Abstract
We study the intergenerational transmission of cognitive and noncognitive abilities using population data and correct for measurement error in abilities using two sets of instruments. The results show that previous estimates are biased downward and that once measurement error is corrected for, the correlation in noncognitive ability is close to that of cognitive ability. By considering both parents, intergenerational ability correlations account for a substantial portion of the sibling correlation. Using adoptees, we find that the social impact of maternal abilities is more important than paternal abilities. Children’s educational attainment and labor market outcomes are strongly related to parents’ cognitive and noncognitive abilities.
I. Introduction
A large literature recognizes the importance of both cognitive and noncognitive abilities for economic and social outcomes (for example, Bowles, Gintis, and Osborne 2001; Heckman, Stixrud, and Urzua 2006; Lindqvist and Vestman 2011). The family plays a crucial role in forming these productive traits: Abilities are correlated across generations, and siblings have a strong resemblance in both intellectual capacity and personality (Black and Devereaux 2011). In theoretical models of intergenerational income mobility and inequality, the transmission of abilities across generations is a key component (Becker and Tomes 1979). This transmission is less than fully understood, as are the sources of estimated sibling correlations. Intergenerational ability correlations are a component of sibling correlations that deepen our understanding of how abilities are passed on from parents. However, traditional estimates suggest that intergenerational ability correlations only account for a fraction of the influence of the family in forming productive traits of children (Björklund and Jäntti 2012; Anger and Schnitzlein 2016). In this paper, we use a novel strategy to correct for measurement errors in cognitive and noncognitive abilities and find that previous studies substantially underappreciate the importance of intergenerational ability correlations, particularly for noncognitive abilities. Because both cognitive and noncognitive abilities are highly rewarded on the labor market, intergenerational ability correlations are a major source of income persistence across generations.
In our analysis, we make use of military enlistment records for 38 cohorts of Swedish men, whose cognitive and noncognitive abilities were all evaluated at age 18 using comparable methods. We correct for measurement error in the fathers’ abilities using two different sets of instrumental variables: For a smaller sample (n ≈ 2,000), we use comparable ability evaluations for fathers at age 13. For a larger sample (n ≈ 50,000), ability evaluations of the son’s uncle (that is, the father’s brother) are used as instruments for the father’s abilities. The two approaches yield similar results. Based on evidence from the genetics literature, simulations of different types of genetic inheritance, and a series of validity checks, we cannot reject the exclusion restriction that uncles have no direct impact on the skills of their nephews. The second IV-strategy also enables us to predict mothers’ abilities by using the ability evaluations of their brothers, thus bringing both parents into the analysis.
Without adjusting for measurement error, we find a father–son correlation of 0.32– 0.35 for cognitive and 0.21 for noncognitive abilities, which are in line with previous studies.1 When adjusting for measurement error, the intergenerational correlation increases to 0.42–0.48 for cognitive abilities and to around 0.42 for noncognitive abilities. This suggests that the difference in estimated intergenerational correlations between cognitive and noncognitive abilities found in previous studies is largely due to a higher degree of measurement error in noncognitive abilities.2
We further find that mother–son correlations in cognitive abilities are somewhat stronger than father–son correlations, whereas no such difference is apparent for noncognitive abilities. Previous studies of the relative ability correlations between mothers and fathers have produced inconclusive results, in part due to small sample sizes (Anger and Heineck 2010; Anger 2011). When taking both parents and assortative matching into consideration, we show that intergenerational ability correlations can account for 67 percent of the sibling correlation in cognitive abilities and 45 percent of the correlation in noncognitive abilities. These shares are orders of magnitudes higher than those obtained from previous comparisons of sibling correlations and intergenerational ability correlations (Björklund and Jäntti 2012; Anger and Schnitzlein 2016).
To address the underlying mechanisms behind our findings, we estimate intergenerational ability correlations for boys adopted from abroad. The results indicate that the social transmission of abilities from fathers is modest, while the nurture of mothers is more important for passing down abilities.
Finally, we find strong associations between both parents’ abilities and educational and labor market outcomes for both sons and daughters. Parents’ cognitive abilities are relatively more important for educational outcomes, and their noncognitive abilities are relatively more important for earnings and labor force participation. Back-of-the-envelope calculations indicate that only a minor part of the earnings premium of parental abilities can be accounted for by increased educational attainment. Such calculations also show that all of the earnings increase associated with higher parental abilities can be attributed to the impact on sons’ abilities, rather than to other channels. These results support findings suggesting that the transmission of productive abilities can explain a substantial part of the intergenerational correlation in economic outcomes (Osborne Groves 2005; Blanden, Gregg, and MacMillan 2007).
The paper starts by proposing a strategy for estimating intergenerational correlations when abilities are measured with error. Section III presents the data. In Section IV, father–son correlations are estimated, and we test the validity of the uncle instrument. Next, we derive maternal abilities and estimate ability correlations using both parents, relate these estimates to sibling correlations, and present the results for adoptees. Section VI estimates the relationship between parental abilities and long-run child outcomes, and Section VII concludes. Online Appendix A derives the conditions for generating an unobserved endogenous regressor. Appendix B discusses and simulates potential biases under different assumptions of genetic heritability. Appendix C describes the Swedish adoption process. Appendix D presents supplementary results, and Appendix E shows how to correct IV estimates for measurement error when variables are standardized. Online Appendixes A–E can be found at http://jhr.uwpress.org/.
II. Methodological Considerations
We ideally want to estimate the true population correlation of cognitive and noncognitive abilities between generations, that is, to estimate the following simple regression model:
(1)where 
, represents the true cognitive or noncognitive ability for the father and son in family j, and εj is an error term. The parameter β is the population correlation for true cognitive or noncognitive abilities between fathers and sons.
A problem for this and most other studies in the area is that the observed cognitive and noncognitive ability measurements include measurement errors. We consider three potential sources of measurement errors in the observed abilities that may bias the estimates of the intergenerational correlations toward zero. First, the evaluation instrument can only test for a subset of the traits characterizing the underlying ability, and individuals may have good or bad realizations of the specific items included in the test. Second, some individuals will perform particularly well or particularly poorly on the day of the test. Finally, individuals may make idiosyncratic errors during the test. The different sources of mismeasurement of individuals’ abilities are likely to result in a random measurement error.
