Intergenerational Health Mobility: Magnitudes and Importance of Schools and Place

Abstract

This paper broadens the literature on intergenerational persistence of socioeconomic status to consider individual, family, and spatial variation in intergenerational health mobility in the United States. Using a school-based representative panel (Add Health), we report overall health persistence of 0.17 with higher mobility in Hispanic families. We find large variation by place; intergenerational health persistence estimates range between 0–0.5, with similarly large ranges for absolute upward and downward health mobility. School- and contextual-level correlates indicate local race/ethnicity composition, proportion of single parents, and average mother’s education may be related to observed variation in intergenerational health mobility.

1. Introduction

A growing literature on intergenerational relationships seeks to understand whether and why (or why not) the United States (U.S.) is truly a “land of opportunity”. There has been significant progress documenting heterogeneity and patterns of intergenerational economic mobility within the U.S., specifically with respect to race/ethnicity (Chetty et al., 2018; Hertz, 2005; Mazumder, 2014) and geography (Chetty et al., 2014). For example, children of parents in the 25^th percentile of parent income in Salt Lake City, UT on average are near the 46^th percentile of income around age 30, whereas their peers in Charlotte, NC only expect to achieve the 36^th percentile (Chetty et al., 2014). A larger gap in expected percentile ranks for children of parents in the 25^th percentile of parent income is identified between non-Hispanic White and non-Hispanic Black children (Chetty et al., 2018). However, knowledge of health relationships across multiple generations is more limited, and knowledge of heterogeneous patterns in this relationship within the U.S. is largely absent. Examining the interconnectedness of generations broadly is important not only to understand present disparities in key socioeconomic outcomes (including health), but also in planning for future generations and identifying potential interventions. The present analysis contributes to the literature by broadly examining intergenerational health mobility in the U.S. and documenting stark heterogeneity within the U.S. by parent or child characteristics and location.

Health throughout the life course is pivotal to many socioeconomic markers, including education, labor market participation, income, and aging. Poor health in childhood is associated with lower educational attainment (Case et al., 2005; Haas & Fosse, 2008), which in turn is associated with lower likelihood of successful aging and higher mortality (McLaughlin, 2017; Meara et al., 2008). Experiencing poor health during prime working ages can also have lasting effects. Healthy men on average are found to work more, earn more, and have higher net worth (Hokayem & Ziliak, 2014). In the event that ill health limits an individual from fully engaging in the labor market, significant drops in earnings and income may be observed up to a decade after onset (Charles, 2003; Jolly, 2013; Meyer & Mok, 2019). Given the relationship of health with education, labor market participation, and income, patterns in health across generations may help better understand the persistence of socioeconomic status in the U.S. However, disparities in health and intergenerational health persistence or mobility are also independently important to understand when persons value good health.

A small existing literature explores intergenerational persistence of health. Early life-course intergenerational health correlations, based on birth weight, are approximately 0.2 (Currie & Moretti, 2007). Using outcomes a little later in the life course, Thompson (2014) examines the intergenerational transmission of specific health conditions, including asthma, hay fever, chronic headaches (migraines), and diabetes, finding a range of estimates from 0.006 for diabetes to 0.276 for hay fever. The intergenerational elasticity of body mass index has been estimated around 0.25 – 0.4 (Classen 2010; Classen & Thompson 2016). An example examining the intergenerational persistence of mental health in Britain also found a correlation of 0.16 (Johnston et al., 2013). What emerges from this literature is a relatively consistent estimate of intergenerational health persistence in the 0.2 – 0.3 range.

A recent paper that is most similar to the present analysis uses the Panel Study of Income Dynamics (PSID) to examine intergenerational health mobility in self-reported health status. That study corroborates previous estimates of intergenerational health persistence and finds a persistence of 0.26 (Halliday et al., 2021).¹ That paper is essential to the analysis we pursue as many properties established in that work counteract limitations in our own data. First, the authors demonstrate that estimates of intergenerational health persistence are attenuated when using a single observation of parent health relative to using an average over multiple years by about 30 – 40 percent. Second, life-cycle biases could also attenuate persistence estimates. For example, the authors report moderate reductions in their estimate of mother-son health persistence—from 0.27 to 0.21—if they use son’s health measures during younger adulthood (age ~30) rather than older adulthood (age ~60). However, mother-daughter estimates are more stable as daughters age. Third, the authors report nearly identical results when using 21 objective health measures instead of self-rated health status (Halliday et al., 2021)—our data only contain the latter for the parent’s generation. Finally, the authors applied the rank-based approach from Chetty et al. (2014), which they found to exhibit improved properties regarding the assumption of linearity for estimation in the health context (Halliday et al., 2020).

