Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data

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Intelligence

Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data Linda Wänström* , Bertil Wegmann Linköping University, Linköping 581 83, Sweden

A R T I C L E

I N F O

Article history: Received 19 February 2016 Received in revised form 5 January 2017 Accepted 19 January 2017 Available online xxxx

A B S T R A C T We examine the effects of child sibship size on intelligence, school performance and adult income for a sample of Swedish school children (n = 1326). These children were measured in grade three in 1965 (age 10) and in grades six (age 13) and nine (age 16), and the women and men were later followed up in adulthood at ages 43 and 47, respectively. Using Bayesian varying-intercept modeling we account for differences between school classes in each of our three response variables: IQ-scores, school grades and adult income, and control for background variables such as gender, socioeconomic status, and maternal- and paternal age. Consistent with previous research, we find patterns of decreasing IQ scores for increasing sibship sizes, specifically for an increasing number of older siblings. No relationships between sibship size and children’s school grades are found. We find, however, patterns of decreasing adult income for an increasing number of younger siblings. In addition, considerable amounts of variations in intelligence scores as well as school grades are found between school classes. Some implications of the findings and suggestions for future research are provided. © 2017 Elsevier Inc. All rights reserved.

1. Introduction Family composition variables, such as children’s sibship size, have been found to be negatively correlated with children’s intelligence and related variables (correlation coefficients around −0.20), e.g. IQ tests and achievement tests, school grades, and educational attainment, in a number of studies (see e.g. Anastasi, 1956; Belmont & Marolla, 1973; Downey, 2001; Fergusson, Horwood, & Ridder, 2005; Higgins, Reed & Reed, 1962; Jæger, 2008, 2009; Kanazawa, 2012; Kristensen and Bjerkedal; Nisbet & Entwistle, 1967; Page and Grandon, 1979; Velandia, Grandon, & Page, 1978; Zajonc, 1975; Zajonc, Markus, Berbaum, & Bargh, 1991). There have not been as many studies on long term effects of sibship size, although Holmgren, Molander, and Nilsson (2006) and Holmgren, Molander, and Nilsson (2007) found negative relationships between sibship size and executive functioning and memory in adulthood, whereas Goodman, Koupil, and Lawson (2012) found negative relations with adult income. Theories have been developed to explain these relationships. According to the confluence model (Zajonc, 1975; Zajonc, 1976; Zajonc, 2001; Zajonc & Mullally, 1997), children’s intellectual development is affected by their intellectual home climates, which, in

* Corresponding author. E-mail address: [email protected] (L. Wänsträm).

turn, are affected by the intellectual levels of the family members. The model predicts lower test scores for children of larger sibship sizes and children of lower birth orders (born early into the family). The resource dilution theory (Blake, 1981; Downey, 1995; Downey, 2001; Armor, 2001) predicts lower IQ test scores, educational performance, and educational attainment for children of larger sibship sizes, because of a dilution of parental resources (e.g. shelter, food, travel, instruction, and money) in these families. The above theories assume, at least partly, a causal relationship between sibship size and IQ test scores and educational performance. Because IQ and educational performance are related to each other (correlation coefficient around 0.54, see Roth et al., 2015), it is interesting to examine if sibship size has any effects on educational performance, taking into account the effect of IQ. Adult income is also related to IQ (correlation coefficient around 0.20, see Strenze, 2007) and educational performance (grades and salary: correlation coefficient around 0.20, see Roth, 1998) and it is therefore also interesting to examine if sibship size has any long term effects on adult income, accounting for IQ, educational performance, and educational attainment. In the present study, we examine the effects of sibship size on intelligence, educational performance, and adult income using a cohort of Swedish children attending grade school in the 1960s. The sibship size effect may be different in different countries, depending on differences in social policies (Downey, 2001; Park, 2008; Xu, 2008). The social system in Sweden is different from the systems in