To illustrate, assume that the observed ability of individual i, in family j, on assessment a, at time t, Yiat , can be expressed as a linear function of the individual’s true latent ability, 
, the individual’s test specific error, λia, time specific error μit, and pure idiosyncratic error, ηiat :
(2)Under the assumption that the measurement error is classical, the OLS-estimate of the intergenerational correlation in true abilities is attenuated by the reliability ratio:
(3)Noisy measurements of the true latent ability of fathers are problematic for our purposes, not least because the extent of measurement error may differ between cognitive and noncognitive ability measures. In particular, we suspect the measurement error problem to be more severe for measures of noncognitive abilities than of cognitive abilities because the methods for testing cognitive abilities are more developed and because the assessment by a psychologist may result in a more subjective valuation than a cognitive paper-and-pen test. This would lead us to draw incorrect conclusions about the relative importance of the intergenerational transmission of different types of abilities.
One way of dealing with measurement error is to find an instrument that is strongly related to fathers’ abilities but not directly related to sons’ abilities (Ashenfelter and Krueger 1994). We use two different sets of instruments to correct the measurement error and estimate the intergenerational correlations in true latent abilities: evaluations of fathers’ abilities conducted at an earlier age and draft evaluations of paternal uncles. The earlier evaluation is conducted at age 13 and reflects the same underlying abilities as the draft evaluation at age 18, but with different items. This measure is strongly correlated with latent ability, 
, but it is uncorrelated with the individual-test-specific, time-specific, and idiosyncratic error terms. Similarly, the draft evaluations of paternal uncles are strongly related to the fathers’ latent ability, 
, due to the sibling correlation in skills. These are, however, uncorrelated with the fathers’ measurement error, as fathers and uncles have different individual-specific errors with respect to the time and assessment items. The main advantage of using this uncle instrument is that it dramatically increases the sample size and hence increases the precision of our estimates. We estimate the following first-stage equation:
(4)where ρ is the correlation between the different ability evaluations. Under the exclusion restriction that there is no direct impact of the father’s ability at age 13 or the uncle’s ability at age 18 on the son’s abilities—other than through its effect on father’s ability at age 18—we correct for measurement error bias and thus estimate the intergenerational correlation in true latent abilities:3
(5)The exclusion restriction is quite innocent when considering the fathers’ own evaluations conducted at an earlier age. The validity of the uncle instrument is less clear; the exclusion restriction may be violated because of genetic similarity or a shared environment. In such cases, the IV-estimate may overestimate the true transmission in abilities. Another potential problem is that the brothers’ measurement errors could be correlated. In that case, the IV-estimate would likely underestimate the intergenerational correlation in true latent skills. In Section IVB, we will address these and related concerns about the validity of the uncle instrument.
Another question is whether the IV-estimates capture the true population correlation of cognitive and noncognitive abilities between generations. In principle, it is possible that the intergenerational transmission depends on the sources of variation in fathers’ abilities. Thus, any difference between the OLS- and the IV-estimates may not only be driven by measurement error but could also be due to the fact that the estimators exploit different parts of the variation in fathers’ abilities. Because we have two sets of instruments, both exploiting different sources of variation, we will shed some light on this issue by comparing the different IV-estimates. Under the assumptions of classical measurement errors and valid instruments, any difference between the IV-estimates would be informative about heterogeneous effects in the intergenerational transmission of abilities. In Section IVB, we discuss this in more detail.
III. Data
Up until 2010, all Swedish men had to enlist in the military if called upon. In most cases, enlistment took place the year men turned 18. Until the late 1990s, over 90 percent of all men in each cohort went through the whole enlistment procedure. Thereafter, the need for conscripts declined, and enlistment became less comprehensive.
The enlistment consisted of a series of physical, psychological, and intellectual evaluations. The evaluation of cognitive ability consisted of tests of the conscript’s logical, verbal, and spatial abilities, as well as a test of technical comprehension. The design of the test was subjected to minor revisions in 1980, 1994, and 2000, but throughout the period it tested for the same four underlying abilities. The test results on these four subtests were combined to generate a normally distributed stanine scale ranging from 1–9 (mean five, standard deviation two), which has been found to be a good measure of general intelligence (Carlstedt 2000). We standardize this composite measure of cognitive ability by enlistment year.4
Our measure of noncognitive abilities is based on a standardized psychological evaluation aimed at determining the conscripts’ capacity to fulfill the requirements of military duty and armed combat. Central to this are the abilities to cope with stress and to contribute to group cohesion. The evaluation was performed by a certified psychologist who conducted a structured interview with the conscript. As a basis for the interview, the psychologist had information about the conscript’s results on the tests of cognitive ability, physical endurance, muscular strength, school grades, and answers from a questionnaire about friends, family, and hobbies. The interview followed a specific, and classified, manual that states topics to discuss and also how to grade different answers.
A conscript’s personality is scored along four domains (Mood, Jonsson, and Bihagen 2012): social maturity (extroversion, having friends, taking responsibility, independence), psychological energy (perseverance, ability to fulfill plans, to remain focused), intensity (the capacity to activate oneself without external pressure, the intensity and frequency of free-time activities), and emotional stability (the ability to control and channel nervousness, tolerance of stress, and disposition to anxiety). It should be noted that motivation for doing the military service was explicitly not a factor that was evaluated. Grades were given on four different subscales along the personality dimensions, which were transformed to a normally distributed stanine scale ranging from 1–9. We standardize this measure by enlistment year. The correlation between cognitive and noncognitive abilities is 0.39; see Appendix Table D4 online.5
Data on enlistment is collected from the Swedish Military Archive and the National Service Administration and includes all Swedish men born between 1950 and 1987. Information from Statistics Sweden on biological parents has been used to link fathers and sons, as well as mothers and siblings. Children adopted from abroad are used for a separate analysis and domestic adoptions are dropped.