Halliday et al. (2021) makes many important contributions to our understanding of intergenerational persistence of general health status. The PSID affords many advantages including regular observations of individuals over time, a genealogical design, up to 50 years of data on multiple generations, and in recent years, the inclusion of rich data on health conditions. However, estimates do not capture the Hispanic population and the sample sizes are too small to explore geographic variation below the level of census region. The latter does not afford the opportunity to examine more granular spatial variation in intergenerational health persistence or mobility, which is likely to exist in the U.S. given documented heterogeneity in intergenerational economic mobility (Chetty et al., 2014).

Using the National Longitudinal Study of Adolescent to Adult Health (Add Health), our analysis complements and extends the previous literature in two important ways. First, the sample size is over 25% larger than the PSID, allowing corroboration of important estimates including race/ethnicity stratifications in addition to specifically examining Hispanics separately. The larger sample also yields a sizable subsample of adoptees which will assist in determining the potential role for non-genetic factors, complementing previous work regarding the genetic role for intergenerational health persistence (Classen & Thompson, 2016; Thompson, 2014). Second, a school-based sample design in addition to the larger sample allows for examining spatial variation of intergenerational health relationships and tying these estimates to spatial/contextual correlates to begin an investigation of potential factors generating persistence or mobility.

Our analysis estimates intergenerational health persistence to be 0.170, while children born to parents in the 25^th (75^th) percentile of health on average achieve the 47^th (56^th) percentile of health. However, based on the results in Halliday et al. (2021), these full-sample estimates are likely biased downward. A key contribution in our estimates is the ability to compare across groups and locations. For example, our results suggest Hispanics may experience less health persistence and more downward mobility relative to non-Hispanic White children. Children without health insurance, whose parents were unmarried, or whose mothers did not complete high school tend to experience poorer expected health relative to their more advantaged peers, although patterns differ based on race-ethnicity. A relatively large sample of adoptive children also suggests that non-genetic factors appear to play a role in determining health mobility.

This analysis also finds significant spatial heterogeneity of intergenerational health mobility—some schools are estimated to have essentially zero health persistence while others are as high as 0.50. Similarly, for some schools the expected health rank for children of parents in the 25^th percentile of parent health is around 30 relative to other schools where the child’s expected health rank is well above the median. We then explore correlates of these vast differences in persistence and mobility across place. For example, we find the West, areas with higher shares of non-Hispanic Blacks, or higher shares of single parents experience less health persistence. Higher local average mother’s education is linked with more health persistence, higher upward health mobility and less downward health mobility. Surprisingly, the percentage of smokers in the area does not appear to be associated with health mobility or persistence. The remainder of this paper is organized into three additional sections. The next section discusses methods and data while the third section presents the main results of the analysis. The final section discusses results and implications.

2. Methods and Data

Intergenerational health mobility (or persistence) is estimated following traditional specifications in the literature of intergenerational economic mobility (Mazumder, 2005; Solon, 1992, 2004), with recent applications to intergenerational health mobility (Akbulut-Yuksel & Kugler, 2016; Classen, 2010; Currie & Moretti, 2007; Halliday et al., 2021; Johnston et al., 2013). Specifically, parent’s self-reported health status (SRHS_p) is regressed on child’s self-reported health status (SRHS_c) using OLS controlling for age in quadratic form in both generations (C_z) as in equation 1.

$$SRH{S}_c={\beta }_0+{\beta }_{1}SRH{S}_p+\sum {\beta }_z{C}_z+\epsilon$$ (1)