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e.g. the U.S. and many European countries, where much of the data used for sibship size studies originate from. Universal child benefits were introduced in Sweden in 1948 (see e.g. Ferrarini, 2009) and students can attend Universities at practically no cost. Park (2008) noted that among 20 OECD countries, Sweden was among those with the highest public expenditure on education and family (as percent of GDP), and was also among those countries with the highest levels of universal child benefits. Dilution of some parental resources, such as money, may therefore not be as influential in Sweden as in other countries. Indeed, Park (2008) found that the sibship size effects on reading scores for countries with high levels of public expenditure on education, and countries with high levels of public expenditure on the family, was approximately one third of the effects for countries with low levels. The sibship size effects for countries with high levels of universal child benefits, and countries with high levels of child care, was about one half of the effects for countries with low benefits and child care. In line with this, Xu (2008) also found weaker sibship size effects in social democratic countries (such as Sweden) on math- and reading scores, and nonexisting effects on science scores. It is therefore interesting to see if we can find any sibship size effects on intelligence, educational performance, and adult income in our Swedish cohort. The effect of sibship size on intelligence and related variables may partly be due to selection, such that parents with high performing children have fewer children on average, compared to parents with low performing children (Page and Grandon, 1979; Velandia et al., 1978; Rodgers, Cleveland, van den Oord, & Rowe, 2000; Rodgers, 2001). Some studies have found that the effects of sibship size decrease, and sometimes disappear, when adjusting for selection bias by accounting for unmeasured variance statistically, using instrumental variables or multilevel multiprocess models (Black, Devereux, & Salvanes, 2005; 2010; de Haan, 2010; Angrist, Lavy, & Schlosser, 2010; Ghilagaber & Wänström, 2015), whereas others have found that some effects persist (Cáceres-Delpiano, 2006; Black et al., 2010; Conley & Glauber, 2006; Mogstad & Wiswall, 2016). In a similar manner, although most studies on birth order effects and intelligence have used between-family data (including one child per family), some studies have found that birth order effects disappear (e.g. Rodgers, 1984; Rodgers et al., 2000) when including all, or some, children of the same family. When within-family data are lacking, researchers have tried to account for possible sources of selection bias by e.g. including important variables in the models or holding variable levels constant. Because we use a cohort of children, i.e. between-family data, we try to account for sources of selection by including them into the models. The variables we are able to control for are socioeconomic background, maternal- and paternal age, gender, concentration difficulties, and educational attainment, and we next provide reasons for including them. Many studies show negative effects of child socioeconomic status on educational performance and on economic situations in adulthood (Dubow, Boxer, & Huessmann, 2009; Fergusson, Horwood, & Boden, 2008; Gibb, Fergusson, & Horwood, 2012; Myrberg & Rosén, 2009). In addition, children from lower socioeconomic backgrounds have, on average, more siblings (Blake, 1981; Downey, 1995; Downey, 2001). Some associations between parental age and child intelligence have also been found (e.g. Myrskylä, Silventoinen, Tynelius, & Rasmussen, 2013). Therefore, we find it necessary to account for differences in children’s socioeconomic backgrounds and maternal and paternal age when examining the effects of sibship size on intelligence and related variables. There have been no previous studies on sibship size and intelligence on the dataset we are using. However, previous studies on this dataset have found some relationships between IQ and educational attainment (Bergman, Corovic, Ferrer-Wreder, & Modig, 2014), between school performance and educational attainment (Ferrer-Wreder, Wänström, & Corovic, 2014), between income and educational attainment as well

as income and gender (Ferrer-Wreder et al., 2014), and between concentration difficulties and educational performance and income (Andersson, Lovén, & Bergman, 2014). We therefore find it necessary to also control for gender, concentration difficulties, and educational attainment in our study. Relationships between sibship size and IQ and related outcomes may not be linear. Rankin, Gaite, and Heiry (1979) found, for example, that American Samoan children with sibship sizes closer to the mean scored higher compared to children of other sibship sizes. There may be differences between families that decide to have a number of children closer to, or farther away, from the “norm”. Ghilagaber and Wänström (2015) found that parents who decided to have additional children differed in their incomes, educational attainment, ethnicities, and maternal age at first child. We therefore examine both linear and nonlinear effects of sibship size. In addition, we examine whether parents with a number of children close to, or far away, from the “norm” differ in their characteristics. Our research questions are as follows: R1: What is the effect of sibship size on intelligence test scores for Swedish school age children? R2: What is the effect of sibship size on Swedish children’s school grades when taking into account the effect of individual differences in intelligence? R3: What is the effect of sibship size on the incomes of Swedish adults when taking into account the effects of school grades, educational attainment, and individual differences in intelligence? 2. Methods 2.1. Data Analyses are based on the longitudinal dataset Individual Development and Adaptation, IDA (Bergman, 2000). The dataset (n = 1326) includes all school children who were in grade three in normal schools in Örebro in 1965, a Swedish town with about 100,000 inhabitants. Swedish children typically started first grade in the fall of the year they turned seven, so these children were around ten years old at that time. Information on e.g. the children’s intelligence, school performance, and school adjustments were collected from the children, and additional information was collected from their teachers and parents. The children were followed up in grades six (age 13) and nine (age 16), and children who had moved to Örebro and were in grades six and/or nine during those times were added to the dataset. The women who were in at least one of these grades were followed up at age 43 (nwomen = 682), and the men who were in grade three were followed up at age 47 (nmen = 543), in which information on e.g. career outcomes was collected. The follow up data collection and construction of a database for the women was very comprehensive (with e.g. personal interviews) resulting in a later follow up for the men. 2.2. Variables 2.2.1. Response variables Intelligence. The response variable of interest for our first research question is childhood intelligence (IQ), measured by an index used in previous intelligence studies on the IDA data (e.g. Bergman et al., 2014; Ferrer-Wreder et al., 2014). The index is the sum of the standardized scores from the Swedish DBA intelligence test (Härnqvist, 1962) in grades three and six, and the Swedish WIT III intelligence test (Westrin, 1969) in grade eight. The DBA test includes the subtests Synonyms, Opposites, Letter groups, Figure sequences, Cube counting, and Mental folding, and the WIT III test includes Analogies, Opposites, Number combinations, and Puzzle (see Magnusson, 1978 for more details). The resulting sums were standardized to have a

