Educational Inequality*

Different fields of study are associated with considerably different payoffs, even after accounting for sorting and variance in the quality of institutions or peer groups.

“These differences are in turn an important source of economic inequality and immobility: different fields of study are associated with considerably different payoffs (Kim, Tamborini, and Sakamoto 2015), even after accounting for sorting and variance in the quality of institutions or peer groups (Dale andKrueger 2014, Kirkeboen, Leuven, andMogstad 2016).”

• cites Kim, Tamborini, and Sakamoto 2015 sourceSupported
• cites Dale andKrueger 2014Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Kirkeboen, Leuven, andMogstad 2016Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In the United States, children whose parents are in the top 1 percent of the income distribution are 77 times more likely to attend an Ivy League college than those whose parents are in the bottom income quintile.

“For example, Chetty et al. (2017) find that in the United States, children whose parents are in the top 1 percent of the income distribution are 77 times more likely to attend an Ivy League college than those whose parents are in the bottom income quintile.”

• cites Chetty et al. (2017) sourcePartly supported

  Section III (Access: Parental Income Distributions) reports the 77-fold difference for attendance at Ivy-Plus colleges. That group includes the Ivy League plus Stanford, MIT, Chicago, and Duke, so the passage does not establish the same figure for Ivy League colleges alone. (LLM, conf=0.90)

  Experimental — accuracy not yet measured

Lee and Seshadri find that parental background has a particularly large impact on early investments in young children.

“Similar to Herrington (2015), the authors find that parental background has a particularly large impact on early investments in young children.”

• cites Lee and Seshadri (2019) sourceSupported

Doepke and Zilibotti (2017) and Doepke, Sorrenti, and Zilibotti (2019) models imply that the choice between parenting styles depends on inequality; when income inequality is high, parents are more likely to adopt a more intensive parenting style.

“The models of Doepke and Zilibotti (2017) and Doepke, Sorrenti, and Zilibotti (2019) imply that the choice between these styles depends on inequality.Specifically, when income inequality is high (including a large wage gap between those with greater and lesser educational attainment), parents are more concerned about their children's success, and hence are more likely to adopt a more intensive”

• cites Doepke and Zilibotti (2017)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Doepke, Sorrenti, and Zilibotti (2019) sourceSupported

The model of Lee and Seshadri (2019) is consistent with empirically observed intergenerational elasticities in terms of lifetime earnings and college attainment.

“The model is consistent with empirically observed intergenerational elasticities in terms of lifetime earnings and college attainment.”

• cites Lee and Seshadri (2019) sourceSupported

Time use studies show that parents today spend many more hours caring for their children compared to the 1970s, particularly when this concerns time spent on education-oriented activities, such as helping children with homework.

“Meanwhile, time use studies show that parents today spend many more hours caring for their children compared to the 1970s, particularly when this concerns time spent on education-oriented activities, such as helping children with homework (Doepke and Zilibotti 2019).”

• cites Doepke and Zilibotti 2019 sourceSupported

Policy interventions at early stages, when poorer parents face considerable constraints, are predicted to increase social mobility.

“Policy interventions at this early stage, when poorer parents face considerable constraints, are predicted to increase social mobility.”

• cites Lee and Seshadri (2019) sourceSupported

These studies point to the importance of the timing of investments in skills and public education funding.

“In addition, they all point to the importance of the timing of investments in skills and public education funding, which we will further discuss in Sections 3.5, 3.6, and 3.8 below.”

• cites Herrington (2015) sourceNot checked — no full text of the source
• cites Lee and Seshadri (2019) sourceSupported
• cites Daruich (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Most carefully designed studies show that the provision of early childcare is beneficial, especially for children from disadvantaged backgrounds.

“though most carefully designed studies show that the provision of early childcare is beneficial, especially for children from disadvantaged backgrounds (Havnes and Mogstad 2015, Cornelissen et al. 2018, Felfe and Lalive 2018, Gormley and Gayer 2005).”

• cites Havnes and Mogstad 2015 sourceNot checked — no full text of the source
• cites Cornelissen et al. 2018 sourcePartly supported

  The Results (§5.2) and Conclusions (§7) find that early child care improves school readiness particularly for minority children, with evidence of larger gains for children from disadvantaged backgrounds. But the Introduction (§1) describes evidence on universal child care as “mixed,” not as showing that most carefully designed studies find benefits. Page numbers are unavailable in our copy. (LLM, conf=0.88)

  Experimental — accuracy not yet measured
• cites Felfe and Lalive 2018 sourceNot checked — no full text of the source

Bursztyn and Jensen (2015) show that students in low-performing peer groups try to avoid social stigma by reducing their educational efforts when those efforts are observable by their peers.

“For example, Bursztyn and Jensen (2015) show that students in low-performing peer groups try to avoid social stigma by reducing their educational efforts when those efforts are observable by their peers.”

• cites Bursztyn and Jensen (2015) sourceSupported

A few programs, for example $5-a-day childcare in Quebec and state-funded pre-K in Tennessee, have been found to have negative effects on children's skill acquisition.

“A few programs, for example $5-a-day childcare in Quebec and state-funded pre-K in Tennessee, have instead been found to have negative effects on children's skill acquisition (Baker, Gruber, andMilligan 2008, Durkin et al. 2022).”

• cites Baker, Gruber, andMilligan 2008Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Durkin et al. 2022 sourceSupported

These studies agree that economic inequality and social mobility are closely linked through the determination of investments in the skill acquisition process.

“These studies agree on the basic insight that economic inequality and social mobility are closely linked through the determination of investments in the skill acquisition process, along the lines of our stylized model.”

• cites Herrington (2015) sourceNot checked — no full text of the source
• cites Lee and Seshadri (2019) sourceSupported
• cites Daruich (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Parents have a crucial impact on the acquisition of both cognitive and noncognitive skills, in part through transmission of their own skills and in part through their engagement and interaction with the child.

“Carneiro and Heckman (2003), Heckman and Masterov (2007), and Cunha et al. (2006) show that parents have a crucial impact on the acquisition of both cognitive and noncognitive skills, in part through transmission of their own skills and in part through their engagement and interaction with the child.”

• cites Carneiro and Heckman (2003) sourcePartly supported

  The Early Childhood Investments section says parental inputs are important correlates of cognitive and noncognitive skills. Family Income and Enrollment in College describes parents shaping children’s expectations and assisting their studies, while Sources of Skill Differences discusses parental environment and genes. But Early Childhood Investments also says the exact causal mechanisms are not well understood, so the claim overstates how firmly this paper establishes the two specified routes of influence. No page numbers are available in our copy. (LLM, conf=0.84)

  Experimental — accuracy not yet measured
• cites Heckman and Masterov (2007)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Cunha et al. (2006)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Huebener, Kuger, and Marcus (2017) find that a German reform extending the school week by two hours improved students' performance in mathematics, science, and reading by slightly more than 0.05 of a standard deviation.

“For example, Huebener, Kuger, and Marcus (2017) find that a German reform extending the school week by two hours improved students' performance in mathematics, science, and reading by slightly more than 0.05 of a standard deviation.”

• cites Huebener, Kuger, and Marcus (2017) sourceSupported

A direct effect of grandparents on their grandchildren is possible through means that do not require contact, such as financial transfers.

“However, there are exceptions (Zeng and Xie 2014), and a direct effect of grandparents on their grandchildren is possible through means that do not require contact, such as financial transfers (Hällsten and Pfeffer 2017).”

• cites Zeng and Xie 2014 sourceSupported
• cites Hällsten and Pfeffer 2017 sourcePartly supported

  The Discussion reports a direct association between grandparental wealth and grandchildren’s educational achievement beyond parent-mediated transmission. The Theoretical Background mentions direct transfers, but our copy does not establish financial transfers as the mechanism for that association or address whether it requires contact. (LLM, conf=0.84)

  Experimental — accuracy not yet measured

Policies that support earlier parental investments in children's skills are more effective than later interventions such as tuition subsidies.

“For these reasons, and in line with the work of Herrington (2015), Lee and Seshadri (2019), and Daruich (2020) discussed above, policies that support earlier parental investments in children's skills turn out to be more effective than later interventions such as tuition subsidies.”

• cites Herrington (2015) sourceNot checked — no full text of the source
• cites Lee and Seshadri (2019) sourcePartly supported

  The Government Policies section finds that early childhood education subsidies can have the largest long-run effect on mobility, though later subsidies can have a more visible short-run effect. Its policy comparison concerns subsidies at different stages of childhood investment; it does not establish a comparison with tuition subsidies as a later intervention. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites Daruich (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Engzell, Frey, and Verhagen (2021) find that in the Netherlands, eight weeks of online rather than in-person learning led to 0.08 of a standard deviation lower test scores for students aged eight to eleven.

“Engzell, Frey, and Verhagen (2021) find that in the Netherlands, eight weeks of online rather than in-person learning led to 0.08 of a standard deviation lower test scores for students aged eight to eleven.”

• cites Engzell, Frey, and Verhagen (2021) sourceSupported

Parolin and Lee (2021) show that school closures in the United States in the fall of 2020 were more common for students from ethnic minorities.

“Parolin and Lee (2021) show that school closures in the United States in the fall of 2020 were more common for students from ethnic minorities.”

• cites Parolin and Lee (2021) sourceSupported

In three schools in China, children with access to online learning through their school scored 0.22 of a standard deviation higher on tests after a seven-week school closure.

“Clark et al. (2021) consider evidence from three schools in China and show that children who have access to online learning through their school do 0.22 of a standard deviation better on tests that follow the end of a seven-week period of school closures.”

• cites Clark et al. (2021) sourceSupported

Aucejo and Romano (2016) and Gershenson, Jacknowitz, and Brannegan (2017) show that individual absences have significantly worse effects on the outcomes of low-income students.

“and Aucejo and Romano (2016) and Gershenson, Jacknowitz, and Brannegan (2017) show that individual absences have significantly worse effects on the outcomes of low-income students.”

• cites Aucejo and Romano (2016) sourceSupported
• cites Gershenson, Jacknowitz, and Brannegan (2017) sourceNot checked — no full text of the source

In Clark et al. (2021), effective online learning is especially beneficial for low achievers.

