Educational mobility across three generations of American women

Economics of Education Review 53 (2016) 72–86

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Educational mobility across three generations of American women Sarah Kroeger, Owen Thompson∗ Department of Economics, University of Wisconsin-Milwaukee, United States

a r t i c l e

i n f o

Article history: Received 27 May 2015 Revised 16 May 2016 Accepted 16 May 2016 Available online 28 May 2016 Keywords: Mobility Education Trends Gender

a b s t r a c t We analyze the intergenerational transmission of education in a three-generation sample of women from the 20th century US. We find strong three-generation educational persistence, with the association between the education of grandmothers and their granddaughters approximately two times stronger than would be expected under the type of first-order autoregressive transmission structure that has been assumed in much of the existing two-generation mobility literature. These findings are robust to using alternative empirical specifications and sample constructions, and are successfully replicated in a second independently drawn data set. Analyses that include males in the youngest and oldest generations produce very similar estimates. A variety of potential mechanisms linking the educational outcomes of grandparents and grandchildren are discussed and where possible tested empirically. © 2016 Elsevier Ltd. All rights reserved.

Introduction Social scientists have a longstanding interest in the extent to which social and economic well-being is transmitted across generations, and a large literature studies the degree of intergenerational mobility across two consecutive generations (see Solon, 1999, and Black & Devereux, 2010, for reviews). However, an emerging literature, which is reviewed in detail below, examines the transmission of earnings, educational attainment, and other characteristics across three or more generations. While extending the study of intergenerational mobility beyond two generations has the potential to substantially enrich our understanding of long-run social mobility, the increased data requirements of such studies have limited the number of contexts for which reliable multigenerational estimates are available.

∗

Corresponding author. Tel.: +1 4142294429. E-mail address: [email protected] (O. Thompson).

http://dx.doi.org/10.1016/j.econedurev.2016.05.003 0272-7757/© 2016 Elsevier Ltd. All rights reserved.

The main contribution of the present study is to assemble a nationally representative sample of approximately 2,0 0 0 American women born in the early 1980s with linked information on the educational outcomes of their mothers and grandmothers, then use this data to estimate the level of educational persistence across three generations in 20th century United States. Only a small number of studies have evaluated multigenerational mobility levels in contemporary Western economies, and most existing work has either focused on European countries with greater data availability, or on occupational class measures rather than education. The present study is also among the first to focus explicitly on the multigenerational mobility levels of women. The paper’s main finding is that there was a high degree of multigenerational educational persistence in the studied context. In particular, our estimates of threegeneration educational associations are approximately twice as strong as those predicted by assuming that transmission follows a simple first-order autoregressive – or AR(1) – structure and then multiplicatively extrapolating two-generation transmission estimates. To demonstrate the

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reliability of our findings, we successfully replicate the baseline results in a second, independently drawn national sample, and present robustness checks that suggest our results are likely not due to the mismeasurement of education and are not sensitive to using alternative empirical specifications or sample constructions. While the structure of our data leads us to focus primarily on transmission within all-female lineages, we are also able to estimate multigenerational transmission strength in limited samples that also include men, and results using these samples are very similar to our baseline findings for women. The remainder of the paper proceeds in six sections. Section 1 briefly reviews relevant previous research; Section 2 describes the utilized data; Section 3 presents our baseline findings; Section 4 conducts a number of robustness checks and auxiliary analyses; Section 5 discusses and tests various mechanisms that may help to explain our findings; Section 6 concludes. 1. The current state of the literature The literature studying socioeconomic mobility across three or more generations is much less developed than the literature on two-generation mobility, owing primarily to data constraints, but several existing studies do analyze multigenerational mobility. Such estimates first appeared in the literature several decades ago, and a number of more recent studies have also estimated transmission for various socioeconomic characteristics and in a variety of historic and geographic contexts. With respect to early multigenerational studies, (Hodge, 1966) used data on the occupations of American men to estimate three-generation transition probabilities, and found that while occupational transition probabilities differed from those predicted by a simple Markov model, the associations in the occupations of grandfathers and grandsons were not quantitatively large after accounting for the occupations of fathers. This led Hodge to conclude that multigenerational models with a “memory” of only one generation were generally adequate, since “grandfather’s occupation does not have any appreciable direct effect upon a person’s occupation beyond the indirect effect induced by its influence upon father’s occupation” (p. 25). Other relatively early multigenerational estimates included Behrman & Taubman (1989), (Peters, 1992) and (Warren & Hauser, 1997), with all of these studies generally failing to find large three-generation effects. Specifically, Behrman & Taubman (1989) used data from the National Research Council Twin Sample and found that in OLS estimation the effect of grandparent’s schooling on grandchild’s schooling – conditional on parent’s schooling – is positive but small in magnitude and statistically insignificant. Similarly, (Warren & Hauser, 1997) used data from the Wisconsin Longitudinal Survey and regressed the occupational status of children on the education and occupational statuses of both parents and all four grandparents, finding grandparent effects that were generally positive but typically not statistically significant. Finally, (Peters, 1992) focused primarily on two-generation income and earnings transmission in the US, but also presented results that regressed child income or earnings on the income or

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earnings of their parents and the educational attainment of their grandparents, finding no significant conditional effect of grandparent’s education on child income or earnings. A more recent set of papers has reexamined the issue of multigenerational mobility, and in contrast to early studies has typically found strong three-generation transmission. For instance (Chan & Boliver, 2013) found strong three-generation persistence in occupational prestige in Britain; (Lindahl, Palme, Sandgren Massih, & Sjögren, 2015) (forthcoming) used exceptional Swedish data to document significant three-generation effects for income and four-generation effects for education; (Johnston, Schurer, & Shields, 2013) found strong three-generation persistence in mental health outcomes in the US; (Zeng & Xie, 2014) documented a strong association between the education of Chinese grandparents and their co-residing grandchildren (but not among non-co-residing children); and (Hertel & Groh-Samberg, 2014) found low levels of occupational class mobility across three generations in both Germany and the US. Additionally, widely discussed work by Clark (2014) used rare surnames to estimate multigenerational mobility levels across multiple centuries and in various countries and reported very high persistence levels, though the reliability of Clark’s conclusions has been questioned (see the discussion in Solon, 2014).1 A smaller number of recent papers fail to find significant associations across three generations. These include (Lucas & Kerr, 2013), who reported three-generation income and earnings mobility estimates in a 20th century Finnish sample; (Erola & Moisio, 2007), who also used Finnish data and find small conditional effects of grandparent’s social class; and (Jæ ger, 2012), who used data from the Wisconsin Longitudinal Survey and found that various socioeconomic characteristics of grandparents (as well as other extended family members) typically do not have strong associations with children’s educational outcomes. There are a number of possible explanations for the divergence in findings across these previous studies. Early studies that did not find large multigenerational effects, such as Behrman & Taubman (1989) and (Warren & Hauser, 1997), often estimated separate coefficients for each parent and each available grandparent (up to six separate coefficients), and since these variables are highly collinear the estimates may become statistically insignificant, especially in the relatively small available samples.2 The methodological approaches of the cited papers also vary significantly, which could partially account for the disparate findings. Perhaps most importantly though, true multigenerational mobility levels may simply not be

1 Several current working papers also find three-generation associations in excess of those implied by AR(1) transmission, including (Long & Ferrie, 2012; Olivetti, Paserman, & Salisbury, 2013; Sauder, 2006) and (Braun & Stuhler, 2015). 2 Braun and Stuhler (2015) also find that in most instances the association between the educational attainment of grandparents and grandchildren is substantially reduced when they condition on the educational attainment of both parents in the intermediate generation. The authors interpret this as suggesting that unconditional grandparent-grandchild associations partially reflect bias from the omission of relevant parental characteristics. We discuss how conditioning on both mother and father education impacts our own three-generation estimates in Section 5 below.

