Cognitive Skills, Non-Cognitive Skills and Family Background: Evidence from Sibling Correlations Silke Anger IAB Nuremberg, University of Bamberg, IZA Daniel D. Schnitzlein * Leibniz University Hannover, DIW Berlin [This version: February 2014] Abstract This paper estimates sibling correlations in cognitive skills and non-cognitive skills to evaluate the importance of family background for skill formation. The study is based on a large representative German dataset, which includes IQ test scores and measures of non- cognitive skills. Using a Restricted Maximum Likelihood model we find substantial influences of family background on the formation of skills. Sibling correlations of non- cognitive skills range from 0.223 to 0.463, indicating that even for the lowest estimate, about one fifth of the variance can be attributed to factors shared by siblings. Calculated sibling correlations in cognitive skills are higher than 0.50, indicating that more than half of the inequality can be explained by family background. Comparing these findings to the results in the intergenerational skill transmission literature suggests that intergenerational correlations are only able to capture parts of the influence of the family on children’s cognitive and non- cognitive skills. This result is confirmed by decomposition analysis and in line with findings in the literature on educational and income mobility. JEL-Codes: J24, J62 Keywords: Sibling correlations, family background, non-cognitive skills, cognitive skills * Corresponding author: Daniel D. Schnitzlein, Leibniz University Hannover, Institute of Labour Economics, Koenigsworther Platz 1, 30167 Hannover, Germany; e-mail: [email protected]; tel: +49- (0)511-762-5298.
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Cognitive Skills, Non-Cognitive Skills and Family Background:
Evidence from Sibling Correlations
Silke Anger
IAB Nuremberg, University of Bamberg, IZA
Daniel D. Schnitzlein*
Leibniz University Hannover, DIW Berlin
[This version: February 2014]
Abstract
This paper estimates sibling correlations in cognitive skills and non-cognitive skills to evaluate the importance of family background for skill formation. The study is based on a large representative German dataset, which includes IQ test scores and measures of non-cognitive skills. Using a Restricted Maximum Likelihood model we find substantial influences of family background on the formation of skills. Sibling correlations of non-cognitive skills range from 0.223 to 0.463, indicating that even for the lowest estimate, about one fifth of the variance can be attributed to factors shared by siblings. Calculated sibling correlations in cognitive skills are higher than 0.50, indicating that more than half of the inequality can be explained by family background. Comparing these findings to the results in the intergenerational skill transmission literature suggests that intergenerational correlations are only able to capture parts of the influence of the family on children’s cognitive and non-cognitive skills. This result is confirmed by decomposition analysis and in line with findings in the literature on educational and income mobility. JEL-Codes: J24, J62 Keywords: Sibling correlations, family background, non-cognitive skills, cognitive skills
* Corresponding author: Daniel D. Schnitzlein, Leibniz University Hannover, Institute of Labour Economics, Koenigsworther Platz 1, 30167 Hannover, Germany; e-mail: [email protected]; tel: +49- (0)511-762-5298.
1
1 Introduction
Recent economic research stressed the importance of cognitive and non-cognitive
skills for both, individual labor market outcomes and social outcomes.1 This finding resulted
in a growing interest in the development of cognitive and non-cognitive skills. Cunha and
Heckman (2007, 2008) present a model of skill formation that links the development of these
skills - among other factors - to parental cognitive and non-cognitive skills, as well as parental
resources. This raises the question of equality of opportunities. Equality of opportunities in
the sense of Roemer (1998) requires that an individual’s economic success only depends on
factors under the individual’s control. Environmental factors – factors beyond an individual’s
control – should have no influence on later success or failure. The family a child is born into
is clearly beyond an individual’s control. Therefore the “accident of birth” (Cunha and
Heckman, 2007, p. 37) should have no influence on individual outcomes. As cognitive and
non-cognitive skills are important determinants of economic success, the normative goal of
equality of opportunity is violated if the formation of these skills is influenced by family
background.
A growing body of literature developed in the field of intergenerational mobility, that
analyzed the transmission of both, cognitive and non-cognitive skills from parents to children
(Black and Devereux, 2011). Intergenerational transmission of cognitive skills has been
analyzed for Scandinavia (Black et al., 2009, Björklund et al., 2010, Grönqvist et al., 2010),
for the US (Agee and Crocker, 2002), for the UK (Brown et al., 2011), and for Germany
(Anger and Heineck, 2010, Anger, 2012). In contrast, there is only scarce evidence on
intergenerational transmission of non-cognitive skills in the economic literature. The
transmission of personality traits from parents to children has been examined for the US
1 See for example Heckman et al. (2006) and Heineck and Anger (2010). An extensive overview can be found in Almlund et al. (2011).
2
(Mayer et al., 2004, Duncan et al., 2005), Sweden (Grönqvist et al., 2010) and Germany
(Anger, 2012).2
A number of authors have recently stressed that estimating intergenerational
correlations or elasticities only reveals part of the impact of family background (see e.g.,
Björklund et al., 2010, Björklund and Jäntti, 2012).3 Especially for the interpretation as an
indicator of equality of opportunity, they suggest instead estimating sibling correlations.