“While effects by family background are not reported, the authors find that effective online learning is especially beneficial for low achievers.”

• cites Clark et al. (2021) sourceSupported

In Jang and Yum (2020), the effects on intergenerational mobility are larger for older children, who have less time to compensate for learning losses through greater time investments.

“In contrast to the findings of Fuchs-Schündeln et al. (2021), these effects turn out to be larger for older children, who have less time to compensate for learning losses through greater time investments.”

• cites Jang and Yum (2020) sourceNot checked — no full text of the source
• cites Fuchs-Schündeln et al. (2021) sourceSupported

In Fuchs-Schündeln et al. (2021), the effects are largest for younger children.

“The effects are largest for younger children, an implication that follows from two features of the skill accumulation technology emphasized in Section 3, namely selfproductivity (investments today increase human capital tomorrow) and dynamic complementarity (investments today increase the marginal productivity of further investments tomorrow).”

• cites Fuchs-Schündeln et al. (2021) sourcePartly supported

  The Results section (“Young and Old Children”) says younger children are more adversely affected when the length of school closures is held constant, and links this to self-productivity and dynamic complementarity. The claim omits that condition: accounting for longer secondary-school closures, the paper says the youngest secondary-school children are most severely affected. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

• AssumptionThe authors state this as an assumption: Educational achievements depend on school inputs, parental effort, parenting style, and peer effects.

Results from Engzell, Frey, and Verhagen (2021) for an eight-week school closure imply that the PISA gap would further increase by around 0.05 of a standard deviation.

“Results from Engzell, Frey, and Verhagen (2021) for an eight-week school closure imply that this gap would further increase by around 0.05 of a standard deviation.”

• cites Engzell, Frey, and Verhagen (2021) sourcePartly supported

  The Discussion reports an average loss of 0.08 SD after the Dutch school closure and says losses among children from less-educated households were up to 60% larger; the implied additional loss is about 0.05 SD. The study measured Dutch primary-school test scores, not a PISA gap, so applying that estimate to the PISA gap is an extrapolation rather than a finding of the cited paper. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

In Fuchs-Schündeln et al. (2021), earnings and welfare losses will be largest for children who started public secondary schools at the onset of the crisis.

“Extending their earlier life cycle model to include the choice of parents between public and private school options, the authors predict that the earnings-and welfare losses will be largest for children who started public secondary schools at the onset of the crisis.”

• cites Fuchs-Schündeln et al. (2021) sourceSupported

In Fuchs-Schündeln et al. (2021), these changes diminish the average lifetime earnings of the affected children by about one percent.

“These changes diminish the average lifetime earnings of the affected children by about one percent.”

• cites Fuchs-Schündeln et al. (2021) sourceSupported

In Fuchs-Schündeln et al. (2021), the welfare loss is non-monotonic in parental education, being strongest for children with high school educated parents rather than for those whose parents did not complete high school.

“This implies that the welfare loss is non-monotonic in parental education, being strongest for children with high school educated parents (who have sizeable college completion rates) rather than for those whose parents did not complete high school (whose attendance rates were low even before the pandemic).”

• cites Fuchs-Schündeln et al. (2021) sourceCould not verify

  The Introduction and Results passages report welfare losses by age, school type, and parental income, but not the claimed ranking by parental education. The Calibration > Preferences passage discusses parental education and college completion without comparing welfare losses for children of high-school-educated parents and parents who did not complete high school. Searches for that comparison and for a non-monotonic pattern found no passage establishing it in our copy. (LLM, conf=0.72)

  Experimental — accuracy not yet measured

A regular income boost improves children's brain development in their first year of life.

“This is supported by recent evidence fromTroller-Renfree et al. (2022), who find that a regular income boost improves children's brain development in their first year of life.”

• cites Troller-Renfree et al. (2022) sourcePartly supported

  The Abstract reports that monthly cash transfers to low-income families may affect infant brain activity at age one, and the Results find higher power in some EEG frequency bands in the higher-cash group. But the Discussion cautions that the evidence does not establish a general improvement in brain development: the observed patterns are associated with later skills, not proof of better developmental outcomes, and not all findings survive multiple-comparison correction. (LLM, conf=0.89)

  Experimental — accuracy not yet measured

During school closures, low-achieving students in Germany disproportionately replace learning time with less productive activities, such as playing video games.

“Similarly, Grewenig et al. (2021) and Werner and Woessmann (2021) find that during school closures, low-achieving students in Germany disproportionately replace learning time with less productive activities, such as playing video games.”

• cites Grewenig et al. (2021) sourceSupported
• cites Werner and Woessmann (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Evidence from the United States and the United Kingdom suggests that inputs from both parents and children rise with schooling inputs.

“Evidence from the United States and the United Kingdom suggests that inputs from both parents and children rise with schooling inputs (Bansak andStarr 2021, Del Bono et al. 2021)”

• cites Bansak and Starr 2021 sourceSupported
• cites Del Bono et al. 2021Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The gap in test scores between the top and bottom quarters of socio-economic status is pronounced in each of the 35 considered countries.

“First, the gap in test scores between the top and bottom quarters of socio-economic status is pronounced in each of the 35 considered countries.”

Beyond test scores, socio-economic differences also extend to educational attainment.

“Beyond test scores, socio-economic differences also extend to educational attainment.”

These socio-economic gaps are large compared to the overall differences in achievement between countries.

“Second, these socio-economic gaps are large compared to the overall differences in achievement between countries.”

The average test score of children of less educated parents is between 0.4 and 0.6 standard deviations lower than that of children with highly educated parents, in both mathematics and reading, across Australia, the United States, England and Germany.

“The results are similar across the four countries and across the school subjects: the average test score of children of less educated parents is between 0.4 and 0.6 standard deviations lower than that of children with highly educated parents, in both mathematics and reading.”

Educational inequality is surprisingly persistent across multiple generations.

“The second finding is that educational inequality is surprisingly persistent across multiple generations.”

• cites Clark 2014 sourceNot checked — no full text of the source
• cites Lindahl et al. 2015 sourceNot checked — no full text of the source

The probability of attending university at age 20 is between 18 (Australia) and 28 (United States) percentage points higher for children of highly educated parents.

“The probability of attending university at age 20 is between 18 (Australia) and 28 (United States) percentage points higher for children of highly educated parents, as defined above.”

Achievement gaps within countries are wide compared to the observed variation in average achievement across countries.

“In addition, achievement gaps within countries are wide compared to the observed variation in average achievement across countries.”

These gaps do not arise solely because children from well-off families perform better in school.

“Moreover, these gaps do not arise solely because children from well-off families perform better in school (as documented in the previous section).”

In all countries considered, there are large achievement gaps between students from families of higher versus lower socioeconomic status.

“We show that in all countries considered, there are large achievement gaps between students from families of higher versus lower socioeconomic status.”

Even in the best-performing countries such as Finland or Canada, the achievement of students from disadvantaged backgrounds is below the OECD average of 500 points.

“Even in the best-performing countries such as Finland or Canada, the achievement of students from disadvantaged backgrounds is below the OECD average of 500 points.”

Using longitudinal data for a smaller set of countries, there are similar socioeconomic gaps in terms of educational attainment.

“Using longitudinal data for a smaller set of countries, we document similar socioeconomic gaps in terms of educational attainment.”

Socio-economic differences are pronounced even conditional on intermediate measures of achievement, such as test scores during high school.

“Socio-economic differences are pronounced even conditional on intermediate measures of achievement, such as test scores during high school.”

Differences in test scores explain about half of the gap in university attendance in the United States, Germany, and Australia.

“Differences in test scores explain about half of the gap in university attendance in the United States, Germany, and Australia.”

The evidence regarding educational attainment over time is mixed.

“The evidence regarding educational attainment is also mixed.”

The gaps in university attendance remain large even conditional on test scores.

“That said, the gaps remain large even conditional on test scores.”

Overall, the relationship between income inequality and mobility in student performance is weak.

“Overall, the relationship is weak.”

Overall, evidence for a systematic decrease in relative educational mobility in response to recent increases in income inequality is mixed.

“Overall, evidence for a systematic decrease in relative educational mobility in response to recent increases in income inequality is mixed.”

Attainment gaps in higher education are large even conditional on observed achievement gaps in secondary school.

“To summarize, attainment gaps in higher education are large even conditional on observed achievement gaps in secondary school.”

Socio-economic gaps in attendance rates are greater when restricting analysis to selective universities.

“Indeed, socio-economic gaps in attendance rates are greater when we restrict our analysis to selective universities (as defined in Table 1), which tend to attract better students.”

In the other countries as well, children of highly educated parents are much more likely to study at a selective institution at age 20.

“Panel (c) of Table 3 provides further details on this result, where we see that in the other countries as well, children of highly educated parents are much more likely to study at a selective institution at age 20.”

There is no clear relationship between income inequality and mobility in student performance in high-income countries.

“We do not observe any clear relationship between income inequality and mobility in student performance in high-income countries”

The right panel in Figure 2 shows a clear positive relationship between income inequality and immobility in educational attainment, measured as the intergenerational correlation in years of schooling, both within developing and developed countries.

“The right panel in Figure 2 plots a measure of immobility in educational attainment, namely the intergenerational correlation in years of schooling against income inequality.”

• Also stated in: § 2.4 Economic Inequality and Intergenerational Mobility · boosted

  “We observe a clear positive relationship, both within devel-”

In Germany, students from more advantaged backgrounds are still 11 percentage points more likely to attend university than their peers with comparable test scores at age 14-15, compared to an overall attendance rate of 46 percent.

“For example, in Germany, students from more advantaged backgrounds are still 11 percentage points more likely to attend university than their peers with comparable test scores at age 14-15, compared to an overall attendance rate of 46 percent.”

There is only a weak positive relationship between income inequality and mobility in student performance for developing economies.

“and only a weak positive relationship for developing economies.”

The evidence on whether social mobility declined over the same period as rising economic inequality is mixed.

“However, the evidence to this regard is mixed.”