A few data restrictions have been imposed in the main analysis. All men included in our sample must have a valid enlistment record and must have enlisted the year they turned 18, 19, or 20. Because over 90 percent of all men in each cohort were enlisted up to the late 1990s, representativeness is a minor concern for most of the period studied. During the early 2000s, however, the share of enlisted men fell: For individuals born in the mid 1980s, only 70 percent were enlisted.6
To correct for measurement error in the fathers’ abilities we use two different sets of instruments, both imposing separate sample restrictions. For a 10 percent sample of fathers born in 1953, we have alternative measures of cognitive and noncognitive abilities at age 13. These data come from the longitudinal study “Evaluation Through Follow-up” (ETF). In the ETF surveys, individuals were given cognitive ability tests reflecting the exact same abilities as those measured during enlistment. Although the ETF data do not include any direct measurement of noncognitive abilities, it contains information capturing such personality traits. Specifically, the ETF data contain information on grade point average in nonacademic subjects and survey information on educational aspirations and peer interaction at age 13. We use the residual of these measures, after regressing them on the ETF-measure of cognitive ability, as instruments of the father’s noncognitive ability at age 18.
Our second strategy is to use the uncles’ abilities as instruments for the father’s abilities, and we therefore restrict the sample to sons with at least one uncle. In addition, by requiring that both the father and the uncle have enlisted before 1980, we guarantee that they have undertaken the same version of the cognitive ability test. To avoid that uncles share more of the same environment with their nephews than with their brothers, we require the age difference between fathers and uncles to be at most seven years. If the father has more than one brother, we use the uncle closest in age.
Subject to these restrictions, our main regression samples consists of almost 2,000 observations (sons) for the ETF-sample and more than 50,000 observations (sons) for the uncle sample. Table 1 shows descriptive statistics for sons, fathers, and paternal uncles in our respective samples. As noted above, men are typically enlisted when they are 18 years old. There is some evidence that the sons in our sample have slightly higher cognitive and noncognitive skills than the population on average, whereas their fathers have slightly lower cognitive and slightly higher noncognitive skills than their sons. This pattern is likely to be caused by the age restrictions in the enlistment data (individuals born 1950–1987), which implies that the fathers in our sample are slightly younger than fathers in the population as a whole. Paternal uncles are slightly younger than fathers because there is no requirement that uncles need to have children. They also have somewhat lower cognitive scores than fathers, possibly due to birth order effects (Black, Dervereux, and Salvanes 2011).
Descriptive Statistics
IV. Father–Son Correlations
We start this section by presenting the results for intergenerational correlations in cognitive and noncognitive abilities between fathers and sons with and without correction for measurement error. In Section IVB, we discuss the validity of the uncle instrument and present a number of consistency checks.
A. Correlations with and without Correcting for Measurement Error
We begin by presenting the first-stage estimates. Table 2 shows a strong relationship between the two sets of instruments and fathers’ cognitive and noncognitive abilities. This reflects that abilities at age 18 are highly correlated to both own abilities at age 13 and to brothers’ abilities at age 18. The only exception is the relation between the noncognitive components of the ETF and the noncognitive measure at age 18, but the noncognitive components of the ETF still classify as strong instruments (Staiger and Stock 1997).
First Stage Estimates
Table 3 presents OLS- and IV-estimates of the intergenerational correlation in abilities between fathers and sons. In the first column in the top panel of Table 3, we see that the OLS-estimate of the relationship between fathers’ and sons’ cognitive abilities is 0.32 for the ETF-sample. For the uncle sample, the same estimate, in Column 3, is 0.35, which is close towhat Black, Devereux, and Salvanes (2009) have found for Norway and Björklund, Hedros-Eriksson, and Jäntti (2010) for Sweden. In the first column in the lower panel, we instrument for fathers’ cognitive abilities using the cognitive ability evaluation conducted at age 13. The point estimate increases to 0.42, implying a reliability ratio of 0.76. In the third column, we instead instrument for fathers’ cognitive abilities using the enlistment evaluations of their brothers, that is, the uncle instrument. The IV-estimate is 0.48, which in turn implies a reliability ratio of 0.73. This ratio is not statistically different from the reliability ratio in Column 1.
OLS- and IV-Estimates of Intergenerational Correlation in Abilities—Alternative Instruments
We next turn to the intergenerational ability correlations in noncognitive abilities. In Columns 2 and 4 in the top panel, we see that the OLS-estimates are 0.21 both for the ETF and the uncle sample, which is in line with previous findings (for example, Loehlin 2005; Dohmen et al. 2012; Anger 2011). In the lower panel, we correct the estimates for attenuation bias using the age 13 measurements. The point estimate increases to 0.41, which means that the reliability ratio equals 0.51. In the final column, we use the uncle instrument to correct for measurement error and get a point estimate of 0.42, very close to the estimate in Column 2. The reliability ratio using the uncle instrument equals 0.50, which is not statistically different from the reliability ratio in Column 2.7
Apart from the substantial increases in the intergenerational correlations when correcting for measurement error, the most striking finding in Table 3 is the similarity between the estimates based on the two different set of instruments for fathers’ abilities. Using a t-test, we cannot reject that the reliability ratios are equal (p-values are 0.679 and 0.932 for cognitive and noncognitive abilities, respectively). Recall that the ETF-instruments are measures of the same traits at age 13 for the same individual, thus constituting a close to perfect instrument. The fact that the uncle instrument and the age 13-instrument yield very similar results is consistent with the assumption that the exclusion restriction holds also for the uncle instrument.
The similarity between the estimates using different instruments has implications for the interpretation of the estimated intergenerational correlation. The ETF-instruments pick up all genetic determinants of cognitive and noncognitive ability and all environmental factors up until age 13. Hence, they capture the true population correlation, unless any change in fathers’ abilities between age 13 and 18 has a differential impact on their sons than that of fathers’ abilities at age 13. The uncle instrument, on the other hand, exploits the variation in fathers’ skills that is common between brothers. Because brothers on average share 50 percent of their genes and part of their environment at age 18, the two instruments exploit rather different sources of variation in the father’s abilities at age 18. Under the assumptions of classical measurement errors and valid instruments, the fact that the two instruments produce similar results is consistent with the notion that the different sources of variation in the father’s abilities—genes and environment—have similar impacts on the transmission of abilities over generations, and that the IV-estimates capture the average intergenerational correlation in abilities in the population.
One concern is that the high father–son correlation in noncognitive ability may be spuriously driven by cognitive ability, as the cognitive ability is omitted in the regressions in Columns 2 and 4, and vice versa. In Table 4, however, we find that the point estimates in the uncle sample (ETF-sample) are only slightly reduced—to 0.45 (0.36) for cognitive abilities and to 0.39 (0.40) for noncognitive abilities—when controlling for the other ability type. These point estimates are not statistically different from the corresponding estimates in Table 3. That the intergenerational ability correlations are only slightly affected by considering cognitive and noncognitive abilities simultaneously is consistent with Duncan et al. (2005).