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constant across different contexts, a point emphasized by Solon (2014). Instead, it is highly plausible that the level of three-generation mobility depends on the studied time period, geographic location, sample characteristics, and outcome measures, and the likelihood of such heterogeneity underscores the importance of producing estimates from as many contexts as possible. In summary, early empirical research on multigenerational mobility typically found small three-generation effects, while a larger set of more recent studies have typically - but not always - found significant multigenerational effects for various socioeconomic outcomes and in a number of historical and geographic contexts. The present paper adds to this emerging literature by being among the first to estimate three-generation mobility levels within the US, whereas the majority of previous research used Western and Northern European data, where there are well established differences with the US population in twogeneration mobility levels. We also add to the literature by utilizing nationally representative data sets, whereas most previous US based work used more specialized and homogenous data sources, by studying educational attainment whereas most existing three-generation work (especially from the US) has analyzed occupational class, and by focusing explicitly on the multigenerational mobility levels of women. 2. Data Our primary data source is the 1997 National Longitudinal Survey of Youth (NLSY97), which was initiated in 1997 and has since fielded 15 annual interviews with approximately 9,0 0 0 members of the 1980–1984 birth cohorts. The most recently available data is from the 2011 wave, when respondents were ages 27–31. In each survey wave all respondents were asked to report the highest grade they had completed and the highest degree they had been awarded. In our baseline estimates we measure each respondent’s education as of age 27, even if they were observed at older ages as well. We take this approach because most individuals have completed formal schooling by age 27 and it allows us to measure education consistently across individuals from different cohorts, and as a robustness check we demonstrate that our results are substantively unchanged if we restrict our analysis to education observed at older ages.3 Because NLSY97 respondents were ages 12–16 when the survey began, almost all participating youths were living non-independently at baseline, typically with their parents, and in the inaugural wave of the NLSY97 a separate survey instrument was completed by a resident parental figure. The survey enumerators made an explicit effort to 3

Education at age 27 is sometimes missing due to individuals not being interviewed at the NLSY97 wave occurring when they were 27. If education at age 27 is not observed but education at an age younger than 27 and an age older than 27 are both observed and are equal to each other, we set education at age 27 equal to this value. If education at 27 is neither observed directly nor directly implied by other observations, we set education at age 27 equal to education at the next available observation. Simply excluding observations with education at age 27 missing does not meaningfully change the results we present below.

have biological mothers complete the parent survey when present, and were able to do so in over 82% of the cases. The parent survey included a question asking the highest grade of schooling that the mother had completed, as well as the highest grade completed by her own parents - i.e. the grandparents of the primary NLSY97 respondent - which allows us to observe educational attainment in three consecutive generations of women. We retain cases in which all three generations had valid education data and were US born, which creates a working sample of 2,034 three-generation female educational lineages.4 One obvious limitation of the data is that, because the parent survey was typically completed by the mothers of the primary NLSY97 respondents, the data does not contain information on the educational attainment of three consecutive generations of men. While this feature of the data leads us to focus primarily on matrilineal transmission, the NLSY97 does contain information on the educational attainment of men in the youngest generation (who were primary NLSY97 respondents themselves) and the education of maternal grandfathers (as reported by mothers in the parent survey), as well as youth-reported information on paternal education, allowing us to estimate a limited set of multigenerational transmission patterns involving men. We present these estimates in Section 3.3 below, and they are very similar to findings with all-female lineages, suggesting that our main findings may have applicability in a broader population, though we make this inference only cautiously given the incomplete nature of the available data on men. A number of valid concerns can also be raised related to sample construction and the measurement of educational attainment in the NLSY97 data. For instance grandmother education is reported by the mother generation rather than by the grandmothers themselves and data on three generations can only be constructed when mothers are coresiding with their daughters at ages 12–16, among other potential issues. While we acknowledge that substantial bias stemming from these and related data issues cannot be ruled out, we do undertake several strategies to mitigate this risk. One of these strategies is to replicate our baseline findings using an independent data set, specifically the 1979 National Longitudinal Survey of Youth (NLSY79) and the linked NLSY79-Young Adult survey (NLSY79YA). Importantly, the three-generation sample from the NLSY79/NLSY79-YA was constructed via a fundamentally different structure than the NLSY97 and additionally contains self-reported education for all three generations. The NLSY79/NLSY79-YA data is described in detail in Section 4. For reasons discussed there the NLSY97 remains

4 The full NLSY97 sample contained 4,385 female respondents. Sample attrition is primarily due to respondents leaving the sample before age 27, cases where someone other than the biological mother completed the parent survey, cases where the responding mother did not know the educational attainment of her own mother, and families where one of the women was foreign born. Non-native women were excluded because education obtained abroad cannot generally be measured comparably to education completed in the US. However, results with immigrants included are broadly similar to those presented below and are available upon request.

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Table 1 Mean female educational attainment by generation.

Grandmothers Mothers Daughters

Years of schooling

College graduate(%)

Some college(%)

High school graduate(%)

Less than high school(%)

Birth year range

10.8 13.3 14.2

10.7 22.3 36.3

10.0 29.6 29.5

43.3 34.8 21.1

35.9 13.3 13.0

1915–1944 1947–1965 1980–1984

Sample contains 2,034 daughter–mother–grandmother triples. Reported birth year ranges are the 5th–95th percentiles in the corresponding generation. Grandmother’s and mother’s education is final attainment. Daughter’s education is measured at age 27. NLSY custom sampling weights are applied.

our preferred data source, but we view replication as a rigorous check of bias arising from sample construction or educational mismeasurement. Section 4 additionally presents a series of robustness checks using the NLSY97 that suggest our baseline results are unlikely to be an artifact of data quality issues. Table 1 reports descriptive statistics on the educational attainment of each generation in our base NLSY97 sample of women, as well as the range of birth years for each generation. For ease of exposition, the results in Table 1 (as well as subsequent results) refer to the oldest generation in our data as “grandmothers,” the next oldest generation as “mothers” and the youngest generation as “daughters.” Table 1 exhibits the well-documented upward trend in female educational attainment over this period. For instance the mean years of education completed increases from 10.8 among the cohorts of grandmothers born from 1915–1944, to 13.3 among the cohorts of mothers born from 1947– 1965, to 14.2 among the cohorts of daughters born from 1980–1984. Large scale increases in female college attendance and graduation rates are also observed. We note that the education levels reported in Table 1 closely resemble those found in large national cross sections of the corresponding birth cohorts (Bailey, Dynarski, Duncan, & Murnane, 2011; Goldin, 2006), which tentatively suggests that despite the data limitations noted above, our sample is reasonably representative of women from these generations and contains broadly accurate measures of educational attainment. 3. Baseline results We measure educational mobility using both regression specifications that summarize intergenerational persistence with a single point estimate as well as by examining the distribution of education in more recent generations conditional on the education of previous generations. This conditional distribution gives the probability of transitioning between multiple points in the educational distribution over the course of two and three generations. Results from these two approaches are presented in turn. 3.1. Intergenerational regression estimates We begin by estimating two-generation mobility models similar to those used in the extensive existent educational mobility literature. These estimates serve as a baseline that can be compared both to previous work and to our subsequent three-generation results. Specifically, we estimate OLS regression models of the following form:

E ducation f g = α + β1 E ducation f (g−1) + γy + ε f g

(1)

where Educationfg denotes the educational attainment of the woman from family f in generation g and Education f (g−1 ) denotes the educational attainment of the woman from family f in the previous generation. To account for secular time effects within generations (for example the secular effect of a “mother” being born in 1947 as opposed to 1965) we also include full sets of birth year indicators for the included generations, denoted γ y , though we show below that our results are very similar if these fixed effects are omitted. Finally, α is a populationwide constant and ε fg is an idiosyncratic error term. Because we are analyzing the educational attainment of women over the course of approximately 100 years, our education measures need to take into account the largescale increase in female educational attainment that occurred over the study period. The basic issue is that years of education do not constitute comparable units across generations. In particular, a year of education completed by a women born in 1920 likely carries a different meaning than a year of education completed by a women born in 1980. To measure education in consistently interpretable units, we convert our years of education variable to a zscore by subtracting the generation-specific mean level of education from each observation and then dividing by the generation-specific standard deviation. This allows us to interpret the coefficients from Eq. (1) in a manner similar to simple correlation coefficients, specifically as the standard deviation change in the education of a women from generation g that is associated with a standard deviation change in the education of her mother and/or grandmother. For completeness, Section 4 additionally reports results from models where education is measured in years. Columns 1 and 2 of Table 2 show results from estimating Eq. (1) for both possible two-generation samples, specifically the association between mother’s education and grandmother’s education and the association between daughter’s education and mother’s education. The results in Column 1 indicate that a one standard deviation increase in grandmother’s education is associated with a .320 standard deviation increase in mother’s education, while the results in Column 2 indicate that a one standard deviation increase in mother’s education is associated with a .350 standard deviation increase in daughter’s education. These results suggest minimal secular trends in mobility rates over our study period, and closely resemble previous US educational transmission estimates (Behrman & Rosenzweig, 2002; Black & Devereux, 2011; Hertz et al., 2007; Huang, 2013). The remainder of Table 2 presents results that measure educational transmission across three generations. Before discussing the empirical estimates, it is valuable to

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Table 2 Intergenerational regression results. (1) Mother education

Observations R-squared

(3) Daughter education

(4) Daughter education

0.231∗∗∗ (0.023) 2,034 0.163

0.299∗∗∗ (0.029) 0.127∗∗∗ (0.025) 2,034 0.251

0.350∗∗∗ (0.027)

Mother education Grandmother education

(2) Daughter education

0.320∗∗∗ (0.023) 2,034 0.262

2,034 0.206

Column headings indicate the dependent variable. Educational attainment is measured using z-scores, and the reported coefficients can therefore be interpreted in standard deviation units. All models contain full sets of birth year dummies for individuals from the included generations. Robust standard errors are in parentheses. Sample size denotes number of daughter–mother–grandmother triples. Grandmother’s and mother’s education is final attainment. Daughter’s education is measured at age 27. NLSY custom sampling weights are applied.

consider on a theoretical basis what would be expected if educational transmission was dictated by the type of process that has been implicitly or explicitly assumed in much of the existing intergenerational mobility literature. To do so, begin by considering a simple theoretical two-generation transmission model similar to the ones estimated empirically above:

E ducation2 = b0 + b1 E ducation1 + e

(2)

where b0 and b1 are constants and e is an idiosyncratic error term. In this specification, educational attainment in generation 2 depends on education in generation 1 but not on education in higher order generations. A similar equation can be used to describe transmission to generation 3 from generation 2:

E ducation3 = b˜0 + b˜1 E ducation2 + e˜

(3)

where the ˜ notation reflects the fact that transmission strength may vary quantitatively across generations without altering the qualitative transmission structure. A key feature of this transmission model is that it has a “memory” of only one generation, and transmission processes with this feature are generally referred to as Markovian. A more specific case is where b1 < 1, so that education is mean reverting across generations, and this case is referred to as first-order autoregressive transmission, or AR(1).5 If educational transmission is dictated by such an AR(1) process, then the relationship between the educational attainment of generations 3 and 1 can be obtained simply by substituting Eq. (3) into Eq. (2) and multiplying through, producing the following:

Education3 = α + (b1 × b1˜ )Education1 + u

(4)

where α is a composite constant and u is a composite error term. In words, under an AR(1) transmission process the relationship between the education of grandmothers and daughters is simply the product of grandmother– mother transmission (b1 ) and mother-daughter transmission (b˜1 ). The most important implication of this framework is that even relatively large two-generation correlations would imply a high degree of mobility over three or four generations. For instance, a two-generation correlation 5 An additional special case occurs when the parameter b1 is less than one and is constant across time periods, which is often referred to as a stationary AR(1) process.

of .3 would imply a modest three-generation correlation of .09 and a near negligible four-generation correlation of .027. Applying these extrapolations to the numerical estimates reported in Columns 1 and 2 of Table 2, an AR(1) transmission process would generate a grandmother– daughter association of .320 × .350 = .112. A closely related prediction of the AR(1) framework is that if daughter education is regressed on both mother’s and grandmother’s education simultaneously, only mother’s education will be statistical or substantively significant, since grandmothers affect daughters only via their influence on the intermediate generation. While this sort of extrapolation from twogeneration estimates is observed on occasion,6 its accuracy is ultimately an empirical question that must be tested with three generations of data. The remaining columns of Table 2 conduct such tests, and the results generally do not support the appropriateness of extrapolating two-generation transmission estimates implied by an AR(1) model. Specifically, Column 3 reports results from estimating a regression model similar to Eq. (1) but with daughter education as the dependent variable and grandmother education as the independent variable of interest. The estimated coefficient is .231, more than twice as large as the .112 that would be expected under AR(1) transmission. The final column of Table 2 reports results from estimating a modified version of Eq. (1) that simultaneously includes both mother’s education and grandmother’s education as independent variables. In contradiction to the prediction of an AR(1) transmission process of zero conditional grandmother effect, grandmother and granddaughter education have a statistically significantly correlation of .127 after conditioning on mother’s education. 3.2. Conditional distributions One shortcoming of intergenerational correlations is that they impose linearity on the relationship between 6 For instance (Becker & Tomes, 1986) use multiplicative extrapolation of two-generation income transmission estimates to assert that “almost all earnings advantages and disadvantages of ancestors are wiped out in three generations” (p. S28) while the popular undergraduate labor economics textbook by Borjas (2013) gives several numerical examples of multiplying two-generation estimates to infer three-generation mobility levels (see Section 7.6).

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Fig. 1. Educational distributions by grandmother education.

educational attainment across generations, but transmission strength may vary at different points in the educational distribution. This issue is perhaps especially important in the current context given the economic and social importance of female college graduation rates specifically. A common alternative mobility measure is the transition probability matrix, which reports the probabilities of transitions between specific points in the educational distribution across generations. Fig. 1 reports information comparable to what is contained in transition probability matrices by showing histograms of educational outcomes in the mother and daughter generations split by grandmother education. For presentational clarity, we collapse the educational attainment of mothers and daughters into four practically important categories: less than high school, high school graduate, some college, and college graduate.7 Because postsecondary schooling among women in the grandmother generation was a relative rarity, we collapse educational attainment in this generation into three categories corresponding to those with less than 12 years of schooling, those with exactly 12 years of schooling, and those with more than 12 years of schooling. Panel A of Fig. 1 shows histograms of educational attainment in the mother generation. The first histogram is for the full sample of mothers, and shows that approximately 13% of mothers did not complete high school, 35% were high school graduates, 30% attended less than four years of college, and 22% were college graduates.