In the German sample, the coefficients on parent education decrease slightly but still remain large when accounting for additional ability measures and test scores.

“In the German sample, for example, the coefficients on parent education decrease slightly but still remain large when accounting for these additional controls.”

In the model with a fixed number of children who can attain high skill, if the solution for parental investment I1(S,X) is interior for both low- and high-skill parents, a marginal increase in returns to education X raises the educational investment I1(H,X) of high-skill parents.

“In the model with a fixed number of children who can attain high skill, if the solution for parental investment I 1 (S, X) is interior for both low-and high-skill parents, a marginal increase in returns to education X will: • Raise the educational investment I 1 (H, X) of high-skill parents.”

• AssumptionThe authors state this as an assumption: In the bottleneck variant, the number of children who are able to attain high skill is fixed, say because of a set number of slots at university.
• AssumptionThe authors state this as an assumption: Higher parental effort I1 increases the chance that a child will become high-skill, but if all parents increase their parenting effort, this raises the bar for success.
• AssumptionThe authors state this as an assumption: The probability that a child will achieve high skill is given by ψI1, where ψ is taken as given by parents and in equilibrium equals φ/P(I1(L,X)+I1(H,X)).

In the model with a fixed number of children who can attain high skill, if the solution for parental investment I1(S,X) is interior for both low- and high-skill parents, a marginal increase in returns to education X increases the probability that a child of a high-skill parent will attain high skill and lowers the probability that a child of a low-skill parent will attain high skill.

“• Increase the probability that a child of a high-skill parent will attain high skill, and lower the probability that a child of a low-skill parent will attain high skill.”

• AssumptionThe authors state this as an assumption: In the bottleneck variant, the number of children who are able to attain high skill is fixed, say because of a set number of slots at university.
• AssumptionThe authors state this as an assumption: Higher parental effort I1 increases the chance that a child will become high-skill, but if all parents increase their parenting effort, this raises the bar for success.
• AssumptionThe authors state this as an assumption: The probability that a child will achieve high skill is given by ψI1, where ψ is taken as given by parents and in equilibrium equals φ/P(I1(L,X)+I1(H,X)).

The absolute change in the investment of low-skill parents is ambiguous.

“The absolute change in the investment of low-skill parents is ambiguous, because even though ψ has to decrease, the product ψX may either rise or fall.”

• AssumptionThe authors state this as an assumption: The probability that a child will achieve high skill is given by ψI1, where ψ is taken as given by parents and in equilibrium equals φ/P(I1(L,X)+I1(H,X)).

In the regression of years of schooling on parent and grandparent schooling, the coefficient on grandparent schooling βgp tends to be positive and, often, sizable.

“the coefficient on grandparent schooling β gp tends to be positive and, often, sizable.”

In the model with a fixed number of children who can attain high skill, if the solution for parental investment I1(S,X) is interior for both low- and high-skill parents, a marginal increase in returns to education X increases the difference I1(H,X) - I1(L,X) between the educational investment of high-skill parents and low-skill parents.

“• Increase the difference I 1 (H, X) -I 1 (L, X) between the (higher) educational investment of high-skill parents and the (lower) investment of low-skill parents.”

• AssumptionThe authors state this as an assumption: In the bottleneck variant, the number of children who are able to attain high skill is fixed, say because of a set number of slots at university.
• AssumptionThe authors state this as an assumption: Higher parental effort I1 increases the chance that a child will become high-skill, but if all parents increase their parenting effort, this raises the bar for success.
• AssumptionThe authors state this as an assumption: The probability that a child will achieve high skill is given by ψI1, where ψ is taken as given by parents and in equilibrium equals φ/P(I1(L,X)+I1(H,X)).

In the United States, students with highly educated parents are 14.5 percentage points more likely to complete college than students with less educated parents.

“By far the largest impact of family background is found in the United States, where students with highly educated parents are 14.5 percentage points more likely to complete college than students with less educated parents.”

The gap between children in the top and bottom quintile of family background in PISA test scores is roughly one standard deviation.

“The gap between children in the top and bottom quintile of family background is roughly one standard deviation.”

In more unequal countries, the intergenerational correlation between parents and children in educational attainment is higher (the Educational Great Gatsby Curve).

“To show that educational inequality contributes to this relationship, we provide evidence for an “Educational Great Gatsby Curve,” meaning that in more unequal countries the intergenerational correlation between parents and children in educational attainment is higher.”

Poorer students put in less effort conditional on attending.

“Moreover, given that poorer students put in less effort conditional on attending, they also experience lower returns to attending college, which lowers the likelihood of attending even more.”

Students with fewer resources will spend more time on working during college.

“Here the marginal benefit of putting effort on the right-hand side does not depend on assets a 2 , but the marginal cost of effort on the left-hand side is decreasing in assets, so that students with more resources will put in higher effort i 2 , and conversely students with fewer resources will spend more time on working during college (n 2 is decreasing in a 2 ).”

n2 is decreasing in a2.

“Here the marginal benefit of putting effort on the right-hand side does not depend on assets a 2 , but the marginal cost of effort on the left-hand side is decreasing in assets, so that students with more resources will put in higher effort i 2 , and conversely students with fewer resources will spend more time on working during college (n 2 is decreasing in a 2 ).”

The right-hand side of the college attendance condition is increasing in assets a2.

“Here the right-hand side is increasing in assets a 2 (because effort i 2 increases in assets) and the left-hand side is decreasing in assets (because of diminishing marginal utility), implying that students with more assets a 2 are more likely to attend (put differently, the threshold for skill s 2 above which a student attends college is decreasing in assets a 2 ).”

Effort i2 is increasing in wealth.

“Moreover, a 3 is increasing in initial wealth a 2 , implying that effort i 2 is also increasing in wealth.”

The integral is increasing in assets a3.

“The integral is therefore increasing in assets a 3 .”

The marginal benefit of putting effort does not depend on assets a2.

“Here the marginal benefit of putting effort on the right-hand side does not depend on assets a 2 , but the marginal cost of effort on the left-hand side is decreasing in assets, so that students with more resources will put in higher effort i 2 , and conversely students with fewer resources will spend more time on working during college (n 2 is decreasing in a 2 ).”

Students with more resources will put in higher effort i2.

“Here the marginal benefit of putting effort on the right-hand side does not depend on assets a 2 , but the marginal cost of effort on the left-hand side is decreasing in assets, so that students with more resources will put in higher effort i 2 , and conversely students with fewer resources will spend more time on working during college (n 2 is decreasing in a 2 ).”

The left-hand side of the college attendance condition is decreasing in assets.

“Here the right-hand side is increasing in assets a 2 (because effort i 2 increases in assets) and the left-hand side is decreasing in assets (because of diminishing marginal utility), implying that students with more assets a 2 are more likely to attend (put differently, the threshold for skill s 2 above which a student attends college is decreasing in assets a 2 ).”

The marginal cost of effort is decreasing in assets.

“Here the marginal benefit of putting effort on the right-hand side does not depend on assets a 2 , but the marginal cost of effort on the left-hand side is decreasing in assets, so that students with more resources will put in higher effort i 2 , and conversely students with fewer resources will spend more time on working during college (n 2 is decreasing in a 2 ).”

a3 is increasing in initial wealth a2.

“Moreover, a 3 is increasing in initial wealth a 2 , implying that effort i 2 is also increasing in wealth.”

Conditional on skills s2, the return to attending college is increasing in effort i2.

“Hence, conditional on skills s 2 , the return is increasing in effort i 2 , so that if richer students put in more effort they also get a higher return.”

Parental decisions about where to live and which schools and extra-curricular activities to enroll their children in add to inequality in school inputs, particularly in settings such as the United States where public school quality varies considerably and there are expensive private school options.

“Their deci-sions in these matters add to inequality in school inputs, particularly in settings such as the United States where public school quality varies considerably and there are expensive private school options.”

The central role of parents in shaping their children's education generates a link between different sources of educational inequality.

“A main insight from our model of skill acquisition during childhood is that the central role of parents in shaping their children's education generates a link between different sources of educational inequality.”

A more probable candidate for persistent endowments is a persistent family culture, capturing, for example, how a family views its position in society.

“A more probable candidate would be a persistent family culture, capturing, for example, how a family views its position in society.”

Conventional measures of social mobility from parents to children may understate persistence because educational advantages cannot be fully captured by simple summary measures such as years of schooling.

“One potential explanation for this puzzle is that conventional measures of social mobility from parents to children may understate persistence because educational advantages cannot be fully captured by simple summary measures such as years of schooling.”

Persistent endowments are unlikely to primarily consist of genetic characteristics, as persistence across generations would be low unless assortative mating on genetic ability were extraordinarily strong.

“Such persistent endowments are unlikely to primarily consist of genetic characteristics, as persistence across generations would be low unless assortative mating on genetic ability were extraordinarily strong.”

A comparison of distant kins suggests that conventional measures understate the contribution of assortative mating to educational inequality and low social mobility.

“Similarly, a comparison of distant kins suggests that conventional measures also understate the contribution of assortative mating to educational inequality and low social mobility (Collado, Ortuño-Ortín, and Stuhler 2022).”

• cites Collado, Ortuño-Ortín, and Stuhler 2022Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

By the age of 15, children in the bottom quarter in terms of socio-economic background are more than two years behind their more advantaged peers.

“The evidence in Figure 1 therefore suggests that by the age of 15, children in the bottom quarter in terms of socio-economic background are more than two years behind their more advantaged peers.”

• cites OECD 2016Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Woessmann 2016Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Horizontal stratification in the learning process, such as variation in the quality of educational institutions attended by children from richer and poorer families, may have an additional impact on intergenerational persistence.

“For example, horizontal stratification in the learning process, such as variation in the quality of the educational institutions attended by children from richer and poorer families, may have an additional impact on intergenerational persistence.”

Empirical findings based on two generations and focusing on standard measures of education may miss some types of endowments and could consequently understate the wider transmission of advantages and disadvantages.

“That said, our analysis in Section 5 of multi-generation transmission suggests that empirical findings based on two generations and focusing on standard measures of education may miss some types of endowments and could consequently understate the wider transmission of advantages and disadvantages.”