IV-Estimates of Intergenerational Correlations in Both Cognitive and Noncognitive Abilities
The results in this section show that OLS-estimates of intergenerational ability correlations are substantially downward-biased, particularly for noncognitive abilities.
B. Can We Trust the Uncle Instrument?
In this section, we perform several consistency checks corroborating the exclusion restriction for the uncle instrument. This is crucial because a direct impact of uncles on their nephews’ abilities would render results based on this instrument to be invalid. In principle, uncles may be related to their nephews either through genetic similarity or shared environment. We address both of these channels.
Even though the average uncle is more than 25 years older than his nephew, uncles could have a direct influence on their nephews. We test for this by using a subsample of “absent uncles,” defined as uncles who either died or emigrated from Sweden prior to the birth of their nephew.8 If uncles have a direct effect on their nephews, IV-estimates based on absent uncles should be lower than for the average uncle.
Despite the drastic reduction in sample size, Column 2 in Table 5 first shows that the OLS-estimates for cognitive and noncognitive skills are essentially unchanged compared to the estimates based on the full sample. More importantly, the IV-estimates for the absent uncle sample are, if anything, larger than the IV-estimates based on the full sample of observations, and the reliability ratios are lower. The precision of these IV-estimates are low, however, and we cannot reject that the IV-estimates for the different samples are equal. Still, the results do not indicate that the IV-estimates for absent uncles are smaller or that the reliability ratios are larger, compared to the estimates based on the full sample. This is consistent with a lack of a direct influence of uncles on their nephews’ abilities.
Intergenerational Correlation in Abilities—Alternative Restrictions
Even if uncles do not influence their nephews directly, they do have a shared environment through the grandparents. Grandparents may have an influence on both their sons and their grandsons, for example, by spending time with their grandchildren. Hence, there may be an association between the uncle and his nephew, not shared with the father, potentially biasing the IV-estimates upward. In order to test for this, we consider subsamples of children with “absent grandparents,” where the direct contact with the grandparents is broken.
We first use a sample of children where either the grandmother or the grandfather died before their grandson was born. In Column 3 of Table 5, we find the IV-estimates for cognitive and noncognitive abilities to be essentially unchanged compared with the original estimates. In Column 4, we instead use the small sample in which both the grandmother and the grandfather died before their grandson was born. For this sample, the IV-estimate for cognitive ability is slightly smaller, while the estimate for noncognitive ability is larger, than for the full sample, but these differences are not statistically significant. It is important to note that the OLS-estimates also differ somewhat from the estimates based on the full sample, most likely due to this sample being a highly selected one. If the original IV-estimates were upward-biased due to a direct influence by grandparents on their grandchildren, we would expect the reliability ratios for the absent grandparents sample to be higher than for the full sample. Again, we find no indication of this. Thus, we fail to find support for an independent association between uncles and nephews through the influence of grandparents.
Although we do not find support for any environmental influence between uncles and nephews, there still may be a direct genetic link between them. Because children receive one complete copy (allele) of their genetic material from each parent, uncles cannot share genes with their nephews that are unshared by the father or the mother. However, there may be a direct link between uncles’ and nephews’ genetic expressions. In the simplest model of inheritance, alleles are assumed to interact additively with each other to form a trait. However, alleles may also mask the contribution of other alleles, and inheritance is then said to be nonadditive. If inheritance is predominantly nonadditive, uncles and nephews may share a genetic expression that is unshared by the parents.
There has been a long controversy concerning the relative proportion of additive and nonadditive genetic variation for complex human traits such as stature, intelligence, and personality. Recent evidence from genome-wide association studies suggests that most of the genetic variation in the population is additive (for example, Zhu et al. 2015). In addition, twin studies typically find little support for substantial nonadditive effects in the heritability of complex human traits (Polderman et al. 2015). Thus, the available empirical evidence suggests that most genetic variation is additive, which implies that a direct link between uncles and nephews genetic expressions poses less of a threat against the validity of the uncle instrument.
In Appendix B, we discuss the genetic inheritance in more detail and quantify the potential bias from a possible direct link between uncles’ and nephews’ genetic expressions by simulating how the uncle instrument performs under different assumptions of nonadditive inheritance. In most cases, we cannot reject that the uncle instrument is valid. Only when inheritance is assumed to be predominately nonadditive—an assumption not supported by the available empirical evidence—are the IV- and OLS estimates significantly different. Even in this case, the potential bias is relatively small (less than 6.5 percent of the true estimate). Thus, under most reasonable assumptions of nonadditive genetic inheritance, we do not find any support for a direct genetic similarity between uncles and nephews.
As a final check for a direct link between uncles and nephews, we study how the uncle instrument performs for another complex human trait, stature. Stature has two features that make it suitable for testing the genetic resemblance over generations. First, height has a strong genetic component, although it also has environmental influences (Polderman et al. 2015). Second, the measurement of stature is less likely to suffer from severe error. If shared genetic (and environmental) factors captured by uncle stature have a direct impact on child stature, we expect the IV-estimates to be significantly larger than the OLS. If, on the other hand, no direct effects are present, the IV- and OLS-estimates should be similar. Indeed, in Table 6 we find the OLS-estimate of the father-son correlation in height to be 0.48, whereas the IV-estimate is 0.50. Thus, we fail to find indications of direct effects by uncles on their nephew’s stature through shared genetic (and environmental) factors.
Instrument Validity: Intergenerational Correlations in Height
Through all the consistency tests performed we fail to find evidence of a direct effect from uncle to nephew, either through a direct influence, a shared environment, or through a common genetic component not shared by the father. Given the results of these tests and the similarity in results between the two IV-strategies, the remaining analysis is based on the uncle instrument.
V. Ability Correlations Using Both Parents
Thus far, we have only studied father–son correlations, even though both parents presumably are important for the transmission of abilities over generations. To bring the mothers into the analysis, we generalize our methodological strategy by predicting maternal abilities using the enlistment records of their brothers.
