educated families at the bottom of the academic-ability distribution, it does not matter how much relative ability a twin may display, because both twins have equally low chances of attending the academic track (“equality to the bottom”). However, at higher levels of the ability distribution, twin differences in cognitive ability may become more noticeable for parents, thus generating inequality patterns as parents attempt to help the higher-ability twin make it to the academic track. The main logic behind this speculation is that disadvantaged families are generally more reluctant to opt for the academic track given their lower resources and lower perceived chances of success. Unless one of their children is exceptionally bright in absolute and relative terms, they are more risk averse.

Robustness Checks

Reverse Causality

Cognitive ability is measured at least one grade (fifth or sixth) after tracking (fourth grade) took place. Previous research shows a positive longitudinal association between academic tracking and gains in cognitive ability (Guill, Lüdtke, and Köller 2017), which could compromise accurate estimations of the effect of cognitive ability on track choice due to potential reverse causality bias (i.e., overestimation). More importantly for this research, in case of reverse causality, reinforcement patterns could be more easily found than compensation.

Reverse causality would ideally be tested by assessing differences in cognitive ability in the academic and vocational tracks before (fourth grade) and after (grade 5 onward) tracking (at 10 years old). Unfortunately, I cannot observe cognitive ability before tracking. Thus, to estimate the direction and magnitude of this potential reverse causality bias, I exploit a feature of German national legislation for enrollment in primary school: children must turn six on or before June 30 to enroll in school, although there is variability by länder (Jürges and Schneider 2007). This cutoff based on birth month generates variation in grade progression in the sample. Those kids who turn six before the cutoff are enrolled in the first grade of primary, while those who turn later on delay their enrollment until the next academic year. Even though allocation to grade is not completely based on random variation coming from pupils’ birth month, as families have a considerable margin of discretion (Bernardi 2014), I exploit this variation in grade progression to assess reverse causality.

The main idea is to assess whether pupils in the academic track increase their advantage in cognitive ability compared to students in vocational tracks between grades 5 and 6. After dropping observations that experienced grade retention and twins in discordant grades, I compare average cognitive-ability differences by track between grades 5 and 6 with naive OLS (equation [4]) and fixed-effects (equation [5]) regressions. The dummies on grade (X_i) and track (Z_i) are interacted, showing whether the difference in cognitive ability between academic and vocational tracks increased, decreased, or remained constant between grades 5 and 6.

y_{i} = α + β_{1} (X_{i}) + β_{2} (Z_{i}) + β_{3} (X_{i} * Z_{i}) + e_{i}

(4)

y_{i 1 j} - y_{i 2 j} = β_{1} (X_{i 1 j} - X_{i 2 j}) + β_{2} [(X_{i 1 j} - X_{i 2 j}) * (Z_{j})] + (e_{i 1 j} - e_{i 2 j})

(5)

As Table 7 and Figure 5 show, pupils in vocational training and academic tracks increased their mean cognitive ability from grade 5 to 6. However, while the advantage in cognitive ability for academic-track pupils at grade 5 stands at 0.67 (naïve OLS) and 0.56 standard deviation units (fixed effects), this advantage does not significantly increase by grade 6. The magnitude of the difference in cognitive ability between tracks remains fairly stable across grades 5 and 6, as shown in the coefficients for the interaction terms in Table 7: −0.11 standard deviation units for the OLS estimator and −0.06 standard deviation units for the fixed-effect estimator. These differences are not statistically significant.

Table 7.

Reverse Causality: Effects of Track and Grade on Cognitive Ability.

Variable	Naive OLS	Twin fixed effects
Grade 6 (ref. = grade 5)	.3357*** (.0893)
Academic track (ref. = vocational track)	.6662*** (.0918)	.5641** (.2047)
Track × grade	−.1070 (.1157)	−.0625 (.2652)
Constant	−.1070*** (.0702)	−.1349 (.0784)
Observations	1,029	1,029
R ²	.1261	.0322

Note: OLS = ordinary least squares; ref. = reference. Standard errors are in parentheses; robust standard errors for the naive OLS model.

p < .05. **p < .01. ***p < .001.

Figure 5.

Cognitive-ability distribution by grade and track.

Even if this robustness check cannot completely rule out reverse causality problems (i.e., unobserved cognitive ability between grades 4 and 5), it shows that overestimation bias might not represent a serious threat for this article’s general finding: children with low cognitive ability from high-SES families experience no compensation.

Additional Robustness Checks

To further assess the credibility of the findings, in Appendix C I discuss additional robustness checks on attenuation bias, external validity, logistic specifications, and extrapolation and linearity of the moderation analysis.