Recent empirical evidence shows that differences in economic status across families persist over many generations.

“Yet, recent empirical evidence shows that differences in economic status across families instead persist over many generations (e.g., Clark 2014, Lindahl et al. 2015).”

• cites Clark 2014 sourceNot checked — no full text of the source
• cites Lindahl et al. 2015 sourceNot checked — no full text of the source

Our model of children's skill acquisition demonstrates the important role played by schools in equalizing educational opportunities between children from different backgrounds.

“Our model of children's skill acquisition demonstrates the important role played by schools in equalizing educational opportunities between children from different backgrounds.”

The choice of inequality measure matters, as educational expansions are associated with systematic changes in both the average level and variance of schooling, which affects some inequality measures more than others.

“The choice of inequality measure matters, as educational expansions are associated with systematic changes in both the average level and variance of schooling (Ram 1990), which affects some inequality measures more than others.”

• cites Ram 1990 sourceNot checked — no full text of the source

Knowledge about the extent to which educational advantages and disadvantages persist is mainly based on simple summary statistics, such as the parent-child correlation in years of schooling.

“Knowledge about the extent to which educational advantages and disadvantages persist is mainly based on simple summary statistics, such as the parent-child correlation in years of schooling (as shown in the right panel of Figure 2).”

In the presence of borrowing constraints, attendance increases in the financial assets of the parents, conditional on skill.

“However, in the presence of borrowing constraints, attendance increases in the financial assets of the parents, conditional on skill.”

The cross-country relationship between income inequality and intergenerational mobility is stronger for educational attainment than for educational performance.

“The cross-country relationship between income inequality and intergenerational mobility is therefore stronger for educational attainment than for educational performance.”

The contrasting pattern in Figure 2 could be indicative of differences in educational investments and choices net of performance in high school being an important driver of the Great Gatsby Curve in income.

“The contrasting pattern in Figure 2 could therefore be indicative of differences in educational investments and choices net of performance in high school being an important driver of the Great Gatsby Curve in income.”

Monetary investments are diverging between families at different places along the income scale.

“monetary investments are likewise diverging between families at different places along the income scale (Corak 2013;Kornrich and Furstenberg 2012;Schneider, Hastings, and LaBriola 2018”

• cites Corak 2013 sourceNot checked — no full text of the source
• cites Kornrich and Furstenberg 2012Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Schneider, Hastings, and LaBriola 2018 sourceNot checked — no full text of the source

Educational outcomes of ancestors remain predictive of child education, even after conditioning on parent education.

“One way to demonstrate this point is to note that educational outcomes of ancestors remain predictive of child education, even after conditioning on parent education (e.g., Lindahl et al. 2015, Braun and Stuhler 2018, Colagrossi, d'Hombres, and Schnepf 2020).”

• cites Lindahl et al. 2015 sourceNot checked — no full text of the source
• cites Braun and Stuhler 2018Not checked — no full text of the source
• cites Colagrossi, d'Hombres, and Schnepf 2020 sourceNot checked — no full text of the source

Ramey and Ramey (2010) document that more educated parents in the United States have increased the time spent on child care much more than less educated parents.

“Ramey and Ramey (2010) document, for example, that more educated parents in the United States have increased the time spent on child care much more than less educated parents”

• cites Ramey and Ramey (2010) sourceNot checked — no full text of the source

In more recent models of human capital investments over multiple stages, additional links between economic and educational inequality arise, implying that cross-sectional inequality is a key determinant of intergenerational persistence.

“In such models, additional links between economic and educational inequality arise, implying that cross-sectional inequality is a key determinant of intergenerational persistence.”

Evidence on the association between income inequality and educational gaps could be indicative of the mechanisms underlying the Great Gatsby Curve in income.

“Evidence on this association could therefore be indicative of the mechanisms underlying the Great Gatsby Curve in income.”

In most high-income countries, economic inequality has risen substantially in recent decades.

“In most high-income countries, economic inequality has risen substantially in recent decades (see for example Krueger et al. 2010).”

• cites Krueger et al. 2010 sourceNot checked — no full text of the source

Correlation estimates that abstract from changes in the variance of schooling tend to be more stable over time than those that do not, such as regression estimates.

“In particular, correlation estimates that abstract from changes in the variance of schooling tend to be more stable over time than those that do not, such as regression estimates (Hertz et al. 2008).”

• cites Hertz et al. 2008 sourceNot checked — no full text of the source

Fregoni, Havari, and Stuhler (2021) report a pronounced negative relation between income inequality and income mobility for Italy, Spain, Sweden, and the Netherlands.

“comparing regional estimates from Italy, Spain, Sweden, and the Netherlands, Fregoni, Havari, and Stuhler (2021) report a pronounced negative relation for all four countries.”

• cites Fregoni, Havari, and Stuhler (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In Sweden, conditional on previous achievement, about 25 percent of the variation in tertiary field choices can be explained by parental background (parents' education, occupation, income, and wealth).

“For example, Hällsten and Thaning (2018) find that conditional on previous achievement, about 25 percent of the variation in tertiary field choices in Sweden can be explained by parental background (parents' education, occupation, income, and wealth).”

• cites Hällsten and Thaning (2018) sourceNot checked — no full text of the source

Conventional parent-child measures may not capture the full extent to which inequalities are transmitted across generations.

“Nevertheless, there are several reasons why conventional parent-child measures may not capture the full extent to which inequalities are transmitted across generations.”

Chmielewski (2019) finds that achievement gaps have increased in most countries.

“Chmielewski (2019) finds that achievement gaps have increased in most countries.”

• cites Chmielewski (2019) sourceNot checked — no full text of the source

The contrasting findings of Reardon (2011) and Hanushek et al. (2020) can be traced to differing data sources and definitions of family background.

“Their contrasting findings can be traced to differing data sources and definitions of family background.”

In economic models in the tradition of Becker and Tomes (1979), a rise in economic inequality can make financial constraints more binding for low-income parents, and hence reduce social mobility.

“In such models, a rise in economic inequality can make financial constraints more binding for low-income parents, and hence reduce social mobility.”

• cites Becker and Tomes (1979) sourceNot checked — no full text of the source

Even if borrowing constraints are not binding, attendance will increase in financial assets if higher education is a risky endeavour, as the disutility of risk is greater for families with low financial resources.

“Even if borrowing constraints are not binding, attendance will increase in financial assets if higher education is a risky endeavour, as the disutility of risk is greater for families with low financial resources.”

As college shares are stabilizing in many countries, the relative importance of qualitative dimensions of stratification in reproducing inequalities could well be on the rise.

“As college shares are stabilizing in many countries, the relative importance of qualitative dimensions of stratification in reproducing inequalities could well be on the rise.”

In most high-income economies, economic inequality, including education wage premia, increased throughout the 1980s and 1990s, with particularly large changes in the United States and the United Kingdom.

“As discussed in Section 2, in most high-income economies, economic inequality, including education wage premia, increased throughout the 1980s and 1990s, with particularly large changes in the United States and the United Kingdom.”

Doepke and Zilibotti (2017, 2019) use evidence from the World Values Survey to show that in countries with high income inequality, there are more authoritarian and authoritative parents and fewer permissive ones.

“In line with these predictions, Doepke andZilibotti (2017, 2019) use evidence from the World Values Survey to show that in countries with high income inequality, there are more authoritarian and authoritative parents and fewer permissive ones.”

• cites Doepke and Zilibotti (2017, 2019)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The direct impact of X on the income gap between workers with less and more skill would further accentuate the income gaps between workers of different education levels.

“Moreover, the direct impact of X on the income gap between workers with less and more skill would further accentuate the income gaps between workers of different education levels.”

Both changes have a negative impact on other parents' incentives to make educational investments.

“Both changes have a negative impact on other parents' incentives to make educational investments.”

Different methods point to the same conclusion: traditional parent-child correlations understate the transmission of advantages and the persistence of educational inequalities across multiple generations.

“Different methods therefore point to the same conclusion: traditional parentchild correlations understate the transmission of advantages and the persistence of educational inequalities across multiple generations.”

Actual bottlenecks do exist in certain areas, such as admission slots in top universities.

“Moreover, actual bottlenecks do exist in certain areas, such as admission slots in top universities (as discussed in Section 2).”

• cites Section 2Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

As spousal correlations tend to be high, assortative mating is an important driver of educational inequality.

“As spousal correlations tend to be high (Fernández and Rogerson 2001), assortative mating is also an important driver of educational inequality.”

• cites Fernández and Rogerson 2001Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Fernández, Guner, and Knowles (2005) show that the spousal correlation in years of schooling tends to be greater in countries where skill premia and income inequality are high.

“Indeed, Fernández, Guner, and Knowles (2005) show that the spousal correlation in years of schooling tends to be greater in countries where skill premia and income inequality are high.”

• cites Fernández, Guner, and Knowles (2005)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In a more general model, the impact of a rise in X would also depend on the functional form through which parental investment I1 affects children's skills s2.

“In a more general model, the impact of a rise in X would also depend on the functional form through which parental investment I 1 affects children's skills s 2 (which is linear in our example).”

Aggregate feedback mechanisms of this kind arise not just from fixed slot constraints, but also from general equilibrium effects on the price of skill and on the cost of education.

“Yet, aggregate feedback mechanisms of this kind arise not just from fixed slot constraints, but also from general equilibrium effects on the price of skill and on the cost of education.”

If returns to parental investments are strongly diminishing, a rise in X could result in a rising gap in parental investment but little or no change in the skills gap between children of high- and low-skill parents.

“If returns to parental investments are strongly diminishing, a rise in X could result in a rising gap in parental investment (as in Propositions 1 and 2) but little or no change in the skills gap between children of high-and low-skill parents.”

Anderson, Sheppard, and Monden (2018) report that estimates of the coefficient βgp tend to be one quarter the size of the coefficient βp.

“Summarizing the results from 40 different studies, Anderson, Sheppard, and Monden (2018) report that estimates of the coefficient β gp tend to be one quarter the size of the coefficient β p , as is the case for the estimates reported in Figure 3.”