A. Deriving Maternal Abilities
To derive maternal abilities, we use the idea behind the uncle instrument to predict abilities for both parents using the first-stage relation; that is, we use enlistment records of both paternal and maternal uncles. Because we do not observe mothers’ abilities, we cannot obtain a direct estimate of the first-stage equation for mothers. However, if the brother–sister correlations at age 18, 
, were known, we could predict mothers’ abilities using maternal uncles:
(6)Predicted maternal abilities, 
, could then be used in the second-stage relation (Equation 1). To perform this exercise, we need an estimate of 
.
In order to produce estimates of the gender-specific sibling correlations, we use alternative sources of data.We scale the brother correlations from Equation 3 by a factor equal to the relative sister–brother to brother–brother correlation for each ability. Specifically, we construct the estimate of the brother–sister correlation to be used in the prediction of mother’s abilities as follows:
(7)For cognitive skills we have ability evaluations at age 13 from the ETF-study for a sample of boys and girls. Using these data, we first regress girls’ cognitive ability at age 13 on their brothers’ cognitive ability at the enlistment at age 18 to obtain the brother– sister correlation 
. We obtain 
by regressing the cognitive ability at age 13 for boys on their brothers’ cognitive ability at enlistment. Relating the brother– sister correlation to the brother–brother correlation gives us a scaling factor for cognitive ability. In the first two columns of Table 7, we find that this sibling correlation in cognitive abilities is 0.41 for brothers and 0.38 for sisters and brothers. This gives a relative sister–brother to brother–brother correlation in cognitive abilities of 0.92.
Sibling Correlations
We do not have any direct measure of noncognitive abilities for women. However, we do have the grade point average (GPA) from the last year of compulsory school at age 16. These grades are used by students to apply for upper-secondary education, and they reflect both cognitive and noncognitive abilities.9 To obtain a scaling factor for noncognitive abilities—and an additional estimate of the scaling factor for cognitive abilities—we regress boys’ and girls’ GPA on their brothers’ enlistment cognitive and noncognitive evaluations, which gives 
and 
.
As can be seen in the third and fourth column of Table 7, male and female students’ GPA results are strongly related to their brother’s cognitive and noncognitive abilities at enlistment. The correlation in cognitive abilities between brothers and sisters relative to the correlation between brothers is 0.92, which is identical to the relative sibling correlations in cognitive abilities obtained from the estimates in Columns 1 and 2. Similarly, the relative sibling correlation in noncognitive abilities from Columns 3 and 4 is 0.93.
Based on these estimates, we assume that the scaling factor (the brother–sister correlation relative to the brother–brother correlation) is 0.92 for cognitive abilities and 0.93 for noncognitive abilities. Using these estimates of the relative gender sibling correlations, we obtain the first-stage relationship between mothers and their brother’s abilities 
. We then predict the cognitive and noncognitive abilities for both fathers and mothers using the abilities of paternal and maternal uncles with enlistment records.
In Appendix A, we derive the conditions for generating an unobserved endogenous regressor, which is unavailable in other samples, but where an alternative measure can be used to generate the missing regressor. In addition to the exclusion restriction that maternal uncles’ abilities have no direct effect on their nephew’s abilities, we show that the scaling in Equation 7 also requires that the alternative ability measure (ability at age 13 or GPA at age 16) is an equally good proxy variable for both mothers’ and fathers’ ability at age 18. In Appendix Table D3, we check this condition for cognitive skills in our data. We find that cognitive abilities at age 13 have essentially the same association with GPA at age 16 for both girls and boys.
B. Results for Maternal and Paternal Abilities
Having derived abilities for both mothers and fathers, we can estimate the intergenerational correlation between sons and both of their parents. Note that the attenuation bias due to measurement error is accounted for in the two-stage procedure. We now require that enlistment records are available for both paternal and maternal uncles, which reduces the sample size to around 25,000 sons. (Sample descriptions are available in Appendix Table D6.) In the first column of Table 8, we estimate the father–son correlation in cognitive ability to be 0.51; the slight difference to the IV-estimates in Table 3 is due to the somewhat different sample.10 In Column 2, we see that the estimated mother–son correlation in cognitive ability is higher, 0.58. The third column shows that the partial correlations for fathers’ (0.33) and mothers’ (0.42) cognitive abilities are both reduced when entered jointly into the regression, indicating positive assortative mating. 11 The difference in the intergenerational correlations for fathers’ and mothers’ abilities is statistically significant both for the bivariate and partial results, which is consistent with the findings in Anger and Heineck (2010).
Father–Son and Mother–Son Correlations
For noncognitive abilities, the mother and father correlations are more similar. The father–son correlation in noncognitive abilities is 0.46 (Column 4), the same as the mother–son correlation in Column 5. When entered jointly, the partial father–son correlation is 0.32, whereas the partial mother–son correlation is 0.29. The difference between these estimates is not statistically significant.
The results in this section show that mother–son correlations in cognitive abilities are higher than father–son correlations, whereas the mother–son and father–son correlations are similar for noncognitive abilities.
C. Intergenerational Correlations versus Sibling Correlation
An alternative strategy for assessing the importance of the family in shaping abilities is to estimate sibling correlations. This is a broad measure capturing the overall importance of the family, community, and neighborhood factors—including joint shocks shared between siblings. It has been suggested that intergenerational ability correlations only account for a limited part of the sibling correlation and that hard-to-measure attributes are important for inequalities in productive traits across families (Björklund and Jäntti 2012; Anger and Schnitzlein 2016).
A novel aspect of our study is that we bring both parents into the analysis and account for measurement error. In Columns 4 and 8 of Table 8, we see that the intergenerational correlation is primarily driven by the skill-to-skill transmission from parents to sons, rather than a transmission across skills. This suggests that children’s abilities are mainly formed by their parents’ abilities, rather than by other factors uncorrelated with parents’ abilities.
Solon (1999) shows that the sibling correlation in abilities, r, can be decomposed as follows (assuming single-parent families):
(8)where β is the intergeneration correlation. Most studies use the correlation in abilities between fathers and sons as the measure of intergenerational transmission. Following this convention, we find that the intergenerational correlation in cognitive skills between fathers and sons (0.35 in Table 3) accounts for (0.35)2/0.460 = 0.266 of the sibling correlation in Column 3 of Table 2. The corresponding share for noncognitive skills is 0.14. This is in line with or slightly higher than previously reported (Björklund and Jäntti 2012).