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

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mean of 100 and a standard deviation of 15 (see Bergman et al., 2014). Educational performance. Within our second research question, the response variable of interest is educational performance (Grade), measured by the average school grades from third (Swedish and mathematics), sixth (Swedish and mathematics) and ninth grade (Swedish, history, civics, biology, chemistry, and physics). Grades in each subject ranged from “1” (lowest) to “5” (highest), see Bergman et al. (2014) for more information. Note that the first response variable, IQ, is included as a control variable for this second research question. Income. For our third research question, the log of adult income (LIncome) is the response variable of interest. It was measured at age 43 for women and age 47 for men. Note that the first and second response variables, IQ and Grade, are included as control variables for this third research question. 2.2.2. Explanatory variables Sibship size. The main explanatory variable of interest is child sibship size, measured by the number of siblings for each child in grade nine. In order to account for birth order, we consistently split up the variable sibship size in our study into two variables: the number of older (Old) and younger (Young) siblings. This split is preferable to using birth order and sibship size, because birth order (which essentially is the same variable as the number of older siblings) is part of the variable sibship size, and the correlation between these variables will therefore be higher than if we instead use the number of older and younger siblings. In order to examine nonlinear effects, we also use a categorical version of the sibship size variable (close/far from the “norm”) for each research question. Most women in Sweden born in the 1930s (when many mothers of the Swedish cohort were born) had two children. Around 14% of the women in Sweden had no children, 19% had one child, 35% had two, 19% had three, and 12% had four or more children (Statistics Sweden, 2011). The “norm” in Sweden at the time can therefore be considered to be two children (sibship size one). We therefore also split sibship size into small (close to the norm: 0–2) coded “0”, and large (3+) coded “1”, for each research question. The explanatory variables we control for in our study are socioeconomic status, maternal- and paternal age, gender, concentration difficulties, and educational attainment. Socioeconomic status. Parental SES (SES) was measured by the sum of the average self-reported family income before taxes in grades three and six, and the educational level of the parent with the highest education measured in grades three, six, and nine. The resulting scores were standardized to have a mean of 0 and a standard deviation of 1, see Bergman et al. (2014). Maternal and paternal age. Maternal age (M.age) and paternal age (P.age) were measured in grade nine and coded “1” (up to 25), “2” (26–30), “3” (31–35), “4” (36–40), “5” (41–45), “6” (46–50), “7” (51–60), or “8” (over 61). Gender. Gender was coded “1” for males and “0” for females. Educational attainment. Educational attainment (Edu.att) was measured at age 43 for women and at age 47 for men and was coded “1” (at least three year high school) or “0” (less than three year high school), see Bergman et al. (2014) for more information. Concentration difficulties. Concentration difficulties (Con.dif) were measured by teacher ratings from sixth grade, ranging from “1” (low) to “7” (high), see Ferrer-Wreder et al. (2014) for more information.

3

Table 1 Summary statistics of the data. Variable

Mean

Std dev

Min

Max

R1

R2

R3

IQ, y(1) Grade, y(2) Income, y(3) Old Young Gender M.age P.age SES Con.dif Edu.att

103.13 3.23 21.02 0.77 0.66 0.51 5.23 5.75 0.13 3.55 0.54

13.87 0.79 15.01 0.94 0.85 0.50 1.15 1.13 0.94 1.57 0.50

57.19 1.11 5.83 0 0 0 2 3 −1.88 1 0

138.14 4.94 200.79 5 5 1 7 8 2.32 7 1

x

x x

x x x x x x

x x x x x x x

x x x x x x x x x x x

Note that variable Income is measured in thousands of Swedish kronor.

Within each research question, we sorted out a complete dataset with no missing values for each of the variables. This resulted in n1 = 665, n2 = 660 and n3 = 373 total number of observations for the variables within research questions 1,2 and 3, respectively. Table 1 presents the means, standard deviations, and the minimum and maximum values for each variable separately. In addition, Table 1 marks out the response variables y(1) , y(2) and y(3) for the three research questions R1 , R2 and R3 and which explanatory variables that were included for each research question. Table 2 presents the correlations between all variables for the complete dataset with no missing values that was used for research question 3. Some of the effects of the explanatory variables may be difficult to separate due to multicollinearity problems that may appear if they are highly correlated with each other. This may especially be the case for IQ and school grades (r = 0.77), school grades and concentration difficulties (r = −0.71), and maternal and paternal age (r = 0.73). Examination of variance inflation factors (VIF) show however that all of them are fairly small (with most of them being between 1 and 2 and the largest one being 4.038 for school grade). Multicollinearity problems therefore do not seem to have any major effects on the estimates in our study. 2.3. Statistical models We assume three cases of a model to explore the effects of the number of older and younger siblings, as well as large/small sibship size, on the response variables 1) IQ, 2) Grade, and 3) LIncome. For each case, we estimate a fully Bayesian varying-intercept model using the 46 different school classes on the group-level. In this type of multilevel model, a regression with different intercepts for the school classes is estimated. We find Bayesian varying-intercept modeling to be a particularly suitable choice of statistical method for several reasons. First, the group-level model is naturally treated as prior information in estimating the individual-level coefficients. Second, the intraclass correlation between school classes, as a percentage of the variance between classes to the total variance of the response variable (or, equivalently, the within-class correlation of scores), is of major interest in our models and in multilevel models in general. Table 2 Correlation matrix of the data. Variable