• cites Anderson, Sheppard, and Monden (2018) sourceNot checked — no full text of the source

Ramey and Ramey (2010) cite competition for college admission as one reason for the widening disparity in parenting investments observed in the United States.

“Ramey and Ramey (2010) cite competition for college admission as one reason for the widening disparity in parenting investments observed in the United States.”

• cites Ramey and Ramey (2010) sourceNot checked — no full text of the source

The results in Proposition 1 provide a possible explanation for the general trends in parental investments in children's education observed in a number of countries since the 1970s.

“The results in Proposition 1 provide a possible explanation for the general trends in parental investments in children's education that have been observed in a number of countries since the 1970s.”

The effect on educational inequality arises from the parental budget constraint: if returns to education rise, the income of highly educated parents increases relative to that of others with less education, which lowers the marginal utility of consumption and hence lowers the marginal cost of investing in children's education.

“The effect on educational inequality arises from the parental budget constraint.If returns to education rise, the income of highly educated parents increases relative to that of others with less education.This rise in income increases consumption, lowers the marginal utility of consumption, and hence lowers the marginal cost of investing in children's education.”

• AssumptionRests on an assumption: Financial markets are imperfect, so parents cannot borrow against their child's future income and investments are constrained by current parental income.

Recent evidence suggests that mating has become more assortative over time in the United States as inequality has risen.

“Moreover, recent evidence suggests that mating has become more assortative over time in the United States as inequality has risen (Greenwood et al. 2014, Greenwood et al. 2016, Chiappori, Dias, and Meghir 2020).”

• cites Greenwood et al. 2014 sourceNot checked — no full text of the source
• cites Greenwood et al. 2016Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Chiappori, Dias, and Meghir 2020Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In the bottleneck model, the parenting investments of one group of parents impose an externality on other parents.

“In this setting, the parenting investments of one group of parents impose an externality on other parents, because the more they invest the higher the bar for success.”

• AssumptionThe authors state this as an assumption: Higher parental effort I1 increases the chance that a child will become high-skill, but if all parents increase their parenting effort, this raises the bar for success.

Even though the total number of students in college more than doubled in recent decades in the United States, elite schools have not expanded enrollment, choosing instead to admit a smaller fraction of applicants.

“Blair and Smetters (2021) document that even though the total number of students in college more than doubled in recent decades in the United States, elite schools have not expanded enrollment, choosing instead to admit a smaller fraction of applicants.”

• cites Blair and Smetters (2021) sourceNot checked — no full text of the source

Proposition 1: If the solution for parental investment I1(S,X) is interior for both low- and high-skill parents, a marginal increase in returns to education X will raise the educational investment of all parents and increase the difference between the investment of high-skill parents and low-skill parents.

“If the solution for parental investment I 1 (S, X) is interior for both low-and high-skill parents, a marginal increase in returns to education X will: • Raise the educational investment I 1 (S, X) of all parents. • Increase the difference I 1 (H, X) -I 1 (L, X) between the (higher) educational investment of high-skill parents and the (lower) investment of low-skill parents.”

• AssumptionThe authors state this as an assumption: Parents agree on their objectives and maximize a joint utility function.
• AssumptionThe authors state this as an assumption: The skill accumulation functions f0, f1, and f2 are increasing in each argument.
• AssumptionThe authors state this as an assumption: The probability that the child will end up with high skill is min{I1,1}.
• AssumptionThe authors state this as an assumption: The parent's concern for the child's future outcome takes the form of a warm-glow preference derived from the child's future wage.
• AssumptionThe authors state this as an assumption: In the special case, skills are determined entirely by parental investment I1 in late childhood, with a single parent and two skill levels.
• AssumptionRests on an assumption: Financial markets are imperfect, so parents cannot borrow against their child's future income and investments are constrained by current parental income.

If one group of parents redoubles their investment and demand for college education among their children rises, all else equal college tuition will rise and returns to college will decline once the increased number of college graduates enters the labor market.

“For example, if one of group of parents redoubles their investment and demand for college education among their children consequently rises, all else equal college tuition will rise and returns to college will decline once the increased number of college graduates enters the labor market.”

For poorer families, the increase in parenting investments of rich families leads to a discouragement effect, which lowers their incentive to invest and further widens educational inequality.

“For poorer families, the increase in parenting investments of rich families leads to a discouragement effect, which lowers their incentive to invest and further widens educational inequality.”

In countries where economic inequality has risen quickly, there is clear evidence of increasing inequality in educational inputs.

“Likewise, in countries where economic inequality has risen quickly, there is clear evidence of increasing inequality in educational inputs.”

Parenting styles also respond to changing inequality within countries: if income inequality goes up over time, so too does the fraction of parents who employ one of the intensive styles of parenting.

“Parenting styles also respond to changing inequality within countries.Namely, if income inequality goes up over time, so too does the fraction of parents who employ one of the intensive styles of parenting.”

Barone and Mocetti (2020) find persistence in earning advantages over nearly six centuries.

“For example, using historical census data from Florence, Barone and Mocetti (2020) find persistence in earning advantages over nearly six centuries.”

• cites Barone and Mocetti (2020) sourceNot checked — no full text of the source

Marital sorting is stronger in the United States (spousal correlation of 0.6) than in England, Germany, and Australia, consistent with the idea that such sorting may be strongest in high inequality environments.

“Notably, marital sorting is stronger in the United States (spousal correlation of 0.6) than in England, Germany, and Australia, consistent with the idea that such sorting may be strongest in high inequality environments.”

The results from Propositions 1 and 2 provide a possible rationale for the empirical phenomenon of the Great Gatsby Curve.

“The results from Propositions 1 and 2 provide a possible rationale for the empirical phenomenon of the Great Gatsby Curve discussed in Section 2.4.”

The model of parental investments suggests that at least part of the shift toward more parental time investment can be seen as a response to a changed economic environment where succeeding in formal education is much more highly rewarded than in earlier times.

“Our model of parental investments in children's education suggests that at least part of this shift can be seen as a response to a changed economic environment where succeeding in formal education is much more highly rewarded than in earlier times.”

Corak (2013), Kornrich and Furstenberg (2012), and Schneider, Hastings, and LaBriola (2018) observe a large increase in the gap in spending on children between high- and low-income households from the 1970s to the 2000s.

“Corak (2013), Kornrich and Furstenberg (2012), and Schneider, Hastings, and LaBriola (2018) observe a large increase in the gap in spending on children between high-and low-income households from the 1970s to the 2000s.”

• cites Corak (2013) sourceNot checked — no full text of the source
• cites Kornrich and Furstenberg (2012)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Schneider, Hastings, and LaBriola (2018) sourceNot checked — no full text of the source

The feedback from aggregate inequality to educational inequality can be further amplified if there are bottlenecks in the education system.

“The feedback from aggregate inequality to educational inequality can be further amplified if there are bottlenecks in the education system.”

• AssumptionThe authors state this as an assumption: In the bottleneck variant, the number of children who are able to attain high skill is fixed, say because of a set number of slots at university.

Evidence on the success of universal childcare programs is more mixed than for the early targeted programs.

“Evidence on the success of universal childcare programs is more mixed than for the early targeted programs (Blanden and Rabe 2021), though most carefully designed studies show that the provision of early childcare is beneficial, especially for children from disadvantaged backgrounds (Havnes and Mogstad 2015, Cornelissen et al. 2018, Felfe and Lalive 2018, Gormley and Gayer 2005).”

• cites Blanden and Rabe 2021 sourceNot checked — no full text of the source

Biasi (2022) observes that equalized funding increases the social mobility of low-income students.

“The link between school funding equalization and higher social mobility is supported by the empirical results of Biasi (2022), who examines the effect of state-level reforms in school financing in the United States and observes that equalized funding increases the social mobility of low-income students.”

• cites Biasi (2022)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

For Denmark, Bingley, Cappellari, and Tatsiramos (2020) document that community background accounts for about one-fifth of the sibling correlation in years of schooling.

“For Denmark, Bingley, Cappellari, and Tatsiramos (2020) exploit within-family variation in exposure to different neighborhoods, and document that community background accounts for about one-fifth of the sibling correlation in years of schooling.”

• cites Bingley, Cappellari, and Tatsiramos (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Together with evidence that skills are particularly malleable early in life, the self-productivity of skill acquisition points to the important role of skill gaps between young children from different backgrounds in generating overall educational inequality.

“Together with evidence that skills are particularly malleable early in life (Carneiro andHeckman 2003, Ermisch andFrancesconi 2005, Heckman and Mosso 2014), the self-productivity of skill acquisition points to the important role of skill gaps between young children from different backgrounds in generating overall educational inequality.”

• cites Carneiro andHeckman 2003Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Ermisch andFrancesconi 2005Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Heckman and Mosso 2014Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Rising economic inequality leads to more residential segregation, as richer parents seek out homogeneous neighborhoods with strong peer effects.

“Rising economic inequality leads to more residential segregation, as richer parents seek out homogeneous neighborhoods with strong peer effects.”

• cites Fogli and Guerrieri (2019) sourceNot checked — no full text of the source

Eckert and Kleineberg (2021) show that a policy that equates school funding across neighborhoods has only limited benefits due to the endogenous response of residential segregation.

“In a similar setting, Eckert and Kleineberg (2021) show that a policy that equates school funding across neighborhoods has only limited benefits due to the endogenous response of residential segregation.”

• cites Eckert and Kleineberg (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Dynamic complementarity of skill acquisition means that early investments in skills make later investments more productive.

“Similarly, dynamic complementarity of skill acquisition means that early investments in skills make later investments more productive.”

Policy choices regarding the financing of public schools play a large part in determining whether aggregate inequality drives educational inequality through variation in the quality of public schooling.

“Clearly, policy choices regarding the financing of public schools (e.g., local versus state-level funding) play a large part in determining whether aggregate inequality drives educational inequality through variation in the quality of public schooling.”

Endogenous peer group formation can amplify educational inequality, because homophily bias implies that socio-economic differences across families are reproduced in the peer connections children make in schools and neighborhoods.