Sibling correlations are – compared to intergenerational correlations – a much broader
measure of the influence of the family. While an intergenerational correlation only covers a
one-dimensional intergenerational association between a parental skill measure and an
offspring’s skill measure, a sibling correlation takes into account all factors that are shared by
siblings of one family. This covers not only family background but also community factors.4
In the context of skill formation this is an important advantage of sibling correlations over
intergenerational correlations as Cunha and Heckman (2007, 2008) suggest the skill
formation not only to be dependent on parental skills but a variety of parental characteristics.
Sibling correlations have been used to estimate the influence of family background on
educational and labor market outcomes, showing remarkable cross-country differences
(Björklund et al., 2002, Schnitzlein, 2014). 5 These cross-country differences might be
attributed to different institutional settings in these countries, but the exact mechanisms are
still unclear. To the best of our knowledge, existing studies on cognitive and non-cognitive
skill correlations within families, until now, cover only the U.S. (Mazumder, 2008) and
2 Although economic research on non-cognitive skill formation is rather scarce, intergenerational correlations have been analyzed by psychologists for decades (e.g. Loehlin, 2005). However, the data sets used by most psychological studies are based on a small number of observations or lack representativeness. 3 Björklund and Jäntti (2012) call this the „tip of the iceberg“. 4 Among others, Solon et al. (2000), Page and Solon (2003), Leckie et al. (2010), Nicoletti and Rabe (2013) and Lindahl (2011) show that the family is the major factor compared to the neighborhood. Bügelmayer and Schnitzlein (2014) present results on German adolescents. Their results suggest that the influence of the neighborhood is not negligible in Germany but still family background is the predominant factor. Thus in the following when we talk about shared family background, this includes shared community factors. 5 For example, using brother correlations, Schnitzlein (2014) reports that about 45 percent of the variance in permanent earnings can be attributed to family or neighborhood factors in the US and Germany, whereas in the corresponding estimate for Denmark is only 20 percent.
3
Sweden (Björklund et al., 2010, Björklund and Jäntti, 2012), and they are based on few skill
measures and only on a single skill measurement at one point in time.6 Moreover, the Swedish
register data are only restricted to males, since they make use of information from military
enlistment tests (Björklund and Jäntti, 2012).
In this recent study, we contribute the following to the literature: first, we estimate
sibling correlations in a variety of cognitive and non-cognitive skills test scores based on
representative German survey data, providing measures of the importance of family factors
for individual skill formation. Thereby, we add the German perspective to the existing
literature, which is an important contribution in the light of the cross-country differentials in
sibling correlations in economic outcomes identified in the existing literature. If the estimated
sibling correlations in cognitive and non-cognitive skills follow the same cross-country
patterns than estimates for economic outcomes this would shed some light on the underlying
mechanisms of these differentials. Our data contains test scores from two ultra-short IQ-tests,
which we use as our measure of cognitive skills. Furthermore, it provides data on Locus of
Control, reciprocity, and the Big Five personality traits (openness, conscientiousness,
extraversion, agreeableness and neuroticism), which act as our measures of non-cognitive
skills. In contrast to the existing literature our data is not restricted to males and we can rely
on two repeated measurements of our non-cognitive skills measures.
Second, following a decomposition approach by Mazumder (2008) we investigate the
factors, which may drive the effect of family background on skill formation. Finally, we
assess to which extent differences in sibling correlations in skills between countries can
explain cross-national differences in the influence of family background on education and
labor market outcomes.
6 Nicoletti and Rabe (2013) report sibling correlations on exam scores, which are similar in size to cognitive skills, but refer to educational attainment.
4
To summarize our main results: We show that family background is important for
cognitive and non-cognitive skills for both men and women. Sibling correlations of
personality traits range from 0.223 to 0.463, indicating that even for the lowest estimate, one
fifth of the variance or inequality can be attributed to factors shared by siblings. All calculated
sibling correlations in cognitive skills are higher than 0.50, indicating that more than half of
the inequality can be explained by family background. Comparing these findings to the results
in the literature on intergenerational skill transmission suggests that sibling correlations are
indeed able to provide a more complete picture of the influence of the family on children’s
cognitive and non-cognitive skills.
Opening the black box of influence of family background supports this result. Parental
skills are important influence factors, but including a rich set of family characteristics
significantly adds to explaining the observed influence of family background.
Comparing our results to previous findings for the US and Sweden provides no
evidence that the differential in sibling correlations in economic outcomes can be explained
by differences in the formation of cognitive skills. The evidence from cross-country
comparisons with respect to sibling correlations in non-cognitive skills is less clear.
The remainder of the paper is structured as follows. In the next section we briefly
discuss the existing theoretical model of skill formation. The third section presents our data
and our main descriptive results. The fourth section contains our estimation strategy. Our
main results are presented and discussed in section 5, before conclusions follow in the last
section.