Measuring intergenerational health mobility or persistence using an OLS specification as in equation 1 requires an assumption of linearity. Research in intergenerational economic mobility suggests logged income or earnings may present some non-linearities that can be largely resolved using a rank-based approach (Chetty et al., 2014). Analogously, a recent paper suggests estimates of intergenerational health mobility using self-reported health status measures² may produce estimates that are slightly biased; however, using ranked self-reported health statuses in each generation in equation 1 has been shown to yield no meaningful bias to estimates when adopting the assumption of linearity for OLS (Halliday et al., 2020). Therefore, the main results in our analysis adopt a rank-based self-reported health status measure as in equation 2.³

$$\mathit{\text{Health}}Ran{k}_c={\beta }_0+{\beta }_1\mathit{\text{Health}}Ran{k}_p+\sum {\beta }_z{C}_z+\epsilon$$ (2)

Two measures of intergenerational mobility are obtained from equation 2. The first, referred to as “relative” mobility in the literature (Chetty et al., 2014; Halliday et al., 2021), is measured by β₁. This slope coefficient can be conceptualized as a measure of health persistence between generations with a similar interpretation as a correlation coefficient.⁴ Higher persistence indicates less mobility and vice versa. This metric captures the similarity of parent and child health without regard to whether that health is good or bad. The second measure estimates the expected outcome for children conditional on a parent’s health status – what Chetty et al. (2014) conceptualize as “absolute” mobility (equation 3). We pay particular attention to the expected outcome for children of parents at the 25^th and 75^th percentile of parent health following literature selecting these percentiles to gauge absolute mobility, which may also be referred to as absolute upward (or downward) mobility respectively (Chetty et al., 2014; Halliday et al., 2021).

$$E\left(\mathit{\text{Health}}Ran{k}_c|\mathit{\text{Health}}Ran{k}_p=x\right)={\beta }_0+{\beta }_1\left(x\right)$$ (3)

In a hypothetical scenario with perfect mobility, the expected health rank for all children regardless of parents’ health would be the median. Although there is not perfect mobility, societies typically exhibit mean reversion of health and income. Thus, children of parents in relatively poor health (i.e. the 25^th percentile) on average achieve better health – giving rise to the concept of upward health mobility. For example, if the predicted health rank for children of parents with health at the 25^th percentile is the 45^th percentile, the average child has 20 percentiles better health, or upward mobility. Conversely, children of parents in relatively good health (i.e. the 75^th percentile) on average will have somewhat worse health – or have downward mobility. If the predicted health rank for children of parents at the 75^th health percentile is the 60^th percentile, then on average there is 15 percentiles of downward mobility.

Data comes from The National Longitudinal Study of Adolescent to Adult Health (Add Health), a school-based nationally representative panel survey of adolescents from grades 7–12. This study incorporates child-generation’s reports of self-rated health status from four waves of data (1994–1995, 1996, 2001–2002, and 2008–2009) and parents’ self-reported health from the first wave from a total of 131 schools. We note observing parent health in a single wave is a considerable limitation of this analysis. However, our results remain reasonably consistent with previous work unburdened by this factor (i.e. Halliday et al., 2021). Additionally, we do not expect this measurement error to systematically vary across groups or schools, meaning comparisons should be relatively unaffected.⁵ The school-based (i.e. highly clustered) design is critical for this analysis, as it allows for examining spatial variation in estimates, which has not previously been explored in the intergenerational health mobility literature within the U.S.⁶

Self-rated health status is measured on a five-point Likert scale with one representing poor health and five representing excellent health. As the marginal distribution of the Likert scale for self-rated health is likely non-constant, this study follows previous work and adopts the HALex health index. This index maps the survey response of self-rated health status to a scale representing quality of life – conceptualizing perfect health with a score of one hundred and death with a score of zero (Erickson, 1998; Erickson et al., 1995). It has also been applied previously in the literature to address concerns surrounding the marginal distribution of health from the Likert scale (Halliday et al., 2021; Johnson & Schoeni, 2011). Following this work, our analysis assigns the midpoint of established HALex interval values of 15, 50, 77.5, 90, and 97.5 to self-rated health statuses of poor, fair, good, very good, and excellent in both generations each wave. These HALex adjusted health measures are then averaged across all waves and the resulting health status is ranked within each generation.⁷ Estimates that follow will incorporate three main measures of health mobility or persistence : (1) Rank slope, the β₁ coefficient from equation 2 using ranked percentiles of HALex adjusted self-rated health in both generations (a measure of persistence), (2) the expected health rank of a child conditional on his/her parent having health rank at the 25^th and (3) 75^th percentile of parent health from equation 3 (measures of mobility).

