Last Updated on October 14, 2023

Richer and more educated parents tend to have smarter children than poorer and less educated parents. That is, there is a positive correlation between parental socioeconomic status (SES) and offspring cognitive outcomes. Some people who observe this correlation infer that parental SES has a large causal influence on offspring cognitive outcomes. However, such a causal inference requires ruling out plausible alternative explanations of this correlation, i.e. this inference requires ruling out plausible confounding. One plausible alternative explanation of the association between parental SES and offspring cognitive outcomes is parental cognitive ability. Smarter parents earn higher incomes and acquire more education, and smarter parents also have smarter children. To the extent that smarter parents have smarter children because of reasons other than the mediating effect of their attained SES, the correlation between parental SES and offspring cognitive outcomes will be (at least partly) due to confounding and therefore not causal.

This post reviews studies that enable us to quantify the magnitude of this potential confounding by reviewing studies that examine the association between parental SES and offspring cognitive outcomes after controlling for parental cognitive ability/skills. The post is broken down into the following sections:

1. I summarize the main findings and explain why they are important.
2. I cover some preliminaries regarding effect sizes, terminology, selection criteria, confounding explanations, etc. to motivate and help interpret the studies that I will review in the later sections.
3. I review studies that allow us to quantify the independent effects of parental education and parental income on offspring cognitive outcomes.
4. I review studies that allow us to quantify the independent effects of parental education, parental income, and parental cognitive ability (and potentially parental occupation and parental wealth) on offspring cognitive outcomes.
5. I report the main findings from my examination of these studies.

Summary

Main findings in brief

Here, I will report the main findings in very brief detail here. For more detail, see the final section.

• Without any controls, parental SES has a modest association with offspring cognitive outcomes.
• In models that include both parental education and parental income (but not parental cognitive ability) as predictors of offspring cognitive outcomes:
  • Parental income has consistently small or statistically insignificant effects (with just 1 exception of all studies considered).
  • Parental education has consistently statistically significant effects, with usually small to medium effect sizes.
• In models that include parental education, parental income/wealth, and parental cognitive ability as predictors of offspring cognitive outcomes:
  • Parental income has usually statistically insignificant effects, with consistently small effect sizes.
  • Parental education has usually statistically significant effects, with usually small effect sizes.
  • Parental cognitive ability/skills has consistently statistically significant effects, with usually large or medium effect sizes. In other words, smarter parents have smarter children, independently of the parent’s education, occupation, income, or wealth.
• The relationship between parental cognitive ability and offspring cognitive outcomes is robust, persisting despite ample controls for plausible confounders/mediators:
  • Parental SES does not explain why smarter parents have smarter children. That is, parental SES neither confounds nor mediates the relationship between parental cognitive ability/skills and offspring cognitive outcomes. In other words, parental SES does not drive the intergenerational transmission of cognitive outcomes.
  • Observable/measurable home and parenting factors (e.g., discipline, books in the home, parental warmth, etc.) do not explain why smarter parents have smarter children. That is, these home/parenting factors neither confound nor mediate the relationship between parental cognitive ability/skills and offspring cognitive outcomes.
  • But these same observable/measurable home and parenting factors do explain why richer or higher-SES parents have smarter children. That is, these home/parenting factors do either confound or mediate the relationship between parental SES and offspring cognitive outcomes.
  • Some evidence suggests that genetics do not entirely explain why smarter parents have smarter children, because exogenous changes in parental cognitive ability (which are presumably independent of genetics) are transmitted to their offspring. Though this evidence is more provisional and should be given low credence.

Why this matters

Let’s assume that my main findings are all correct. That is, assume that parental SES does have only a weak association with offspring cognitive outcomes, net of parental cognitive ability. And assume that parental income in particular doesn’t even have a statistically significant association with offspring cognitive outcomes after such controls. So what? Why does this matter? Well, I’ve previously demonstrated that one’s childhood cognitive ability is a powerful predictor of basically everything we care about, including educational attainment, occupational prestige, income, health, avoiding crime, etc. Moreover, we have reason to believe that much of this is because cognitive ability has a causal influence on these outcomes. So knowing what does (and what does not) influence offspring cognitive ability is very important.

Furthermore, people commonly assume that parental SES (especially parental income) has a very large effect on one’s outcomes in life, especially their socioeconomic outcomes. But I have previously shown that offspring cognitive ability is a much better predictor than their parent’s SES for their socioeconomic outcomes. In fact, parental SES is usually a quite weak predictor of offspring socioeconomic outcomes after controlling for offspring cognitive ability.

For example, I have shown that, after controlling for offspring cognitive ability, parental SES has a weak association with offspring income (β ~ 0.10) in the United States and no statistically significant association in studies in Sweden and Germany. Thus, in order for parental SES to have a strong causal influence on offspring income, this effect must be mediated through offspring cognitive ability. But the findings of this post show that not to be the case: parental SES does not have a strong effect on offspring cognitive ability (net of parental cognitive ability), thus parental SES cannot have a strong effect on offspring income (or any other outcome for that matter) that is mediated through offspring cognitive ability*.

* One might object that this inference is invalid because parental SES might have a strong effect on offspring cognitive ability that is mediated through parental cognitive ability. We can reject this hypothesis because, as I show below, studies show that parental SES has weak effects on offspring cognitive ability after controlling for parental cognitive ability even when their abilities are measured at childhood.

Therefore, if the findings in this post are correct, it would undermine the common notion that parental SES has a strong effect on one’s socioeconomic outcomes. It also undermines the notion that parental SES has a strong effect on any other outcomes that are largely driven by cognitive ability.

Preliminaries

Interpreting effect sizes

I will rely heavily on standardized regression coefficients (β) in order to compare effect sizes and to interpret whether a given effect size is small, medium, or large. See this previous post by me for more detail on standardized regression coefficients.

Throughout the post, I will refer to effect sizes as “small” or “weak”, “medium” or “modest”, and “large” or “strong”. To determine whether a standardized regression coefficient is small/weak, medium/modest, or large/strong, I will use the same empirically derived guidelines that are recommended for correlation coefficients (as I mentioned in my previous post). So I will treat 0 < |β| < 0.15, 0.15 < |β| < 0.30, and |β| > 0.30, respectively, as small/weak, medium/modest, and large/strong effect sizes (Now, the precise boundaries are not important for this post. I could have chosen slightly different thresholds without significant change in meaning or accuracy. I just want to be consistent in my interpretation of effect sizes across different posts/studies, and I want the reader to know why I label certain effect sizes as “small” vs “large”).

I use the same guidelines for both correlations and standardized regression coefficients because both effect sizes have a similar interpretation: both indicate the change (in standard deviation units) of one variable that is associated with a one standard deviation increase in the other variable (again, this is explained in my previous post). The difference between simple correlations (r) and standardized regression coefficients (β) is that the former estimates this association without any controls whereas the latter estimates this association after (potentially) controlling for other independent variables.

One complication with using this guideline is that it may give the impression that logged independent variables (such as logged income or wealth) are larger than they actually are. For example, if logged income has a standardized regression coefficient of 0.3, this may not actually be a large effect. This complication will be mentioned in some later studies when it is relevant.

Variables of concern

By “parental socioeconomic status”, I mean a combination of parental education, occupation, and income/wealth. As I’ve demonstrated in previous posts, this is a commonly used measure of SES. It also contains the factors that many suppose play a large role in determining one’s life outcomes.

By “cognitive outcomes”, I refer broadly to what are sometimes considered “cognitive ability”, “cognitive outcomes”, “cognitive skills”, “intelligence”, “academic achievement”, etc. Some of the studies covered will focus on conventional IQ scores or general intelligence (g). Other studies will focus on tests of achievement in reading, literacy, mathematics, etc. Other studies will measure more raw abilities such as working memory. When summarizing findings across different studies, I will try to use the phrasing “cognitive outcomes” or “cognitive skills”, though I admit I’m not always consistent.

Despite the diverse range of outcomes considered, each outcome is likely measuring similar abilities. As I have demonstrated in previous posts such as this one and this one, all measures of “cognitive ability”, “academic achievement”, “intellectual performance”, etc. correlate substantially. Specifically, standardized tests correlate so strongly with conventional IQ tests that some researchers have considered SAT and ACT tests to be adequate measures of general intelligence (Koenig et al. 2008, Frey and Detterman 2004). Since all of the outcomes considered here are measured via standardized tests (as opposed to e.g. teacher-reported grades), they can be considered solid proxies for cognitive ability as measured by conventional IQ tests.

Basic correlations

I’ll start by noting the raw correlations between parental SES and offspring achievement. Meta-analyses reveal that the correlation between parental SES and offspring achievement is fairly modest. A recent meta-analysis by Harwell et al. (2016) reported a correlation of just r = 0.22 between parental SES and offspring achievement from approximately 300 effect sizes across over 100 studies. The observed correlations were also much lower for older children. The correlation between parental SES and achievement was r = 0.33 for students in kindergarten, r = 0.23 for students in elementary school, and r = 0.16 for students in middle and high school (Table 2).

There were not large differences in correlation based on the measure of parental SES. The correlation between achievement and parental SES were all modest, whether parental SES was measured using parental income (r = 0.26), parental education (r = 0.17), parental occupation (r = 0.21), or a composite (r = 0.23). Modest correlations were found regardless of the type of outcome measured (r = 0.27 when IQ is used as outcome and r = 0.20 when not, Table 2). These results led the authors to conclude that the “most important finding was that the SES-achievement relationship assuming a random-effect model was relatively weak (M = .22).”

The association, albeit modest, between parental SES and offspring achievement is found in all countries, not just the United States. For example, Selvitopu and Kaya (2021) [archived] meta-analyzed 62 samples from 48 studies that were published between 2010 and 2019. In line with the results from Harwell, they found an average correlation between parental SES and achievement of r = 0.25 (see page 5). The moderator analysis found similar effect sizes regardless of the location of the study, although the effect sizes were a bit lower in China:

One finding from both of these meta-analyses is that parental education is a similar or stronger predictor of offspring cognitive outcomes than is parental income. However, when simultaneously comparing the effect of parental education and parental income in the same model for a specific sample, parental education is consistently a stronger predictor (as I show below). The findings in the meta-analytic data may be due to heterogeneity in the studies that focus on parental income vs parental education.

When analyzing other specific countries not considered above, we also find that correlations between parental SES and offspring achievement tends to hover between r = 0.20 and r = 0.30:

• United Kingdom: von Stumm et al. (2022) [archived] examined the association between parental SES and primary school performance across 16 British cohorts and over 90k children from 1921 to 2011. The authors found that the average correlation between parental SES and school performance was r = 0.28.
• Australia: In the Longitudinal Study of Australian Children (LSAC), Marks (2016) [archived] finds correlations between a composite measure of parental SES and year 9 standardized test scores that are between r = 0.25 and r = 0.37 depending on the type of achievement measured (numeracy, reading, writing, grammar, or spelling).
• Germany: Linberg et al. (2019) compared academic achievement gaps by family SES in the United States and Germany. They found similar sized gaps in both countries. On math scores, low-SES students scored about 0.48 SD below the mean in the United States and 0.55 SD below the mean in Germany. For language scores, the SES gaps were actually larger in Germany (0.75 SD in Germany vs 0.43 SD in U.S.).

Plausible confounders

Much of the association reported here between parental SES and cognitive outcomes is not in fact causal, but is instead due to confounding. For example, we know that much of the association between parental SES and cognitive outcomes must be due to genetic confounding, because high-SES parents are more likely to have high intelligence and because individuals with high intelligence have higher intelligence largely due to genetics. Therefore, high-SES parents will likely have high-achieving offspring not merely because SES is causal, but because high-SES parents will transmit to their offspring genes that are conducive to cognitive outcomes.

As a general rule, bivariate correlations between parental variables and offspring outcomes will greatly overestimate the causal impact due to genetic confounding. In fact, one of the most replicated findings in behavioral genetics is that “most associations between environmental measures and psychological traits are significantly mediated genetically”. Furthermore, we have evidence that the specific correlation between parental SES and offspring achievement is confounded by genetics. For example, several studies have shown that genes drive the correlation between parental SES and offspring IQ (Trzaskowski et al. 2014) and between parental SES and offspring educational attainment (Krapohl and Plomin 2016).