IQ

IQ Grade LIncome Old Young M.age P.age SES Con.dif

1.00 0.77 1.00

Grade

LIncome

Old

Young

M.age

P.age

SES

0.21 0.18 1.00

−0.11 0.03 −0.13 0.04 −0.03 −0.08 1.00 −0.16 1.00

0.03 0.03 0.05 0.38 −0.44 1.00

0.03 0.00 0.03 0.37 −0.41 0.73 1.00

0.28 −0.53 0.34 −0.71 0.11 −0.13 0.07 0.12 −0.04 −0.06 0.04 0.04 0.01 0.07 1.00 −0.22 1.00

Con.dif

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The higher the correlation, the more important it is to use varyingintercept modeling in order to obtain correct credibility intervals. In our Bayesian modeling the distribution of the intraclass correlation is easily estimated directly from the sampled parameter draws of the estimated posterior distribution. From this we can describe the uncertainty by means of posterior intervals for the intraclass correlation in contrast to other non-Bayesian estimation methods where it is not straightforward to obtain uncertainty intervals around a point estimate of the intraclass correlation. Third, because we account for birth orders by splitting up sibship size into the number of older and younger siblings it is of interest to examine the relationships of the corresponding two parameters. This is easily done in our Bayesian models by examining the bivariate distribution of the parameters for each model. Fourth, the posterior distributions of the model parameters describe how likely the values of the parameters are in different intervals, which does not force us into hypothesis testing for certain values with the choice of specifying significance levels. Our varying-intercept model can be written as yij = aj + bxij + 4ij ,

(1)

where yij is the response for the ith child in the jth class, a j is the intercept for the jth class, b is the parameter vector for the explanatory variables xij , and 4ij is the error term for the ith child in the jth class. We assume the following Gaussian distributions for the response variable and intercepts: aj ∼ N(la , sa2 ) yij ∼ N(aj + bxij , sy2 ),

(2)

where the normal distribution for a j can be viewed as a prior distribution for the intercepts. In order to determine whether parents with many or few children differ in their characteristics, we also estimate a multilevel logistic regression with family size as response variable. Family size is coded “1” if sibship size is large (3+) and coded “0” if sibship size is small (close to the norm: 0–2). Our multilevel logistic regression model can be written as  log

hij 1 − hij

 = aj + bxij ,

(3)

where hij is the probability of large family size for the ith child in the jth class, a j is the intercept for the j th class, b is the parameter vector for the explanatory variables xij , and the same Gaussian distribution for the intercepts as for the varying-intercept model above is assumed. 2.3.1. Prior distributions In our Bayesian framework, we need to assign prior distributions to all unknown parameters: l a , s a , b, and s y . We assume non-informative prior distributions for all the parameters as a standard of comparison. We specify our prior distributions in a range that is ten times as large as we expect the estimated coefficients to be in, as recommended by Gelman and Hill (2007). A larger range can result in computationally unstable estimation using the statistical software BUGS (Bayesian Inference Using Gibbs Sampling). On the other hand, a lower range might result in prior distributions that don’t meet our criteria for non-informative prior distributions. Therefore, we also experimented with much wider ranges, e.g. hundred times as large range for the expected range of the coefficients, to examine if our choice of prior distributions can be considered to be non-informative. This resulted in only very small differences in estimation results, which suggests that our choice of prior distributions are non-informative.

Uniform prior distributions on [0, cs ], are used for the standard deviations s y and s a , where our choices of cs = 100 for model case 1) and cs = 2 for model cases 2) and 3) result in good model convergence and non-informative prior distributions. The prior distribution for h = (l a , b) is h ∼ N(0, sh2 • I), where I is the identity matrix, and our choices of sh2 = 10, 000 for model case 1) and for the multilevel logistic regression model, and sh2 = 100 for model cases 2) and 3) also here result in good model convergence and non-informative prior distributions. 2.3.2. Estimation routines We use the statistical software BUGS to estimate the unknown model parameters of our statistical models using MCMC (Monte Carlo Markov chain). We estimate each multilevel model by using four MCMC chains and run the chains until the distribution of the parameter draws converges to the underlying posterior distribution. We use convergence criteria in Gelman and Hill (2007) for two measures to check for convergence. First, Rˆ is a convergency measure for each parameter and is approximately equal to the square root of the variance of the mixture of all the chains divided by the average within-chain variance. We estimate all models such that Rˆ ≤ 1.1 holds as an indication that the chains have mixed well. Second, we also use the measure neff as the effective number of simulation draws for each parameter. If all simulation draws were independent, the effective sample size would equal the number of saved draws from the MCMC chains. However, the parameter draws are usually autocorrelated in the MCMC chains, which typically makes the effective number of simulation draws considerably smaller than the saved draws. We estimate all models such that neff ≥ 100 for good convergence to the posterior. We use the first half of the draws in the MCMC as a burn-in period to avoid starting values in the MCMC chains to affect the results, i.e. we save the second half of the posterior draws from each of the four MCMC chains to our results. 3. Results Because we divided sibship size into the number of older and younger siblings, it is of interest to examine the bivariate distribution for the model parameters of the explanatory variables Old and Y oung within each research question. However, the correlations between these two parameters are almost zero in all our models, which leads us to only summarize the estimation results for the univariate posterior distributions of each parameter. In the next sections, we first show some descriptive preanalyses of the relationship between each response variable and sibship size and the number of older and younger siblings. Then, we show the results from each estimated Bayesian varying-intercept model for each research question. 3.1. Effects of sibship size on intelligence test scores Fig. 1 shows mean scores of the children’s intelligence for each sibship size from zero to five+. Because only one child had six siblings and two children had eight siblings, sibship sizes five to eight have been grouped together in the graph in order not to disclose any individual information. As seen, mean values of IQ scores tend to decrease for larger sibship sizes, which suggests that children who grew up in large families seem to have lower IQ scores on average. In a similar manner as in Fig. 1, children with four or more older/younger siblings have been grouped together in Fig. 2. A similar pattern can be seen, at least for the number of older siblings. However, these findings do not examine the simultaneous effects of the number of older and younger siblings as we next examine by estimating our Bayesian varying-intercept model. In order to justify our use of a multilevel model, we estimate the intraclass correlation within school classes from our estimated