When abilities are measured with error, both the sibling correlation and the intergenerational correlation will be biased to the same extent. However, because the intergenerational correlation is squared in the decomposition of the sibling correlation, measurement errors will understate the role of parents. Using the estimated reliability ratio for cognitive skills (0.731) in Table 3, we find that the intergenerational correlation accounts for (0.350/0.731)2/(0.460/0.731) = 0.364 of the sibling correlation when correcting for measurement error. The corresponding share for noncognitive skills is 0.283.
When we explicitly consider two-parent families, the decomposition of the sibling correlation expands to:12
(9)With an assortative mating of 0.464 for cognitive abilities in our data (0.508 for noncognitive), the terms related to intergenerational correlation in Equation 9 sum to (0.332)2 + (0.424)2 + 2 × 0.332 × 0.424 × 0.464 = 0.421, when using the error-corrected estimates for cognitive ability in Table 8. This is 67 percent of the error-corrected sibling correlation. The corresponding number for noncognitive ability is 45 percent.
In summary, when including both parents in the analysis and accounting for measurement errors, we find that a substantial part of the sibling ability correlation can be accounted for by the intergenerational transmission of parents’ abilities. This leaves less room for community factors or hard-to-measure attributes of the family than has previously been assumed.
D. The Social Transmission of Abilities: Results Using Adoptees
To study the mechanisms that underlie the intergenerational correlations, we make use of data on international (male) adoptees to Sweden. This enables us to compare the social transmission of skills to the combined influence of social and genetic factors. Adoptees have previously been used to separate nurture from nature, primarily in the intergenerational transmission of income and educational outcomes (Björklund, Lindahl, and Plug 2006; Sacerdote 2007; Holmlund, Lindahl, and Plug 2011; Lundborg, Nordin, and Rooth 2011).
We use data on children adopted to Sweden before the age of two, where none of the adoptive parents are born in the same country as the child. Data are restricted to observations with enlistment information on the adoptee and either the father or an uncle. Ninety percent of the children we observe are born in 1973–87. In total, we have information on 1,591 adoptees for whom we can observe the father (n = 567) and/or a paternal uncle (n = 677) and/or a maternal uncle (n = 833).13 For the sample of fathers, we estimate the OLS-relation between fathers and sons and correct for measurement errors using the reliability ratios in Table 3. For the samples of uncles, we use predicted parental abilities, exploiting the first-stage relationships in Table 2.
Neither the parents nor the adopted children are randomly distributed, and the choice of country to adopt from is likely based on elaborate consideration, but for a given country and year, the allocation of children to parents is plausibly exogenous with respect to abilities.14 We therefore control for the interaction between children’s country of origin and year of birth.
There are limitations to bear in mind when using adoption data to separate the social and genetic influences of parents. The analysis may understate the importance of environmental factors, as it will not capture in-utero environmental factors or events that took place before the adoption, periods that are considered critical (Currie and Almond 2011). Moreover, adoptive children may have difficulties with attachment to their new parents, and adoptive parents also may be non-representative in their investments in their child. With these caveats in mind, we report the intergenerational correlation of cognitive and noncognitive abilities for adoptive sons in Table 9.
Intergenerational Correlations in Abilities for Foreign Adoptees
In Columns 1 and 2, we find the transmission of cognitive ability from fathers to adoptive sons to be 0.12–0.13, while the mother–son correlation is 0.20. That is, nurture accounts for about a quarter of the total transmission of cognitive ability from fathers found in Table 8, whereas social factors account for more than a third of the transmission from mothers. In Columns 4 and 5, we find that the intergenerational correlation of noncognitive ability between fathers and adoptive sons is small or negligible (point estimates are insignificant), but the mother–adoptive son correlation is 0.32. This implies that nurture accounts for more than two-thirds of the total transmission of noncognitive skills from mothers.
Although our adoptive samples are relatively large compared to previous studies, they are small compared to our main analysis, which warrants some caution in interpreting the size of the point estimates. We therefore confine ourselves to concluding that the social transmission of abilities from fathers is modest and that the nurture of mothers is considerably more important for handing down cognitive, and in particular, noncognitive abilities to their sons.
VI. Long-Run Outcomes for Children
In this section, we estimate the relationship between predicted parental abilities and educational and labor market outcomes for both sons and daughters. In particular, we estimate the relationship between parental abilities on children’s compulsory school achievement, years of education, earnings, and labor force participation. In principle, these estimates will capture a composite influence from two sources: The first is the payoff of the abilities transmitted from parents to children. The second is the impact of parental abilities on their children’s outcomes, through channels such as residential choice, help with homework, and professional networks.
We perform this analysis separately for sons and daughters, thus allowing mothers’ and fathers’ abilities to be differently related to sons’ and daughters’ outcomes. Such differences can be due to either a gender-specific transmission of parental abilities, differences in the payoffs of a given ability for men and women,15 or a differential direct impact of parental abilities on sons’ and daughters’ labor market prospects or educational success.
In this analysis, we only require the children to have a paternal uncle and a maternal uncle with a valid enlistment record. We can therefore also predict cognitive and noncognitive abilities for fathers and mothers born before 1950. For these longterm outcomes to be representative of life success, we require the labor market outcomes and years of schooling to be observed when sons and daughters are between 30 and 40 years old.
Table 10 presents the results for educational outcomes of sons and daughters. In Column1 of the upper panel, we regress standardized test scores in English, Swedish and mathematics at age 16 on paternal abilities. The association between paternal cognitive ability and test scores is strong: 0.40 for sons and 0.38 for daughters. For noncognitive ability, the relationship is considerably weaker: 0.07 among sons and 0.10 among daughters. Column 2 performs the same analysis using maternal abilities. The association between maternal cognitive ability and student achievement is stronger for sons (0.43) than for daughters (0.37), while the reverse is true for noncognitive abilities (0.07 for sons and 0.14 for daughters). In Column 3, we include both maternal and paternal abilities and find that the same patterns hold: Mothers’ cognitive abilities are relatively more important for sons, while mothers’ noncognitive abilities are relatively more important for daughters. There is no difference between sons and daughters based on their fathers’ abilities. Children whose both parents have abilities one standard deviation above the mean on average achieve 0.66 standard deviations higher test scores.