Many authors specifically studying the effects of parental SES on offspring cognitive outcomes have noted potential problems of confounding, including genetic confounding. For example, in a systemic review of studies examining the causal impact of money on child outcomes, Cooper and Stewart (2013) mention a number of factors that plausibly confound the relationship between income and offspring outcomes:

On average, children growing up in low-income households have poorer health than children from richer backgrounds and score worse on tests of cognitive, social and behavioural development (e.g. Duncan and Brooks-Gunn, 1997; Mayer, 1997; Bradshaw, 2001; Ermisch et al., 2001). They go on to do less well in education, have lower self-esteem as adolescents, and are more likely to become involved in crime or delinquent behaviour (e.g. Haveman et al., 1997; Hobcraft, 1998; Ermisch et al., 2001).
However, the extent to which these associations reflect causal relationships is not well understood. A number of confounding factors may explain the apparent link between financial resources and outcomes. Genetic endowment including health and cognitive ability may plausibly be one part of the explanation. Beyond that, parents in low-income households tend to have lower levels of education and parental education itself is likely to influence child outcomes through a variety of pathways. Higher-educated parents will be better placed to help with school work, they may give more priority to educational achievement, and they are likely to be better able to negotiate public services

Another possible confound between parental SES and offspring cognitive outcomes is genetic nurture. That is, high-SES parents may be genetically disposed to engage in parenting practices that benefit the cognitive development of their offspring. If so, this will create a correlation between parental SES and offspring cognitive outcomes that is not due to a causal influence of parental SES. We have evidence that this occurs for certain outcomes. For example, Willoughby et al. (2021) found that a parent’s polygenic score for educational attainment predicted their offspring’s educational attainment, independently of the child’s own polygenic score (although this association was largely driven by parental IQ and parental SES). Even a sibling’s polygenic score for educational attainment predicts a child’s educational attainment, independently of their own polygenic score (Cawley et al. 2020).

One way to partially control for these confounds is to control for parental cognitive ability. By controlling for parental cognitive ability, we implicitly account for genetic confounding and genetic nurture. We implicitly control for genetic confounding because studies routinely show that parent-offspring correlations in cognitive ability are substantially greater in biological families rather than in adoptive families, which suggests that much of the association is mediated genetically (or at least through a mechanism that is independent of parental SES). For example, see findings by Willoughby et al. (2021) on the parent-offspring IQ correlation in biological vs adoptive families:

Of course, controlling for parental cognitive ability is not a perfect control for genetic confounding since a parent’s cognitive ability is not completely determined by their genes. Thus, controlling for parent’s cognitive ability does not completely control for the genes they pass on to their children. The same point applies to genetic nurture (parents of similar cognitive abilities likely differ substantially in their parenting practices). Nevertheless, it will be fruitful to know the degree to which the association between parental SES and offspring cognitive outcomes reduces after controlling for parental cognitive ability/skills. If the association is eliminated completely, then that suggests that parental SES does not have a causal influence of their offspring’s cognitive outcomes; rather, parental cognitive ability (or something correlated with their parent’s cognitive ability, e.g. genes) would confound the correlation between parental SES and offspring cognitive outcomes.

Many researchers have mentioned parental cognitive ability as a plausible confounder of parental SES and offspring cognitive outcomes. For example, in a literature review criticizing the idea that educational inequalities are primarily driven by SES, Marks (2021) argues the following:

The associations between parents’ socioeconomic characteristics and their children’s scores in achievement tests cannot naively be interpreted as the effects of parenting, socialisation, and economic and cultural resources since they are confounded by parents’ cognitive abilities and genetic transmission from parents to their children. Ability measured during childhood or adolescence is strongly correlated with family SES during adulthood (r ≈ 0.5), highest level of education reached (r ≈ 0.6), occupational status (r ≈ 0.5) and to a lesser extent income (r ≈ 0.2) (See section, ‘Cognitive ability is strongly associated with adult socioeconomic attainments’). Therefore, to an unknown extent, part of the effects of SES can be accounted for by parents’ abilities and their genetic transmission. This serious threat to the validity of standard analyses from genetic confounding is almost universally ignored (Freese, 2008; Harden, 2021; Murray, 2020, p. 237)

Similar remarks were made by Schulz et al. (2017) in a study examining the drivers of adolescent cognitive outcomes in Germany. The authors report that the effect of parental resources might be overstated given the parental cognitive ability as a possible confounder:

It remains unclear to what extent associations between parental resources and children’s cognitive ability and educational attainment might be overstated when parental resources are products of unmeasured parental ability. Parental cognitive ability jointly influences the socioeconomic resources they can offer their children and the children’s cognitive ability as well as their educational attainment – both genetically and environmentally. Parents with higher cognitive ability are more likely to have attained higher levels of education, more success in the occupational sphere and, consequently, a higher income (Deary et al. 2007) (Strenze 2007). The few studies that have controlled parental cognitive ability when assessing the relations between parental resources and offspring outcomes have found much smaller associations between measures of parental education, occupation, and income, and children’s cognitive ability (Blau 1999; Johnson and Nagoshi 1985; Mayer 1997). Likewise, Doren and Grodsky (2016) observed that parental cognitive ability largely accounted for the relation between parental income and offspring college attendance and completion.

In a report of the effects of parental income on child outcomes, Mayer (2002) explicitly notes that estimates of the effects of parental income that do not control for parent’s cognitive skills will suffer from omitted variable bias:

Estimating the effect of parents’ income on children’s cognitive skills without controlling for parents’ cognitive skills is likely to over-state the importance of parents’ income, because part of the apparent effect of income will be due to shared genetic factors. Because there is no agreement about how large the genetic component of cognitive ability is, the size of the bias is unknown. However, as we will see, studies that control for parental cognitive skills always find that the effect of parental income on children’s cognitive test scores is quite small. This suggests that omitting parental skills (and unmeasured correlates of their skills) is an important source of bias.

The same point was made by Crawford et al. (2011) in a study examining the intergenerational transmission of cognitive skills in the United Kingdom:

In line with other studies, we have found that parental cognitive ability is a very important predictor of children’s cognitive skills (the most important, along with educational attitudes and aspirations). Because parents’ cognitive ability and socio-economic position are in turn also very strongly related, studies which examine the relationship between parental SEP and children’s ability, but do not control for parental ability – or in some other way attempt to account for these factors – will suffer from a serious omitted variables problem. Indeed, our estimates suggest that parental cognitive ability accounts for 16 percent of the gap in cognitive test scores between children from rich and poor families after controlling for a wide range of mechanisms through which ability may be transmitted across generations (for example, differences in the home learning environment that parents provide for their children), and 50 percent of the gap if we do not include such factors.

For that reason, I have gathered studies estimating the association between parental SES and offspring cognitive outcomes after controlling for parental cognitive ability/skills.

Selection criteria

I searched for all studies that I could find that meet the following criteria:

• Must contain a large sample of participants from a developed country, ideally nationally representative.
• Must have data on offspring cognitive outcomes that are measured through standardized tests, because these correlate very highly with cognitive ability measured via conventional IQ tests (r > 0.70). Cognitive outcomes measured via other means (e.g., teacher or parent report) may not be capturing similar abilities and skills, so they were ignored.
• Must have data on parental SES. To be included in the first review of studies (comparing parental education vs income), studies must have data on at least parental income (or wealth) and parental education. To be included in the second review (comparing parental SES vs parental cognitive ability), studies must have data on parental cognitive ability/skills and some measure of parental SES (ideally with several components including education, occupation, and income).
• Must model the simultaneous effect of parental SES and parental cognitive ability/skills on offspring cognitive outcomes (e.g., with regression models that include both parental SES and parental cognitive ability as independent variables). This is necessary in order to quantify the associations of each explanatory variable that is independent of the other explanatory variables.
• Ideally, offspring cognitive outcomes are measured when they are older, at adolescence or young adulthood. Cognitive tests for younger children are less important, because the tests are less reliable, cognitive ability is less stable, and the influence of environmental forces fade as children age. For all these reasons, data that focuses on the predictors of cognitive outcomes of young children may be misleading if we are interested in knowing what predicts long-term cognitive outcomes of offspring.
• Ideally, uses simple models that do not suffer from overadjustment bias (i.e. do not control for mediators or colliders). For example, it will not be desirable if a study assesses the relative predictive power of, say, parental education and parental cognitive ability in a model that controls for, say, number of books in the home. That’s because it’s plausible that the number of books in the home is downstream of parental education or parental cognitive ability; thus, controlling for number of books might introduce overadjustment bias. So I’ll prefer models that include parental SES, parental cognitive ability, and any confounding variables that are highly unlikely to be mediators (e.g., offspring sex, race, or age).
• However, I admit that it is unclear whether some variables are confounders or mediators. For example, number of siblings is often negatively associated with offspring cognitive outcomes (children perform worse with more siblings). But more educated and smarter parents have fewer children. The association between parental education/intelligence and number of offspring may be due to some third variable that causes both, but it’s probably also causal (i.e. many individuals likely have fewer children because they are more intelligent/educated). So should number of siblings be controlled for when analyzing the relative predictive power of parental SES vs parental cognitive ability on offspring cognitive outcomes? It’s not really clear. In cases like this, I’ll just try to be transparent about the models used, and readers can be cautious of possible overadjustment bias.

Parental education vs parental income

In this section, I review studies that allow us to quantify the independent effects of parental education and parental income on offspring cognitive outcomes. These studies construct models to predict offspring cognitive outcomes which include both parental income and parental education as explanatory variables. The studies mostly find that parental income has a weaker influence than does parental education. In fact, the effect of parental income is often insignificant when parental education is controlled. I’ll start by considering a review of 19 samples by Rindermann and Ceci (2018), and then consider other studies in the United States, the United Kingdom, Australia, and Scandinavia.

Rindermann and Ceci (2018). “Parents’ Education Is More Important Than Their Wealth in Shaping Their Children’s Intelligence: Results of 19 Samples in Seven Countries at Different Developmental Levels”. The authors examined the relative effects of parental education and parental wealth/income on offspring cognitive ability. They considered 19 samples of subjects from seven different countries. The standardized effect sizes of parental education typically hovered between 0.2 and 0.3 whereas the standardized effect sizes for parental income/wealth hovered between 0.1 and 0.2 (Table 2). They described the main results as follows:

Results from 18 cross-sectional and one longitudinal subsamples comparing the effect of parental educational level and parental income in seven countries, in developed and developing countries, for kindergarten, primary, and secondary school children and for young adults (see Tables 2 and 3) reveal a clear pattern: To explain differences in children’s intelligence, differences in parental education are more important than are differences in familial income (direct: βEd = .40 vs. βIn = .16, total: βEd = .45 vs. βIn = .12; Table 2). Because of the large differences between studies, both in size and mediating variables, the three methods (regardless of weighting N) led to somewhat different results ranging from βEd = .25 to βEd = .45 and from βIn = .12 to βIn = .16 (Table 2). However, the pattern suggesting a larger educational effect remains stable across the studies: With the exception of four subsamples, education (in direct effects) was found to be more important than income, in total effects except in only two subsamples (correlations become stable from Ns of 250 onward; Schönbrodt & Perugini, 2013). Differences between wealth measures (wealth in natural units, in monetary or logged units) are negligible.

United States

Ganzach (2014). “Adolescents’ intelligence is related to family income” [archived]. The author tests whether family income is associated with offspring intelligence after controlling for parental education.

• Dataset: The 1979 National Longitudinal Survey of Youth (NLSY79) and The 1997 National Longitudinal Survey of Youth (NLSY97). These were nationally representative longitudinal studies published by the U.S. Bureau of Labor Statistics for 2 cohorts of Americans. Both surveys collected data on several thousand subjects (approximately 10,000) from a representative sample of the noninstitutionalized civilian population in the United States. For both surveys, data was collected at the start of the survey when participants were in their youth.
• Parental SES: Mother’s and father’s education were measured by the number of years of full-time education completed. Income was measured as the logarithm of family income reported by the parents.
• Offspring outcomes: Intelligence was measured as the sum of the standardized scores from four tests from the Armed Forces Qualifying Test (AFQT). The four tests assessed arithmetic reasoning, paragraph comprehension, word knowledge, and mathematics knowledge.

The author reported medium-sized associations between family income and offspring intelligence even after controlling for parental education in both the NLSY79 and the NLSY97. In a regression model including mother education, father education, and family income, the standardized coefficient for log family income was around β = 0.22 and β = 0.24.

It’s not clear why these findings differ from the NLSY79 findings reported by Rindermann and Ceci (2018). Other researchers have left the following comments about the relatively large coefficients for family income reported by Ganzach:

• Rindermann and Ceci (2018) reports that the education effects will be underestimated if the mother’s and father’s educational variables are not combined (page 5).
• Marks (2022) reports that the higher effects for family income may have been because “there was no adjustment for age”.

Marks and O’Connell (2023). “The importance of parental ability for cognitive ability and student achievement: Implications for social stratification theory and practice” [archived]. The authors analyzed the relationship between parental SES and academic achievement after taking into account HOME environment measures, mother’s cognitive ability, and the offspring’s prior cognitive ability.

