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: schnitzlein@aoek.uni-hannover.de; tel: +49- (0)511-762-5298.

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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).

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(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.

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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.

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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

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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

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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.

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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.

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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.

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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.

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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

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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

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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

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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.

Cognitive skillsCrystallized intelligence 0.558 -1.812 2.962 443 443 364Fluid intelligence 0.118 -2.135 3.118 501 501 399General intelligence 0.342 -1.890 2.572 443 443 364

Non-cognitive skillsLocus of Control 0.047 -3.660 2.407 6,290 4,352 3,014Positive reciprocity -0.067 -5.332 1.276 6,346 4,380 3,034Negative reciprocity 0.151 -1.442 2.780 6,346 4,380 3,034Openness 0.073 -2.895 2.131 6,415 4,237 2,942Conscientiousness -0.215 -4.866 1.241 6,415 4,237 2,942Extraversion 0.085 -3.373 1.947 6,415 4,237 2,942Agreeableness -0.100 -4.554 1.690 6,415 4,237 2,942Neuroticism -0.070 -2.425 2.604 6,415 4,237 2,942

Non-cognitive skillsLocus of Control 0.044 -3.660 2.407 2,832 1,906 1,226Positive reciprocity -0.070 -5.332 1.276 2,847 1,914 1,232Negative reciprocity 0.173 -1.442 2.780 2,847 1,914 1,232Openness 0.070 -2.895 2.131 2,882 1,868 1,205Conscientiousness -0.214 -4.866 1.241 2,882 1,868 1,205Extraversion 0.097 -3.373 1.947 2,882 1,868 1,205Agreeableness -0.112 -4.554 1.690 2,882 1,868 1,205Neuroticism -0.064 -2.425 2.604 2,882 1,868 1,205

A: Main sample

B: Sample with parental characteristics

  27

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)

High educated mother 0.626 0.560 0.544 0.295 0.358 0.185 0.470 n.s.(0.133) (0.190) (0.118) (0.091) (0.106) (0.100) (0.114) n.s.

Low educated mother 0.458 0.447 0.441 0.217 0.363 0.193 0.286 0.356(0.065) (0.117) (0.072) (0.064) (0.069) (0.060) (0.067) (0.071)

All ind. with nonmis, 0.497 0.464 0.480 0.244 0.366 0.190 0.335 0.266par. characteristics (0.057) (0.099) (0.061) (0.052) (0.058) (0.052) (0.058) (0.059)

Full sample 0.463 0.434 0.382 0.293 0.412 0.223 0.349 0.308(0.042) (0.063) (0.044) (0.037) (0.041) (0.037) (0.041) (0.043)

  29

Table 4: Decomposition of sibling correlations

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)

Positive reciprocity 0.434 0.464 0.367 0.459 0.298 20.95% 1.01% 35.85%(0.063) (0.099) (0.112) (0.099) (0.119)

Negative reciprocity 0.382 0.480 0.380 0.467 0.322 20.90% 2.68% 32.90%(0.044) (0.061) (0.066) (0.062) (0.070)

B5: Openness 0.293 0.244 0.165 0.216 0.131 32.46% 11.65% 46.48%(0.037) (0.052) (0.053) (0.053) (0.053)

B5: Conscientiousness 0.412 0.366 0.322 0.353 0.290 12.07% 3.47% 20.88%(0.041) (0.058) (0.060) (0.058) (0.061)

B5: Extraversion 0.223 0.190 0.161 0.189 0.149 15.27% 0.28% 21.71%(0.037) (0.052) (0.053) (0.052) (0.052)

B5: Agreeableness 0.349 0.335 0.281 0.335 0.257 16.17% 0.03% 23.40%(0.041) (0.058) (0.059) (0.058) (0.060)

B5: Neuroticism 0.308 0.266 0.247 0.265 0.228 7.14% 0.32% 14.12%(0.043) (0.059) (0.059) (0.059) (0.060)

All siblings controling for percentage reduction

  30

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.

Crystallized Fluid Generalintelligence intelligence intelligence

Sibling correlation 0.609 0.549 0.579(s.e.) (0.062) (0.068) (0.067)

Family component 0.408 0.429 0.454(s.e.) (0.057) (0.068) (0.069)

Individual component 0.262 0.352 0.330(s.e.) (0.040) (0.050) (0.051)

Transitory component - - -(s.e.)

  34

Table A.2: Basic estimates – 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.

Locus of Positive Negative Big Five Big Five Big Five Big Five Big FiveControl reciprocity reciprocity O C E A N

Sibling correlation 0.463 0.434 0.382 0.293 0.412 0.223 0.349 0.308(s.e.) (0.042) (0.063) (0.044) (0.037) (0.041) (0.037) (0.041) (0.043)

Family component 0.210 0.131 0.161 0.162 0.215 0.142 0.168 0.148(s.e.) (0.021) (0.019) (0.020) (0.021) (0.023) (0.024) (0.021) (0.022)

Individual component 0.243 0.172 0.260 0.390 0.307 0.496 0.313 0.333(s.e.) (0.022) (0.024) (0.023) (0.024) (0.025) (0.028) (0.023) (0.024)

Transitory component 0.466 0.610 0.480 0.360 0.499 0.370 0.444 0.415(s.e.) (0.015) (0.019) (0.015) (0.011) (0.015) (0.011) (0.013) (0.012)