2 Theoretical background
The model of the family as formalized by Becker and Tomes (1979, 1986) underlies most
empirical analyses of both intergenerational mobility and sibling correlations in economic
5
outcomes. For an analysis of skill formation this model has two weaknesses. First, only one
single composite skill measure is contained. Therefore, complementarity and substitution of
different skills cannot be analyzed. Second, in the original model, parental investment and
complete skill formation takes place in one single period (childhood). This abstracts from the
possibility that investments in skill formation can be more important in some periods of
childhood compared to others.
Cunha and Heckman (2007) suggest an extension of the model addressing these
issues. In their model, an individual’s human capital stock contains both, cognitive and non-
cognitive skills. Cunha and Heckman (2007) present a production function for this part of
accumulated human capital. According to their model the vector of cognitive and non-
cognitive skills (𝜃) of an individual in period (t+1) is a function of the individual’s stock of
both cognitive and non-cognitive skills in the previous period (t), individual and parental
investments in skill formation in the previous period, and parents’ cognitive and non-
cognitive skills as well as other parental or environmental characteristics (h):
θ!!! = f!(θ! , I!, h) (1)
Cunha and Heckman (2007) propose that (i) ∂ f!(θ!, I!, h)/ ∂ θ! > 0 and (ii)
∂! f!(θ!, I!, h)/ ∂ θ! ∂ I!′ > 0. This means that the skill formation process is characterized by a
multiplier effect through self-productivity (i) and dynamic complementarity (ii) of skills. The
former mechanism implies that higher skills in one period create higher skills in the
subsequent period, which is also true between different skills through cross effects. The latter
mechanism means that the productivity of an investment in cognitive and non-cognitive skills
is increasing in higher existing skills. Cunha and Heckman (2008) present empirical evidence
6
corroborating these assumptions. They identify early childhood as most productive period for
investments in cognitive and non-cognitive skills.
This paper focuses on the importance of family background for an individual’s skill
formation. Family background enters the above production function via two channels. First,
the accumulation of cognitive and non-cognitive skills is directly determined by previous
parental investments, and second, the skill formation depends on the parental stock of
cognitive and non-cognitive skills. As we cannot directly observe the arguments in the above
function, we apply an indirect approach. If these channels – parental investments and parents’
stock in cognitive and non-cognitive skills – are important, siblings should have very similar
outcomes, as they share the same family background. We estimate sibling correlations in
cognitive and non-cognitive skills to assess how similar siblings are in skill levels. In a
second step, we decompose the sibling correlations into different input factors of individual
skill formation. This allows us to identify channels through which family background affects
cognitive and non-cognitive skills.
3 Data
3.1 Our estimation sample
We use data from the German Socio-Economic Panel Study (SOEP), which is a
representative household panel survey that started in 1984 (Wagner et al., 2007).7 The SOEP
conducts annual personal interviews with all adult household members and provides rich
information on socio-demographic characteristics, family background, and childhood
environment on about 20,000 individuals in more than 11,000 families in the most recent
wave (2012). Measures of cognitive and non-cognitive skills are included in the years 2005
(Big Five, Locus of Control, reciprocity), 2006 (short IQ tests), 2009 (Big Five), 2010 (Locus
7 We use SOEPv29 (DOI: 10.5684/soep.v29). For more information see http://www.diw.de/soep.
7
of Control, reciprocity), and 2012 (short IQ tests). While the non-cognitive skill measures are
surveyed via several questions in the main SOEP questionnaire, the short IQ-test were
performed only in the CAPI based subsamples of the SOEP. As CAPI interviews are standard
for the newer SOEP subsamples, the initial subsamples are still interviewed via PAPI mode.
This results in a significant lower number of observations available compared to the non-
cognitive skill measures. Unfortunately, for the repeated measurement in 2012 the sample
was further split up to conduct three instead of the original two short IQ tests. Therefore we
will only use the 2006 measurement for cognitive skills in this study.
The information on family relations between household members and the follow-up
concept of the SOEP allow us to observe children over time and to identify them as siblings
even when they are grown up and live in different households. In the survey, children need to
be observed in the same household as their parents only once in order to assign them correctly
to their mother and father. We consider two children to be siblings if they are assigned to the
same father and mother.8
We include all adult children of SOEP households with identified mothers and fathers
who either participated in one of the cognitive tests in 2006 or have successfully answered at
least one of the question sets on non-cognitive skills in one of the respective waves. We
restrict the sample to individuals aged 20 to 54 to avoid the risk of observing noisy skill
measures at very young or old age (Baltes et al., 1999, Cobb-Clark and Schurer, 2012, 2013).
The descriptive statistics of our main sample are shown in panel A of Table 1. All skill
measures are standardized to have mean zero and a standard deviation of one for each year.