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

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5

110 108 106

mean(IQ)

104 102 100 98 96 94 92 90 0 (127)

1 (275)

2 (167)

3 (61)

4 (21)

5+ (14)

Sibship size (number of children per sibship size) Fig. 1. Mean values of intelligence scores for each sibship size.

110 Old Young

108 106

mean(IQ)

104 102 100 98 96 94 92 90 0

1

2

3

4+

number of older (Old) and younger (Young) siblings Fig. 2. Mean values of intelligence scores for each number of older and younger siblings.

Bayesian varying-intercept model in Eqs. (1)–(2) with IQ as response variable and with no explanatory variables. Table 3 shows the estimated results from this model. The lower limit of the posterior interval for the intraclass correlation qic is relatively high, which indicates that a considerable part (at least 31.8%) of the variance in IQ is between school classes. Table 4 shows the estimation results of the Bayesian varyingintercept model for research question 1 with IQ as the response

variable and Old and Young as sibship size variables. For this estimation, as for all the estimations that follow, children with all sibship sizes are included. However, as noted in Fig. 1, because only three

Table 4 Posterior results for the Bayesian varying-intercept model in Eq. (2) with IQ as response variable. Variable/parameter

Table 3 Posterior results for the Bayesian varying-intercept model in Eq. (2) with IQ as response variable and with no explanatory variables. Parameter

la sy sa qic

Posterior

Posterior percentiles

Mean

sd

2.5%

50%

97.5%

99.889 11.359 10.129 0.440

1.601 0.328 1.326 0.065

96.692 10.735 7.835 0.318

99.897 11.351 10.016 0.438

103.029 12.018 13.031 0.573

Old Young Gender SES M.age P.age la sy sa

Posterior

Posterior percentiles

Eff. size

Mean

sd

2.5%

50%

97.5%

Mean

−1.507 0.342 −0.773 2.561 0.119 0.347 98.623 11.195 9.240

0.528 0.577 0.965 0.517 0.596 0.585 3.240 0.323 1.278

−2.543 −0.786 −2.659 1.544 −1.091 −0.777 92.038 10.584 7.028

−1.507 0.342 −0.777 2.560 0.117 0.341 98.704 11.188 9.139

−0.468 1.470 1.121 3.576 1.271 1.534 104.794 11.845 12.010

−0.102 0.021 −0.028 0.174 0.010 0.028

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children had six or more siblings, analyses were also conducted with these children omitted. The estimates did not change (except marginally) and they are therefore not reported. As shown in Table 4, children with a larger number of older siblings are very likely to have a lower intelligence score, while the number of younger siblings does not matter. In addition, children from higher socioeconomic status backgrounds are also very likely to have higher intelligence scores compared to children from lower socioeconomic status backgrounds. Table 4 also shows effect sizes (eff.size), computed as bk  = • bk sxk /sy where bk is the posterior mean for variable k, sxk is the sample standard deviation for explanatory variable k, and sy is the sample standard deviation for the response variable. As shown, the effect size for socioeconomic status is larger than the effect size for the number of older siblings. The explanatory  variables  together explain around 2.8% of the .192 , and 16.8% of the variance between variance within 1 − 11 2 11 . 35   9.142 classes 1 − 10 , which are obtained from the medians of the pos.022 terior distributions for the variances in Tables 3 and 4. Our Bayesian framework allows us to use medians instead of means which is preferable for variance distributions that are generally skewed. When we substitute Old and Y oung by Sibship size (large/small), estimates from our Bayesian varying-intercept model indicate that a small or large sibship size is not very likely to matter with regards to IQ scores (95% credibility interval for Sibship size slope: −4.877; 0.150). Table 5 shows the estimation results from the Bayesian multilevel logistic model with Sibship size (large/small) as response variable. As shown, parents with a smaller number (0–3) and a larger number (4+) of children are not likely to differ in their socioeconomic backgrounds or ages. 3.2. Effects of sibship size on school grades Figs. 3 and 4 show mean values of the children’s grades for each sibship size from zero to five+, and for the number of older and younger siblings. As for research question 1, mean values of grades tend to decrease for larger sibship sizes, which suggests that children who grew up in large families seem to obtain lower grades on average. As for research question 1, we justify our use of a multilevel model by estimating the intraclass correlation within school classes using the Bayesian varying-intercept model in Eqs. (1)–(2) with Grade as response variable and with no explanatory variables. Table 6 shows the estimated results from this model. As for IQ scores, a considerable part of the variance in grades is between school classes (at least 31.5%). Table 7 shows the estimation results of the Bayesian varyingintercept model for research question 2 with Grade as the response variable and Old and Young as the sibship size variables. As seen in the table, the number of older and younger siblings do not seem to have any effects on children’s school grades. Children