“Endogenous peer group formation can amplify educational inequality, because homophily bias (the tendency to associate with peers who are similar to oneself) implies that socio-economic differences across families are reproduced in the peer connections children make in schools and neighborhoods (Agostinelli et al. 2020).”

• cites Agostinelli et al. 2020 sourceNot checked — no full text of the source

The effects of Moving to Opportunity were much smaller than observational differences in outcomes between children across neighborhoods.

“That said, the effects were much smaller than observational differences in outcomes between children across neighborhoods (Harding et al. 2021).”

• cites Harding et al. 2021 sourceNot checked — no full text of the source

Higher returns to education can incentivize parents to relocate to more expensive neighborhoods with stronger schools.

“In addition, higher returns to education can incentivize parents to relocate to more expensive neighborhoods with stronger schools (see Nechyba 2006 for an analysis of the impact of residential sorting on educational inequality).”

• cites Nechyba 2006Not checked — no full text of the source

If economic inequality between rich and poor families rises, spending on private schools attended by the rich would increase without a corresponding increase in the quality of public schools.

“If economic inequality between rich and poor families rises, we would expect to see an increase in spending on private schools attended by the rich without a corresponding increase in the quality of public schools.”

Laliberté (2021) estimates that 50-70 percent of the benefits of moving to a better area for educational attainment is due to access to better schools.

“For example, Laliberté (2021) take advantage of the fact that school catchment areas in Montreal differ across language groups, and estimate that 50-70 percent of the benefits of moving to a better area for educational attainment is due to access to better schools.”

• cites Laliberté (2021) sourceNot checked — no full text of the source

Chetty and Hendren suggest that local inputs do matter, as prospects for upward mobility differ systematically across neighborhoods and regions in the US data.

“Research by Chetty andHendren (2018a, 2018b) suggests that such local inputs do matter, as prospects for upward mobility differ systematically across neighborhoods and regions in the US data.”

• cites Chetty andHendren (2018a, 2018b)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Skill deficits that arise early on in a child's development are difficult to later compensate.

“This feature implies that skill deficits that arise early on in a child's development are difficult to later compensate.”

Early childhood is likely to be a phase when interventions aimed at compensating deficits are particularly productive.

“Conversely, early childhood is likely to be a phase when interventions aimed at compensating deficits are particularly productive.”

Vouchers that give low-income families access to schools in districts with high housing prices can be an effective policy response.

“In line with the evidence from the Moving to Opportunity program (Chetty, Hendren, and Katz 2016), their model shows that vouchers that give low-income families access to schools in districts with high housing prices can be an effective policy response.”

• cites Zheng and Graham (2022) sourceNot checked — no full text of the source
• cites Chetty, Hendren, and Katz 2016 sourceNot checked — no full text of the source

Hanushek and Woessmann (2011) and Woessmann (2016) find no relationship between the level of school funding and test scores at the national level among OECD countries.

“Perhaps contrary to popular expectation, they find no relationship between the level of school funding and test scores at the national level among OECD countries.”

• cites Hanushek and Woessmann (2011)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Woessmann (2016)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Based on randomization and natural experiments, the literature shows that the estimated impacts of money spent on reducing class size are at the upper range of the equivalent estimates from the school funding literature.

“Based on randomization and natural experiments, the literature shows that the estimated impacts of money spent on reducing class size are at the upper range of the equivalent estimates from the school funding literature (Gibbons and McNally 2013).”

• cites Gibbons and McNally 2013Not checked — no full text of the source

The evidence on the importance of school funding for student outcomes is mixed.

“The evidence on the importance of school funding for student outcomes is mixed.”

Evidence summarized by Berlinski and Vera-Hernández (2019) indicates that paid maternal leave beyond three months has no additional benefit for early childhood development.

“Evidence summarized by Berlinski and Vera-Hernández (2019) indicates that paid maternal leave beyond three months has no additional benefit for early childhood development.”

• cites Berlinski and Vera-Hernández (2019) sourceNot checked — no full text of the source

Björklund and Jäntti (2020) and Mogstad and Torsvik (2021) conclude that family income does have a direct impact on children's outcomes, in particular for children from low income or disadvantaged families.

“Empirical evidence on the causal impact of changes in parental income on child achievement is reviewed by Björklund and Jäntti (2020) and Mogstad and Torsvik (2021), who conclude that family income does have a direct impact on children's outcomes, in particular for children from low income or disadvantaged families.”

• cites Björklund and Jäntti (2020) sourceNot checked — no full text of the source
• cites Mogstad and Torsvik (2021) sourceNot checked — no full text of the source

A preference channel for intergenerational persistence in educational attainment is supported by the observation that preferences and aspirations are transmitted from parents to children.

“A preference channel for intergenerational persistence in educational attainment is also supported by the observation that preferences and aspirations are transmitted from parents to children (see for example Dohmen et al. 2012).”

• cites Dohmen et al. 2012 sourceNot checked — no full text of the source

Public investments may not reach those groups who would most benefit from them.

“Moreover, public investments may not reach those groups who would most benefit from them.”

Evidence from the Well-Being Modules of the American Time Use Survey does not show significant differences in the enjoyment of childcare by the mother's education.

“Evidence from the Well-Being Modules of the American Time Use Survey does not, however, show significant differences in the enjoyment of childcare by the mother's education.”

• cites American Time Use SurveyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The early acquisition of non-cognitive skills may result in higher productivity in acquiring cognitive skills later on.

“Moreover, the early acquisition of non-cognitive skills may result in higher productivity in acquiring cognitive skills later on.”

For the most advantaged students, the effects of school funding are smaller.

“For the most advantaged students, the effects are smaller.”

• cites Jackson and Mackevicius (2021) sourceNot checked — no full text of the source

Carneiro et al. (2021) find that income in early and late childhood is more important than income during the middle years for enhancing children's outcomes as adults.

“Carneiro et al. (2021) investigate the optimal timing of parental income for enhancing children's outcomes as adults and find that income in early and late childhood is more important than income during the middle years, casting some doubt on recent models that emphasize early investment above all else.”

• cites Carneiro et al. (2021) sourceNot checked — no full text of the source

Deming (2017) and Edin et al. (2022) document an increase in the economic returns to social and non-cognitive skills in the United States and Sweden in recent decades.

“Deming (2017) and Edin et al. (2022) document an increase in the economic returns to social and non-cognitive skills in the United States and Sweden in recent decades.”

• cites Deming (2017) sourceNot checked — no full text of the source
• cites Edin et al. (2022)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

An important role for either credit constraints or information frictions is supported by the observation that measured returns to parental investment are higher among low-income families.

“An important role for either credit constraints or information frictions (i.e., low-income parents being less informed about the returns to parental investments) is supported by the observation that measured returns to parental investment are higher among low-income families.”

To the extent that differences in preferences and beliefs matter, these are more likely to relate to the returns to investments in children's skills rather than the cost of investment.

“Hence, to the extent that differences in preferences and beliefs matter, these are more likely to relate to the returns to investments in children's skills rather than the cost of investment.”

Inequality in parental investment in education can arise from differing beliefs about the productivity of such investment.

“Inequality in parental investment in education can arise from differing beliefs about the productivity of such investment.”

Lekfuangfu and Odermatt (2020) show that parental aspirations are strong predictors of the educational aspirations of their children, even conditional on the socio-economic status of the parents and the cognitive and non-cognitive skills of the child.

“Lekfuangfu and Odermatt (2020) show that parental aspirations are strong predictors of the educational aspirations of their children, even conditional on the socio-economic status of the parents and the cognitive and non-cognitive skills of the child.”

• cites Lekfuangfu and Odermatt (2020) sourceNot checked — no full text of the source

Apascaritei, Demel, and Radl (2021) find that self-reported personality scales such as locus of control or conscientiousness are at best weakly associated with real effort.

“In real-effort experiments with fifth graders in Spain, Apascaritei, Demel, and Radl (2021) find that self-reported personality scales such as locus of control or conscientiousness are at best weakly associated with real effort.”

• cites Apascaritei, Demel, and Radl (2021) sourceNot checked — no full text of the source

There is evidence that increases in hours of teaching through lengthening the school day, extending the school term, or lowering the school starting age can have modestly beneficial effects.

“There is evidence that increases along all of these margins can have modestly beneficial effects.”

These basic facts are consistent with an important role of financial constraints in educational inequality at the college level in the United States.

“In line with the structural models discussed above, these basic facts are consistent with an important role of financial constraints in educational inequality at the college level in the United States.”

In the case of perfect financial markets, unequal financial resources among families will not result in additional educational inequality.

“Hence, in the case of perfect financial markets, unequal financial resources among families (captured by a 2 ) will not result in additional educational inequality.”

The English higher education funding system mitigates risk for low income students.

“Nevertheless, it does mitigate risk for low income students.”

The combination of rising fees and the switch to income-contingent loans in England has had no appreciable impact on inequalities in higher education participation.

“Indeed, it appears that the combination of rising fees and the switch to income-contingent loans in England has had no appreciable impact on inequalities in higher education participation (Murphy, Scott-Clayton, andWyness 2019 andAzmat andSimion 2017).”

• cites Murphy, Scott-Clayton, and Wyness 2019 sourceNot checked — no full text of the source
• cites Azmat and Simion 2017Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

If the probability of actually attaining a degree is sufficiently small, attending college is an inherently risky decision because it involves an up-front cost with an uncertain outcome.

“If the probability of actually attaining a degree is sufficiently small, attending college is an inherently risky decision, because it involves an up-front cost with an uncertain outcome.”

Differences in pre-college investments play a key role in generating socio-economic differences in college completion.

“Differences in pre-college investments turn out to play a key role in generating socio-economic differences in college completion.”

• cites Blandin and Herrington (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Blandin and Herrington (2021) document that college attendance has risen over time for children from richer and poorer families alike.

“They document that college attendance has risen over time for children from richer and poorer families alike.”

• cites Blandin and Herrington (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

When students with fewer assets face a binding borrowing constraint, their marginal utility of consumption when young is high, which increases the utility cost of paying tuition T to attend college.