The remaining histograms split the mother sample by grandmother education. In the absence of intergenerational transmission, these conditional histograms would be identical to that of the full sample, and unsurprisingly this is not the case. For instance, women in the mother generation whose own mothers did not complete high school transition to being college graduates with a probability of just .11, while for women whose own mothers were high school graduates this probability is .18 and for women whose own mothers had any post-secondary education it is .47. Panel B of Fig. 1 estimates three-generation transition probabilities by repeating this exercise for the daughter generation. The histogram corresponding to the full population of daughters shows substantial gains relative to the previous generation, with especially notable increases in the college graduation rate. However, the conditional histograms indicate that these gains were disproportionately concentrated among women with relatively well educated grandmothers. For example, women in the daughter generation whose grandmothers did not complete high school transitioned to being college graduates themselves with a probability of .24, but those whose grandmothers were high school graduates had a .37 probability of graduating from college, and those whose grandmothers had any post-secondary education graduated from college with probability .55.

7 For mothers we define these groups based on reported years of education completed. For daughters we use reports of highest degree received, counting GED recipients as having less than a high school diploma and counting associates degree recipients as having some college. The basic nature of the results in Fig. 1 are not sensitive to the utilized classification of GED and associates degree recipients.

As noted in Section 2 above, while we are only able to observe educational attainment in three consecutive generations for women, the NLSY97 does contain information on the educational attainment of men in the youngest generation (i.e. sons) and in the oldest generation (i.e. maternal

3.3. Transmission estimates with sons and paternal grandfathers

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Table 3 Estimates including males. (1) Daughter education

(2) Son education

(3) Son education

Mother education

AR(1)-based prediction Observations R-squared

(5) Son education

(6) Son education

0.300∗∗∗ (0.030)

0.338∗∗∗ (0.024) 0.119∗∗∗ (0.023)

0.330∗∗∗ (0.024)

0.246∗∗∗ (0.022)

Grandmother education Grandfather education

(4) Daughter education

0.229∗∗∗ (0.024) .137 1,856 0.153

0.14 2,115 0.140

0.236∗∗∗ (0.022) .141 1,911 0.121

0.104∗∗∗ (0.025) – 1,831 0.251

– 2,078 0.268

0.103∗∗∗ (0.022) – 1,882 0.248

Column headings indicate the dependent variable. Educational attainment is measured using z-scores, and the reported coefficients can therefore be interpreted in standard deviation units. Reported AR(1) based predictions are the product of the transmission coefficients from the relevant two-generation models. All grandparents are maternal grandparents. All models contain full sets of birth year dummies for individuals from the included generations. Robust standard errors are in parentheses. Grandmother’s, grandfather’s and mother’s education is final attainment. Daughter’s and son’s education is measured at age 27. NLSY custom sampling weights are applied.

grandfathers). Given this, the NLSY97 actually allows for the estimation of four distinct patterns of three-generation educational transmission: daughter–mother–grandmother (as in the main results), daughter–mother–grandfather, son–mother–grandmother, and son–mother–grandfather.8 Educational transmission estimates within each of the lineages that include men are presented in Table 3. Columns 1–3 report the results of regressing education in the child generation on education in the grandparent generation directly (without controlling for maternal education), while Columns 4–6 report the results of regressing child education on mother and grandparent education simultaneously. As in the baseline estimates from Table 2, these models include birth year indicators for the relevant individuals and apply individual level sampling weights. For the estimates in Columns 1–3, we additionally report the product of coefficients from models estimating grandparent–parent and parent–child associations, which estimates the grandparent–child association that would be expected under AR(1) transmission.9 The results in Table 3 indicate that three-generation transmission patterns are very similar across all estimable lineages, and uniformly depart from the expectations of AR(1) transmission. For instance, in the baseline female results from Table 2 we found that a standard deviation increase in the educational attainment of grandmothers was associated with a .231 standard deviation increase in the educational attainment of daughters, while Columns 1–3 of Table 3 indicate that the analogous estimates are .229 for daughter–grandfather pairs, .246 for son–grandmother pairs, and .236 for son–grandfather pairs. In all cases the estimated relationships substantially exceed those predicted by AR(1) transmission. Likewise, the estimates reported in Columns 4–6 all find large and statistically significant grandparent effects after conditioning on mother

education that are very similar to the baseline all-female results from Table 2.10 These findings provide suggestive evidence that our main findings, based on women, apply to a broader set of populations that include men, though such a conclusion can be drawn only tentatively given that we are not able to directly estimate transmission involving fathers or paternal grandparents. The uniformity of transmission strength across different types of three-generation lineages is also useful in analyzing which type of transmission mechanism best explains our baseline findings, a point we return to in Section 5 below.

8 The main NLSY97 respondents also reported information on the education of their fathers, and we present results that incorporate this information in Section 5.1 below. 9 Note that to conserve space only the product of the grandparent– parent and parent–child coefficients are reported, not the coefficients themselves.

10 It is also possible to estimate models that simultaneously include mother education, maternal grandmother education, and maternal grandfather education. In such models the coefficient on maternal education is virtually unchanged from the levels reported in Table 4, while the coefficients for both grandmother and grandfather education decline to approximately .075. Full results are available upon request.

4. Robustness and replicability Before discussing the possible interpretations or implications of the findings in Section 3, it is important to establish their reliability. In this section we present results from a number of basic robustness checks and conduct a replication exercise using a second, independently drawn national sample. For brevity we focus on demonstrating the reliability of the intergenerational regression estimates in our all-female sample, but results when using conditional distributions rather than regressions and in samples that include men are very similar to those presented here and are available upon request. 4.1. Basic robustness One potential concern is that our results are sensitive to the inclusion of birth year fixed effects as controls. Panel A of Table 4 reports results from re-estimating our four baseline models excluding these controls, and while there are modest differences – specifically an increase in the magnitude of the mother–daughter coefficient in Column 2 – the basic findings are unchanged. In particular, we continue to

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Table 4 Basic robustness. (1) Mother education Panel A: no controls Mother education Grandmother education Observations Panel B: unweighted Mother education Grandmother education Observations Panel C: daughter education at age 30 Mother education Grandmother education Observations Panel D: education measured in years Mother education Grandmother education Observations Panel E: fertility weights Mother education Grandmother education Observations Panel F: white sample Mother education Grandmother education Observations Panel G: non-white sample Mother education Grandmother education Observations

(2) Daughter education

(3) Daughter education

(4) Daughter education

0.215∗∗∗ (0.024) 2,034

0.387∗∗∗ (0.027) 0.092∗∗∗ (0.024) 2,034

0.228∗∗∗ (0.021) 2,034

0.312∗∗∗ (0.026) 0.125∗∗∗ (0.023) 2,034

0.233∗∗∗ (0.037) 743

0.246∗∗∗ (0.052) 0.146∗∗∗ (0.040) 743

0.164∗∗∗ (0.017) 2,034

0.352∗∗∗ (0.034) 0.090∗∗∗ (0.018) 2,034

0.232∗∗∗ (0.021) 2,034

0.315∗∗∗ (0.025) 0.125∗∗∗ (0.022) 2,034

0.231∗∗∗ (0.032) 1,245

0.272∗∗∗ (0.036) 0.137∗∗∗ (0.033) 1,245

0.166∗∗∗ (0.036) 789

0.333∗∗∗ (0.045) 0.102∗∗∗ (0.036) 789

0.415∗∗∗ (0.025) 0.319∗∗∗ (0.024) 2,034

2,034 0.367∗∗∗ (0.024)

0.320∗∗∗ (0.022) 2,034

2,034 0.300∗∗∗ (0.051)