We follow the economic mobility literature leveraging various stratifications of equation 2 to help understand the heterogeneity of U.S. intergenerational health mobility and persistence. In particular, this analysis first examines heterogeneity based on individual characteristics beginning with race/ethnicity, which is found to be influential in intergenerational economic mobility (Chetty et al., 2018; Hertz, 2005; Mazumder, 2014). Additionally, we incorporate other family level factors including lack of health insurance, parent education (as in Halliday et al., 2021), and parent marital status. This sample highlighting variation by individual characteristics incorporates 10,112 parent-child pairs.⁸

Intergenerational economic mobility is also found to vary geographically in the U.S. (Chetty et al., 2014). Thus, spatial variation in intergenerational health mobility and persistence is estimated by stratifying equation 2 by schools in Add Health.⁹ Fortunately, we are able to rely on the Add Health sampling design to assure unbiased estimates of school-level phenomenon, as students were randomly sampled within schools (the “Core” sample). Our school-based results use schools with a minimum of 20 Core parent-child pairs, resulting in a total of 9,497 parent-child pairs identified in 131 schools.¹⁰First, we estimate equation 2 school-by-school and present summary measures of spatial variation in intergenerational health mobility and persistence. Next, we estimate associations between school-level intergenerational health measures and a set of Census-tract specific characteristics (demographic, socioeconomic, and/or school-specific programs). Our study was approved by our institution’s IRB.

3. Results

Descriptive statistics for the analytic sample are found in Table 1. In our sample, parents are typically observed around age 42, while children’s average age over the waves with reported health is around 20 years old¹¹. Parents generally have worse health – HALex adjusted health score around 83 relative to children’s HALex adjusted health score of 86. Non-Hispanic Black and Hispanic parents are slightly younger but in worse health relative to non-Hispanic White parents. Minority children on average are also in slightly worse health. More than half of non-Hispanic White parents have more than a high school education, and 77% are married. On the other hand, just under half of non-Hispanic Black mothers have more than a high school education or are married. A little less than half of Hispanic mothers have less than a high school education, with only a quarter reporting more than a high school education, but 74% are married. Most children regardless of race-ethnicity are covered by health insurance in waves 3 or 4; however, minority children are more likely to lack coverage.

Table 1:

Descriptive statistics of sample

Sample Size	Full Sample 10,112	nH White 5,856	nH Black 1,966	Hispanic 1,658
Parent Health & Age
HALex Health	80.4	82.5	78.4***	75.8***
Rank	50.2	54.1	46***	41.5***
Age	42.0	42.2	40.9***	41.7+
Child Health & Age
HALex Health	86.2	86.8	85.9*	85**
Rank	51.1	52.5	50.7***	47.4**
Age	19.8	19.8	19.6***	19.8***
Other Characteristics
Mother < HS	16.9	8.6	12.5*	46.3***
Mother HS	34.9	36.8	38.2***	28.9*
Mother > HS	48.2	54.6	49.3***	24.7***
Married Parents	72.5	77.4	48.9***	73.5***
Child without Health Insurance	34.9	33.3	35.9***	42.5***

Source:Authors’ calculations using Add Health

Notes:Not all parent-child pairs observe “other characteristics”. Between 90% and 95% of parents observe educational attainment, while more than 99% observe marital status. 80% to 90% of children observe health insurance in wave 3 or 4. Sample sizes for each race-ethnicity group separately do not add up to the full sample (n = 10,112) because other race-ethnicity subsamples do not have group-specific reported estimates. Statistical significance in columns 3 and 4 is relative to non-Hispanic White estimates with *** p<0.001, ** p<0.01, * p<0.05, and + p<0.1.