• Dataset: NLSY79-C. The NLSY79 Child and Young Adult cohort. This survey interviewed the biological children of the female participants of the NLSY79, which was described above. This survey is referred to with many different abbreviations, including CNLSY (children of the NLSY79), NLSY-CS (NLSY79 Child Supplement), NLSY-Child, NLSY-CYA (NLSY79 Child and Young Adult), and perhaps others. The NLSY79 was described earlier. By 2014, 11,521 children had been identified as born to 6,281 mothers in the NLSY79.
• Parental SES: information on parental SES was reported by mothers during their interviews for the NLSY79 survey. Parental SES was measured based on total net family income, and the educational attainment and occupational status for both the mother and father. Educational attainment was measured by years of education. Occupational status was measured by Duncan SEI (socioeconomic index scores).
• Offspring outcomes: Cognitive outcomes were measured each year for children who were between 3 and 15 years of age. Five cognitive outcomes were analyzed. The Peabody Picture Vocabulary Test (PPVT) and the Wechsler digit memory span tests were measures of verbal intelligence and working memory, respectively. Academic achievement was measured via Peabody Individual Achievement Tests (PIAT) for reading comprehension, reading recognition, and math.

Note: the bivariate correlations between parental SES and offspring cognitive outcomes (r = 0.24 to 0.39) were slightly greater than the meta-analytic correlations cited earlier:

The authors analyzed the relationship between parental SES and offspring cognitive outcomes by first constructing a simple model with child test scores as the dependent variable and parental SES and age as the only independent variables. The authors later constructed more models with different combinations of more independent variables as plausible confounders, including mother’s cognitive ability, HOME environment ratings, and prior offspring ability. For the purposes of this section, only the simple model is relevant, as I am interested in comparing the predictive power of family income vs parental education.

The first column of Table 2 shows the effects of each individual component of parental SES on offspring cognitive outcomes when each component is treated as an independent variable.

The results show that family income is consistently the weakest predictor of offspring cognitive outcomes whereas mother’s education is consistently the strongest predictor. In fact, the standardized coefficient (β) for family income ranges between β = 0.00 and 0.02 for 4 of the 5 outcomes, and reaches just β = 0.05 for 1 outcome. By contrast, the standardized coefficient for mother’s education ranges between β = 0.18 and β = 0.24 depending on the outcome. Father’s education has the next biggest association, with effect sizes ranging between β = 0.06 and β = 0.12.

The authors also emphasize the weakness of family income in explaining cognitive outcomes:

Of the four SES measures, mother’s education shows the largest standardized coefficients followed by father’s education (Table 2). Father’s and especially mother’s occupational status have only small, or very small, standardized effects. Family income has only weak effects on test scores: a doubling of family income is associated with increases of only 0.6 score points for the PPVT and no significant association with digit memory scores. The predicted change in achievement in reading comprehension and recognition, and math for a doubling of family income is less than half a score point. For the PPVT, a doubling of income is associated with an average increase of only 0.85 score points.

United Kingdom

Sullivan et al. (2021). “The intergenerational transmission of language skill” [archived]. The authors analyze the relationship between parent and offspring language skills in the Millennium Cohort Study (MCS) in the United Kingdom.

• Dataset: the Millennium Cohort Study (MCS). The MCS is a national birth cohort study following 19,517 children born in the United Kingdom in 2000 to 2001. Data was collected on the children at ages 9 months, 3, 5, 7, 11, 14, and 17 years (the last wave was not available at the time of the study). The authors focus on the 10,781 members who completed the vocabulary test at age 14.
• Parental SES: Parent’s education was measured as the highest qualification of either parent. Economic circumstances were captured in wave 1 (or wave 2 if wave 1 is not available) based on parental social class, home ownership, and family income. Parental occupational status was measured as parental “social class” based on the National Statistics SocioEconomic Classification (NS-SEC) scale.
• Offspring outcomes: Child’s vocabulary scores were assessed when the cohort member was 14 years of age. Vocabulary scores were measured with a shortened version of the Applied Psychology Unit (APU) Vocabulary Test. The test involved 20 questions where participants were instructed to match a stimulus word to a synonym from five alternatives.

Raw correlations were only presented between parent and offspring vocabulary (Table 2). The parent-offspring correlation was in line with expectations (r = 0.32 to 0.35).

The authors constructed a series of regression models to measure the independent associations of many different independent variables (e.g., parental SES measures, books in the home, reading frequency, etc.) on offspring vocabulary score. However, for this section, we will focus solely on model 1 (which the authors call the “Demographics” model), which includes only the parental SES measures, demographic information (e.g., age, sex, ethnicity, country of origin), parental age, siblings, and language spoken at home. The regression results for this model allows comparing the relative importance of different components of parental SES (see Table 3). The results show that parental education has a strong association with offspring vocabulary, but parental income does not have a statistically significant association with vocabulary. In fact, the effect size for log household income is just 0.01.

The authors mention this finding when describing the results as follows:

Model 1 includes socioeconomic and demographic information and provides an indication of the magnitude of the associations between these variables and the child’s vocabulary scores before any potential mediating factors have been accounted for. Parental education is strongly linked to the child’s vocabulary. Having an undergraduate (bachelors) university degree or a higher (postgraduate) degree (compared to no qualifications) provides roughly three times the advantage associated with having a parent with a higher managerial or professional occupation (compared to a routine occupation) when both are included in the same model. Income and home ownership are not significantly associated with vocabulary, taking the other factors in the model into account.

Australia

Marks (2021). “Is the relationship between socioeconomic status (SES) and student achievement causal? Considering student and parent abilities” [archived]. The author here analyzed the relationship between parental SES and offspring achievement after taking into account offspring and parent cognitive ability in Australia. For my purposes, I am not interested in how the parent or offspring cognitive ability influences the parental SES – achievement relationship. I’m merely interested in which components of parental SES are most strongly linked to offspring achievement.

• Dataset: The Longitudinal study of Australian Children (LSAC). A longitudinal sample of Australian children born between 1999 and 2000. The participants were studied across six waves, starting when children were aged 4 or 5 with another wave every 2 years. Over 3,000 children from this dataset were analyzed.
• Parental SES: Family income was measured as an average of weekly income reported by the parents across all waves. Father’s and mother’s educational attainment was measured by the highest level of schooling completed and post-school qualifications recorded across the six waves of data. Father’s and mother’s occupational status were coded according to the Australian Socioeconomic Index 2006.
• Offspring outcomes: Academic achievement of students were measured based on their test scores in  years 3, 5, 7, and 9 based on assessments conducted by the National Assessment Program–Literacy and Numeracy (NAPLAN). This study focuses on student scores in numeracy and reading in year 9, which children were aged 14 or 15.

The basic correlations between the parental SES measures and student achievement measures resembles that reported in the meta-analytic literature. Though the correlation between the parental SES composite and student achievement was slightly greater than expected:

The author conducted a series of regression analyses for year 9 numeracy and reading achievement. The first model (Model 1) only included the parental SES measures as independent variables. The later models incorporated childhood cognitive ability and prior achievement, but those aren’t relevant to my question here, so we can ignore those models. The results of the first model shows that family income is a particularly weak predictor of year 9 achievement compared to the other parental SES measures (see Table 3):

The results here differ slightly from the U.S. results in that parental occupation seems to predict offspring achievement about as well as parental education does. Regardless, family income is clearly a weak predictor of offspring achievement after one controls for only parental education and parental occupation. The standardized effect size for family income is weak, ranging from β = 0.03 to β = 0.06, whereas parental education has small-to-modest effects, ranging from β = 0.10 to β = 0.17. In fact, the effect of family income on reading achievement is not even statistically significant. These findings are emphasized by the author:

Table 3 presents the estimates from regression analyses of student achievement in numeracy and reading in Year 9 on the SES components, early childhood cognitive ability, and prior achievement. Model 1 shows that the five SES components account for 16% and 17% of the variance in Year 9 numeracy and reading. Of the SES components, family income has the weakest relationship indicated by the standardised coefficients.

It should be noted that an earlier study of the same dataset conducted by Khanam and Nghiem (2016) [archived] found a moderate-to-large effect of log family income on “cognitive outcomes” (β = 0.23 to β = 0.29, depending on the outcome, see Table 3). These results are somewhat in tension with the findings by Marks. I say the findings are only “somewhat” in tension, because the results do not technically contradict the findings by Marks. There are a few reasons for this:

• The authors measured different outcomes from Marks. The authors measured cognitive outcomes based on (1) PPVT and matrix reasoning test scores (which were measured in earlier waves) and (2) mathematical and literacy skills according to teacher report on a Likert scale survey instead of standardized tests. By contrast, Marks measured achievement via standardized test scores at age 14 or 15.
• These authors found that family income did not have a statistically significant association (at the 5% level) with any of the outcomes in the simplest model that controlled only for basic demographics (age, sex, ethnicity), parental education, parental working hours, household size, birth weight, parental age, and language spoken at home. This is compatible with the finding reported above by Marks. However, these authors found that family income surprisingly has a significant association with cognitive outcomes after introducing controls for what the authors call “parental investment” variables (which includes factors such as number of books in the home, index of activities that the family does together, has computer at home, etc.).

It’s not clear why family income would develop a stronger association with student achievement after controlling for parental investment. This is certainly unexpected given that virtually all studies show that the effect of parental income diminishes after introducing additional controls (as I show below). An explanation is certainly required for why the findings for this study seem so unique.

Regardless, in a comment on this study, Marks (2017) [archived] points out that standardized effects for logged variables should not be interpreted in the same way that we interpret standardized effects for non-logged variables. That is, whereas a standardized effect of 0.3 may be large for non-logged variables, this is not so large for logged variables. He notes:

Before discussing the results, I note that the estimates reported by Khanam and Nghiem (2016) seem larger than they are. Standardized effects of between 0.23 and 0.29 are comparatively large in studies of the effects of parental measures (apart from parental cognitive ability) on cognitive outcomes. However, the effects cannot be interpreted in the same way that standardized effects are for nonlogged independent variables. To simplify, assume that the estimates were all 0.30. That means that for a doubling of family income, the predicted achievement score would increase by 0.17 of a standard deviation. A tripling of family income would translate to an increase of 0.27 of a standard deviation. Therefore, large changes in family income are associated with only moderate changes in test scores, even when assuming an estimate of 0.30.

In response, Khanam and Nghiem (2017) [archived] agree that their effects appear larger than they really are and should be translated into a non-log format for easier interpretation:

We agree with Marks that KN’s statement (2016:608), “. . . an increase of log family income by 1 [standard deviation] is associated with an improvement on the PPVT, MR, literacy, and mathematical scores of children by about 0.29, 0.26, 0.23, and 0.24 SD, respectively” should be translated to nonlog format to make the magnitude smaller. KN’s interpretation is technically correct but is cumbersome (1 standard deviation of log income) and makes the magnitude of income parameter larger than it is. We could make the interpretation easier by transforming to a nonlog format, which would lead to a smaller magnitude. In this case, the same result can be translated as a 10 % increase in household income is associated with an increase in PPVT, MR, literacy, and mathematical score by 1 % of a standard deviation.

These results suggest that the association between income and achievement is small, even using their own large estimates in their study.

Scandinavia

Kristensen et al (2009). “Educational attainment of Norwegian men: influence of parental and early individual characteristics”. These authors analyzed the relative influences of parental income, parental education, and youth cognitive ability on educational attainment in young adulthood in a very large sample of Norwegian males. The authors conducted path analysis which reveals the relative independent influences of parental income and parental educational level on cognitive ability.

• Dataset: All males born in Norway in 1967 to 1971 who were alive at 28 years of age (N = 160,914). The national identification numbers of citizens allowed linking children and parents through national registers. Parental data (income education), and offspring outcome (cognitive ability, education) were available through the Central Population Register, the Education Register of Statistics Norway, the Armed Forces Personnel Data Base, and the benefit and income registers of the National Insurance Administration.
• Parental SES: Parental education was defined as the sum of educational years for both parents when the subject was 16 years old. Mother’s and father’s income levels were measured when the subject was 16 years old.
• Offspring outcomes: Due to compulsory military service at the time, these men were required to complete a test of general cognitive ability as a conscript examination, usually when they were 18 years old.

The authors conducted path analyses to explore the relationships between parental education, parental income, offspring cognitive ability, and offspring educational attainment. The analyses also adjusted for various background factors, such as birth order, year of birth, municipality, etc. The results indicated that parental educational level has a much larger impact on offspring cognitive ability than does parental income level:

The path from parental education to cognitive ability is twice the path from parental income to cognitive ability (0.22 vs 0.11), revealing that cognitive ability has a moderate association with parental education but only a weak association with parental income.

Similar findings were reported in a much smaller sample of Norwegian children (N=255) aged 8-12 years by Eilersten et al. (2016) [archived]. The authors analyzed the association between parental SES and cognitive function as measured by the third edition of the Wechsler Intelligence Scale for Children (WISC-III). Parental SES was defined based on parental education and family income. The authors concluded that parental education, but not parental income, was significantly associated with the cognitive test scores of the children:

The analyses showed that SES explained a significant part of the variance of the full-scale WISC-III score and two WISC-III indices (Verbal Comprehension and Freedom from Distractibility). Overall, the strength of the relations was weaker than expected from reports from other non-Nordic countries. Parental education was the only significant individual predictor, suggesting that income was of minor importance as a predictor of cognitive functioning. Further studies should investigate how diverse political and socioeconomic contexts influence the relation between SES and cognitive functioning.