8 The SOEP data provides different parental identifiers. In this study, we use the identifiers provided in the SOEP file BIOPAREN. These parental identifiers are based on cohabitation at age 17 (or older if respondent is older at first interview). The SOEP also provides information on biological children for all women in the survey but only since 2000 information on men are provided. As our children are mainly children from the initial SOEP households using the biological identifier for men would significantly reduce our sample size. However, for mothers, for about 92 percent of the mother-child pairs in our sample the social mother is also the biological mother. That means nearly all of our siblings share at least their biological mother. If genetics is an important factor, considering social instead of biological parents would lead to an underestimation of the estimated sibling correlations. Therefore, our estimates can be considered to be a lower bound.
8
Presented are figures for the pooled sample. In addition the number of observations, the
number of individuals, and the number of families are reported for each skill measure. As we
only include one observation for cognitive skills, number of observations and number of
individuals is identical for these outcomes.
Our data not only allows identifying parents and siblings, but also provides
information on parents’ characteristics, family background, and childhood environment. To
identify factors through which family background affects skills, we use data on parental
socio-economic characteristics. In particular we use father’s and mother’s years of education,
father’s and mother’s individual labor earnings,9 information on father’s and mother’s
migration background, mother’s age at first birth, whether the family is originally from East
Germany, and the number of children reported by the mother. As measures of parental non-
cognitive skills we include father’s and mother’s 2005 measures.10 Given the low number of
available observations for cognitive skills we are only able to perform the decomposition
analysis for the non-cognitive skill scores. The descriptive statistics for the subsample with
available parental information are presented in panel B of Table 1 and an overview on the
parental characteristics is shown in Table 2.
3.1 Cognitive and non-cognitive skill measures
In 2006 information on cognitive skills was collected from adult respondents and
comprises test scores from a word fluency test and a symbol correspondence test. Both are
ultra-short tests and were especially developed for the SOEP, as fully fletched IQ tests cannot
be implemented in a large-scale panel survey (Lang et al., 2007). Since the symbol
correspondence test is carried out using a computer, these tests were only conducted with
9 We also include years with zero earnings. As we use log earnings in most specifications. We actually computed log (earnings+1). 10 Due to the low number of observations we cannot include parental cognitive skill measures in the analysis. The effect of cognitive skills will – at least to some part – be captured by parental education.
9
respondents with a computer assisted personal interview (CAPI) – about one third of all
respondents. Both tests correspond to different modules of the Wechsler Adult Intelligence
Scale (WAIS) and produce outcomes, which are relatively well correlated with test scores
from more comprehensive and well-established intelligence tests.11
The symbol correspondence test is conceptually related to the mechanics of cognition
or fluid intelligence and comprises general abilities. The test involved asking respondents to
match as many numbers and symbols as possible within 90 seconds according to a given
correspondence list which is permanently visible to the respondents on a screen.
The word fluency test is conceptually related to the pragmatics of cognition or
crystallized intelligence. It involves the fulfillment of specific tasks that improve with
knowledge and skills acquired in the past. The word fluency test implemented in the SOEP
was based on the animal-naming task (Lindenberger and Baltes, 1995): respondents name as
many different animals as possible within 90 seconds. While verbal fluency is based on
learning, speed of cognition is related to an individual’s innate abilities (Cattell, 1987).
In addition, we generate a measure of general intelligence by averaging the two types
of ability test scores.12
Measures of non-cognitive skills for adult respondents are available for 2005 (Dehne
and Schupp, 2007, Richter et al., 2013), and were repeated in 2009 and 2010. The personality
measures in 2005 include self-rated measures that were related to the Five Factor Model
(McCrae and Costa Jr., 2011) and comprise the five basic psychological dimensions –
openness to experience, conscientiousness, extraversion, agreeableness, neuroticism (Big
Five) – which are each measured with 3 items. In addition, self-rated measures of Locus of
Control (7 items) and reciprocity (6 items) are included in 2005.
11 Lang et al. (2007) carry out reliability analyses and find test–retest coefficients of 0.7 for both the word fluency test and the symbol correspondence test. 12 Using average test scores is expected to reduce the error-in-variable bias by diminishing the random component of measured test scores. Furthermore, average test scores could be interpreted as an extract of a general ability type, which captures both coding speed and verbal fluency.
10
Locus of control is the extent to which an individual believes that he or she has control
over what happens in his or her life. Psychologists differentiate between external locus of
control, i.e. individuals believe that events are mainly the result of external effects, and
internal locus of control, i.e. individuals believe that events are the results of their own action.
Reciprocity measures the extent to which an individual is willing to respond to
positive or negative behavior. One can distinguish positive reciprocity, i.e. the extent to which
individuals respond positively to positive actions and negative reciprocity, i.e. the extent to
which individuals respond negatively to negative behavior.
All items related to non-cognitive skills are answered on 7-point Likert-type scales (1
– “disagree completely” to 7 – “agree completely”). The scores are summed up among each
dimension to create an index ranging from 1 to 7, and standardized for each year. In 2009,
respondents were repeatedly asked to rate their personality according to the dimensions of the
Five Factor Model. Self-ratings of Locus of Control and of reciprocity were repeated in
2010.13
As discussed above, we only include individuals in our sample for whom we can
identify the parents. Naturally, as in all analysis on intergenerational mobility or family
background, this reduces the number of individuals in the estimation sample. Figures A.1 and
A.2 in the appendix show distributions for our cognitive and non-cognitive skill measures for
the full SOEP sample and our full estimation sample. For all skill measures the graphs show
very similar distributions in the two samples. Therefore, our results should not be
contaminated. This is in line with results by Richter et al. (2014) who only find minor effects
of personality traits on panel attrition.