0.290∗∗∗ (0.037) 743

743 0.413∗∗∗ (0.032)

0.193∗∗∗ (0.014) 2,034

2,034 0.370∗∗∗ (0.023)

0.323∗∗∗ (0.022) 2,034

2,034 0.325∗∗∗ (0.034)

0.321∗∗∗ (0.031) 1,245

1,245 0.373∗∗∗ (0.042)

0.223∗∗∗ (0.036) 789

789

Column headings indicate the dependent variable. All models contain full sets of birth year dummies for individuals from the included generations except for those in Panel A, which contain no controls. All models apply NLSY custom sampling weights except for those in Panel B, which are unweighted, and those in Panel E, which apply fertility based inverse probability weights as described in Section 4.1 of the text. Grandmother’s and mother’s education is final attainment, while daughter’s education is measured at age 27 except for in Panel C, where it is measured at age 30. Educational attainment is measured using z-scores except in Panel D, where education is measured in years. Robust standard errors are in parentheses. Sample size denotes number of daughter–mother–grandmother triples.

find a strong direct three-generation correlation (Column 3) and a significant conditional grandmother effect (Column 4). Another possible specification related concern is the application of sampling weights. Especially given that we are using a subsample of NLSY97 participants, the appropriateness of applying these weights is unclear. Panel B of Table 4 presents results that forgo sampling weights, and they are virtually identical to the baseline results from Table 2. In our baseline models we measured educational attainment in the daughter generation as of age 27, primarily because this maximized our sample size and most individuals complete their formal schooling by age 27. However, this is not universally the case, especially for the increasing number of women pursuing graduate degrees. To test

the sensitivity of our results to late completion of schooling, Panel C of Table 4 re-estimates our baseline specifications with the subsample of daughters for whom we observe education as of age 30. While this restriction substantially reduces the sample size, the basic nature of the results is unchanged, suggesting that in this case educational attainment at age 27 is a good proxy for ultimate attainment.11 As discussed above, our baseline models were estimated with education measured as z-scores, which allowed for a consistent interpretation of coefficients despite

11 We have also estimated models that exclude daughters who were currently enrolled in school and the results are not substantively changed.

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strong secular trends over the study period. For completeness Panel D of Table 4 reports results from re-estimating our specifications using education measured in years. The most noticeable change from this rescaling is that the grandmother–mother coefficient in Column 1 becomes much smaller than the mother–daughter coefficient in Column 2. Specifically, a year increase in grandmother education is associated with a .193 year increase in mother education, while a year increase in mother education is associated with a .413 year increase in daughter education. This reflects the fact that earlier cohorts of women had lower and less variant levels of educational attainment than later cohorts, causing the value of an educational year to decline over time when measured in standard deviation units. However, the three-generation findings with education measured in years are substantively identical to our baseline findings. Specifically, the two-generation estimates with education measured in years imply a predicted grandmother–daughter association of .193 × .413 = .08, but we observe an association of .164, which is again approximately twice the magnitude predicted by AR(1) transmission. Also, a significant grandmother–daughter association of .09 remains after controlling for maternal attainment. These results demonstrate that for present purposes conducting the analysis in z-scores is a matter of presentational convenience only. Another potentially important consideration is that because women with higher educational attainment have lower average fertility levels, the women in our sample consist disproportionately of the descendants of relatively less-educated grandmothers and mothers. Put differently, we have measured educational mobility within the threegeneration sets of women that actually exist, but education also affects which types of three-generation sets are formed. This raises the question of whether the high level of three-generation educational persistence we observe results from population-level differences brought about by differential fertility patterns (see Lam, 1986). This question can be framed as a counterfactual by asking what level of educational mobility would havebeen realized if fertility patterns did not vary by educational attainment, so that all educational lineages were equally represented in the youngest generation of our sample. To help address this issue, we first use Census and CPS data to calculate the total fertility rates of women with varying levels of educational attainment from the cohorts that correspond to the grandmother and mother generations in our data, and then use these fertility levels to calculate the approximate probability of observing a granddaughter with a given combination of grandmother and mother education.12 As a numerical example of this calculation, the total fertility rate of women with no formal schooling in the grandmother and mother generations were 4.61 and 3.54, respectively. If we assume that 50% of surviving children are female, then the probabil-

12 Specifically, grandmother fertility information is calculated from from US Census 1960–1990 using the 1914–1945 birth cohorts while mother fertility information is calculated from the Current Population Survey Fertility Supplement 1992–2014 using the 1946–1966 birth cohorts. In both cases women sampled are aged 45 and older.

ity that this educational lineage will produce at least one woman in the third generation is equal to the probability of the grandmother having at least one female offspring multiplied by the probability of the mother having at least one female offspring, which is given by [1 − ( 12 )4.61 ] × [1 − ( 12 )3.54 ] ≈ .877. In contrast, the total fertility rates for college-educated women in the grandmother and mother generations were 3.19 and 1.63, respectively, and the probability that this educational lineage will produce at least one female in the third generation is [1 − ( 12 )3.19 ] × [1 − ( 12 )1.63 ] ≈ .603. We repeat this procedure for each possible permutation of grandmother and mother education, then re-estimate our baseline three-generation models weighting the observations by the inverse of these probabilities. The intuition behind this approach is that if differential fertility causes us to observe relatively few women with college-educated mothers and grandmothers, we can correct for this selection by placing more weight on the cases of this kind that we do observe, and vice versa. The inverse probability weighting procedure therefore yields estimates of what transmission strength would have been if there were no fertility differences by education, so that all educational lineages had equal representation in the youngest generation. Inverse probability weighted regression results are reported in Panel E of Table 4, and they are very similar to baseline findings from Table 2, with most point estimates numerically identical to two decimal places. This suggests that although fertility does differ by education, such fertility differences are not a quantitatively important determinant of the three-generation persistence documented in Section 2. A final robustness-related issue is that our baseline models combined women from all racial and ethnic backgrounds, but it is well known that both mean levels of education and intergenerational mobility vary by race and ethnicity in the US (Bhattacharya & Mazumder, 2011; Kearney, 2006). To partially allow for racial and ethnic heterogeneity in our results, Panels F and G of Table 4 show results from re-estimating our baseline models using the white and non-white portions of the sample, respectively.13 While some modest differences in transmission strength are observed across the white and non-white subpopulations, strong three-generation transmission is present in both groups. Although a more thorough analysis of transmission within subpopulations using larger samples would be desirable, the results in Panels F and G suggest that our findings are broadly applicable to both white and non-white US populations. 4.2. Replicability While the robustness checks presented above address a variety of potential issues, the most scientifically rigorous test of robustness and reliability is replication in an independently drawn sample. Such a replication is difficult to

13 Race and ethnicity are defined using a self-report in the daughter generation. Unfortunately sample size limitations prevent us from analyzing more specific racial and ethnic minority groups.