For our nationally representative sample of the U.S. (Table 1), relative intergenerational health persistence as measured by a rank-rank slope is estimated at 0.170 (95% confidence interval: 0.137 – 0.204). Children whose parents are in relatively poorer health (at the 25^th percentile of parent health) are anticipated to reach near the 47^th percentile of health on average, while children whose parents are in relatively better health (the 75^th percentile of parent health rank) are expected to achieve near the 56^th percentile of health as adults.¹² Estimates using the PSID suggest the rank slope coefficient to be 0.261 and expected child health rank for those whose parents are at the 25^th (75^th) percentile of parent health is 44.3 (57.4) (Halliday et al. 2018). Our Add Health sample also uncovers a higher rank slope for mother-child health relative to father-child rank slope (consistent with Halliday et al., 2021), and parent-daughter persistence is greater than parent-son persistence (see Appendix Table A.1.2).¹³

In order to both replicate and extend results in the PSID by Halliday et al., we next consider heterogeneity of these estimates by race/ethnicity, parent and child characteristics, and geography. Heterogeneity in intergenerational health mobility and persistence is present by race/ethnicity (Figure 1 and Table A.1.1 in the Appendix). Like Halliday et al., point estimates suggest that non-Hispanic Black children experience less health persistence, or greater relative mobility, relative to non-Hispanic Whites. Extending PSID results, we also present the first evidence of Hispanic health persistence, which we find is lower than non-Hispanic Whites. Indeed, Figure 1 suggests only Hispanic parent-child pairs have statistically more relative mobility (i.e. less health persistence) than non-Hispanic Whites. Children born to parents in relatively poor health (at the 25^th percentile of parent health) are generally not expected to reach median health as adults, and point estimates are generally consistent across race-ethnicity categories. While Hispanic children are found to have the best chances of achieving median health as adults, these differences are not statistically significant. Meanwhile children born to parents in relatively good health (the 75^th percentile of parent health rank) exhibit a bit more heterogeneity in terms of expected child rank. Estimates suggest non-Hispanic Black children and Hispanic children experience more mean reversion, landing nearer to the 50^th percentile of health rank relative to their non-Hispanic White counterparts. However, only Hispanic estimates are statistically different than non-Hispanic White estimates. Coefficient results are somewhat in contrast to results from Halliday et al. (2021), who find Black parent-child pairs not only experience a coefficient of health persistence approximately half that of their White counterparts, but also observe a ten-percentile gap in expected health rank for children whose parents are at the 25^th percentile of parent health rank. We expand on this observation in the discussion.

Figure 1:

Intergenerational health persistence and mobility stratified by race-ethnicity

Source: Authors’ calculations using Add Health

Notes: Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c|rank_p = 25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p = 75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). Estimates are weighted and use the full Add Health sample (sample sizes in Table A.1.1). Red dots represent point estimates and vertical lines are the corresponding 95% confidence intervals.

We next consider additional heterogeneity in absolute mobility based on individual/family level characteristics in Table 2. For example, like Halliday et al. (2021), we find that children who ever were without health insurance as young adults (in waves three or four) typically have lower expected health ranks relative to those who always had health insurance when holding parent health rank constant, although disadvantage appears concentrated in non-Hispanic White populations and to a limited degree among non-Hispanic Blacks at lower parent health ranks (gaps are not statistically significant, but in the hypothesized direction). Children whose parent(s) were unmarried or whose mothers had less than a high school education similarly tend to have lower expected health relative to children of married parents and mothers with more than a high school credential net of parent health. The gap observed between “advantaged” and “disadvantaged” parent-child pairs though is not constant throughout the parent health distribution, or by race/ethnicity. Generally speaking, the gap in each of these characteristics increases as parent health increases, which reflects a typically flatter slope for “disadvantaged” parent-child pairs (signaling higher relative mobility or lower health persistence) or that such characteristics may matter more when the parent is in better health. However, while non-Hispanic White parent-child pairs have an increasing gap over parent health rank with respect to parent marital status, the gradient appears much stronger for Hispanics, and inverted for non-Hispanic Blacks.

Table 2:

Expected absolute mobility conditional on parent health rank & personal characteristics