Parental Abilities and Educational Success, Sons and Daughters
In the middle panel, the outcome is the child’s grade GPA when completing compulsory school. The relationship between paternal cognitive (noncognitive) abilities and sons’ GPA is 0.31 (0.19), and it is almost identical for daughters. For maternal abilities, the correlation is 0.35 (0.17) for sons and 0.31 (0.21) for daughters. Parental noncognitive abilities are thus relatively more important for GPA than for test scores, and the combined impact of a one-standard-deviation increase in both abilities for both parents is a 0.69 standard deviation increase in the GPA for both sons and daughters.
In the lower panel, we document a strong relationship between years of schooling and parental abilities. Both paternal and maternal cognitive abilities are more strongly related to sons’ than to daughters’ years of schooling, while both parents’ noncognitive abilities are more important for daughters than for sons. Sons (daughters) whose both parents have abilities one standard deviation above the mean attain on average 1.3 (1.2) additional years of schooling. Both GPA and years of schooling have a stronger correlation with parent’s noncognitive skills than test scores, as they may require a broader set of abilities than achievement tests.
We next turn to children’s labor market outcomes. In the top panel of Table 11, we regress annual earnings on fathers’ and mothers’ abilities (zero earnings are included). To facilitate interpretation, we divide the estimates by the average earnings of sons and daughters in the sample. Parental noncognitive abilities are substantially more important than their cognitive abilities for the earnings of their children. Sons (daughters) whose both parents have abilities one standard deviation above the mean on average earn almost 18 (15) percent more. The middle panel shows that one of the reasons for this result is that parental noncognitive abilities are strong predictors of labor force participation, but cognitive abilities are not. This holds true for both sons and daughters. Among sons, a one standard deviation increase in fathers’ and mothers’ noncognitive ability is associated with about a 6.5 percentage point higher probability of being employed. Among daughters, the corresponding number is 7.6 percentage points.
Parental Abilities and Labor Market Success, Sons and Daughters
In the bottom panel, we estimate the relationship between log earnings and parental abilities. For sons, the relationship between log earnings and the cognitive and noncognitive abilities of their fathers is 0.045 and 0.038, respectively. For mothers’ cognitive abilities the point estimate is 0.031, and the point estimate is 0.035 for noncognitive abilities. The estimated correlation between daughters’ log income and parental noncognitive abilities suggests a somewhat different pattern: The estimate for fathers’ cognitive abilities is 0.053, but the association is close to zero for noncognitive abilities. The relative importance of cognitive abilities also holds for maternal abilities: The point estimate is 0.045 for cognitive abilities and 0.011 (not statistically significant) for noncognitive abilities.
The relationship between parental abilities and child earnings might be mediated by educational attainment. To get a sense of the importance of this channel, we conduct a back-of-the-envelope calculation of the implied earnings effect of the relationship between parental abilities and child educational attainment. The estimates in Table 10 show that a one-standard-deviation increase in fathers’ cognitive and noncognitive abilities is associated with 0.91 (0.61 + 0.30) additional years of schooling for sons. Given that the return on an additional year of schooling on the Swedish labor market is 2.5 percent (Öckert 2010), this corresponds to an earnings increase by 0.023 percentage points. As shown in Table 11, the total earnings effect of a one-standard-deviation increase in paternal cognitive and noncognitive abilities is 0.132 (0.037 + 0.095) percentage points. Thus, only a minor part of the earnings premium of parental abilities can be accounted for by increased educational attainment. This pattern is more or less the same for daughters and if we use mothers’ rather than fathers’ abilities.
If we turn to the estimates in Table 4, a one-standard-deviation increase in fathers’ cognitive and noncognitive abilities is associated with a 0.502 (0.445 + 0.057) standard deviation increase in the cognitive abilities of sons, and the corresponding number for noncognitive abilities is 0.443 (0.052 + 0.391). Using the error-corrected estimates of own-ability returns from Lindqvist and Vestman (2011), this corresponds to a total ability return of 0.502 × 0.083 + 0.443 × 0.086 = 0.08 log points. Table 11 shows that increasing fathers’ cognitive and noncognitive abilities by one standard deviation is associated with an increase of the sons’ earnings by 0.045 + 0.038 = 0.083 log points. Thus, the entire earnings increase associated with higher paternal abilities can be attributed to the impact on son’s abilities rather than to other channels.
VII. Conclusions
This paper makes several contributions to the literature on the intergenerational transmission of cognitive and noncognitive abilities. First, we compare intergenerational correlations in cognitive and noncognitive abilities using large and representative samples of men who are evaluated using the same methods and at the same age. Second, we correct for measurement error bias by using two different sets of instruments. In particular, we make a methodological contribution by suggesting that the evaluations of the abilities of uncles can be used as instruments to correct for measurement error in the father’s abilities. We find evidence of measurement error bias in both ability dimensions, and once this is corrected for, the intergenerational transmission of noncognitive abilities is almost as high as that of cognitive skills. Third, we bring mothers into the analysis by predicting their abilities using the evaluations of maternal uncles, and we provide the formal conditions for 2SLS when data on the endogenous regressor are unavailable. Fourth, by considering the joint impact of both parents, we show that intergenerational ability-to-ability correlations can account for a substantial portion of sibling ability correlations. Fifth, using international adoptees, we find that the social transmission of abilities from fathers is modest, whereas the nurturing provided by mothers is more important in shaping child abilities. Sixth, we find that the abilities of both parents are strongly related to later life outcomes for children.
Studies on sibling correlations have shown that the family is important in forming the abilities of children. Our results suggest that abilities are to a large extent handed down ability-by-ability from parents to children and that parental sorting plays an important role in the transmission. This high degree of persistence in abilities across generations may be somewhat surprising given the relatively low intergenerational income correlations found in Sweden (Black and Devereux 2011). Because the labor market returns to skills depend on factors such as the overall wage distribution, the equity of the educational system, and the industry composition, these findings are not contradictory. Hanushek et al. (2015) report that the returns to skills in Sweden are the lowest among OECD countries. Indeed, we find a strong correlation between parents’ cognitive and noncognitive abilities and educational and labor market outcomes for both sons and daughters. Back-of-the-envelope calculations suggest that the association between parental abilities and child earnings runs entirely through the abilities of children and not through other channels. Higher levels of educational attainment associated with higher abilities can only account for a fraction of this increase in earnings.