Humlum (2010). “Timing of family income, borrowing constraints, and child achievement” [working paper] [archived]. The author analyzed the effects of the timing of family income on offspring academic achievement. For my purposes, the timing isn’t really relevant. What’s relevant is the estimated impact of family income after controlling for parental education.

• Dataset: The Danish subset of the children sampled in the OECD PISA 2000 survey. This survey sampled nearly 4,000 Danish children born in 1984. Information was collected each year from 1984 to 2005.
• Parental SES: Parental income was measured as annual disposable income (i.e. income available for consumption after taxes and interest payments) at each year in the survey. Parental education was measured as the maximum education level observed from 1984 to 1999.
• Offspring outcomes: Academic achievement was measured via PISA reading test scores when children were approximately 15 years of age on average. The test evaluates the ability to “understand, use and reflect on written texts, in order to achieve one’s goals, to develop one’s knowledge and potential, and to participate effectively in society”.

The author finds that timing of family income does not appear to be very important for child outcomes in this sample. More importantly, the authors find that the effects of family income are small and insignificant after introducing controls (control variables include: single-parent family, parental unemployment, sex, siblings, age, parental age, region, immigrant status, and parental education). The author summarizes the main findings as follows:

Table 6 displays the estimated coefficients and standard errors from a specification that includes stage-specific family income, stage-specific controls, basic background controls, and parental education. The estimated coefficients on family income are generally small and insignificant. Even a 100,000 DKK increase in permanent income (through an increase in income at ages 12–15) only increases the reading score by 2.6 points…Generally, a higher parental education level is associated with higher achievement scores. Specifically, having parents with long-cycle higher education increases the reading score by as much as 60 points. Thus, parental education appears to be a much stronger determinant of adolescent outcomes than family income.

For reference, 2.6 points is rather low given that the standard deviation for reading scores is 95.5 points.

Summary

In summary, I considered 7 main studies in this section that examined the relative effects of parental education and parental income on offspring cognitive outcomes: 2 from the United States (Ganzach 2014, Marks and O’Connell 2023), 2 from the Australia (Sullivan et al. 2021, Marks 2021), and 3 from Scandinavia (Kristensen et al 2009, Eilersten et al. 2016, Humlum 2010). Each study finds statistically significant effects of parental education after controlling for parental income. The effect sizes are typically small to medium. For the effects of parental income after controlling for parental education, 3 studies find no statistically significant effect (Sullivan et al. 2021, Eilersten et al. 2016, Humlum 2010), 3 studies find small effects (i.e. β = 0.10 or lower; Marks and O’Connell 2023, Marks 2021, Kristensen et al 2009) and just 1 study finds medium effects (β = 0.22 to 0.24 from Ganzach 2014).

If one includes Khanam and Nghiem (2016), then that would count as 2 studies finding medium effects of logged income, although I prefer excluding this study because (as stated earlier) family income had a significant effect only after introducing controls for parental investment variables. Moreover, as Marks (2017) argues (with agreement by Khanam and Nghiem 2017), the effect sizes reported for logged family income appear larger than they actually are.

Therefore, these studies (in combination with the samples analyzed by Rindermann and Ceci 2018) suggest that parental education is a larger and more consistent independent predictor of offspring cognitive outcomes than is parental income. In fact, parental income is often not even significantly associated with offspring cognitive outcomes after controlling for parental education.

Another study analyzing the relative effects of parental education vs parental income comes from Lemos et al. (2011). These authors studied a sample of Portuguese students involved in the standardization sample of the Reasoning Tests Battery (RTB). The authors found that there is no relationship between family income and offspring intelligence after controlling for parental education. However, there were serious limitations of this study, as mentioned by Ganzach (2014): Lemos et al. used a binary measure of income (either high or low income) based upon student-reports of their parents’ occupations. Students were categorized as low income if their parents worked as: trades people, personal and household services, agriculture and fishery (smallholders), non-qualified jobs, or unemployed. They were categorized as high income if their parents worked as: managers, business executives, intellectual and scientific professionals, or technical professionals.

Parental SES vs parental cognitive ability

In this section, I review studies that allow us to quantify the independent effects of parental education, parental income, and parental cognitive ability on offspring cognitive outcomes. These studies construct models to predict offspring cognitive outcomes which simultaneously include parental cognitive ability and some measure of parental SES (usually a composite including parental education, occupation, and income) as explanatory variables. I’ll consider studies focusing on the United States, the United Kingdom, and Germany. At the end, I’ll also mention some other studies that I found related to this subject and explain why I did not cover them.

United States (NLSY-C)

Marks and O’Connell (2023). “The importance of parental ability for cognitive ability and student achievement: Implications for social stratification theory and practice” [archived]. I described this study earlier, so I’ll only briefly describe the dataset here.

• Dataset: NLSY79-C. The NLSY79 Child and Young Adult cohort. This survey interviewed the biological children of the female participants of the NLSY79, which was described above.
• Parental SES: Family income, mother’s and father’s educational attainment, and mother’s and father’s occupational status.
• Parental cognitive ability: Parental cognitive ability was measured based on the mother’s AFQT test that she conducted in the initial wave of the NLSY79 (when she would have been between 14 and 22 years of age).
• Offspring cognitive outcomes: the Peabody Picture Vocabulary Test (PPVT), Digit Memory span, PIAT reading comprehension, PAIR reading recognition, and PIAT math.

Earlier, I considered the effect of different parental SES components on offspring cognitive outcomes. Now, I want to consider this study’s findings when incorporating parental cognitive ability when analyzing the association between parental SES and offspring academic achievement.

Recall earlier that when parental SES variables were the only independent variables in a model to predict offspring cognitive outcomes (Model 1), mother’s education had moderate effects (β = 0.18 and β = 0.24) whereas family income had very small effects (β = 0.00 and β = 0.05). When mother’s cognitive ability is also entered as an independent variable (Model 2), the effect of the parental SES variables diminish even further. Compare the effect sizes for the parental SES composite in Model 1 and Model 2 in Table 1 to see the impact of introducing mother’s cognitive ability as an explanatory variable:

As you can see, the effect size for the parental SES composites decreases by about 50 to 60% after mother’s ability is included in the model. Without mother’s ability in the model, the effect size for parental SES is usually modest (around β ~ 0.20) except for the PPVT where the effect size is large (β = 0.33). The effect size for parental SES becomes weak after controlling for mother’s ability (around β ~ 0.10). By contrast, the effect size for mother’s ability is usually large (β > 0.30) except for Digit Memory where it is only moderate (β = 0.19). Consistently, the effect size for mother’s ability is 2 to 3 times the effect size for the parental SES composite. The effect of parental ability would likely be even greater if the dataset included findings on both mother’s and father’s ability.

The author emphasize the same findings:

SES coefficients decline by at least a half with the addition of mother’s ability (model 2). The declines were largest for reading comprehension (63%) followed by the PPVT (57%), reading recognition and math (54%) and digit memory (53%). Controlling for mother’s ability, the standardized SES coefficients are small: 0.14 for the PPVT and around 0.10 for the other four domains.

Table 2 shows the same models except where each SES component is included instead of using the parental SES composite:

As you can see, the effect of mother’s ability remains the same regardless of whether parental SES is included as a composite rather than individual components. In model 1 (without mother’s ability), mother’s education was consistently the biggest predictor of cognitive outcomes. After introducing mother’s ability (model 2), the effect sizes for mother’s education decreased by about 60 to 85%. Interestingly, the effect sizes for father’s education decreased by a smaller amount, just 15 to 35%. This is perhaps unsurprising since mother’s cognitive ability probably has a stronger association with mother’s education than with father’s education. It would be interesting to see the same findings after controlling for father’s cognitive ability in addition to mother’s cognitive ability.

The author concludes as follows:

These analyses suggest that in the context of children’s cognitive development and student achievement in reading and math, the emphasis placed on SES or aspects of SES in research and policy is undeserved. There is little point in developing theoretical explanations for the associations of SES with children’s test scores when they are so small. Similarly, policies aiming to reduce the SES-student performance relationship are likely to fail since the contemporaneous impact of SES is too weak. The small effect of SES, once mother’s ability is considered, is a compelling explanation for the lack of success in substantially reducing socioeconomic inequalities in education over the last few decades.

In a review by the same authors, Marks and O’Connell (2021) cite other research relying on the NLSY-C which also find that parental SES has only weak effects on offspring achievement, after controlling for mother’s AFQT scores:

The effects of SES measures on achievement, net of mother’s ability, are weak. Currie and Thomas (1999, p. 302) reported a standardised effect (β) around 0.2 for SES and between 0.6 and 0.7 for mother’s Armed Forces Qualification Test (AFQT) score, a commonly used measure of ability, on Peabody Picture Vocabulary Test score among children aged 6 and older. Similarly, Carlson and Corcoran (2001) found that mother’s AFQT score had strong effects on their 7- to 10-year-old children’s reading and mathematics scores, with much smaller effects for family income and no effects for mother’s education. Mother’s AFQT score accounts for about half of racial test score gaps in reading and mathematics whereas ‘home inputs’ account for 10–20% (Todd & Wolpin, 2007). Mayer (1997, pp. 90–91) reported a standardised, but not statistically significant, effect of 0.10 for family income on children’s test score, net of parents’ education, mother’s AFQT score and other factors.

Orr (2003) [archived] also analyzed the relationship between parental SES and academic achievement in the same dataset. But this author also included wealth as an explanatory variable, so it would be interesting to see if wealth has a larger effect than the other parental SES measures. The primary goal of the paper was to test how much wealth could explain the racial achievement gap. However, the findings of this paper are relevant for my purposes because the author addressed this question by constructing various regression analyses with academic achievement (particularly PIAT math scores) as the dependent variable and various parental SES measures as independent variables. Wealth was measured as an average of net worth over 5 years (1990 to 1994), where net worth for a given year was the sum of the value of all household assets minus the household debts. Family income was also measured as an average of family income over the same 5-year period. The primary results of the analysis are presented in Table 3:

The results show that, in the model including wealth (Model 3), the only statistically significant independent variables were number of siblings, mother age, mother’s AFQT, black, parental education, parental occupation, and log wealth. However, the effect sizes are unstandardized, which prohibits comparison of effect sizes. Fortunately, we can convert unstandardized coefficients into standardized coefficients by multiplying by the standard deviation of the independent variable and dividing by the standard deviation of the dependent variable. Table 1 lists the standard deviations for PIAT math scores (12.97), number of siblings (1.03), mother’s age (2.46), mother’s AFQT (193.80), parental education (2.03), parental occupation (13.07), log family income (0.89), and log wealth (2.70). Thus, the standardized effects for select independent variables above can be estimated as follows:

• Number of siblings: β = −0.57 * 1.03 / 12.97 = −0.05
• Mother’s age: β = −0.35 * 2.46 / 12.97 = −0.07
• Mother’s AFQT: β = 0.02 * 193.8 / 12.97 = 0.30
• Parental education: β = 0.39 * 2.03 / 12.97 = 0.06
• Parental occupation: β = 0.06 * 13.07 / 12.97 = 0.06
• Family income: β = −0.35 * 0.89 / 12.97 = −0.02
• Net worth: β = 0.34 * 2.70 / 12.97 = 0.07

These findings are in line with the estimates provided by Marks and O’Connell (2023), despite incorporating income measures across 5 years and wealth measures. That is, mother’s AFQT has a large association with offspring achievement (β = 0.30), whereas each of the parental SES components has a weak association with offspring achievement (β < 0.08), including net worth. Of course, the estimates of the standardized effects should be treated with caution (particularly for mother’s AFQT) due to the lack of significant digits available, which could introduce rounding errors. However, the author reported the standardized coefficients for a few select variables in text that agrees with my estimates here. She notes the following when discussing the results shown in Table 3:

Model 3 adds wealth (log of total net worth) to the equation. The results indicate that wealth affects mathematics achievement, even after SES (parental education, occupation, and income) are controlled. Children who come from families with little or no wealth score lower on the PIAT Mathematics Assessment than do those from wealthier families, regardless of the parents’ income, education, and occupation. Compared to other indicators of SES, wealth has the largest standardized effect on a child’s scores (the standardized coefficients for wealth, parental education, and parental occupation are, respectively, 0.077, 0.057, and 0.058).

One interesting finding is that family income has a negative association (though not statistically significant) with math achievement, even before controlling for wealth. This finding is likely just noise. Regardless, these effect sizes are in line with the findings by Marks and O’Connell (2023), i.e. parental SES components are only weak indicators of offspring achievement after accounting for parental ability. Again, it should be emphasized that we have only controlled for the cognitive ability of one parent. Parental SES would likely have an even weaker effect if we controlled for father’s cognitive ability (studies below show that father’s cognitive ability is associated with offspring achievement, even after controlling for mother’s cognitive ability).