Table 5 Posterior results for the Bayesian multilevel logistic regression model in Eq. (3) with family size as a binary response variable. Variable/parameter

SES M.age P.age la sa

Posterior

from higher socioeconomic backgrounds, children with higher intelligence scores, and children with fewer concentration difficulties, are however very likely to have higher school grades, and we note that the effect of IQ is larger than the effect of concentration difficulties, which in turn, is larger than the effect of SES. The variance in Grade has decreased considerably both between and within classes when the explanatory variables have been added, and the explanatory variables explain around 59.4% of the variance in Grade within, and 96.9% of the variance between classes. When a Bayesian varying-intercept model with sibship size (large/small) is estimated, the results are similar and indicate that a small or large sibship size is not very likely to matter with regards to Grade (95% credibility interval for Sibship size slope: −0.140; 0.038). 3.3. Effects of sibship size on adult income Figs. 5 and 6 show mean values of the log of the income that the children obtained in adulthood for each sibship size from zero to five+, and for the number of older and younger siblings. As for research questions 1 and 2, mean values of income decrease for larger sibship sizes, and the decreasing pattern appears stronger for the number of younger siblings. This suggests that children who grew up in large families, and specifically with more younger siblings, seem to obtain lower incomes, on average, in their adult lives. As for the previous two research questions, we justify our use of a multilevel model by estimating the intraclass correlation within school classes using the multilevel model in Eqs. (1)–(2) with LIncome as response variable and with no explanatory variables. Table 8 shows the estimated results from this model. The upper part of the posterior interval for qic is relatively low. Hence, there does not seem to be much variation in income between school classes. However, for sake of easy comparison between research questions, we also estimate our multilevel model with LIncome as response variable. Table 9 shows the estimation results of the Bayesian varyingintercept model for research question 3 with LIncome as the response variable and Old and Young as sibship size variables. Individuals with a larger number of younger siblings are very likely to have lower log incomes in adulthood, whereas the number of older siblings does not seem to matter. To exemplify this, the mean of the posterior distribution (−0.041) indicates that the effect of one more younger sibling, for an individual with a median income 18,000, is a decrease in income of 723.08 SEK (18, 000 − exp(ln(18, 000) − 0.041)). In addition, men are very likely to have higher incomes than women, as are those who have completed high school, and those with younger mothers. As shown in the table, the gender effect is much larger than the other effects, and the effect of the number of younger siblings is fairly small. The explanatory variables together explain around 51.6% of the variance in log income within classes, and around 78.5% of the variance between classes. Results from a Bayesian varying-intercept model with Sibship size (large/small) indicate that a large or small sibship size is not likely to matter when it comes to adult income (95% credibility interval for Sibship size slope: −0.104; 0.072). 4. Discussion

Posterior percentiles

Mean

sd

2.5%

50%

97.5%

0.083 −0.005 0.195 −2.943 0.325

0.117 0.142 0.149 0.687 0.184

−0.150 −0.280 -0.098 −4.310 0.035

0.084 −0.007 0.196 −2.923 0.313

0.311 0.276 0.487 −1.601 0.712

The purpose of our study was to examine the effects of sibship size on intelligence test scores, school grades, and adult income for a Swedish cohort of children. Our main findings show some negative effects of sibship size on intelligence and on adult income, but not on school grades. Next, we elaborate on our findings for each of our three research questions.

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

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7

3.5 3.4 3.3

mean(Grade)

3.2 3.1 3 2.9 2.8 2.7 2.6 0 (126)

1 (273)

2 (166)

3 (60)

4 (21)

5+ (14)

Sibship size (number of children per sibship size) Fig. 3. Mean values of grades for each sibship size.

3.5

Old Young

3.4 3.3

mean(Grade)

3.2 3.1 3 2.9 2.8 2.7 2.6 0

1

2

3

4+

number of older (Old) and younger (Young) siblings Fig. 4. Mean values of grades for each number of older and younger siblings.

4.1. Effects of sibship size on intelligence test scores Consistent with previous research, our results show that mean intelligence scores tend to decrease for children of larger sibship sizes. Specifically, we account for variance within and between school classes in our multilevel model and show that children with one additional older sibling score, on average, 1.5 points lower on IQ tests compared to other children with comparable number of

Table 6 Posterior results for the Bayesian varying-intercept model in Eq. (2) with Grade as response variable and with no explanatory variables. Parameter

la sy sa qic

Posterior

Posterior percentiles

Mean

sd

2.5%

50%

97.5%

3.073 0.626 0.547 0.431

0.087 0.018 0.069 0.062

2.900 0.592 0.429 0.315

3.073 0.625 0.542 0.429

3.244 0.662 0.699 0.559

younger siblings and background. We also found a considerable variation in IQ scores across school classes. Thus, even though Sweden has high levels of public expenditure on school and the family, which Table 7 Posterior results for the Bayesian varying-intercept model in Eq. (2) with Grade as response variable. Variable/parameter