Our results indicate that the degree of assortative matching has important implications for the distribution of abilities and therefore the earnings distribution of the next generation. The finding that families play an important role in shaping both cognitive and noncognitive abilities raises some doubts concerning the general perception that noncognitive abilities are relatively malleable, and hence a more appropriate target for policy interventions than cognitive abilities (Knudsen et al 2006; Cunha and Heckman 2008). Moreover, the difference between the social influence of mothers and fathers challenges a deterministic view of how abilities are transmitted. Before drawing any strong conclusions on these matters, however, more research is clearly needed.
Acknowledgments
We are grateful for financial support from IFAU and Riksbankens Jubileumsfond. The data used in this article combines information from three Swedish agencies and is restricted by national regulations. Readers interested in obtaining the data can obtain advice on the matter from the authors; contact Björn Öckert: IFAU, P.O. Box 513, SE-75120 Uppsala, Sweden, bjorn.ockert{at}ifau.uu.se.
Footnotes
Erik Grönqvist is a researcher at the Institute For Evaluation of Labour Market and Education Policy (IFAU) and the Department of Economics at Uppsala University. Björn Öckert is a researcher at the Institute For Evaluation of Labour Market and Education Policy (IFAU) and the Department of Economics at Uppsala University. Jonas Vlachos is a professor at the Department of Economics at Stockholm University and the Research Institute of Industrial Economics (IFN).
We have benefitted from comments and suggestions from the referees, Nikolay Angelov, Peter Fredriksson, Per Johansson, Mikael Lindahl, Matthew Lindquist, Erik Lindqvist, Petter Lundborg, Per Pettersson-Lidbom, Martin Nybom, Erik Plug, Analia Schlosser, Peter Skogman-Thoursie, Ingeborg Wärnbaum, and seminar participants at the EEEPE conference in London, the EALE-SOLE meetings in London, UCLS workshop in Öregrund, ELE workshop in Sitges, the National Conference of Swedish Economists in Lund, the Institute for Evaluation of Labour Market and Education Policy (IFAU), the Research Institute for Industrial Economics (IFN), Zentrum für Europäische Wirtschaftsforschung (ZEW), CAFO Linnaeus University, Lund University, Aarhus University, and Tel Aviv University.
↵* Supplementary materials are freely available online at: http://uwpress.wisc.edu/journals/journals/jhr-supplementary.html
↵1. Black, Devereux, and Salvanes (2009) and Björklund, Hederos Eriksson, and Jäntti (2010) find intergenerational correlations in cognitive abilities of 0.35–0.38, whereas the meta-study by Plomin and Spinath (2004) reports 0.4. For noncognitive abilities, the meta-study by Loehlin (2005) reports an intergenerational coefficient of 0.15, Duncan et al. (2005) reports correlations of 0.05–0.16, and Anger (2011) and Dohmen et al. (2012) find coefficients of 0.12–0.25.
↵2. Other studies have also found that measurement errors are larger for noncognitive than cognitive abilities (for example, Mueller and Plug 2006).
↵3. This may not be achieved when using more conventional error correction models, such as test-retest or parallel-test. While retests may be correlated with the test-specific error of the first test, kia, parallel-tests are likely to be correlated with the time-specific error, lit . Hence, in both cases, the reliability of the skill measure tends to be overstated.
↵4. Standardization of a variable with random measurement error will overstate the true variability. To interpret the IV-estimates as the impact of moving one standard deviation in the true distribution of the standardized regressor, the point estimate (and the standard error) must be corrected for the inflated variance. As shown formally in Appendix E, when both the regressand and the regressor have measurement errors and are standardized, the correction term is the square root of the ratio between the reliability ratio of the regressor and the reliability ratio of the regressand. Consequently, if the degree of measurement error can be assumed to be the same for the regressor and the regressand, the correction term cancels out. Therefore, we do not correct the IVestimates in the main analyses, where we use the same ability measures for both parents and sons. In Tables 4 and 8, where we regress one ability measure on another ability measure, we correct the estimates by the square root of the relative reliability ratios. In Tables 10 and 11, where we use regressands that are either not standardized or measured without error, we correct the estimates by the square root of the reliability ratio of the regressor.
↵5. In Appendix Table D1, we show the relationship between the noncognitive draft measures and survey questions evaluating school adaptation and motivation at age 13 for a subsample of draftees.
↵6. Appendix Table D6 shows that sons and fathers with a valid enlistment record are positively selected. This is consistent with the fact that individuals could be exempted from the draft if they were not fit for military service. In Table D7, we find that the intergenerational correlation may be slightly larger in the full population of sons than for the sample of sons with valid draft records, but the difference is not statistically significant.
↵7. As discussed, the composite measures of cognitive and noncognitive skills consist of four different subtests. The intergenerational correlation does not differ substantially between the different subtests, and we therefore focus only on the composite measures. In Appendix Table D2, we present the intergenerational correlations for each of these tests.
↵8. Appendix Table D6 shows that sons and fathers with an uncle who died or emigrated before the son was born are positively selected in cognitive and noncognitive abilities.
↵9. Regressing standardized GPA at age 16 on both abilities at age 18 yields (n = 232,567) a coefficient of 0.48 (SE 0.002) on cognitive abilities and 0.13 (SE 0.001) on noncognitive abilities. Almlund et al. (2011) also find that GPA reflects both types of abilities.
↵10. As shown in Appendix Table D8, the intergenerational correlation in cognitive ability is slightly larger in families for which both the paternal and maternal uncles have valid draft records. Still, the difference is small and not statistically significant.
↵11. In Appendix Table D5, we report the intergenerational correlation between both parents and their sons for the different cognitive and noncognitive subtests.
↵12. For simplicity, we assume equal variance in skills for mothers, fathers and sons.
↵13. Descriptive statistics for the adoptee sample are provided in Appendix table D9.
↵14. Adopting fathers have on average 0.25 (0.28) standard deviations higher cognitive (noncognitive) ability than the average parent, and adopted sons have 0.35 (0.09) standard deviations lower cognitive (noncognitive) ability than the average son. In Appendix C, we discuss the process of foreign adoptions in Sweden.
↵15. Heckman, Stixrud, and Urzua (2006) provide an analysis of gender-specific payoffs of cognitive and noncognitive abilities. Mueller and Plug (2006) find that women with an antagonistic personality are at a substantial earnings disadvantage compared to women who are more agreeable. For men, this pattern is reversed.
- Received January 2015.
- Accepted June 2016.
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