“When students with fewer assets face a binding borrowing constraint, their marginal utility of consumption when young is high, which increases the utility cost of paying tuition T to attend college.”

If better insurance markets could be provided, educational inequality between students of low and high wealth would decrease.

“If better insurance markets could be provided, educational inequality between students of low and high wealth would decrease.”

For young adults with little wealth, college completion is a key margin.

“Nevertheless, as our model emphasizes, for young adults with little wealth college completion is a key margin-many more students begin college than finish it, and dropout rates are closely related to socio-economic status.”

In high-income economies, educational inequality is also shaped by inequality in higher education.

“However, in high-income economies, educational inequality is also shaped by inequality in higher education.”

Such interventions potentially offer an effective means of reducing inequality.

“Such interventions thus potentially offer an effective means of reducing inequality.”

The impact of wealth on education is even more severe when there are binding borrowing constraints in addition to imperfect insurance markets.

“The impact of wealth on education is even more severe when there are binding borrowing constraints in addition to imperfect insurance markets.”

All else equal, a student with fewer assets will put less effort into college and work more while studying, which lowers the probability of graduating.

“Hence, all else equal a student with fewer assets will put less effort into college and instead work more while also studying, which lowers the probability of graduating.”

Student loans would not completely eliminate educational inequality between children from families with more and less resources.

“Nevertheless, student loans would not completely eliminate educational inequality between children from families with more and less resources.”

Public school systems considerably lessen the extent of educational inequality compared to what would prevail if all investments were provided or paid for by the family.

“Nonetheless, public school systems do considerably lessen the extent of inequality compared to what would prevail if all investments were provided or paid for by the family.”

Even if the borrowing constraint is fully eliminated through generous student loans, the risk of attending college with uncertain returns can introduce an impact of wealth on college attendance and returns.

“Furthermore, even if the borrowing constraint is fully eliminated through generous student loans, it still matters that attending college is a risky decision with uncertain returns, which can also introduce an impact of wealth on college attendance and returns (Proposition 4).”

Educational mobility across multiple generations is lower, and perhaps much lower, than a naive extrapolation from conventional parent-child measures would suggest.

“A key finding from the studies reviewed in Section 2.6 is that educational mobility across multiple generations is lower, and perhaps much lower, than a naive extrapolation from conventional parent-child measures would suggest.”

The English system is expensive, with the state predicted to pay almost 43 percent of the value of the loans made, owing to low interest rates and non-repayment.

“This is an expensive system, with the state predicted to pay almost 43 percent of the value of the loans made, owing to low interest rates and non-repayment (Crawford, Crawford, and Jin 2014).”

• cites Crawford, Crawford, and Jin 2014 sourceNot checked — no full text of the source

Many more students begin college than finish it.

“many more students begin college than finish it”

The risk of attending college is accentuated if student loans need to be repaid regardless of success in college.

“The risk of attending college is accentuated if student loans need to be repaid regardless of success in college.”

Dropout rates are closely related to socio-economic status.

“dropout rates are closely related to socio-economic status”

For students with fewer assets facing a binding borrowing constraint, the opportunity cost of putting effort into college is also high.

“Similarly, the opportunity cost of putting effort i 2 into college is also high.”

If students can borrow and there is actuarially fair insurance for income uncertainty, college attendance, effort in college, and the return to college depend only on initial skill s2 and not on resources a2.

“Proposition 3 (Higher Education under Perfect Financial Markets).If students can borrow and there is actuarially fair insurance for income uncertainty, college attendance, effort in college, and the return to college depend only on initial skill s 2 but not on resources a 2 .”

• AssumptionThe authors state this as an assumption: In the higher education model, attending college only affects earnings if college is successfully completed.
• AssumptionThe authors state this as an assumption: In the higher education model, basic skills do not evolve throughout adulthood; s3 = s2.
• AssumptionThe authors state this as an assumption: In the higher education model, the probability of completing college p_d(1,s2,i2) is increasing in both arguments and strictly concave in i2.
• AssumptionThe authors state this as an assumption: In the higher education model, the period utility function u(•) is strictly increasing, strictly concave, and features decreasing absolute risk aversion.

Lavy (2020) observes that an additional hour of weekly instruction on mathematics, science, and language improves students' performance by 0.03 to 0.05 of a standard deviation.

“Lavy (2020) observes that an additional hour of weekly instruction on mathematics, science, and language improves students' performance by 0.03 to 0.05 of a standard deviation.”

• cites Lavy (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The complementarity of investments at different stages implies that policies relaxing borrowing constraints in higher education have larger effects if they are anticipated.

“The same complementarity also implies that policies that relax borrowing constraints in higher education have larger effects if they are anticipated.”

The model developed in Section 4.1 generates a positive ability-enrollment relationship even with a fixed borrowing constraint, because high-ability students have a higher return to college and are therefore more willing to endure temporarily limited resources to attend.

“The model developed in Section 4.1 does generate a positive ability-enrollment relationship even with a fixed borrowing constraint, because high-ability students have a higher return to college and are therefore more willing to endure temporarily limited resources to attend.”

A gap in completing college conditional on attending has emerged.

“However, consistent with the evidence discussed above, a gap in completing college conditional on attending has emerged.”

• cites Blandin and Herrington (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

There is considerable heterogeneity in outcomes conditional on completing college, relating to choice of college major and post-college career and occupation choices.

“Beyond college attendance and completion, there is also considerable heterogeneity in outcomes conditional on completing college, relating to issues such as choice of college major and post-college career and occupation choices.”

Neidhöfer and Stockhausen (2019) find similarly high latent persistence in a comparison of three data sets from the United States, the United Kingdom, and Germany.

“Neidhöfer and Stockhausen (2019) find similarly high latent persistence in a comparison of three different data sets from the United States, the United Kingdom, and Germany”

• cites Neidhöfer and Stockhausen (2019) sourceNot checked — no full text of the source

Collado, Ortuño-Ortín, and Stuhler (2022) estimate that in Sweden, spousal correlations in latent advantages would have to be around 0.75 to explain the correlation pattern in educational attainment between distant siblings-in-law.

“Collado, Ortuño-Ortín, and Stuhler (2022) estimate that in Sweden, spousal correlations in latent advantages would have to be around 0.75 to explain the correlation pattern in educational attainment between distant siblings-in-law.”

• cites Collado, Ortuño-Ortín, and Stuhler (2022)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Lavy's results would predict a 0.06 of a standard deviation fall in math scores as a result of a 12-week school closure.

“As noted by Burgess and Sievertsen (2020), Lavy's results would predict a 0.06 of a standard deviation fall in math scores as a result of a 12-week school closure.”

• cites Burgess and Sievertsen (2020)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Lavy 2015 sourceNot checked — no full text of the source

Colagrossi, d'Hombres, and Schnepf (2020) find similarly high latent persistence in comparing 28 European countries.

“as do Colagrossi, d'Hombres, and Schnepf (2020) in comparing 28 European countries.”

• cites Colagrossi, d'Hombres, and Schnepf (2020) sourceNot checked — no full text of the source

By June 2020, nearly all countries had imposed some form of school closure to halt the progression of the pandemic.

“By June 2020 (Panel (a)), nearly all countries had imposed some form of school closure to halt the progression of the pandemic.”

Estimates of the magnitude of summer learning loss vary widely between studies, from 0.06 to 0.6 of a standard deviation in skills for a 12-week closure.

“However, estimates of the magnitude of the loss vary widely between studies, from 0.06 to 0.6 of a standard deviation in skills for a 12-week closure (Kuhfeld et al. 2020a, Cooper et al. 1996, McCombs et al. 2014).”

• cites Kuhfeld et al. 2020aNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Cooper et al. 1996 sourceNot checked — no full text of the source
• cites McCombs et al. 2014 sourceNot checked — no full text of the source

For a genetic model to explain high multigenerational correlations, there would also have to be high assortative mating in terms of genetic endowments.

“As a result, for a genetic model to explain high multigenerational correlations there would also have to be high assortative mating in terms of genetic endowments (Clark 2021).”

• cites Clark 2021Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Summer learning loss has been found to be less severe for reading skills, where children have more opportunity for independent practice, compared to mathematics or spelling.

“In particular, summer learning loss has been found to be less severe for reading skills, where children have more opportunity for independent practice, compared to mathematics or spelling (Shinwell andDefeyter 2017, Paechter et al. 2015).”

• cites Shinwell andDefeyter 2017Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Paechter et al. 2015Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Halloran et al. (2021) show that shares of in-person schooling time varied from 9 percent in Virginia to 98 percent in Florida.

“Halloran et al. (2021) use school district-level data from 12 US states for the 2020-2021 academic year and show that shares of in-person schooling time varied from 9 percent in Virginia to 98 percent in Florida.”

• cites Halloran et al. (2021) sourceNot checked — no full text of the source

Students around the world experienced highly unequal exposure to school closures.

“Students around the world accordingly experienced highly unequal exposure to school closures.”

By May 2021, schools across countries had been fully closed for an average of 17 weeks.

“By May 2021, schools across countries had been fully closed for an average of 17 weeks (UNESCO 2021).”

• cites UNESCO 2021Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Parent-child correlations may not be very informative about the extent to which educational or socio-economic advantages persist across multiple generations.

“A robust conclusion is that parent-child correlations may not be very informative about the extent to which educational or socio-economic advantages persist across multiple generations.”

All of these inputs are affected by school closures in ways that are likely to differ across families.

“All of these inputs are affected by school closures in ways that are likely to differ across families.”

In a model where observed education Y_t = αS_t + ε_t and skills S_{t+1}=λS_t+ν_t with standardized variances, the parent-child correlation in schooling is ρ1 = α^2 λ.

“In this model, the parent-child correlation in schooling is given by ρ 1 = Cov(Y t+1 , Y t ) Var(Y t ) = α 2 Cov(S t+1 , S t ) = α 2 λ,”

• AssumptionThe authors state this as an assumption: True skills S_t are unobserved; observed educational outcome Y_t is related to true skills by Y_t = αS_t + ε_t, with ε_t an i.i.d. random variable.
• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.
• AssumptionThe authors state this as an assumption: The variances of Y_t and S_t are standardized to one.