13 Personal traits and Locus of Control have been shown to be relatively stable over the adult lifespan (Cobb-Clark and Schurer, 2012, 2013).
11
4 Estimation strategy
Let 𝑦!" be a cognitive or non-cognitive tests score for child j of family i. We assume that this
score can be decomposed into two orthogonal components (Solon et al., 1991, Solon, 1999).
𝑦!" = 𝛼! + 𝜇!" (2)
where 𝛼! covers the combined effect of all factors that are shared by siblings from
family i. 𝜇!" covers all factors that are purely idiosyncratic to sibling j. Orthogonality arises as
we observe each child only in one family. Therefore, the variance of the observed test score
σ!! can be expressed as the sum of the variances of the two components:
σ!! = σ!! + σ!! (3)
The correlation coefficient 𝜌 of the skill measure of two siblings j and j’ then equals
the ratio of the variance of the family component σ!! and the total variance of the measure
σ!! + σ!!:
ρ = corr y!", y!"! = !!!
!!!!!!! with j ≠ j′ (4)
The interpretation of 𝜌 is that the correlation in skills between two siblings (therefore
sibling correlation) equals the proportion of the variance (or inequality) in that skill that can
be attributed to factors shared by siblings, e.g. family factors or neighborhood factors. σ!! and
σ!! cannot be negative, so 𝜌 can take on values between 0 and 1. A correlation of 0 indicates
that there is no influence from family and community factors and 1 indicates that there is no
12
influence from the individual. The first case would describe a fully mobile society and the
latter a fully deterministic one.
Solon (1999) shows that the relationship of the sibling correlation defined above and
the often-estimated intergenerational correlation is:
ρ!"#$$ = IGC!"#$$! + other shared factors uncorrelated with parental skill measure (5)
The sibling correlation in a specific cognitive or non-cognitive skill equals the square
of the intergenerational correlation in this skill plus the influence of all shared factors that are
uncorrelated with the corresponding parental skill measure. Although a sibling correlation is a
much broader measure of family background than an intergenerational correlation, as there
are factors related to the family that are not shared by siblings, the sibling correlation is still a
lower bound of the true influence of family background (see discussion in Björklund and
Jäntti, 2012).
Following Mazumder (2008), we estimate the sibling correlation in our skill measures
as the within-cluster correlation in the following linear multilevel model,
𝑦!"# = 𝛽𝑋!"# + 𝛼! + 𝜇!" + 𝜈!"# (6)
with y being an annual (𝑡) observation of a specific outcome, 𝑋 being a matrix of fixed
year, age and gender effects (including year dummies; age; age2; a gender dummy and
interaction terms of the gender dummy and the age variables), the family component (α!), the
individual (µμ!") component, and a transitory component (𝜈!"#). The sum of the family and
individual component represents the permanent part of the observed outcome. We apply
Restricted Maximum Likelihood (REML) to estimate this model and to estimate the variances
13
of α! and µμ!". The standard error for the sibling correlation is calculated using the delta
method. For specifications with only one observation in time, the model is estimated with
only two levels.
To identify the relative importance of different inputs in the skill formation process,
we follow the decomposition approach suggested by Mazumder (2008). We further include
family background characteristics in the 𝑋 matrix in the above model. If these characteristics
are important determinants in the formation of the respective skill, this should reduce the
variance of the family specific component and therefore reduce the sibling correlation. This
reduction can be seen as an upper bound estimate of the importance of the added family
background characteristic.
5 Results
5.1 Sibling correlations in cognitive and non-cognitive skills
We begin the discussion of our results with our measure of cognitive skills. Figure 1 shows
the estimated sibling correlations and Table A.1 shows the variance of the family and
individual components. We find a strong influence of family background on all dimensions of
cognitive abilities. The sibling correlation in crystallized intelligence is 0.609, in fluid
intelligence 0.549, and in general intelligence 0.579. Hence, family and community
background explains more than 50 percent of the variation in cognitive test scores.
Figure 2 and Table A.2 show the results for non-cognitive skills. The estimated sibling
correlation in Locus of Control is 0.463. Again, this indicates a strong effect of family
background on Locus of Control. 46 percent of the variation in Locus of Control can be
attributed to factors shared by siblings. The corresponding estimates for positive and negative
reciprocity are 0.434 and 0.382, which still indicates substantial influence of family
background. The estimates for Big Five personality traits show more variation. While shared
14
background factors seem to be important for conscientiousness (0.412) the estimated sibling
correlation in extraversion is only 0.223. Agreeableness (0.349), openness (0.293) and
neuroticism (0.308) range in-between.