	Mother’s Education
	Full Sample			non-Hispanic White			non-Hispanic Black			Hispanic
	A	D	Gap	A	D	Gap	A	D	Gap	A	D	Gap
10th	46.2	44.5	1.7	47.7	37.0	10.7**	44.3	37.4	6.9	44.5	51.1	−6.6
25th	49.3	44.4	4.9*	50.6	38.8	11.8***	46.8	37.7	9.2*	48.0	49.5	−1.6
50th	54.4	44.1	10.3***	55.4	41.8	13.6***	51.2	38.2	13*	53.7	46.9	6.8+
75th	59.6	43.9	15.7***	60.3	44.8	15.5***	55.5	38.7	16.8*	59.5	44.3	15.2***
90th	62.7	43.7	19***	63.2	46.6	16.6**	58.1	39.0	19*	63.0	42.8	20.2***
	Marital Status
	Full Sample			non-Hispanic White			non-Hispanic Black			Hispanic
	A	D	Gap	A	D	Gap	A	D	Gap	A	D	Gap
10th	45.4	43.2	2.2	44.0	43.9	0.1	50.6	38.5	12.1***	47.2	46.9	0.2
25th	48.1	45.1	3.1	47.2	46.2	1.0	51.6	41.3	10.3***	48.9	46.7	2.2
50th	52.7	48.1	4.5**	52.4	50.0	2.4	53.2	45.9	7.3*	51.7	46.3	5.4+
75th	57.2	51.2	6***	57.7	53.8	3.9*	54.8	50.6	4.3	54.5	45.9	8.7*
90th	60.0	53.1	6.9***	60.8	56.1	4.7*	55.8	53.4	2.4	56.2	45.6	10.6*
	Child’s Health Insurance
	Full Sample			non-Hispanic White			non-Hispanic Black			Hispanic
	A	D	Gap	A	D	Gap	A	D	Gap	A	D	Gap
10th	46.6	41.7	4.8**	46.5	40.1	6.4**	46.1	39.5	6.7	48.6	46.3	2.2
25th	49.4	43.5	5.9***	49.8	42.0	7.8***	48.0	42.7	5.2	50.0	47.3	2.7
50th	54.2	46.5	7.7***	55.2	45.2	10***	51.0	48.2	2.8	52.3	48.9	3.4
75th	59.0	49.5	9.5***	60.7	48.4	12.3***	54.1	53.6	0.4	54.6	50.6	4.1
90th	61.9	51.3	10.5***	63.9	50.3	13.6***	55.9	56.9	−1.0	56.0	51.5	4.5

Source:Authors’ calculations using Add Health

Notes:Not all 10,112 parent-child pairs observe these characteristics. Between 90% and 95% of parents observe educational attainment, while more than 99% observe marital status. 80% to 90% of children observe health insurance in wave 3 or 4. A represents the “advantaged” group (i.e. Mothers with more than a High School credential, married parents, or a child always with health insurance). D represents the “disadvantaged” group (i.e. Mothers with less than High School, unmarried parents, or a child who was ever uninsured). The Gap is the absolute difference in expected rank conditional on parent rank. In the case of parent health rank at the 25^th (75^th) percentile, the gap represents less upward (more downward) health mobility.

^***p<0.001,

^**p<0.01,

^*p<0.05,

⁺p<0.1

One particular advantage of Add Health is the ability to observe a sufficient number of adoptive parent-child pairs relative to biological parent-child pairs to better understand the potential role genetics may play in the intergenerational transmission of health. For this exercise, the main focus is on the β₁ coefficient from equation 2, or health persistence, to explore intergenerational transmission. Results from this analysis suggest that while intergenerational transmission is stronger for biological parent-child pairs, reflecting both genetic and environment factors, intergenerational transmission among adopted children is non-negligible with a statistically significant rank slope estimate of 0.115 (see Table A.1.3), suggesting considerable environmental effects on health transmission. This represents a 33% reduction in rank slope relative to the biological parent-child pair full sample; although, this decrease is not statistically different from biological parent-child pairs. Adopted non-Hispanic White children though have statistically less health persistence relative to their biological counterparts – lending support to the presence of genetic factors. Estimates from this sample also suggest adopted Hispanic children may have more health persistence relative to their biological counterparts; however, we caution that sample sizes particularly for minority adopted children are quite small.¹⁴

Since pooled or stratified estimates for intergenerational health mobility and persistence may mask underlying heterogeneity in geography, our last analysis undertakes a novel examination of spatial variation in intergenerational health mobility and persistence. Essentially, we estimate equations 2 and 3 school-by-school in the data, leveraging the school-based design of Add Health. Figure 2 (and Table A.1.4 in the Appendix) demonstrates the differences in mobility and persistence measures when observed at the school level.¹⁵ Regardless of the measure considered, some schools experience high mobility while some experience low mobility. In some cases of particularly high health persistence, rank slope estimates can approach 0.5 while other places experience rank slopes near zero.¹⁶ Similarly, in some locations, children born to parents in relatively poor health (at the 25^th percentile of parent health) can expect around a five-percentile improvement over his/her parents’ health rank while in other locations children born to parents experiencing such health may achieve greater than median health as adults. Meanwhile children born to parents in good health (at the 75^th percentile) may be expected to maintain a similar health status as adults for some schools while they could also be expected to experience health that is below the median as adults in other locations.