In the extreme case of full persistence (λ=1), there is no further regression to the mean after the first generation, so ρ1=ρ2=...=ρk.

“In the extreme case of full persistence, λ = 1, we would observe no further regression to the mean after the first generation, so that ρ 1 = ρ 2 = ... = ρ k .”

• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.

More generally, the correlation k generations ahead equals α^2 λ^k.

“More generally, the correlation k generations ahead is equal to α 2 λ k .”

• AssumptionThe authors state this as an assumption: True skills S_t are unobserved; observed educational outcome Y_t is related to true skills by Y_t = αS_t + ε_t, with ε_t an i.i.d. random variable.
• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.
• AssumptionThe authors state this as an assumption: The variances of Y_t and S_t are standardized to one.

Multigenerational estimates offer direct evidence on the persistence of educational advantages in the long run, on which parent-child correlations are less informative.

“First, they offer direct evidence on the persistence of educational advantages in the long run, on which parent-child correlations are less informative.”

The observation ρ2 > ρ1^2 is the flip side of the observation that the coefficient β_gp on grandparents' education in the child-parent-grandparent regression tends to be positive.

“As shown in Braun and Stuhler (2018), this observation ρ 2 > ρ 2 1 is simply the flip side of the observation that the coefficient β gp on grandparents' education in the child-parent-grandparent regression (1) tends to be positive”

• cites Braun and Stuhler (2018)Not checked — no full text of the source

Collado, Ortuño-Ortín, and Stuhler (2022) show that distant-kin as well as more traditional measures of educational inequality, such as parent-child and sibling correlations, can all be integrated within a consistent transmission model.

“They show that distant-kin as well as more traditional measures of educational inequality, such as parent-child and sibling correlations, can be all integrated within a consistent transmission model.”

• cites Collado, Ortuño-Ortín, and Stuhler (2022)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The authors argue that assortativeness in genetic advantages is unlikely to be sufficiently high to explain the high multigenerational persistence in educational advantages documented by recent economic literature.

“While this is an active area of research, we would argue that the assortativeness in genetic advantages is unlikely to be sufficiently high to explain the high multigenerational persistence in educational advantages documented by the recent economic literature.”

A higher degree of multigenerational persistence implies an intergenerational persistence parameter λ closer to 1.

“Interpreted from the perspective of the model outlined above, a higher degree of persistence implies an intergenerational persistence parameter λ closer to 1.”

• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.

Multigenerational estimates may provide indirect information on hidden aspects of intergenerational transmission, such as latent skills.

“Second, they may provide indirect information on more hidden aspects of the intergenerational transmission process between parents and children, such as the latent skills S t in the model above.”

• AssumptionThe authors state this as an assumption: True skills S_t are unobserved; observed educational outcome Y_t is related to true skills by Y_t = αS_t + ε_t, with ε_t an i.i.d. random variable.

A comparison of distant kin suggests that sibling correlations still understate the importance of family influences, as most advantages siblings share are not reflected in observables such as years of schooling.

“Moreover, a comparison of distant kin suggests that sibling correlations still understate the importance of family influences, as most of the advantages that siblings share are not reflected in observables such as years of schooling (Collado, Ortuño-Ortín, and Stuhler 2022).”

• cites Collado, Ortuño-Ortín, and Stuhler 2022Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Many schoolchildren affected by the pandemic are likely to enter adult life with fewer skills and lower educational attainment than they would have otherwise.

“Many of the schoolchildren affected by the pandemic are therefore likely to enter adult life with fewer skills and lower educational attainment than they would have otherwise.”

The simple latent factor model can be identified from linked data on just three generations, as λ is identified by the ratio ρ2/ρ1.

“Indeed, this simple latent factor model can be identified from linked data on just three generations, as the intergenerational persistence of skills λ is identified by the ratio ρ 2 /ρ 1 .”

• AssumptionThe authors state this as an assumption: True skills S_t are unobserved; observed educational outcome Y_t is related to true skills by Y_t = αS_t + ε_t, with ε_t an i.i.d. random variable.
• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.

This evidence suggests that assortative mating would need to be far stronger than that reflected in conventional measures, such as the spousal correlation in years of schooling.

“This evidence suggests that assortative mating would need to be far stronger than that reflected in the conventional measures, such as the spousal correlation in years of schooling.”

The dynamic nature of skill acquisition implies that learning losses, once incurred, are subsequently difficult to compensate.

“This dynamic nature of skill acquisition implies that learning losses, once incurred, are subsequently difficult to compensate.”

Carlsson et al. (2015) find that among 18-year-olds, an extra ten days of school instruction increases scores on crystallized intelligence tests by approximately 0.01 of a standard deviation.

“Even among 18-year-olds (for whom we might expect investment effects to be weaker) an extra ten days of school instruction increases scores on crystallized intelligence tests (synonyms and technical comprehension tests) by approximately 0.01 of a standard deviation.”

• cites Carlsson et al. (2015) sourceNot checked — no full text of the source

Assuming linearity, Carlsson et al.'s estimate implies effects of around 0.06 of a standard deviation for a 12-week closure.

“Assuming linearity, this implies effects of around 0.06 of a standard deviation for a 12-week closure.”

• AssumptionThe authors state this as an assumption: The extrapolation from Carlsson et al.'s estimate to a 12-week closure assumes linearity.

A limitation of applying the summer-learning-loss literature to the pandemic is that the impacts are measured over a short period and hence are not necessarily informative for long-term outcomes.

“A limitation of applying the summer-learning-loss literature to the pandemic is that the impacts are measured over a short period of time (from just before to just after summer) and hence are not necessarily informative for long-term outcomes.”

Public health measures in response to the Covid-19 pandemic led to an unprecedented shock to investments in education.

“Public health measures in response to the Covid-19 pandemic have led to an unprecedented shock to investments in education.”

If λ is sufficiently large, multigenerational persistence can be high even if the parent-child correlation ρ1 is only modest.

“Indeed, if λ is sufficiently large, multigenerational persistence can be high even if the parent-child correlation ρ 1 itself is only modest in size.”

• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.

In the same model, the three-generation (grandparent-child) correlation is ρ2 = α^2 λ^2.

“while the three-generation (grandparent-child) correlation is given by ρ 2 = Cov(Y t+2 , Y t ) Var(Y t ) = α 2 Cov(S t+2 , S t ) = α 2 λ 2 .”

• AssumptionThe authors state this as an assumption: True skills S_t are unobserved; observed educational outcome Y_t is related to true skills by Y_t = αS_t + ε_t, with ε_t an i.i.d. random variable.
• AssumptionThe authors state this as an assumption: Skills evolve over generations according to S_{t+1} = λS_t + ν_t, with ν_t an i.i.d. random variable and 0 < λ < 1.
• AssumptionThe authors state this as an assumption: The variances of Y_t and S_t are standardized to one.

Fitzpatrick, Grissmer, and Hastedt (2011) estimate a drop of around 0.3 of a standard deviation in math scores and 0.4 in reading scores as the result of a 12-week school closure.

“Fitzpatrick, Grissmer, and Hastedt (2011) estimate stronger impacts for the early years of schooling, implying a drop of around 0.3 of a standard deviation in math scores and 0.4 in reading scores as the result of a 12-week school closure.”

• cites Fitzpatrick, Grissmer, and Hastedt (2011) sourceNot checked — no full text of the source

Eyles and Eliott Major (2021) show that in the fall of 2020, localized measures led to nine days of missed schooling in the poorest areas of the United Kingdom compared to only two days in the most affluent municipalities.

“Eyles and Eliott Major (2021) show that in the fall of 2020, these localized measures led to nine days of missed schooling in the poorest areas of the United Kingdom compared to only two days in the most affluent municipalities.”

• cites Eyles and Eliott Major (2021)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Lavy (2015) finds that disadvantaged children are more strongly affected by cross-country differences in instruction time.

“Lavy (2015), for instance, finds that disadvantaged children are more strongly affected by cross-country differences in instruction time.”

• cites Lavy (2015) sourceNot checked — no full text of the source

The results of Engzell et al. (2021) and Maldonado and De Witte (2020) suggest that school closures during the pandemic had greater effects on test scores than one might have expected based on extrapolations from prior evidence.

“The results of Engzell, Frey, and Verhagen (2021) and Maldonado and De Witte (2020) suggest that school closures during the pandemic had greater effects on test scores than one might have expected based on extrapolations from prior evidence.”

Cornelissen and Dustmann (2019) find large effects of the effective length of the first school year on cognitive and noncognitive outcomes at the end of the first school year, implying a fall of around 0.2 of a standard deviation in test scores as a result of a 12-week school closure.

“Cornelissen and Dustmann (2019) see large effects of the effective length of the first school year on cognitive and noncognitive outcomes at the end of the first school year, implying a fall of around 0.2 of a standard deviation in test scores as a result of a 12-week school closure.”

• cites Cornelissen and Dustmann (2019)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

This evidence suggests that variation in the incidence of school closures could exacerbate educational inequalities.

“This evidence suggests that variation in the incidence of school closures could exacerbate educational inequalities.”

Inequalities in access to online learning may in part drive inequalities in the impact of school closure.

“This observation suggests that inequalities in access to online learning may in part drive inequalities in the impact of school closure.”

Halloran et al. (2021) confirm that districts with a greater share of black students and a higher share of students receiving free lunches offered less in-person schooling.

“Halloran et al. (2021) confirm this picture in a sample of 12 states, documenting that districts with a greater share of black students and a higher share of students receiving free lunches offered less in-person schooling.”

• cites Halloran et al. (2021) sourceNot checked — no full text of the source

Halloran et al. (2021) show that proficiency rates in English and math were on average 14 percentage points lower during the pandemic.

“grade, Halloran et al. (2021) show that proficiency rates in English and math were on average 14 percentage points lower during the pandemic.”

• cites Halloran et al. (2021) sourceNot checked — no full text of the source

Students performed worse than if they had simply retained their initial knowledge, suggesting a slide in skills.

“Students performed worse than if they had simply retained their initial knowledge, suggesting a slide in skills.”