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Table 5 Replication of baseline results. NL SY79/NL SY79-YA Mother education (1) Mother education Grandmother education 0.369∗∗∗ (0.040) Observations 998 R-squared 0.257

Daughter education (2)

NLSY97 Daughter education (3)

Daughter education (4)

0.266∗∗∗ (0.043) 998 0.236

0.243∗∗∗ (0.047) 0.178∗∗∗ (0.044) 998 0.290

0.316∗∗∗ (0.045)

998 0.181

Mother education (5)

Daughter education (6)

Daughter education (7)

0.371∗∗∗ (0.026) 0.317∗∗∗ (0.023) 2,178 0.260

2,178 0.226

0.237∗∗∗ (0.023) 2,178 0.163

Daughter education (8) 0.322∗∗∗ (0.027) 0.125∗∗∗ (0.024) 2,178 0.266

Columns 1–4 use data from the NLSY79 and the linked NLSY79 Young Adult sample, while columns 5–8 use data from the NLSY97. Education in the youngest generation is measured as of age 24 in both data sets. Column headings indicate the dependent variable. Educational attainment is measured using z-scores, and the reported coefficients can therefore be interpreted in standard deviation units. All models contain full sets of birth year dummies for individuals from the included generations. Robust standard errors are in parentheses. Sample size denotes number of daughter–mother–grandmother triples. Custom sampling weights are applied in both samples.

implement in the present case, as it requires data collection that spans three generations over a reasonably large female sample of 20th century cohorts. One data set that meets these basic requirements is the 1979 National Longitudinal Survey of Youth (NLSY79) and the corresponding Young Adult survey (NLSY79-YA). The main NLSY79 survey began in 1979 with a nationally representative sample of 12,686 individuals who were born between 1957 and 1964. Participants were eligible to be interviewed annually until 1994 and biennially thereafter, with the most recent available wave occurring in 2012. The initial wave of the NLSY79 included a separate interview with the main survey respondent’s mother, which among other items collected information on their educational attainment. Starting in 1986, an additional longitudinal survey of all biological children of female NLSY79 respondents began, and the NLSY79-YA sample consists of respondents in this survey who were at least age 15 at the time of interview. By combining the education questions from the NLSY79-YA survey with the information on their mothers from the NLSY79 as well as the parent questionnaire from the initial round of the NLSY79, we are able to construct an additional three-generation sample of American women. Notably, the NLSY79/NLSY79-YA employed a structurally different data collection procedure than the NLSY97. In particular, the NLSY79/NLSY79-YA sample is anchored on a nationally representative sample of women from the “mother” generation, with data then collected on these women’s own mothers and their daughters, whereas the NLSY97 is anchored on a nationally representative sample of women from the “daughter” generation with subsequent data collection on previous generations. The structure of the NLSY79/NLSY79-YA also has two advantages over the NLSY97 in terms of educational measurement. First, the educational attainment of grandmothers is measured directly with a self-report, whereas in the NLSY97 this information is reported retrospectively by their daughters. Second, the educational attainment of the mother generation is measured by repeated contemporaneous surveying, whereas in the NLSY97 maternal education was measured with a single retrospective report.

However, a major shortcoming of the NLSY79/NLSY79YA data is that at the time of the most recent survey wave, the youngest generation had a mean age of just 22.1 years and approximately 87% of these respondents were under age 27, leaving us unable to reliably ascertain final educational attainment for a large portion of the daughter generation. Given this, we conduct our replication using the portion of the NLSY79/NLSY79-YA sample where women in the daughter generation were observed at age 24 rather than age 27.14 This restriction is necessary but has two major disadvantages. The first is a substantially reduced sample size, and when restricted to include only daughters age 24 or older our working NLSY79/NLSY79-YA data contains just 998 complete grandmother–mother–daughter observations. The second disadvantage is that focusing on daughters age 24 or older causes us to disproportionately exclude families where the daughter was born to a relatively old mother. This is due to the fact that the NLSY79-YA survey collected information on the children of mothers from a fixed range of cohorts (1957–1964), so that daughters born to older NLSY79 participants are younger in any given calendar year of data collection. These considerations lead us to prefer the results based on the NLSY97 sample. However, replication is a sufficiently useful exercise that we present results using the NLSY79/NLSY79-YA as well in Table 5. The first four columns of Table 5 show estimates of our four baseline specifications using the NLSY79/NLSY79-YA data. For purposes of comparison, the remaining columns of Table 5 show results from re-estimating our baseline models with the NLSY97 data, but using daughter education observed at age 24 rather than age 27 in order to generate broadly comparable estimates across data sets.

14 An age cutoff of 24 was chosen because it allows women approximately 6 years after the typical age of high school graduation to complete post-secondary education while still retaining a reasonably large sample, though we acknowledge that this choice of age cutoff is in part arbitrary. However, results using a cutoff of age 25 or 23 are similar to those reported below and are available upon request. We use imputation procedures identical to those employed in the NLSY97 data as described in footnote 3.

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The results from the two data sets are very similar to one another, and are also very similar to the preferred estimates from Table 2. The two-generation coefficients for grandmother–mother pairs and mother–daughter pairs in the NLSY79/NLSY79-YA are equal to .369 and .316, respectively, and when we estimate these models with the NLSY97 data using daughter education as of age 24 the analogous coefficients are .317 and .371. The two data sets also produce very similar grandmother–daughter coefficients, specifically .266 and .237, respectively. Finally, when daughter education is regressed on both mother and grandmother education, a statistically and substantively significant grandmother–daughter association is present even after conditioning on maternal education in both the NLSY79/NLSY79-YA and the NLSY97 data. While the data limitations discussed above warrant caution in interpreting the results from Table 5, our core finding of strong three-generation persistence is broadly replicable in a second independent data set. This gives us greater confidence that our preferred NLSY97 results are not an artifact of idiosyncratic sampling and data collection procedures or of the discussed education measurement issues in the NLSY97.

5. Transmission mechanisms While the baseline results presented above improve our empirical understanding of multigenerational mobility levels, we emphasize that they are wholly descriptive in nature and are not in themselves informative regarding transmission mechanisms. One possible set of transmission mechanisms is “direct,” meaning that they derive from direct interactions between grandparents and grandchildren, such as rearing by grandparents or education-targeted bequests. Another set of potential transmission mechanisms is “indirect,” meaning that they derive from the structure of multigenerational transmission or from features of commonly used estimation approaches, rather than actual interactions between individuals from nonconsecutive generations. In this section, we discuss these two classes of transmission mechanisms in turn, both by drawing on the existing literature and when possible by testing mechanisms in our own data. Which type of mechanisms best explain our findings has important implications. In particular, if our three-generation findings are due to direct interactions between grandparents and grandchildren, then the effect would likely dissipate across four or more generations, since individuals rarely interact with their greatgrandparents. Direct transmission mechanisms would also leave open some possibility that policy interventions could effectively promote multigenerational mobility, since public programs could in principle serve functions similar to those provided by affluent grandparents. On the other hand, if our findings are largely due to “indirect” structural mechanisms, then mobility across four or more generations is probably severely underestimated by extrapolating two-generation estimates, and the scope for effective mobility promoting policy interventions would be very limited.