For the sake of transparency and completeness, I should note some other studies I found for this dataset that estimate the effect of parental SES on cognitive outcomes after controlling for maternal AFQT scores (Guo 1998, Carlson and Corcoran 2004, and Miller et al. 2021). However, these studies focused specifically on the effects of income or wealth and so do not allow easy comparison of the effect of different parental SES components or the effect of maternal AFQT. These studies typically found statistically significant effects of family income or wealth. However, they had other issues that prevent me from using them here:

• The studies did not control for the father’s characteristics (e.g., father’s education or occupation) when estimating the effect of family income/wealth on cognitive outcomes. This is likely a serious omission because the earlier studies show that father’s characteristics are significantly associated with offspring outcomes even after controlling for family income/wealth.
• The studies did not provide the information necessary (i.e., standard deviations) to determine whether the reported effect sizes were small, medium, or large (Carlson and Corcoran 2004 and Miller et al. 2021 both reported the standard deviation for non-logged income/wealth, but the effect sizes were reported in log format).

In a review of the influence of parental income on offspring outcomes by Mayer (2002) [archived], the author provides a summary of older studies investigating the NLSY-C (which the author calls CNLSY) which estimate the impact of parental income on cognitive outcomes in the same dataset. These older studies are not ideal as they focus on the children when they are very young (aged 3 to 7), which is when environmental influences tend to be stronger. Nevertheless, even at this young age, all of the studies find that very large increases in permanent income were associated with just small increases in offspring cognitive test scores after controlling for mother’s AFQT scores. The results were summarized in the following table:

Focus on the results that control for mother’s AFQT score (in addition, the studies also controlled for factors such as child’s age, gender, mother’s education, number of siblings, etc.). The findings show that large increases in income are only associated with small increases in test scores after including these controls. For example, Blau (1999) found that a $10,000 increase in permanent income was associated with only 1.6 and 2.0 increase in standardized scores on PIAT math and reading (which is only about 0.10 to 0.13 SDs, as the standard deviation for standardized scores is 15 points, see page 72). For reference, $10,000 in 1979 dollars is equivalent to $42,290 in 2023 dollars, and the median household income in 1980 was only $17,710 (Census 1982 [archived]). The results of this section were summarized as follows:

Low parental income has been consistently shown to be associated with lower scores of children’s cognitive ability. However, some of this effect is likely to be due to other factors that give rise to both low incomes among parents and low test scores among their children. Genetic inheritance is one such factor. Studies that control for parental cognitive skills show that the effect of parental income on children’s cognitive test scores is quite small. On average, doubling family income would probably increase children’s cognitive test scores by a couple of points, or somewhere in the neighbourhood of 10 percent of a standard deviation. The effects are likely to be larger for low-income children: the two studies that test for non-linearities in the effect of parental income on PPVT scores both show that the effects are greater for low-income children (Hill and O’Neill 1994, Lefebvre and Merrigan 1998).

Before moving on from the NLSY-C, I want to share an illuminating pair of graphs that I found in Cunha et al. (2006) [archived]. The authors discuss economic models of child development that had garnered empirical support at the time. Most relevant for my purposes here is their discussion on the empirical findings based on the NLSY-C. In particular, they discuss how achievement gaps by parental income are greatly reduced after controlling for a few key controls, as has been indicated above. The following graph shows the average PIAT math percentile rank by parental income quartile:

This shows rather large achievement gaps by parental income. The gap between the top and bottom quartiles is roughly 15 percentile points at age 6 and 24 percentile points at age 12. However, the following graph shows the same gaps after controlling just for mother’s AFQT, mother’s education, and whether the child is in a broken home at each age:

There are still clear achievement gaps by parental income, but they are much smaller. At age 6, the gap between the top and bottom quartiles is maybe 2 to 3 percentile points. At age 12, the gap seems to be about 5 to 6 percentile points, which implies that just a few controls reduces the income achievement gap by about 75%.

United States (PSID)

Yeung and Conley (2008). “Black–White Achievement Gap and Family Wealth” [archived]. The authors of this paper were focused on analyzing how family wealth influences the black-white gap in academic achievement. However, their findings are relevant here because they conduct their analysis by running regression analyses that estimate the effect of parental SES variables (and other variables, such as e.g. race and mother’s ability) on academic achievement.

• Dataset: Panel Study of Income Dynamics (PSID). The PSID is a longitudinal study of a nationally representative sample of 5,000 American families that began in 1968. In 1997, the PSID started the Child Development Supplement (CDS), which collects data on children’s development from PSID families with children aged 0-12 years. The CDS sample contained about 3,500 children from about 2,400 families.
• Parental SES: Family wealth was collected in 1994 and 1989 which represent the total assets minus total debts for the family in the 5 years prior to the data collection. Family income was measured as the logarithm of total pretax income of all family members, averaged over all years from the child’s birth to 1996. Parental education was measured as the highest years of education by either parent. Parental occupational prestige was collected based on the family head.
• Parental cognitive ability: Mother’s cognitive ability was assessed with a passage comprehension test of the W-J Achievement Test-Revised. Thus, the measure of parental cognitive ability was limited to a test of verbal ability and did not include father’s ability.
• Offspring cognitive outcomes: Academic achievement was assessed in 1997 through the W-J Achievement Test – Revised. Preschool-aged children (aged 3 to 5) were assessed using the Applied Problems (AP) and Letter-Word subscales. School-age children (aged 6 to 12) were assessed with the Broad Mathematics and Broad Reading subscales. I’ll focus on the results for the school-age children because they are older.

Before getting to the regression results, it is useful to note the basic correlations for the variables used:

The correlation between the parental income variables and achievement measures is around r = 0.30 to r = 0.35, which is in line with the correlations that have been presented so far. The family wealth variables have slightly smaller associations, at around r = 0.26 (except for the non-logged wealth measure without home equity).

The authors conduct 4 different regression analyses that correspond to each of the following outcomes: reading scores for preschool children (Table 4), math scores for preschool children (Table 5), reading scores for school-aged children (Table 7), and math scores for school-aged children (Table 8). Because I give higher priority to outcomes for older children, we only need to consider Tables 7 and 8. For each outcome, the authors consider many different models with different explanatory variables. They start with just race as an explanatory variable (Model 1), then add non-financial parent and grandparent characteristics (Model 2), then add family income (Model 3), different measures of wealth (Models 4 to 7), and finally add possible mediators of the wealth effects (Models 8 to 9). Since I’m just interested in the total (not direct) effects of the parental SES components, I will ignore the mediator models, and focus just on models 1 through 7.

Here are the results for reading scores of school-aged children:

As you can see, there is no statistically significant association between either family income or family wealth with reading scores. The effect sizes for wealth seem particularly small: A child from a family in the top wealth quartile only scores 0.87 points higher on the reading test than a child in the bottom wealth quartile, and this difference is not significant. This is rather small, given that the standard deviation from the reading score is over 15 points (I don’t know the exact standard deviation for the total sample, because the authors only presented the descriptive statistics separate by race in Table 1).

One way to note the small impact of family income/wealth is to note the R^2 of the different models. In Model 2 without any family income/wealth measures, 27% of the variance is explained by the independent variables. After adding family income and different measures of family wealth in models 3 to 7, this only increases the R^2 by 1 percentage point. Thus, introducing family income and wealth provides very little incremental predictive power once one already knows the child’s sex/race, the parent’s education, parent’s occupation, parent’s reading scores, etc.

Parental education, parental occupation, and the mother’s reading score were all significant predictors of reading score as well, but it’s hard to assess their standardized effects without data on the standard deviations of the total sample (again, the standard deviations are presented in Table 3, but they are broken out by race, but the standard deviations differ significantly by race).

Here are the results for math scores of school-aged children:

Ignoring wealth, the results here are mostly similar to the results for the reading scores. Parental education, occupation, and mother’s reading score are all significantly associated with the child’s math scores (however, parental occupation is no long significant in the mediator model). Family income has no statistically significant association with math scores.

The wealth effects, however, are statistically significant depending on the wealth measure used. Net worth has a statistically significant effect, though the authors note that this is “modest” (page 319). Interestingly, the gap in math scores between children from the top vs bottom quartile of wealth is not significant at the 5% level (though it is significant at the 10% level). The effect size of wealth quartile doesn’t seem particularly large though. Moving from the bottom quartile to the top quartile of wealth is only associated with 3.44 points higher math score. Assuming the standard deviation for the math score is around 16 points or so (based on Table 1), this corresponds to about a 0.2 standard deviation increase in math scores after moving across wealth extremes.

The authors reported the standardized coefficients for some key variables of model 4 in the text (page 319):

• Mother’s verbal score: β = 0.26
• Net worth: β = 0.22
• Parents’ education: β = 0.17
• Family head’s occupation: β = 0.11

The only surprise here is the modest sized wealth effects. It’s not clear why wealth has a significant effect on math scores but not reading scores. One possibility is that net worth is just picking up unmeasured cognitive ability of the parents. One piece of support for this hypothesis is the fact that there was no test of parental math ability, which might be a strong confounder particularly for the child’s math scores (the authors mention this on page 319 as a possible explanation for why the math results differ from the reading results).

United Kingdom

Crawford et al. (2011). “Explaining the socio-economic gradient in child outcomes: the inter-generational transmission of cognitive skills” [archived]. The authors examine the role that parental cognitive skills play in explaining the cognitive skills gap between children from different socioeconomic backgrounds.

• Dataset: The British Cohort Study. This survey sampled all people born in Great Britain during a particular week in April of 1970. The participants were surveyed from seven waves: at birth, at age 5, 10, 16, 26, 29, and 34. This study focused on a randomly selected half of the cohort members (called “CMs” in the study) from the final wave who lived with children. The sample was further restricted to CMs with 3 to 16-year-old children, leaving them with 3,416 children and 2,059 families.
• Parental SES: Parental socioeconomic position (SEP) was measured as an index composed of permanent family income, housing tenure, parental occupational class, and financial difficulty. Parental education was measured based on the age the mother and father left full-time education.
• Parental cognitive ability: Parental cognitive ability was measured via tests completed by the parents when they were age 5 and age 10. At age 5, the cognitive ability measure includes tests on vocabulary, copying designs, human figure drawing, and profile recognition. At age 10, the cognitive ability measure includes tests from the British Ability Scales (BAS), and tests of reading, vocabulary, writing, spelling, math, copying, sentence formation, and sequence recognition.
• Offspring cognitive outcomes: The CM’s child’s cognitive ability was measured in 2004 based on the British Ability Scales. Children aged 3 to 5 were tested on vocabulary and number concepts. Children aged 6 and older were tested on word reading, spelling, and number skills.

The first thing to note is that there seems to be a relatively small association between parental SEP and offspring cognitive ability in this sample. Children in the top SEP quintile had test scores that were only 8.7 percentiles higher than children in the bottom SEP quintile (Table 4). After controlling for parental cognitive ability, this association was reduced even further. This is shown in the following figure:

Across all SEP quintiles, smarter parents tend to have smarter children. However, among children with parents of middle or high cognitive ability, there seems to be no association between parental SEP and offspring cognitive ability. This point was made by the authors:

Figure 1 allows us to disentangle the correlations documented in Tables 2 and 3, by showing children’s cognitive test scores in subgroups defined by both parental ability and SEP. The gradients across SEP quintiles suggest that children whose parents are of low ability tend to do significantly better in cognitive tests if they are in a high SEP group (an average percentile rank of 51 in cognitive test scores for those in the top SEP quintile, compared to 37 in the bottom SEP quintile); however, there is no discernible SEP gradient for those whose parents are of middle and high ability. This could be because we only observe the cognitive ability of one parent. Low ability CMs who are in a high SEP group may be relatively likely to have high ability partners (which is unobservable in our data), and that may explain the better cognitive ability of their children.

Regression analyses give a more precise quantification of the effect of parental cognitive ability on the association between parental SEP and offspring cognitive ability. These analyses show that parental cognitive ability alone can explain about half of this association. As stated earlier, the gap in offspring cognitive ability between children in the top vs bottom SEP quintiles is 8.7 percentiles. After simply controlling for parental cognitive ability, this gap reduces to 4.8 percentiles (see model 2 in the bottom panel of Table 4). After further controlling for whether the CM reported that they were good at math at age 16, the gap further reduces to just 3.8 percentiles (model 3).

After further controlling for parental education, whether the father is self-employed, and some basic demographic information (maternal age at birth, number of siblings, whether the child has a twin) (see model 5 in table 4), the effect of parental SEP is no longer significant at the 5% level. The effect of mother’s education is still significant, but the CM’s cognitive ability measured at age 10 has a larger effect: the gap in test scores between children with the most educated mothers vs the least educated mothers is 7.2 percentiles, whereas the gap in test scores between children with parents who scored in the top quintile vs the bottom quintile at age 10 is 10.8 percentiles.