Conclusion

The main aim of this article was to test whether high-SES families compensate for children’s low ability in the transition to secondary education in the stringent setting of German early-ability tracking. This article was motivated by the lack of dialogue and limitations of the literature on educational inequalities between (i.e., misspecification of social background and ability) and within (i.e., stratification by SES and the endowment distribution) families. I used a twin fixed-effects design that controls for more unobserved confounding (i.e., school, genes, neighborhood, and family environment) and provides a more credible test of the compensatory hypothesis than most previous research using between-family estimates or sibling fixed effects.

I find that twins with greater cognitive ability than their co-twins enjoy larger transition rates to the academic track. This finding aligns with previous research that finds reinforcement patterns for this association in the United States, Mexico, Ethiopia, and Burkina Faso. Does parental SES moderate the effect of twin differences in cognitive ability on track choice (research question 1)? The positive association between cognitive ability and transition to the academic track, generating within-family inequality or reinforcement of abilities, holds for advantaged and disadvantaged families alike. In other words, in contrast to some previous hypotheses and findings (Conley and Glauber 2008), within-family inequality in educational outcomes is not heterogeneous across parental SES. This result is in line with Grätz’s (2018) study in Germany that finds no SES heterogeneity in the level of siblings’ similarity in admission to the academic track.

The main contribution of this article was to test the compensatory advantage hypothesis within families at the bottom of the absolute cognitive-ability distribution (research question 2). Results show that highly educated families are not able to compensate for children’s low academic ability: lower-ability twins at the bottom of the ability distribution show the largest differences in transition rates compared to their relatively more able twin. Rational action theories (i.e., risk aversion to downward mobility), mainly applied to understanding between-family inequalities, may also help us understand these within-family patterns.

In the German educational tracking system, in which the recommendation or transition to secondary education is chiefly a function of early academic ability, highly educated parents may have serious difficulty deploying compensatory strategies at the bottom of the academic-ability distribution. It remains a question whether patterns of compensation for low cognitive ability may emerge in educational systems without early-ability tracking, in which transitions to upper-secondary education are less linked to observed performance.

The absence of compensatory patterns in cases of low academic ability might be interpreted as positive evidence for equality of opportunity, but children from highly educated families with the same level of cognitive ability as children from less educated ones still have substantially larger transition rates (27 percentage points) to the academic track. From a normative standpoint, these inequalities net of cognitive ability represent a waste of academic potential for disadvantaged students, which compromises upward social mobility. Moreover, this scenario is at odds with the role of cognitive ability as a prominent criterion of merit for liberal theories of equality of opportunity (Bowles and Gintis 2002; Fishkin 2014).

Overall, results point to the importance of other unobserved factors, rather than cognitive ability, in influencing learning, academic performance, and transition rates that vary between families with different socioeconomic resources. Potential candidates to explain this residual association between parental background and educational outcomes include risk aversion to downward mobility, noncognitive skills, and teachers’ bias. Further research is needed to explore these mechanisms.

After carrying out several robustness checks on reverse causality, attenuation and sample selection bias, moderation, confounding, and alternative specifications, I generally conclude that the study’s main findings are consistent. A substantive limitation of this study is that no direct indicators of parental investment or responses to children’s endowments are used. Future research should disentangle the particular mechanisms that may account for the associations between children’s endowments, parental response, and educational outcomes across families with different socioeconomic resources. Recognizing these limitations to be improved in future research, this article contributes to the literature on educational inequality between and within families in theoretical, methodological, and empirical terms.

Footnotes

Appendix A

Appendix B

Appendix C

Acknowledgements

For feedback, support, and stimulating discussions, I thank Fabrizio Bernardi, Juho Härkönen, Marco Cozzani, Mario Spezio, Irene Pañeda, Ildefonso Marqués, Pablo Gracia, Felix Tröpf, Nevena Kulik, Volker Lang, David Martínez, David Andrés, María José Serrano, Diana Galos, and Lea Kröger. This article was presented at the European Consortium for Sociological Research conference “Causes and Consequences of Inequalities in Europe” celebrated in Paris at Sciences Po between October 29 and 31, 2018. I thank the participants in the session for very accurate feedback. I also thank the four anonymous reviewers and the editor of Sociology of Education, Linda Renzulli, for the constructive remarks to improve the quality of the manuscript.

Research Ethics

The data set used here comes from the TwinLife study, a publicly available (GESIS) study in which families and children voluntarily participated. All data were properly anonymized.

Notes

Author Biography

Carlos J. Gil-Hernández is a PhD researcher at the Department of Political and Social Sciences of the European University Institute in Florence, Italy. He graduated in MSc studies at Pompeu Fabra University and the University of Tilburg. His research interests include child development, educational inequalities, intergenerational social mobility, and social policies. He has worked as a research assistant in international projects on the European Values Survey, a volume on social mobility and education edited by Stanford University Press, and as a consultant for Eurofound. He has published his work in journals such as Research in Social Stratification and Mobility and Demographic Research.

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