Figure 2:

School-stratified estimates of intergenerational health persistence and mobility

Source: Authors’ calculations using Add Health

Notes: Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c|rank_p = 25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p = 75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). Estimates are not weighted, but use only children identified in the Core sample to produce school-specific results. Solid red lines represent the full (national) estimates, while dashed red lines indicate perfect mobility (i.e. β₁ = 0 or absolute mobility = 50). Black dots/line represent school-specific estimates. Vertical lines are the corresponding 95% confidence intervals for school estimates.

Finally, following Chetty et al. (2014)’s work on spatial variation in economic mobility, we explore contextual correlates of school-specific mobility and persistence estimates in Table 3.¹⁷ All non-binary covariates are standardized to mean zero, standard deviation one for ease of interpretation. Table A.1.5 in the Appendix provides descriptions of the distribution and number of schools for each covariate of interest. We examine correlates previously identified as possibly related to intergenerational mobility: local race-ethnicity makeup, portion of single parents, and the local income distribution (Chetty et al., 2014). Halliday et al. (2021) also suggest the U.S. South experiences differentiated health mobility, and we therefore also examine regional differences. In our sample, we do not find the South to experience altered health mobility relative to non-Southern schools (row 1), although the West specifically may have lower health persistence and greater downward health mobility relative to the South (row 2). Areas with higher shares of non-Hispanic Black residents tend to experience lower health persistence, and more absolute downward mobility (row 4). Point estimates characterizing the area’s income distribution suggest higher median income may be associated with more health persistence and less absolute upward health mobility. Meanwhile more income inequality (as measured by the area’s standard deviation of income) could be associated with less health persistence (row 5), although the coefficient declines and becomes insignificant if urbanicity is also controlled (see Table A.1.6). Finally, a larger portion of single parents in the area is associated with lower health persistence and more absolute downward mobility (row 7).

Table 3:

Correlates of intergenerational health persistence and mobility

		Rank Slope	E(rankc|rankp=25)	E(rankc|rankp=75)
	Full Sample Estimate:	0.170	47.4	55.9
1	South (ref. not South)	0.029	0.232	1.702
		(0.026)	(1.616)	(1.546)
2	West (ref. South)	−0.072*	−0.105	−3.725+
		(0.034)	(2.091)	(2.007)
	Midwest	0.014	−2.826	−2.125
		(0.034)	(2.067)	(1.984)
	Northeast	−0.032	3.352	1.744
		(0.038)	(2.351)	(2.256)
3	Rural (ref. Urban)	0.052	−4.096	−1.503
		(0.041)	(2.522)	(2.440)
	Suburban	0.038	−1.535	0.377
		(0.029)	(1.772)	(1.714)
4	% non-Hispanic Black	−0.031*	−0.683	−2.232**
		(0.014)	(0.863)	(0.806)
	% Hispanic	−0.018	−0.057	−0.934
		(0.014)	(0.873)	(0.815)
	% Other race-ethnicity	−0.008	0.681	0.302
		(0.015)	(0.936)	(0.873)
5	Median Income	0.020	−1.337	−0.352
		(0.027)	(1.658)	(1.606)
	σ Income	−0.042+	2.150	0.066
		(0.024)	(1.468)	(1.422)
6	Average mother’s education	0.028*	1.607*	2.987***
		(0.013)	(0.783)	(0.716)
7	% Single Parents	−0.033*	0.301	−1.330+
		(0.013)	(0.832)	(0.790)
8	Hospital Beds	−0.015	1.585+	0.841
		(0.013)	(0.821)	(0.796)
9	School PTA	−0.100*	4.086	−0.922
		(0.046)	(2.840)	(2.752)
10	Health Ed. Requirement	−0.001	3.061	3.024
		(0.045)	(2.788)	(2.675)
11	% Smokers	−0.002	−0.879	−0.993
		(0.017)	(1.093)	(1.014)