Equation (5) shows that sibling correlations cover much more of the influence of
family background than intergenerational correlations. As argued in the introduction this is
one reason why sibling correlations are a preferable measure for equality of opportunity. In
Figure 3, we draw on the intergenerational correlations reported by Anger (2012) who uses
the same dataset and outcomes as we do.14 It is apparent that, for all analyzed outcomes, the
estimated sibling correlations are considerably higher than the corresponding squared
intergenerational correlations. This finding suggests that intergenerational correlations are in
fact only able to capture parts of the influence of the family on children’s cognitive and non-
cognitive skills. This result is in line with findings in the literature on educational and income
mobility.
To summarize, we showed that family background has a significant and in most cases
substantial influence on an individual’s cognitive and non-cognitive skills. As these skills are
important determinants of economic success this finding violates the normative goal of
equality of opportunity.
5.2 Decomposition of the influence of family background
As Cunha and Heckman (2007) show, the formation of skills is influenced by different input
factors. In this section we shed light on the question which channels are most important in
determining the influence of the family on skill formation.
In a first step, we estimate sibling correlations for different subgroups of our
estimation sample. Table 3 shows results divided by family income and education. Siblings
14 Note that Anger (2012) does not report results for reciprocity.
15
with high income parents15 show (with the exception of negative reciprocity) higher sibling
correlations than low income families, indicating stronger influence of the family. Children of
high educated mothers16 show higher sibling correlations in most outcomes as well again
indicating higher influence of family background on skill formation.17 Overall, the results in
Table 3 indicate that the influence of the family differs for different family types. While the
size of our estimation sample doesn’t allow us to investigate this in more detail, we can shed
light on the question which parental characteristics best explain the influence of family
background on skill formation.
Table 4 shows the results of the decomposition approach described in section 4. The
first column shows the estimated sibling correlations for the full estimation sample and the
second column shows the estimated sibling correlations for the subsample with non-missing
parental characteristics. With the exception of the estimate for negative reciprocity – which
increases from 0.382 to 0.480 – the sibling correlations are very similar in both samples.
The middle part of Table 4 presents the results for our decomposition. In the first
column, we add the respective parental (father’s and mother’s) skills to the fixed effects
matrix in equation (6). The resulting decline in the estimated sibling correlation indicates the
importance of the parental skill in the influence of the family on the skill formation process.
In the second column, instead of parental skills, we add parental education. Parental education
acts as both, an indicator for parental resources but also as indicator for parental cognitive
skills. Finally, in the third column in the middle part of Table 4 we add the full set of parental
characteristics (as presented in Table 2) to our model.
For each of these decompositions, the right part of Table 4 shows the respective
percentage reduction in the estimated sibling correlation. The results give two important
15 We use the sum of mother’s and father’s earnings (including zero earnings). Families above the median are labeled high income. 16 Mothers with at least 12 years of education. 17 See Conley et al. (2007) for a more detailed analyses of sibling correlations among different subgroups.
16
insights: first, for all outcomes, the corresponding parental skill is important but adding the
full set of parental characteristics clearly adds in explaining the observed sibling correlations.
Second, even our rich set of parental characteristics is only able to capture 14 to 46 percent of
the influence of family background captured by the estimated sibling correlations.
To summarize, we showed that the influence of family background on an individual’s
skill formation process differs along parental resources. Our decomposition approach
revealed, that parental skills are important factors in determining the influence of family
background but – as also suggested in section 5.1 – only looking at intergenerational skill
transmission does not capture the full picture. In addition, our results show that even a rich set
of parental characteristics does only capture less than half of the influence of the family on the
skill formation process.
5.3 Cross-national comparisons
Finally, we discuss how our findings compare to the existing results in the literature. Can
differences in the influence of family background on cognitive and non-cognitive skills
explain the observed differences in the importance of family background for economic
outcomes?
Björklund et al. (2002) and Schnitzlein (2014) report significant cross-country
differences in sibling correlations in earnings. In particular they find that in the US and
Germany, family background is more important than in the Scandinavian countries. Whereas
in the US and Germany about 45 percent of the variance in earnings can be attributed to
family factors, this share is only 20 percent in Denmark based on brother correlations
(Schnitzlein, 2014).18
18 Cross-country differences in the importance of family background are also found for educational attainment. Whereas in Nordic countries about 45 percent of the variance in education can be attributed to the family and neighborhood (Raaum et al., 2006, Lindahl, 2011), this is more than 60 percent in Germany (Schnitzlein, 2014) and up to 70 percent in the US (Mazumder, 2011).
17
However, the sibling correlation in cognitive skills for the US reported by Mazumder
(2008) is 0.619. Hence, compared to the estimates presented in Table A.1 the influence of
family background on the formation of cognitive skills is only slightly different in the US
than in Germany.19 Björklund and Jäntti (2012) find brother correlations of about 0.5 for
cognitive skills in Swedish data. Again these estimates differ only slightly from the ones
presented in Table A.1. Based on these findings we find no evidence that differences in the
influence of family background on the formation of cognitive skills can explain the cross-
country differentials in sibling correlations in earnings.