5.1. Direct transmission mechanisms Several potentially important direct transmission pathways are discussed by Mare (2011) and Solon (2014). Many of these involve face to face interactions between grandparents and grandchildren. For instance, grandparents (especially grandmothers) frequently engage in significant amounts of grandchild rearing, ranging from modest “babysitting” arrangements to being primary caretakers (Cherlin & Furstenberg, 1986). Grandparent co-residence, while less common in the contemporary US than in many other contexts, is still a relatively frequent arrangement for at least some portion of children’s lives, and may be more important than is suggested by its simple prevalence given that grandparents often “step in” during a crisis period, for instance the death or incarceration of a parent or after a separation or divorce (Biblarz & Raftery, 1993; DeLeire & Kalil, 2002). The most obvious way that direct interactions could increase the association between the educational attainment of grandparents and grandchildren is by influencing the human capital formation of grandchildren. More highly educated grandparents may be more inclined towards or effective at activities like reading their grandchildren books, helping them with their homework, taking them on educational outings, or assisting them in navigating school systems and college admissions processes (Jæ ger, 2012; King & Elder, 1997). More abstractly, interactions with grandparents could influence three-generation transmission via social norms, specifically the extent to which grandchildren perceive that high (or low) levels of educational attainment are normal or expected. Such pathways may be particularly germane within the matrilineal sets we focus on here, given that female college attendance in particular was a relative rarity over much of the study period, which could magnify the influence of highly educated grandmothers as role models. Unfortunately our data contains few measures of direct interactions between grandmothers and granddaughters. Because the primary NLSY97 respondents were ages 12–16 at the first wave of the survey, no detailed information was collected regarding child care arrangements or household structure during their childhoods. However, the parent survey fielded in the initial wave of the NLSY97 did ask women from the “mother” generation whether they had ever lived with any of the primary respondent’s grandparents for three or more months after the child’s birth, and approximately 25% of respondents reported that they had. This measure of grandparent co-residence faces serious limitations. One important shortcoming is that respondents did not specify which grandparent(s) had coresided with the granddaughter, for how long, or under what circumstances. Additionally, the available sample of co-residing families is relatively small and self-selected into those living arrangements, making it difficult to distinguish between any actual effects of co-residence and effects deriving from other characteristics of families with three co-residing generations. Still, previous research in other contexts has found a strong effect of grandparent co-residence on three-generation educational transmission

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Table 6 Testing direct transmission mechanisms. (1) Not co-resident

(2) Co-resident

(3) Not co-resident

(4) Co-resident

(5) Controlling for paternal education

0.229∗∗∗ (0.055)

0.312∗∗∗ (0.029) 0.123∗∗∗ (0.026)

0.235∗∗∗ (0.083) 0.153∗∗ (0.061)

472 0.220

1.47 0.23 1,562 0.272

0.196∗∗∗ (0.033) 0.090∗∗∗ (0.026) 0.231∗∗∗ (0.028) –

472 0.290

1,747 0.288

Mother education Grandmother education

0.236∗∗∗ (0.026)

Father education Chi-Square of test for difference P-value of difference Observations R-squared

0.69 0.41 1,562 0.167

The dependent variable for all models is daughter education. The models in Columns 1 and 3 use the sample where daughters never co-resided with a grandparent for three or more months, while the models in Columns 2 and 4 use the sample where daughters did co-reside with a grandparent for three or more months. Reported Chi-Square statistics and P-values are from a test that the coefficients on grandmother education are equal for co-residing and non co-residing families. The model in Column 5 controls for youth-reported paternal education. Educational attainment is measured using z-scores, and the reported coefficients can therefore be interpreted in standard deviation units. All models contain full sets of birth year dummies for individuals from the included generations. Robust standard errors are in parentheses. Sample size denotes number of daughter–mother–grandmother triples. Grandmother’s, mother’s, and father’s education is final attainment. Daughter’s education is measured at age 27. NLSY custom sampling weights are applied.

(Zeng & Xie, 2014), and some insight into the potential importance of direct grandmother–granddaughter interactions may be gained by comparing three-generation transmission strength in extended families that did and did not co-reside at some point.15 Given this, Table 6 reports results of re-estimating our baseline three-generation models split by grandparentgrandchild co-residence. Columns 1 and 2 show the direct (unconditional) grandmother–granddaughter educational correlation for non-co-residing and co-residing observations, respectively. The estimates indicate that transmission strength is very similar in families where the youngest generation did and did not live with any grandparent, with coefficients of .236 and .229, respectively. Columns 3 and 4 of Table 6 report results from models that regress daughter education on mother and grandmother education simultaneously, again split by co-residence. These estimates indicate that relative to families that never co-resided, the association between mother education and daughter education is approximately .077 standard deviation units weaker among co-residing families (.312 versus .235) while the association between grandmother education and daughter education is approximately .03 standard deviation units stronger among co-residing families (.123 versus .153). Chi-Square statistics and corresponding Pvalues for these differences are also reported, and none of the differences in transmission strength across co-residing and non-co-residing families are statistically significant at conventional levels. We interpret these results as suggestive evidence that three-generation co-residence – and more speculatively direct interactions between grandparents and grandchildren – are at most modest mediators of three-generation educational transmission in our sample.

15 In addition to the evidence on co-residence-based heterogeneity provided by Braun and Stuhler (2015); Zeng and Xie (2014) use variation in the timing of grandparents’ deaths induced by World War II in German data, and find that three-generation mobility estimates are not sensitive to whether grandparents died before a grandchild’s birth.

However, the limitations discussed above make it difficult to draw firm conclusions from this exercise. It should be noted that not all direct transmission mechanisms require actual interactions between grandparents and grandchildren. For instance grandparents may transfer financial resources directly to their grandchildren through a variety of common financial instruments even if they are deceased or absent, and financial support for educational expenses such as college tuition is an especially common form of three-generation financial transfer (Coate, Dalton, Hotz, & Thomas, 2010). Legacy-based admission into preparatory schools, colleges and universities, or social clubs of various forms can also lead to relationships between the educational opportunities of grandparents and grandchildren that are not transmitted via the intermediate generation, and can do so without any actual grandparent-grandchild interactions. Another potentially important transmission mechanism relates to the characteristics of men from the middle generation (i.e. fathers); such a mechanism can be viewed as a direct effect despite not requiring actual interactions between grandparents and grandchildren. Essentially, grandparents can have a direct effect on the quality of their sons-in-law. In particular, if the grandparent generation is highly educated, this may increase the likelihood that women in the middle generation (i.e. mothers) will have children with a more-educated mate, which in turn could influence the education of children in the youngest generation. As an example, consider two women who are both college graduates themselves, but one of whom has a mother who also graduated from college while the other is a firstgeneration college graduate whose mother completed only high school. If social network effects or cultural norms lead the woman with a college-educated mother to have children with a more highly educated man than the woman whose own mother was not a college graduate, and if more highly educated fathers in turn positively affect the average education of the youngest generation, this will strengthen the association between the education levels

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of grandmothers and granddaughters, even conditional on mother education. A transparent method of testing the importance of fathers as a link between grandmothers and granddaughters is to add controls for paternal education to a specification that already contains mother and grandmother education, then observe how the coefficient on grandmother education is affected. If paternal education is an important mediator of grandmother–granddaughter educational associations, then we would expect the grandmother effect to be reduced after controlling for father education. While the NLSY97’s parent survey, which we rely on for maternal education data above, was completed almost exclusively by mothers, the NLSY97 youths themselves reported the educational attainment of their biological fathers (if known) in the initial wave of the survey.16 This data on paternal education has serious limitations. In particular, over 16% of youths in our working sample did not know the educational attainment of their fathers, and greater measurement error in this youth reported data seems likely as well. Despite these shortcomings, having even limited information on father outcomes allows us to add controls for paternal education to our baseline all-female models and then observe any changes in the coefficients on mother and grandmother education, and estimates from this specification are reported in the final column of Table 6. These results suggest that fathers are indeed a non-trivial mediator of grandmother–granddaughter educational associations. In particular, Column 5 of Table 6 shows that the coefficient on grandmother education falls from .127 when paternal education was not included (as reported in Column 4 of Table 2) to .09 after its inclusion. This reduction in the grandparent effect reflects the fact that, conditional on their own education, the daughters of highly educated women marry more-educated men. This can be seen directly by regressing father education on mother and grandmother education simultaneously. When we do so (not shown), the coefficient on grandmother education is .106 and highly statistically significant, indicating that even after accounting for women’s own education, having a more highly educated mother substantially increases the average education of their reproductive partners in adulthood. These more-educated fathers would in turn be expected to increase daughter’s education. In addition to providing evidence on multigenerational transmission mechanisms, the results that include fathers strengthen the general case that using an AR(1) framework to extrapolate two-generation mobility estimates is inappropriate. In particular, depending on the signs and strengths of the associations between father’s education and the education of the women in our baseline specifications, significant omitted variable bias in the coefficients on mother and grandmother education was a possible concern. However, the results in Column 5 of Table 6 indicate that while controlling for father’s education reduces the 16 Note that while youths report the educational attainment of their fathers, no information on the education of paternal grandparents is available, so that three consecutive generations of educational attainment is only observed for female lineages.