Posterior Mean

Old Young Gender SES M.age P.age Con.dif IQ la sy sa

−0.018 0.006 0.058 0.087 0.010 −0.003 −0.191 0.030 0.798 0.399 0.095

Posterior percentiles

Eff. size

sd

2.5%

50%

97.5%

Mean

0.018 0.020 0.033 0.018 0.020 0.020 0.013 0.001 0.190 0.012 0.037

−0.054 −0.033 −0.007 0.051 −0.030 −0.042 −0.216 0.027 0.421 0.376 0.013

−0.018 0.006 0.058 0.087 0.010 −0.003 −0.191 0.029 0.803 0.398 0.096

0.018 0.046 0.124 0.122 0.049 0.038 −0.167 0.032 1.158 0.423 0.166

−0.022 0.007 0.037 0.104 0.015 −0.004 −0.390 0.528

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

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10.1 10

mean(LIncome)

9.9 9.8 9.7 9.6 9.5 9.4 9.3 0 (67)

1 (167)

2 (86)

3 (33)

4 (12)

5+ (8)

Sibship size (number of children per sibship size) Fig. 5. Mean values of log of income for each sibship size.

10.1 Old Young

10

mean(LIncome)

9.9 9.8 9.7 9.6 9.5 9.4 9.3 0

1

2

3

4+

number of older (Old) and younger (Young) siblings Fig. 6. Mean values of log of income for each number of older and younger siblings.

may have decreased the influences of familial factors on intellectual development, Swedish children with many older siblings have, on average, lower intelligence scores. This is in contrast to Holmgren et al. (2006) and Holmgren et al. (2007) who found sibship size and birth order effects on executive functioning and episodic memory, but not on intelligence for Swedish adults. We examined a global intelligence measure on a child cohort. Future research can benefit Table 8 Posterior results for the Bayesian varying-intercept model in Eq. (2) with LIncome as response variable and with no explanatory variables. Parameter

la sy sa qic

Posterior

Posterior percentiles

Mean

sd

2.5%

50%

97.5%

9.834 0.425 0.081 0.043

0.027 0.016 0.040 0.035

9.781 0.394 0.006 0.000

9.835 0.424 0.082 0.036

9.886 0.458 0.159 0.127

from examining potentially differing sibship size effects on different aspects of intelligence. Our measure of intelligence can be divided into scores from subtests, so this should be possible to do using the IDA data. The number of older siblings is measuring the same thing as birth order, indicating the existence of a birth order effect in our data. This effect was found controlling for the number of younger siblings. We need to keep in mind, however, that our results are based on scores of children in ninth grade. We are thus (most often) comparing a child with birth order one from one family, to a child with birth order two from another family, to a child with birth order three from yet another family etc., which many birth order effect studies do. Rodgers et al. (2000) pointed out that birth order effects necessarily operate within the family, i.e. affect children within a family, at one point in time, differently, and the existence of such effects can only be validated using sibling data. We might otherwise be measuring differences between families instead of differences within families. Unfortunately, this could not be done using our data and we

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

ARTICLE IN PRESS L. Wänsträm, B. Wegmann / Intelligence xxx (2017) xxx–xxx Table 9 Posterior results for the Bayesian varying-intercept model in Eq. (2) with LIncome as response variable. Variable/parameter

Old Young Gender SES M.age P.age Con.dif IQ Edu.att Grade la sy sa

Posterior percentiles

Eff. size

Mean

Posterior sd

2.5%

50%

97.5%

mean

−0.006 −0.041 −0.602 0.016 −0.041 0.010 −0.002 0.000 0.167 0.068 10.036 0.296 0.039

0.019 0.021 0.033 0.020 0.021 0.021 0.014 0.002 0.039 0.039 0.199 0.011 0.023

−0.043 −0.082 −0.666 −0.022 −0.082 −0.032 −0.029 −0.003 0.090 −0.009 9.658 0.274 0.002

−0.006 −0.041 −0.602 0.016 −0.041 0.010 −0.002 0.001 0.167 0.068 10.042 0.295 0.038

0.030 0.000 −0.538 0.055 0.000 0.049 0.026 0.004 0.244 0.146 10.427 0.319 0.087

−0.013 −0.079 −0.687 0.032 −0.110 0.026 −0.007 0.000 0.194 0.123

cannot determine whether the negative effect of the number of older siblings is, fully or partly, causal. We controlled for parental socioeconomic status, which had a larger effect on intelligence than the number of older siblings. We also controlled for maternal and paternal age and child gender, which did not show any effects on the intelligence scores. All explanatory variables were together able to explain almost 17% of the variance in IQ scores across school classes, but only about 3% of the variance within classes. There may be other variables, not accounted for here, that affect both children’s intelligence and parental decisions on family size. Ghilagaber and Wänström (2015) used multilevel multiprocess models to explore the existence of selection bias in the relationship between sibship size and intelligence and found that parents differed in socioeconomic indicators, ethnicity and maternal age at first child. For sibship sizes zero to two, the previously negative effects of sibship size disappeared when controlling for unmeasured heterogeneity affecting both decisions on family size and child intelligence. There may thus be, unmeasured, differences between families of children with many, and few, older siblings that we could not account for. Two such variables may be maternal- and paternal intelligence (see e.g. Rodgers et al., 2000), which, unfortunately, were not available in the data. 4.2. Effects of sibship size on school grades We found no sibship size effects on school grades controlling for intelligence, SES, maternal- and paternal age, gender, and concentration difficulties. Lawson, Makoli, and Goodman (2013), studying a large sample of Swedish individuals born between 1915–1924, found however sibship size effects on school grades and educational attainment. They did not, however, control for individual differences in intelligence. Thus, it could be that children with different sibship sizes differ in how well they perform in school, but given a certain intelligence level there are no differences in performance. Indeed, when we checked this and dropped the intelligence variable in our multilevel model, the number of older siblings was very likely to have an effect on school grades. We found that Swedish children with favorable socioeconomic backgrounds, higher intelligence, and fewer concentration difficulties, achieve higher grades in school and that the average grades vary between classes. This, in turn, can be due to some segregation such that children with similar backgrounds and characteristics (socioeconomic backgrounds, intelligence, and levels of concentration difficulties) to a certain extent end up in the same school classes. The Swedish school system in the 1960s was very centralized and regulated, and children went to the school they lived closest to. The decentralization from the government to the municipalities and