Turning to non-cognitive skills, Mazumder (2008) uses the Rotter scale for Locus of
Control and finds correlations of 0.11 for brothers, 0.07 for sisters, and 0.09 for all. These
estimates are much lower than the ones presented in Table A.2 for Germany. However, the
Rotter questionnaire in the NLSY used by Mazumder (2008) is only a four-item version of the
original 60-item scale (instead of 7 items in the SOEP) and each item is only scored on a scale
of 1 to 4 (instead of 1 to 7 in the SOEP). In addition, Mazumder (2008) had only one
observation available in the data and therefore could not control for transitory fluctuations.
Solon et al. (1991) showed that using multiple measurements reduces transitory fluctuations
and measurement error that leads to underestimation of the sibling correlation.20. Figure A.3
in the appendix shows this effect for our non-cognitive skill measures. For all skill measures
the estimated sibling correlations in permanent outcomes – the model in equation (6)
estimated with two available observations – are clearly higher than the corresponding sibling
correlations using only data from the first (2005) or the second (2009 or 2010) wave.21
Björklund and Jäntti (2012) present the second available estimate in the literature for
non-cognitive skills. They used an aggregate measure of leadership skills, derived from
19 However, it may be problematic to directly compare these results to Mazumder (2008), since he uses a different measure of cognitive skills (AFQT test scores). 20 This is similar to the findings of Solon (1989, 1992) and Zimmerman (1992) for intergenerational mobility estimates. 21 In these cases the model in equation (6) is estimated without the transitory component.
18
interviews during the military enlistment test. They report a brother correlation of 0.32, which
is in the range of sibling correlation in personality traits revealed by our estimates for
Germany. Again, however, it is not clear if this measure is comparable to one of our
measures.
To summarize, our results on cognitive skills are remarkable similar to existing results
for brothers for the US and Sweden. We find no evidence that differences in the influence of
family background on cognitive skills explain differences in the importance of family
background for economic success. The picture for non-cognitive skills is not as clear, as the
different measures used are not directly comparable.
6 Conclusion
In this study, we investigate the importance of family background for cognitive and non-
cognitive skills based on sibling correlations in order to provide a broader measure of the role
of family background in the process of skill formation than the previously used
intergenerational transmission estimates. Our estimates are based on data from the German
Socio-Economic Panel Study (SOEP), which is a large representative household survey and
provides measures of cognitive skills from two ultra-short IQ-tests, and self-rated measures of
Locus of Control, reciprocity, and the Big Five personality traits. Previous analyses on
Sweden and the US are restricted in as much as they are based only on males (Björklund et
al., 2010, Björklund and Jäntti, 2012), use only Locus of Control out of many personality
traits (Mazumder, 2008), and use only a single measurement at one point in time. Hence, this
study contributes to the literature by providing evidence on sibling correlations in broader
measures of non-cognitive skills including men and women.
We show that family background is important for cognitive and non-cognitive skills.
Sibling correlations of personality traits range from 0.223 to 0.463, indicating that even for
19
the lowest estimate, one fifth of the variance or inequality can be attributed to factors shared
by siblings. All calculated sibling correlations in cognitive skills are higher than 0.50,
indicating that more than half of the inequality can be explained by shared family
background. Comparing these findings to the results in the intergenerational skill transmission
literature suggests that sibling correlations are indeed able to provide a more complete picture
of the family influence on children’s cognitive and non-cognitive skills. This result is in line
with findings in the literature on educational and income mobility.
Opening the black box of influence of family background supports this result. Parental
skills are important influence factors, but including a rich set of family characteristics
significantly adds to explaining the observed influence of family background.
Comparing our results to previous findings for the US and Sweden provides no
evidence that the differential in sibling correlations in economic outcomes can be explained
by differences in the formation of cognitive skills. The evidence from cross-country
comparisons with respect to sibling correlations in non-cognitive skills is less clear.
20
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23
Figures and tables
Figure 1: Sibling correlations in cognitive skills
Note: Presented are sibling correlations for cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared); a gender dummy and interactions of the gender dummy and the polynomials of age. Source: SOEPv29.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Crystallized intelligence Fluid intelligence General intelligence
Sibl
ing
corr
elat
ion
24
Figure 2: Sibling correlations in non-cognitive skills
Note: Presented are sibling correlations for non-cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared), a survey year dummy. and a gender dummy and interactions of the gender dummy and the polynomials of age. Source: SOEPv29.
0
0.1
0.2
0.3
0.4
0.5
0.6
Locus
of Con
trol
Positiv
e reci
procit
y
Negati
ve re
ciproc
ity
Openn
ess
Consci
entio
usness
Extrav
ersion
Agreeab
leness
Neurot
icism
Sibl
ing
corr
elat
ion
25
Figure 3: Comparison of sibling and intergenerational correlations
Note: Presented are sibling correlations and squared intergenerational correlations for cognitive and non-cognitive skills. Squared intergenerational correlations are taken from Anger (2012).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Crystal
lized
intel
ligen
ce
Fluid i
ntellig
ence
Genera
l intel
ligen
ce
Locus
of Con
trol
Big Five
O
Big Five
C
Big Five
E
Big Five
A
Big Five
N
Sibling correlation
Squared IGC
26
Table 1: Descriptive statistics - Main sample and sample with parental characteristics
Note: the table shows descriptive statistics for our main sample and the subsample with non-missing parental characteristics. Source: SOEPv29.