The difference between 7.2 and 10.8 percentiles may not seem like much, but this actually understates the effect of parental cognitive ability relative to parental education. There are a few reasons for this:

1. The effect of parental cognitive ability was split across 2 variables, one for age 5 parental cognitive ability and one for age 10 cognitive ability. An index of parental cognitive ability based on both measures would have likely resulted in a greater association between parental cognitive ability and offspring cognitive ability.
2. The difference between the top and bottom quintiles (for cognitive ability) is likely less extreme than the difference between the highest and lowest level of education (since, presumably, fewer than 20% of individuals have either the highest or lowest level of education).
3. The cognitive ability measure for the parent is likely to be noisy as it was measured when parents were just between 5 and 10 years of age. A later measure of parental cognitive ability would have likely had a greater association with offspring outcomes. For example, an analysis of the same dataset has shown that parental cognitive skills at adulthood predict offspring cognitive outcomes, even after controlling for their parental cognitive skills measured at childhood (de Coulon 2011).
4. Cognitive ability was only measured for one of the parents, which greatly undersells the overall effect of parental cognitive ability.

Anyway, despite these handicaps, parental cognitive ability still turns out to be a better predictor of offspring cognitive ability than any of the parental SES measures. The authors conclude by noting that parental cognitive ability is the most important predictor of offspring cognitive skills:

In line with other studies, we have found that parental cognitive ability is a very important predictor of children’s cognitive skills (the most important, along with educational attitudes and aspirations). Because parents’ cognitive ability and socio-economic position are in turn also very strongly related, studies which examine the relationship between parental SEP and children’s ability, but do not control for parental ability – or in some other way attempt to account for these factors – will suffer from a serious omitted variables problem. Indeed, our estimates suggest that parental cognitive ability accounts for 16 percent of the gap in cognitive test scores between children from rich and poor families after controlling for a wide range of mechanisms through which ability may be transmitted across generations (for example, differences in the home learning environment that parents provide for their children), and 50 percent of the gap if we do not include such factors.

Brown et al. (2011). “Following in Your Parents’ Footsteps? Empirical Analysis of Matched Parent–Offspring Test Scores” [full pdf of earlier version] [archived]. This article analyzes the relationship between parent’s cognitive skills and offspring cognitive outcomes.

• Dataset: British National Child Development Study. This survey followed a cohort of participants born in Great Britain during a particular week in March of 1958. The participants were surveyed in later waves at age 7, 11, 16, 23, 33, 42, and 46. Their children were also analyzed when the participants were 33.
• Parental SES: Parental SES measures included log of total household labor income and the highest educational attainment of the parent.
• Parental cognitive ability: The parent’s cognitive ability was measured when they were 7 years old. The parents were tested on problem-based arithmetic, and word recognition and comprehension. The authors note that this test was designed to identify low attainment and “less successful at distinguishing between individuals at higher levels of attainment.” As a result, the authors infer that “the lack of variation at the top end of the distribution in the parents’ tests” may under-estimate the true correlation.
• Offspring cognitive outcomes: The children’s cognitive ability was measured when they were aged 5 or older and their parents were aged 33. The children were assessed using the Peabody Individual Achievement Tests (PIATs) math, reading recognition, and comprehension. The mean age of children taking the tests was 9.

The authors conducted regression analyses for the child’s test scores. One of the specifications included the following as independent variables (specification 2): parent’s age 7 test scores, the parental SES variables mentioned earlier, health problems for the child, siblings, number of books, single-parent household, and home ownership status. These analyses showed that very few of these variables had a statistically significant effect. The exceptions included number of books owned by the child and parent’s age 7 test scores. Thus, “other variables included, in particular those measuring the parents’ income and educational attainment, appear unrelated to their children’s age 7 test scores.” Interestingly, the authors noted that, if parent’s test scores are omitted from the analysis, parents’ education does become significantly related to children’s test scores.

The analysis also shows that the aforementioned control variables have barely any impact on the relationship between parent’s test scores and offspring test scores:

We now focus on the intergenerational relationship between parents’ and children’s test scores in all three specifications described above. The coefficients on the parents’ test scores in each equation are reported in Table 5.

The raw intergenerational test score correlation, controlling only for the gender of the child, is 0.165 for reading test scores, as shown in the first row of results (Specification 1). This means that for a one standard deviation increase in parents’ age 7 reading scores, there is an associated one-sixth of a standard deviation increase in their children’s reading scores, relative to other children of the same age. This relationship is economically and statistically significant.

Specification 2 adds a range of control variables for characteristics of the child, as well as parental income and the highest qualification of the NCDS respondents. The results show, however, that this has essentially no impact on the intergenerational coefficient in reading test scores. Thus, any effect of parents’ ability in reading on the reading skills of their children is not being transmitted via these control variables. Whilst parents’ test scores are, as expected, correlated with their educational achievement (with correlation coefficients of 0.29 and 0.28 for reading and maths scores, respectively) and to a lesser extent with family income (correlation coefficients of 0.10 and 0.06 for reading and maths scores, respectively), the impact of parents’ test scores on their children’s test scores appears to be independent of such relationships. Thus, the source of the success of the children of high-scoring parents is not the fact that their parents’ ability led to higher educational achievements or family income.

Sullivan et al. (2021). “The intergenerational transmission of language skill” [archived]. I described this study earlier, so I’ll only briefly describe the dataset here.

• Dataset: the Millennium Cohort Study (MCS).
• Parental SES: Parental SES measure included parent’s education, parental social class, home ownership, and family income.
• Parental cognitive skills: The mother’s (and mother’s partner) language skills were measured using the same test given to the children.
• Offspring cognitive outcomes: Child’s vocabulary scores were assessed when the cohort member was 14 years of age.

As discussed earlier, parental income had no association with child’s vocabulary in Model 1 (which controlled for other parental SES measures, demographic information, parental age, siblings, and language). However, parental education had a significant association with vocabulary. In particular, the gap in vocabulary between children with the most educated parents (Higher Degree) and the least educated parents (No academic qualification) was 0.75 standard deviations (Model 1, Table 3).

Unfortunately, the next models (Models 2 and 3) introduce mediating variables into the model. Model 2 adds “family cultural capital” variables (e.g., number of books in the home) and Model 3 adds “child cultural capital” variables (e.g., how often the child reads for pleasure). The problem is that these variables might mediate the effect of our independent variables of interest (i.e. they might mediate the effect of parental SES or parental cognitive ability), so controlling for these variables may interfere with our ability to compare the relative effects of these independent variables). However, these findings are still useful because parental education still has a significant association with offspring cognitive skills even after introducing these mediator variables. For example, the gap in vocabulary between children with the most vs least educated parents reduces from 0.75 points (0.29 SD) in Model 1 to 0.47 points (0.18 SD) in Model 3.

Model 4 adds parental vocabulary skills to the model (Model 4), which substantially reduces the remaining effect of parental education. Here’s a snippet of Table 3 showing how the effect of parental education on offspring vocabulary changes as additional variables are controlled for.

Note: I didn’t include the coefficients for the lower levels of parental education, because they were on the previous page, which would make the screenshot rather large. The coefficients for those levels of education were typically lower than all of the effect sizes visible here, and they were always lower than the effect sizes for First Degree and Higher Degree.

As you can see, all of the parental education variables (except for the highest 2) are no longer statistically significant after controlling for parental vocabulary (Model 4). The effect sizes are also significantly reduced after controlling for parental vocabulary. Parental occupational status (or “social class”) also no longer has a significant association with offspring test scores in this model. The authors describe the effects as follows:

In model 4, we introduce the mother’s and partner’s vocabulary scores. Both, especially the mother’s, are strongly independently associated with the child’s score. Including parental vocabulary reduces the apparent influence of parental education, reducing the coefficients for a degree and higher degree by about half, and reducing lower levels of education to statistical insignificance. Social class also becomes statistically non-significant in this model. The coefficients for the home literary climate are also substantially reduced, but the association with the child’s own cultural activities is unaffected.

For example, the gap in vocabulary between children with the most vs least educated parents reduces from 0.47 SDs in Model 3 to 0.16 SDs in Model 4. For reference, a 1 SD increase in parent’s and parent’s partner’s vocabulary is associated with an increase in child’s language skills by about 0.19 and 0.14 SDs, respectively, in Model 4. I wouldn’t place too much emphasis on comparing effect sizes though, since these are the results after controlling for plausible mediators.

Germany

Schulz et al. (2017). “Pathways of Intergenerational Transmission of Advantages during Adolescence: Social Background, Cognitive Ability, and Educational Attainment” [archived]. The authors analyzed the relationships between socioeconomic resources, parental cognitive ability, offspring cognitive ability, and academic tracking in Germany.

• Dataset: The TwinLife dataset is a longitudinal study of twins and their families in Germany. The first wave comprised four birth cohorts, each containing approximately 500 pairs of monozygotic and 500 pairs of same-sex dizygotic twins, their parents, and one full sibling (if present). The authors focused on assessments during the first wave in 2015-2016. Specifically, they focused on the 2 cohorts that were about 11 and 17 years old at the time. This resulted in around 4,000 twins and about 800 siblings who were at least 10 years of age.
• Parental SES: Parental SES was measured based on the family’s educational level, parental occupational status, and monthly net household income adjusted by household size. Family’s educational level was measured as the highest educational attainment of the parent in the household. The authors used three educational levels: ISCED levels 1 and 2 (primary and lower secondary education), levels 3 and 4 (upper secondary and post-secondary non-tertiary education), and levels 5 and 6 (first and second stage of tertiary education).
• Cognitive outcomes: Twin, sibling, and parental cognitive ability was measured using the Culture Fair Intelligence Test (CFT). The CFT assesses non-verbal intelligence, comprising four subtests of figural reasoning, figural classification, matrices, and reasoning.

Table A2 displays the basic correlations between the variables of interest. Offspring CFT scores had expected correlations with parental CFT scores (r = 0.33), but it had slightly lower than expected correlations with household income (r = 0.14) and slightly greater than expected correlations with parental occupational status (r = 0.27).

Using both the twin and sibling data, the authors estimated the association between parental cognitive ability and offspring cognitive ability (both measured using CFT scores), after iteratively introducing additional parental SES variables into the model. The results showed that parental cognitive ability maintained significant association with offspring cognitive ability even after controlling for all parental SES variables:

The results also show statistically significant effects of parental cognitive ability, parental education (ISCED levels), parental occupation (mean parental ISEI), and parental income (when comparing the bottom income quintile to the top two quintiles). To meaningfully compare the effect sizes, the coefficients should be converted to standardized coefficients. Based on the standard deviations reported in Table 1, the standardized effects can be calculated as follows:

• Parental cognitive ability: β = 0.83 * 0.303 / 0.9 = 0.28
• Parental occupational level (ISEI): β = 0.003 * 26 / 0.9 = 0.09
• Parental education level 1/2 – 5/6 (ISCED): d = 0.165 / 0.9 = 0.18 SD
• Parental income top – bottom quintile: d =  0.118 / 0.9 = 0.13 SD

These results are mostly in line with the findings reported so far. For the continuous measures, we see almost large effects of parental cognitive ability (β ~ 0.3) and small effects of parental occupational level (β ~ 0.1). Giving from the bottom quintile of income to the top quintile is only associated with a 0.13 SD increase in offspring test scores, which is rather minor. The effects of parental education are slightly larger. The bottom two education levels (ISCED = 1 & 2) represent the bottom 6% of the population, whereas the top two education levels (ISCED = 5 & 6) represent the top 57% of the population. Thus, moving from the bottom 6% of households to the top half (in terms of parental education) is associated with a 0.18 SD increase in offspring test scores.

As an aside, the authors also investigated the relative effects of parental socioeconomic resources and parental CFT on whether the child attends the academic track. Interestingly, here it seems that parental SES plays a larger role in explaining child outcomes (see Table 4).

Anger and Heineck (2010). “Do Smart Parents Raise Smart Children? The Intergenerational Transmission of Cognitive Abilities” [archived]. The authors examined parent-offspring correlations for cognitive ability in Germany.

• Dataset: German Socio-Economic Panel Study (SOEP) is a longitudinal study that provides information on a representative sample of households since 1984. The wave in 2006 provides information on cognitive abilities of the respondents. The sample had to be restricted to participants who completed an IQ test in 2006 and who had a parent in the study who also completed an IQ test in the same year. This reduced the overall sample to 504 adult children who completed a test and who could be matched to a parent who also completed a test.
• Parental SES: Parental SES was measured based on the educational attainment of both parents.
• Cognitive ability: Cognitive ability of parents and offspring were measured using 2 very short tests developed specifically for the SOEP: a symbol correspondence test (SCT) and a word fluency test (WFT). Both tests correspond to different modules of the Wechsler Adult Intelligence Scale (WAIS). The SCT measured non-verbal ability whereas the WFT test measured verbal ability.

Unfortunately, the parental SES measure only includes measures of parental education. However, this shouldn’t distort findings too much since previous studies show that parental education is typically the SES component that has the largest association with offspring cognitive ability.