conditional association between grandmother and granddaughter education, the estimated coefficient on grandmother education is still well above the value of zero that is predicted by an AR(1) model.17 A final set of direct transmission mechanisms relate to shared genetic profiles across generations. While it is true that genetic material is transferred from grandparents to grandchildren exclusively via parents, actual genetic transmission structures are sufficiently complex that unmediated three-generation effects are certainly possible. For instance many genetic traits only lead to a corresponding phenotypic outcome in the presence of specific environmental circumstances, other genes, or both. Such “gene-environment interactions” and “gene-gene interactions” could cause a genetic trait held by a grandparent to be physiologically present in both their children and grandchildren, but to only have practical consequences for their grandchildren (see Rutter, 2006). Additionally, the ova that eventually were fertilized and became granddaughters were created while the mother herself was still in-utero, so that a physiological shock to a grandmother while pregnant (for instance sustained fever or malnutrition) could have a direct physiological effect on eventual granddaughters (see Van den Berg & Pinger, 2014; Gluckman & Hanson, 2005) While the importance of these and other direct transmission mechanisms cannot be directly tested in our data, they are likely to at least partially explain our findings, and investigating their importance would be a potentially fruitful direction for future research if suitable data became available. 5.2. Indirect transmission mechanisms While direct linkages between grandparents and grandchildren could generate strong three-generation educational persistence, a number of theoretical transmission structures are also consistent with strong three-generation transmission even without invoking any direct interactions between grandparents and grandchildren. In this section we briefly discuss these potential indirect explanations for our findings. The most influential formal theoretical model of intergenerational transmission is due to Becker and Tomes (1979), and their proposed transmission structure predicts a small or even negative conditional effect of grandparent characteristics on those of grandchildren.18 However, as pointed out by Solon (2014), models in the tradition of Becker–Tomes are highly stylized, and quite plausible

17 An alternative specification is to control for the average of maternal and paternal education, rather than having each enter separately as in Table 6. When we estimate such a specification (not shown) the coefficient on the mean parental education variable is .415 and, more importantly, the coefficient on grandmother education is .093 and highly statistically significant. 18 It should be noted, however, that geometrically declining transmission coefficients do not follow directly from the Becker–Tomes model. Solon (2014) derives three-generation transmission coefficients based on a Becker–Tomes framework, and shows that after conditioning on parental outcomes, the association between the outcomes of grandparents and grandchildren is actually predicted to be negative in this framework.

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alternatives or extensions of their theoretical framework can lead to larger three-generation effects. One theoretical transmission model with this feature is presented by Stuhler (2012), who models intergenerational transmission as a two step process (Stuhler focuses on income transmission, but the argument readily applies to educational transmission as well). In the first step, parents transmit relevant characteristics to their children. For education, examples of these characteristics could include IQ, non-cognitive skills, or general health. In the second step, children convert the transmitted characteristics into the actual outcome of interest, in our case educational attainment. Stuhler (2012) points out that while the transmission of characteristics may decline geometrically as they are iteratively inherited across generations, the rate at which those traits are converted into education will not in general do so. Critically, empirical estimates of two-generation transmission reflect both the transmission of characteristics from parents to children and the conversion of those characteristics into actual educational attainment. Since only the portion of two-generation estimates that is due to shared characteristics can reasonably be expected to decline geometrically, three-generation transmission strength will typically exceed the simple product of two-generation transmission estimates, as we found empirically above. We note that indirect transmission mechanisms of this general form are broadly consistent with the uniformity of our results when sons and paternal grandfathers are included in the analysis, as reported in Table 3. This is because mechanisms deriving from direct interactions with grandparents would likely vary to some degree by gender, so that nearly identical transmission strength across grandparent and grandchild gender is suggestive of transmission occurring though indirect pathways. An additional explanation for large three-generation associations that does not invoke direct transmission is classical measurement error, and this explanation is most easily demonstrated through a numerical example presented by Solon (2014). Specifically, Solon considers a hypothetical case where intergenerational transmission is indeed governed by an AR(1) process and the true parent-child correlation is .5, implying a true grandparent-child association of .25, but where measured educational attainment in all three generations consists of 80% true variation and 20% noise. In this case the estimated correlations will be subject to an attenuation factor of .8, leading to an estimated parent-child correlation of .4 and an estimated grandparent-child correlation of .2. Since the estimated grandparent-child correlation of .2 exceeds the AR(1) based expectation of .42 = .16, observed three-generation associations will be larger than those expected under AR(1) transmission, which is qualitatively similar to what we find in Table 2 above. While this example demonstrates how measurement error may impact our estimates, there are two reasons we believe it is not a primary explanation for our findings. First, rather than the educational attainment of all three generations being measured with identical error as in the (Solon, 2014) example, the measurement error in our data would likely be most severe in the grandmother

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generation. This implies that the attenuation in our estimated daughter–grandmother associations would be the most severe, which strengthens rather than weakens our main finding of strong three-generation persistence.19 Second, our findings using the NLSY79/NLSY79-YA are very similar to our main NLSY97-based results. As discussed above, the NLSY79/NLSY79-YA data likely suffers less from measurement error than the NLSY97 data, so that similar findings across the two data sets suggest measurement error does not strongly influence the results. Still, measurement error may lead to an overstatement of threegeneration persistence in our estimates, even if it is not the primary explanation for our findings. 6. Conclusion This paper has estimated the intergenerational persistence of educational attainment across three generations of women in the US. The core finding has been that there was a high degree of multigenerational persistence in this historical context, with grandmother–granddaughter educational associations approximately twice as strong as would be expected under an AR(1) transmission structure. This finding was replicated in a second independently constructed national data set, and is present across a variety of specifications and subpopulations. Additional estimates that included men in the oldest and youngest generations yielded similar findings. Finally, a variety of transmission mechanisms that are potentially applicable to three generation contexts were discussed, and some suggestive tests of these mechanisms were presented as data allowed. Multigenerational transmission remains an understudied aspect of social mobility. Research documenting the level of multigenerational mobility in additional contexts, as well as empirical and theoretical research on the mechanisms of multigenerational transmission, would produce a richer understanding of long-run social mobility. If future research using other data sources and in alternative historical and geographic contexts yields findings similar to those described here, researchers may need to reconsider the extent to which intergenerational transmission measures based on two consecutive generations can accurately quantify the prevailing level of social and economic mobility. Acknowledgment We thank John Parman, Gary Solon, participants at the 2016 ASSA meetings and UW-Milwaukee labor lunch, as well as two anonymous referees for thoughtful comments. Data and code to replicate this study are available at https: //pantherfile.uwm.edu/thompsoo/www/.

19 Stronger measurement error in the grandmother generation would also attenuate the mother–grandmother association relative to the daughter–mother association. While the mother–grandmother and daughter–mother associations reported in Table 2 are very similar, the effect of measurement error on their relative strength cannot be distinguished from the possibility of a secular trend in transmission strength.

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