Outcome Mean Min Max N of Obs. N of Ind. N of Fam.
Table 2: Descriptive statistics of parental characteristics
Note: the table shows descriptive statistics for our parental characteristics. Source: SOEPv29.
Locus of Reciprocity Big FiveControl
Locus of Control -0.236 -0.232 -0.240Positive reciprocity 0.035 0.037 0.021Negative reciprocity -0.104 -0.108 -0.109Openness -0.110 -0.107 -0.116Conscientiousness 0.146 0.145 0.145Extraversion -0.068 -0.067 -0.075Agreeableness 0.161 0.161 0.164Neuroticism 0.284 0.285 0.285Years of education 11.18 11.18 11.17Earnings 6.727 6.730 6.715East German 0.314 0.314 0.310Migration background 0.209 0.208 0.212Number of kids 2.610 2.606 2.610Age at first birth 23.31 23.31 23.30
Locus of Control -0.083 -0.079 -0.074Positive reciprocity 0.029 0.027 0.031Negative reciprocity 0.147 0.149 0.139Openness -0.210 -0.214 -0.211Conscientiousness 0.041 0.039 0.034Extraversion -0.208 -0.210 -0.212Agreeableness -0.240 -0.240 -0.238Neuroticism 0.015 0.012 0.014Years of education 11.78 11.78 11.80Earnings 8.457 8.452 8.422East German 0.310 0.311 0.307Migration background 0.212 0.211 0.215
A: Mothers' characteristics
B: Fathers' characteristics
28
Table 3: Sibling correlations by parental background
Note: Presented are sibling correlations for non-cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared); a gender dummy and interactions of the gender dummy and the polynomials of age. Samples are divided along family income (sum of father’s and mother’s earnings including zeros) with high income family indicating families above the median and mothers education (high educated mother: 12 or more years of education). Source: SOEPv29
Locus of Positive Negative Big Five Big Five Big Five Big Five Big FiveControl reciprocity reciprocity O C E A N
High income family 0.526 0.489 0.341 0.335 0.431 0.282 0.401 0.321(0.095) (0.147) (0.129) (0.078) (0.086) (0.077) (0.085) (0.091)
Low income family 0.468 0.457 0.525 0.161 0.312 0.120 0.280 0.222(0.074) (0.133) (0.068) (0.070) (0.077) (0.067) (0.079) (0.077)
Note: Presented are sibling correlations for non-cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared); a gender dummy and interactions of the gender dummy and the polynomials of age. Source: SOEPv29
All siblings All siblingsfull sample par. sample parental parental all parental parental all
skill education factors skill education factors
Locus of Control 0.463 0.497 0.379 0.478 0.317 23.68% 3.84% 36.15%(0.042) (0.057) (0.064) (0.059) (0.069)
Appendix Figure A.1: Distribution of cognitive skills; full SOEP-sample vs. estimation sample
Source: SOEPv29
0.1
.2.3
Dens
ity
-4 -2 0 2 4 6Crystallized intelligence
0.1
.2.3
Dens
ity
-4 -2 0 2 4 6Fluid intelligence
0.1
.2.3
Dens
ity
-4 -2 0 2 4 6General intelligence
Full SOEP distribution
Full estimation sample
31
Figure A.2: Distribution of non-cognitive skills; full SOEP-sample vs. estimation sample
Source: SOEPv29
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Locus of Control
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Positive reciprocity
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Negative reciprocity
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Openness
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Conscientiousness
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Extraversion
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Agreeableness
0.1
.2.3
Dens
ity
-6 -4 -2 0 2 4Neuroticism
Full SOEP distribution
Full estimation sample
32
Figure A.3: Sibling correlations in non-cognitive skills – permanent and annual measures
Source: SOEPv29.
0 .1 .2 .3 .4 .5
Neuroticism
Agreeableness
Extraversion
Conscientiousness
Openness
Negative Reciprocity
Positive Reciprocity
Locus of Control
First wave Second wavePermanent Outcome
33
Table A.1: Basic estimates – cognitive skills
Note: Presented are sibling correlations for cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared); a gender dummy and interactions of the gender dummy and the polynomials of age. Source: SOEPv29.
Note: Presented are sibling correlations for non-cognitive skill measures. The models are estimated via REML. Standard errors of the sibling correlations are calculated via the delta method. All estimations control for fixed aged profiles (age and age squared), a survey year dummy. and a gender dummy and interactions of the gender dummy and the polynomials of age. Source: SOEPv29.
Locus of Positive Negative Big Five Big Five Big Five Big Five Big FiveControl reciprocity reciprocity O C E A N