Anyway, in regression models that control for parent’s cognitive ability, parental education, sex, own education, and some other controls (e.g., siblings, height, region, etc.), the authors found that parent’s cognitive test scores, but not parental education, are significantly associated with offspring test scores. These results are described as follows:

Table 3 provides estimates of these extended specifications including family background and childhood environment (Table 3, columns 1 and 4), as well as the controls related to labor market experience, marital status, region, and health (Table 3, columns 2 and 5). Interestingly, the estimates show barely any significant effects of the family background, childhood environment, and other control variables on children’s cognitive abilities. In contrast, the regressions show a very robust finding for parents’ cognitive abilities which is in line with the results by Brown et al. (2009) who find a very robust transmission effect for reading and maths test scores in their study on the U.K., independently of additional controls.

The effect sizes for parent’s cognitive abilities are large. In particular, the results show that a 1-point increase in parent’s test scores are associated with about a 0.45 to 0.50 point increase in children’s test scores after introducing all control variables. Since parent’s test scores and offspring test scores have roughly equal standard deviations (about 9.5 to 11.5 points), the standardized effect sizes are around this range as well.

Interestingly, even a participant’s own education is not significantly associated with their test scores after controlling for their parent’s test scores:

As could be expected, the regression results indicate a positive relationship between education and both types of ability test scores (Table 2, columns 1 and 3), although the explained variation is very small. Particularly individuals with a college or university degree attain significantly higher speed test scores compared to their counterparts with lower secondary schooling. This positive association however vanishes once parents’ cognitive skills are included.

Other studies

Here are some other studies that I found which I did not cover for various reasons (e.g., they covered countries I don’t compare about, didn’t provide enough information to interpret effect sizes as small vs large, didn’t model the effects as desired, etc.). They typically reported similar findings as the above findings (i.e. weak effects of parental SES).

• Johnson and Nagoshi (1985). “Parental ability, education and occupation as influences on offspring cognition in Hawaii and Korea”. The authors compared the relative influence of parental cognitive ability vs parental socioeconomic status (education and occupation) on offspring cognitive ability in a sample of families in the Hawaii Family Study of Cognition. They conclude that “parent ability and parent status each independently influence offspring performance on measures of cognition”, but “the influence of status generally is far weaker than is the influence of parental cognitive ability”. Similar findings were reported in a later sample by Nagoshi and Johnson (2005).
• Campos-Vazquez (2018). “Intergenerational Persistence of Skills and Socioeconomic Status”. The study described the association between parental socioeconomic status and the cognitive and non-cognitive skills of their teenage offspring in a sample of Mexican families. The exact effect sizes were difficult to determine, but it appears that, controlling for parental SES, a 1-standard deviation increase in parental cognitive ability was associated with about a 0.26 SD increase in offspring cognitive ability (Figure 1) whereas a comparable increase in parental wealth or parental years of education was only associated with a 0.1 SD or less increase in offspring cognitive ability (Figures 2-3).
• Dui (2020). “Research on the influence of family resources on children’s cognitive ability.” This article analyzed the impact of family resources on children’s cognitive abilities based on the data from the China Family Panel Studies (CFPS). They found that economic resources (e.g., family income, education expenses) had a significant association with offspring cognitive ability prior to controlling for non-economic resources. However, after accounting for non-economic resources, the study finds that “family economic resources have no significant impact on children’s cognitive abilities” whereas “family non-economic resources have significant effects on children’s cognitive abilities, especially parents’ cognitive abilities, academic expectations and family environment”.
• Marks (2021). “Is the relationship between socioeconomic status (SES) and student achievement causal? Considering student and parent abilities”. I mentioned this study earlier when showing that family income had the weakest association with offspring achievement, compared to other SES components like education or occupation). However, I did not include the analysis that considers parental cognitive ability, because the sample used does not actually observe parental cognitive ability. Instead, the authors infer parental cognitive abilities based on empirical established correlations with the observed variables in the study.
• Xu et al. (2023). “Parental socioeconomic status and children’s cognitive ability in China”. The authors examined the influence of parental socioeconomic status and parental cognitive abilities on their offspring’s cognitive ability. In analyses that test the independent influences of both parental income and parental education, the authors found that “parents’ education levels rather than income levels are positively associated with their children’s cognitive abilities”. The authors also found significant effects of parental cognitive ability.

Main findings in detail

Net of parent’s cognitive ability, parental SES is a weak predictor of offspring cognitive outcomes

I summarized the effect sizes from the main studies in the previous section into the following table. Each column corresponds to the effect size for a different predictor: parental cognitive ability/skills, parental education, wealth, and income. Each row corresponds to a model from a different study. If an effect size was statistically insignificant, I did not include the effect size (and instead left n.s.). The first column describes the dataset, model, and dependent variables (one outcome is listed per bullet/line in a row). For each dataset, I selected one of the models that were described in my analysis above.

The effect of parental cognitive ability vs parental SES on offspring cognitive outcomes

Some notes about the table:

• * The first row of values corresponds to the reading score from the PSID sample (Yeung and Conley 2008). Because standardized effect sizes were not reported for reading scores, I simply reported whether or not the effect sizes were significant or not.
• ** 2 effect sizes are given for 1 outcome in the British Cohort Study. The effect sizes describe the effect of parent’s cognitive ability at ages 5 and 10, respectively.
• *** The MCS and NCDS samples likely underestimate the effects of the independent variables due to overadjustment bias. Both control for variables that are likely downstream of parental cognitive ability, parental education, or even offspring cognitive outcomes: e.g., number of books owned by the child, whether the child reads for pleasure, plays a musical instrument, etc.
• For some variables, multiple effect sizes were reported in the original study. In particular, the effect sizes for parental education or parental cognitive ability/skills were sometimes reported separately by the mother and father. In those cases, I listed the larger of the effects to avoid complicating the table.

The main findings are as follows:

• Parental income: usually insignificant, consistently small effects. There were 13 effect sizes reported for parental income. Only 3 (23%) of the effect sizes were statistically significant. The 2 significant standardized regression coefficients from the NLSY-C were very small (β = 0.01 and β = 0.03). The significant effect size from the TwinLife dataset was also small (students from the top quartile of income only outscored students in the bottom quartile by merely 0.12 standard deviations).
• Parental wealth: inconsistent effects. The findings for wealth are inconsistent. There were 3 effect sizes reported. 1 was insignificant, 1 was significant and small (β = 0.07), and 1 was significant and modest (β = 0.22). This certainly does not provide sufficient evidence for the commonly espoused idea that wealth has large effects on offspring cognitive ability. Moreover, it should be noted that, because wealth is logged in the PSID study, the standardized effect size may give the impression that the effect is larger than it actually is (see the points by Marks (2017) above).
• Parental education: usually significant, usually small effects. There were 15 effect sizes reported for parental education. 11 (73%) of the effect sizes were statistically significant. 9 of the effect sizes were standardized (either standardized regression coefficients or standardized mean difference). Of the 7 significant standardized regression coefficients, 6 were small (β < 0.1) and 1 was modest (β = 0.17). For the 2 standardized mean differences reported, both were small/medium (d ~ 0.16 between students from most and least educated parents).
• Parental cognitive ability/skills: consistently significant, usually large/medium effects. There were 16 effect sizes reported for parental cognitive ability/skills. All of the effect sizes were statistically significant. Of the 13 standardized regression coefficients, 6 were large (β > 0.30). 6 were modest (β = 0.15 to β = 0.28), and 1 was small (β = 0.065).

Each study with standardized effect sizes reported the same rank order pattern: parental cognitive ability had a larger effect size than parental education, which had a larger effect size than parental income. Parental wealth typically had a similar or slightly larger effect size than parental education, but smaller effect size than parental cognitive ability.

One might be concerned that parental cognitive ability/skills may mediate the relationship between parental SES and offspring cognitive outcomes. That is, perhaps parental SES enhances parental cognitive ability, which in turn enhances offspring cognitive outcomes. If this were true, then estimating the impact of parental SES after controlling for parental cognitive ability would commit overadjustment bias and thus underestimate the true impact of parental SES. I have two statements in response:

• Even if parental cognitive ability mediated the relationship between parental SES and offspring cognitive outcomes, it is still useful to know that the parental SES – offspring ability relationship is very weak after controlling for parental cognitive ability. This would at least show that we can dismiss proposed mechanisms linking parental SES and offspring cognitive outcomes that are not mediated through parental cognitive ability, which is an important finding.
• Some of the studies measured parental cognitive ability when the parents were rather young, well before their SES would plausibly have a large effect on their cognitive development. For example, in Marks and O’Connell (2023), mother’s AFQT was measured between 14 and 22 years of age, though one could argue that some of the variation of AFQT scores at this time was caused by differences in college attendance. However, Crawford et al. (2011) and Brown et al. (2011) both measured parent’s cognitive abilities when they were between the ages of 5 and 10, well before they can acquire an income/occupation and well before large variation in attained levels of education. Even in these studies, before variation in parental SES can cause significant variation in parental cognitive ability, parental SES (particularly parental income) still has weak effects on offspring cognitive outcomes.

Parental SES does not explain why smarter parents have smarter children

The fact that parental cognitive ability/skills has a large association with offspring cognitive outcomes after controlling for parental SES suggests that parental SES does not explain why smarter parents have smarter children. For example, Brown et al. (2011) report that the association between parent’s and offspring test scores are independent of parental SES (parent’s education and income):

Whilst parents’ test scores are, as expected, correlated with their educational achievement (with correlation coefficients of 0.29 and 0.28 for reading and maths scores, respectively) and to a lesser extent with family income (correlation coefficients of 0.10 and 0.06 for reading and maths scores, respectively), the impact of parents’ test scores on their children’s test scores appears to be independent of such relationships. Thus, the source of the success of the children of high-scoring parents is not the fact that their parents’ ability led to higher educational achievements or family income.

They go on to state the following:

Thus, we can rule out the cause of the positive intergenerational relationship in reading test scores being due to parents with higher test scores as children achieving higher education levels and higher income, and so being able to purchase more learning resources for their children, as well as ruling out parenting style such as the frequency with which parents read to their children, since such parental behaviour has also been shown to be highly correlated with income and education (see Ermisch, 2008).

Many other studies had the same findings. 4 studies reported the association between parent’s and offspring cognitive outcomes before and after controlling for parental SES. I’ll summarize the results in the following table. The 2nd column shows the effect size for parental cognitive ability/skills on offspring cognitive outcomes, before controlling for parent’s SES. The 3rd column shows the effect size after controlling for parent’s SES (thus, the same effect sizes reported in the “Cognitive ability/skills” column of the previous table). The 4th column shows the % reduction in effect size after controlling for parent’s SES. I mention the parental SES variables in the last column.

The effect of parental cognitive ability on offspring cognitive outcomes before vs after SES controls

• * I am justified in comparing correlation coefficients and standardized regression coefficients because the two values are identical in a simple linear regression model with no other independent variables (as explained here).

The results indicate that the association between parental and offspring cognitive outcomes only reduces by at most about 20% to 30% after controlling for parental SES. Thus, the vast majority of the parent-offspring cognitive ability association is not confounded by nor mediated through parental SES. Parental SES plays, at best, only a small role in explaining the association between parental and offspring cognitive ability.

Observable home/parenting factors do not explain why smarter parents have smarter children

If parental SES does not explain why smarter parents have smarter children, then perhaps various home or parenting factors explain the relationship. For example, one might think that the number of learning materials in the home, the number of books in the home, whether the child attends a private school, etc. explains why smarter parents have smarter children. However, the studies above (and additional studies not yet considered, which I’ll present below) show that, while such factors may explain why richer parents have smarter children, those same factors do not explain why smarter parents have smarter children.

For example, in the analysis of the British Cohort Study, Crawford et al. (2011) found that the effect of parental SEP (socioeconomic position) was largely eliminated after controlling for observable home/parenting factors such as whether the child goes to private school, whether the child uses a computer, whether the child reads for enjoyment, etc. This suggests that the effect of parental SES is either confounded by or mediated through these factors (or something correlated with those factors). By contrast, the effect of parental cognitive ability was largely unaffected by these controls. This suggests that the effect of parental cognitive ability on offspring cognitive ability is neither confounded by nor mediated through the same home/parenting factors. The authors mention this when discussing these findings:

Columns 4-6 of the upper panel show how the residual SEP gap is reduced by controlling for the kinds of factors observed in the other papers in this Special Issue: parental education, demographics and other family background characteristics, and attitudes, educational aspirations, behaviours and the home-learning environment. Once we account for these, the residual SEP gap in cognitive skills is not statistically significant. This does not necessarily diminish the importance of SEP for cognitive development, as many of the factors we control for are plausible transmission mechanisms between SEP and cognitive skills…It is striking that, in contrast to SEP, the apparent importance of parental cognitive ability is relatively insensitive to the number of factors we control for (as shown by the coefficients on parental ability at the bottom of Table 4). We cannot rule out the possibility that there are unobserved covariates which would change this story if included in our model. However, given the very rich set of information we do observe, the results are at least suggestive of the fact that parental ability plays some kind of role in determining children’s cognitive skills.