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the implementation of free choice and the rise of private schools in the 1990s may have increased the segregation in Swedish schools (see discussion in Yang Hansen & Gustafsson, 2016) such that differences in educational performances have increased. It will therefore be particularly important for any future studies on performances of Swedish school children, to account for variances between and within school classes as we have done here. 4.3. Effects of sibship size on adult income We found a small negative effect of the number of younger siblings on adult income, such that an individual with a median income and one additional younger sibling has, on average, a 4% lower income compared to another individual with a comparable number of older siblings and background. Our results support Grinberg’s (2015) findings that sibship size, more so than birth order, was negatively associated with having a managerial position in adulthood. It however somewhat disagrees with previous findings on Swedish data. Goodman et al. (2012) found negative sibship size effects on income, however when Lawson et al. (2013) split sibship size into the number of older and younger siblings, they found that the relative ages of the siblings (older or younger) did not have any effects. The individuals were between five and 15 years old when information on their siblings was collected however, which means that the total number of younger siblings was not complete for many of them, which may account for some of the differences. As for short term effects of the number of older siblings on intelligence, we cannot be sure that the effects of the number of younger siblings on adult income is causal. This variable may reflect unmeasured differences between families of many and few children. Neither intelligence, SES, nor school grade seem to have long term effects on income. However, not unexpectedly, those who completed three years of high school have, on average, higher incomes, and variables such as intelligence, SES, and grades may of course affect educational attainment (see e.g. results in Bergman et al., 2014 on the same data). Men have higher incomes than women, a fairly large effect that is somewhat enhanced because their incomes were collected later than women’s incomes. In addition, those with younger mothers have higher incomes than those with older mothers. There is not much variation in income between those who were in different school classes in ninth grade, which is somewhat expected because of the time lap between ninth grade and the ages of 43 (for women) and 47 (for men). It is, however, interesting to note that any segregation effects present in childhood, manifested as differences between school classes, do not show up in adulthood when it comes to income. An interpretation of this may be that although Swedish classmates where somewhat similar with regards to IQ and school grades when they were still in school, school class belongingness in itself did not have much effect on their adult careers, as manifested in their incomes. 4.4. Small vs large sibship size We noted (in Figs. 1 and 3) that the mean intelligence scores are about the same for the three smallest sibship sizes, and the mean grades increase slightly for these sibship sizes before they decrease. There were, however, no effects of large/small sibship size when they were analyzed in a multilevel model. The effects of the number of older and younger siblings found in this study therefore do not seem to come from differences between families with sizes close to the “norm” (small size) and farther from the “norm” (large size). In support of this, no differences in parental characteristics were found for parents with small and large family sizes, suggesting that Swedish parents of different socioeconomic statuses or ages do not produce different size (small/large) families. These

Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004

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variables may therefore not be important sources of selection in Sweden. Future research would benefit from finding, and controlling for, other possible sources of selection. In trying to find such sources, researchers could search for parental characteristics correlated with child intelligence, as we found that there were no sibship size effects on educational performance, after controlling for child intelligence. As mentioned previously, one such variable may be parental IQ. 5. Conclusions We studied a Swedish cohort of school children and found negative effects of the number of older children on intelligence, as well as of the number of younger siblings on adult income. These sibship size effects were found even though the children grew up in a country with high levels of public expenditure on the school and the family. Non-linear effects of large vs small families were not found. A substantial amount of variation in intelligence and school grades was found between classes, and future studies on these variables should therefore account for this class variance. Finally, there may be other types of sibship size effects not examined here. Both the confluence model and the resource dilution theory (e.g. Powell & Steelman, 1990; Zajonc & Mullally, 1997) predict some spacing effects such that close spacing have more detrimental effects than wide spacing. Future studies, using larger samples than ours, may divide the number of older and younger siblings further into spacing categories to examine possible differential effects. Acknowledgments The authors would like to thank four anonymous reviewers for their valuable comments. The paper was partly supported by the Jan Wallander and Tom Hedelius Foundation (grant no. W2011-0408:1).

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Please cite this article as: L. Wänsträm, B. Wegmann, Effects of sibship size on intelligence, school performance and adult income: Some evidence from Swedish data, Intelligence (2017), http://dx.doi.org/10.1016/j.intell.2017.01.004