The authors go on to speculate that the strong relationship between parent’s and offspring’s cognitive ability that persists despite robust controls suggests that the relationship may be transmitted genetically:

In addition, we could conjecture that higher parental ability increases children’s cognitive skills by making the time spent on children’s cognitive development more productive (e.g. reading with one’s children may be more productive if the parent is a good reader). However, the importance of parental cognitive ability does not seem to be largely driven by a complementarity with observed aspects of parenting, in as much as most interaction terms between parental cognitive ability and environmental factors are not statistically significant when added to the model (not shown). Thus, although our findings are based on a simple linear regression model in which endogeneity cannot be ruled out, we interpret the large contribution of parental cognitive ability in Figure 2 – which remains even after controlling for a very wide range of plausible transmission mechanisms between parental and child cognitive ability – as being suggestive of the possibility of some kind of genetic link between the cognitive skills of parents and their children, although we acknowledge that the interactions between genetics and the environment are necessarily complex.

Many other studies had the same findings. 3 studies reported the association between parent’s and offspring cognitive outcomes before and after controlling for observable home/parenting factors. I’ll summarize the results in the following table. The 2nd column shows the effect size for parental cognitive ability/skills on offspring cognitive outcomes, after controlling for parent’s SES (thus, the same effect sizes reported in the “After SES controls” column of the previous table). The 3rd column shows the effect size after also introducing controls for the observable home/parenting variables. The 4th column shows the % reduction in effect size after controlling for these home/parenting factors. The last column lists the home/parenting variables used in the study.

The effect of parental cognitive ability on offspring cognitive outcomes before vs after home/parenting controls

Thus, of the parent-offspring cognitive ability association that persists after controlling for parental SES, the observed parenting/home factors seem to account for about 10 to 25% of this association. Thus, the observed home/parenting factors (at best) play only a small role in explaining why smarter parents have smarter children. I say “at best” because we cannot assume this 10 to 25% reduction is due to a causal effect of these home/parenting factors (due to possible confounding). On the other hand, the 10 to 25% figure may underestimate the influence of home/parenting factors due to possible unobserved home/parenting factors (but there is no evidence supporting this currently).

Other studies have also reported similar dynamics. Other studies have found that, whereas the effect of parental SES is often eliminated after controlling for observed home/parenting factors (suggesting mediation or confounding), the effect of parental cognitive ability persists after controlling for these same factors.

For example, Mandara et al. (2009) notes that “several studies find that the effects of various SES factors on child and adolescent achievement are almost completely mediated by family functioning and parenting” (page 868). This same pattern does not hold for parental cognitive ability.

For example, in a study examining the mechanisms of the effect of poverty on child outcomes, Guo and Harris (2000) [archived] find that “Both AFQT and mother’s education have a significant indirect effect on intellectual development through cognitive stimulation, but only AFQT exerts a significant direct effect on intellectual development” (page 441). They find that “the influence of family poverty on children’s intellectual development is mediated completely by the intervening mechanisms measured by our latent factors”. By contrast, when analyzing the effect of parental cognitive ability (i.e. mother’s AFQT score), these effects are largely unaffected by their mediating variables:

It is also informative to compare AFQT with poverty. In the baseline reported in Table 2, both AFQT and poverty exert a significant effect on intellectual development. Once the mediating variables are included in the analysis, the effects of poverty disappear completely, whereas the direct effect of AFQT on intellectual development remains almost as large as in the baseline model (Table 3). These results indicate a substantial component in mother’s cognitive ability, which influences the child’s cognitive development and which passes on from mother to child without being mediated by mother’s learned behavior or environmental influences. Without explicit genetic analysis on genetic data, however, we cannot draw any further conclusions about the effect of AFQT.

This same pattern was found in other datasets. For example, consider Cottrell et al. (2015) [archived] which examined factors explaining the black-white gap in cognitive test scores in the NICHD Study of Early Child Care and Youth Development. This dataset included a longitudinal sample of 1,364 families studied from age 4 to 15 years. Cognitive ability was measured based on the general cognitive ability / knowledge based on the math, vocabulary, and reading facets of the Woodcock-Johnson Psycho-Educational Battery-Revised. To estimate which factors explain the racial cognitive ability gap, the authors constructed various models to explain cognitive ability. Each model stipulates that race influences “maternal advantage” (i.e. SES and maternal cognitive ability), which influences “parenting factors” (e.g., learning materials, maternal sensitivity), which in turn influences offspring cognitive ability. Some of the models also allow for maternal cognitive ability to have a direct effect on offspring cognitive ability (i.e. not mediated through parenting factors). The authors describe these models as follows:

As such, we now additionally offer two alternative, partial mediation model specifications that we suspect might possibly, but not necessarily, play a role in explaining the race gap in cognitive test scores. These two alternative models (i.e., partial mediation models) are presented in Figure 1, Models B and C. Figure 1, Model B, specifies a direct effect from maternal verbal ability/knowledge to g, and we label this direct effect a verbal socialization effect. The notion of verbal socialization implies a direct impact of a mothers’ language knowledge and usage on a child’s knowledge of reading, vocabulary, and mathematics (Dollaghan et al., 1999; Schady, 2011). That is, because a mother’s degree of verbal capability represents the complexity of the medium through which the child learns cognitive knowledge and skills at home, children of mothers with higher verbal ability should directly acquire more advanced cognitive skills and knowledge. Although this relationship is virtually self-evident in the case of vocabulary (i.e., children learn the vocabulary words their mothers use), we assert it is also true for children’s development of reading comprehension and mathematics skills, which mothers often explain to children verbally.

Each of the three hypothesized models are illustrated as follows:

Notice that Model B allows maternal cognitive ability to directly influence offspring cognitive ability (not mediated through parenting factors). Also Model C allows race to directly influence parenting factors (not mediated through maternal advantage), though Model C isn’t really relevant here. When testing which model best fit the data, the authors found that Model C was the most strongly supported, suggesting a direct link between maternal cognitive ability and offspring cognitive ability that is not mediated through parenting factors:

Figures 2a and 2b present our 3-Step Models. The 3-Step Model examines the process by which race leads to cognitive test score gaps. In particular, we show that race gives rise to a set of group differences in maternal advantage factors: income, maternal education and maternal verbal ability/knowledge (Step 1), which in turn lead to parenting factors of maternal sensitivity, acceptance, physical environment, learning materials, birth weight, and birth order (Step 2), which in turn promote cognitive ability/knowledge in children (Step 3). We also found that maternal verbal ability/knowledge directly impacts a child’s cognitive ability/knowledge, a phenomenon we refer to as verbal socialization. Finally, we examined differences in parenting by race, a phenomenon we refer to as culturally specific parenting. The 3-Step Model with Verbal Socialization and Culturally Specific Parenting was most strongly supported in our data.

Moreover, the authors also conducted simpler models that allowed each explanatory variable to have a direct effect on the child’s cognitive ability. That is, each explanatory variable was allowed to have an effect on the outcome without demanding a particular pattern of relations among the explanatory variables (unlike the 3-Step models considered above, whereby e.g. income can influence offspring ability only via parenting factors). The simpler model shows that, in a model including race, parent’s SES, mother’s verbal ability, and parenting factors, mother’s ability but not parental SES has a statistically significant association with child cognitive ability. The coefficients of each explanatory are reported in the column corresponding to Model 3 in Table B1:

As you can see, maternal verbal ability has a strong association with offspring cognitive ability in this model (β = 0.33), far stronger than any other variable. By contrast, family income and maternal education do not have a statistically significant association with offspring cognitive ability, and their effect sizes are small.

All of the studies in this section have converged on the same conclusion: when it comes to explaining offspring cognitive outcomes, observable home/parenting factors can explain either the entirety or almost the entirety of the effect of parental SES, but such factors cannot explain the effect of parental cognitive ability. Smarter parents have smarter children, and this is not just because they are richer or because of observable/measurable aspects of their parenting practices or home environment. Even after controlling for parental SES and observable home/parenting factors, there is a large association between parental cognitive ability and offspring cognitive outcomes.

Genetics do not (entirely) explain why smarter parents have smarter children?

Finally, I found two studies (one of which was considered above) which suggest that the link between parent’s and offspring’s cognitive outcomes may not be (merely) due to genetic transmission. These studies suggest that exogenous changes in parental cognitive ability (which are presumably independently of genetic effects) are transmitted to their offspring. Both of the studies rely on an instrumental variables (IV) design to infer this conclusion. I am admittedly unfamiliar with IV designs, nor do I know the most prominent sources of bias for IV designs. Thus, I’m not sure how much credence should be given to causal estimates that are inferred from this kind of methodology. Nevertheless, the results were interesting, so I decided to place them here:

Brown et al. (2011) use an IV design that relies on variation in parent’s reading ability that is due to the local education policies. This variation is estimated to be transmitted to their offspring (page 51):

The final specification uses instrumental variables to assess the intergenerational relationship, as described above. Specifically, since a linear equation is estimated in the second stage, Two-Stage Least Squares is used. Again, the estimated coefficient on the parents’ age 7 reading test score variable (in this case, instrumented) is left unchanged. This specification isolates any exogenous variation in parents’ reading ability due to the local education policies of where they live, and as such could not be passed on genetically to children. These results show, however, that having removed any genetic effect, the intergenerational relationship in reading test scores is as strong as ever, suggesting that the source of the relationship is not a genetic effect.

The authors use this to infer the absence of a genetic transmission of reading skills from parent to offspring (page 56):

With respect to reading, nothing we try reduces the size of the intergenerational relationship, which remains essentially unchanged after adding controls for parental education and income (amongst others), and after instrumenting parents’ test scores to isolate exogenous variation in such scores owing to local education policy in the area in which they happen to live…the IV results suggest that the cause of the relationship is not a genetic effect, since even exogenous changes in parents’ reading scores seem to be passed on to their children, to the same extent as before. Perhaps, the cause of the intergenerational relationship is that parents with better reading skills are simply better able to help their children learn to read within the home for a given set of resources, and so irrespective of income, education, learning resources and time spent on reading, etc.

However, the same IV estimation strategy finds that exogenous changes in math (as opposed to reading) are not transmitted to their offspring, which they use to infer the presence of a genetic transmission from parent to offspring (page 56):

A different cause of the intergenerational relationship seems to be at work with respect to maths scores, however, where the estimated coefficient in the IV specification is essentially zero. This suggests that exogenously increasing the maths skills of the parents (in this case via starting full-time school or the systematic learning of ‘sums’ earlier) will have no effect on the maths skills of their children. This in turn suggests that genetic effects are very important for the intergenerational transfer of maths skills. As before when discussing the relative sizes of the maths and reading effects, a possible explanation of such findings is that maths skills cannot be passed on from one generation to the next via teaching in the home, in the same way that reading skills can be. Moreover, parents’ maths skills acquired as children may be less easily transferred to their own children within the home, compared with their childhood reading skills, since their maths skills are much less likely to have been used, maintained and developed through their adult lives, compared with reading skills.

It’s unclear why math skills would be transmitted through genes but not reading skills. The more parsimonious explanation seems to be that the IV estimates are unreliable.

Anyway, similar findings were reported by Hanushek et al. (2021) [archived]. These authors study the Intergenerational transmission of math and language skills in the Netherlands. They purport to show that variation in parent’s cognitive skills due to their peer’s achievement is transmitted to their offspring’s cognitive outcomes. Like the previous study, they use this finding to infer that the association between parent and offspring cognitive outcomes is not (entirely) transmitted through genetic mechanisms (page 2):

Our data also provide a unique opportunity to investigate how the formal education environment influences parent skills and results in spillovers to the next generation. Through instrumental variables (IV) estimation, we isolate parent skills developed outside the family by using information about subject specific achievement of the parents’ classroom peers. Because differences in the subject-specific skills of parents’ classmates are – as we show – unrelated to dynastic predispositions for either subject within families, they provide exogenous variation in parents’ skill differences. Estimates derived from just the parent skill variation coming from these peer-based measures of the quality of the formal education environment are very similar to those obtained from using the total variation in parent skills in our basic between-subject model – thus, reinforcing a causal interpretation of our baseline estimates. These IV estimates eliminate concerns that observed skill patterns reflect just predetermined traits such as those arising from genetic configurations (e.g., a ‘math’ gene). They also demonstrate that policies that improve school quality not only enhance the skills of the current generation but also have lasting impact on family outcomes through the transmission of higher skills to children.

These studies suggest that the association between parent and offspring cognitive ability is not just a result of genetic transmission, because variation in parent’s cognitive ability due to childhood environmental factors is associated with their offspring’s cognitive outcomes. This is an interesting finding, but this finding should probably be given the lowest confidence of anything else in the post. It is based only on 2 studies, and one of the studies finds inconsistent results for math vs reading. Moreover, as stated earlier, I’m also not familiar with the reliability of the IV design in general.