Source:Authors’ calculations using Add Health

Notes:Each numbered row corresponds to a separate regression. Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c|rank_p=25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p=75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). All models control for regional fixed effects except estimates for just the South (row 1). Standard errors in parentheses,

^**p<0.01,

^*p<0.05,

⁺p<0.1

We investigate a few additional correlates that could be pertinent particularly for health mobility. Whether a community is urban or rural could relate to different patterns in health and healthcare, while the availability of local hospital beds and portion of smokers could be indicative of healthcare availability and behaviors respectively. Average parent education, school health education requirements, or Parent Teacher Associations could also be suggestive of local parent involvement in children’s education and/or local priorities around health.¹⁸ In our school sample, we do not detect significant differences across urbanicity; however, the point estimate for upward mobility of rural schools suggests these areas have 4 percentiles less upward mobility relative to urban schools (row 3). One of the strongest correlates of health mobility and persistence appears to be the average educational attainment of mothers at the school. One standard deviation increase in average maternal education is linked to 0.028 greater health persistence, 1.6 percentiles more upward mobility and 3 percentiles less downward mobility (row 6). Schools located in areas with more hospital beds are estimated to have higher upward health mobility (row 8). Finally, there are specific school characteristics that are associated with health mobility or persistence. Schools with a Parent-Teacher Association (PTA) have lower health persistence (row 9), although we note that relatively few schools in this sample lack a PTA (see Table A.1.5 in Appendix). Point estimates for health education requirements suggest such policies are associated with an increase in upward health mobility and decrease in downward mobility by around 3 percentiles each, although these estimates are not statistically significant (row 10). Surprisingly, the portion of smokers in the area appears unrelated to health persistence or mobility (row 11).

4. Discussion

The results of this study rely heavily on a number of properties established in Halliday et al. (Halliday et al., 2020, 2021) due to limitations in Add Health. First, the analysis relies on self-rated health status as a valid measure of actual health status. To alleviate some concerns with the marginal distribution of a five-point Likert scale, the HALex index (Erickson, 1998; Erickson et al., 1995; Halliday et al., 2021; Johnson & Schoeni, 2011) is incorporated to better capture health as reported in five self-rated health categories. Fortunately, Halliday et al. (2021) leverage rich health data in PSID to help further validate self-reported health status as a suitable proxy for general health specifically in the intergenerational health persistence context. In addition to using self-reported health status, they also estimate intergenerational health persistence using a more objective measure of health that includes 21 indicators of physical and mental health and find similar estimates. Thus, the use of self-reported health status remains a plausible option for examining heterogeneity of intergenerational health relationships in the U.S.

Second, these results assume measurement error in both generations predictably attenuates results semi-consistently across context and space. More specifically, Halliday et al. (2021) are able to construct a series of health persistence estimates while varying the number of observations and the age at which an individual is observed in the data. They demonstrate mother-daughter (and father-daughter) health persistence increases from 0.21 (0.17) to around 0.31 (0.29) when increasing the number of years parent health is observed from one to eight years. Our analysis estimates health persistence at 0.170 with one year of parent health and up to four waves of child health. We then assume that the measurement error does not otherwise systematically vary across schools in further analysis.¹⁹ Therefore, we expect attenuation bias may reduce national health persistence estimates in Add Health by 30–40%. However, the main contribution of this analysis is examining heterogeneity of intergenerational health mobility. Findings of significant heterogeneity by parent and child characteristics and geography are not likely to be significantly altered as long as such biases operate similarly across schools. In spite of these limitations, Add Health remains an excellent source to broadly explore heterogeneity of intergenerational health mobility and persistence because of its relatively large sample size and spatial clustering in the school-based design.

If national persistence estimates from this study (i.e. β₁ = 0.170) are attenuated by 30–40%, estimates would be broadly consistent with previous research. For example, the few studies that have estimated intergenerational health persistence have found β₁ coefficients from equations 1 or 2 to be 0.2 – 0.3 for self-rated health status using the PSID (Halliday et al., 2020, 2021), 0.163 for mental health using the 1970 British Birth Cohort Study (Johnston et al., 2013), around 0.2 for birth weight in California (Currie & Moretti, 2007), and 0.284 – 0.42 for Body Mass Index using the National Longitudinal Survey of Youth and National Health Interview Survey (Classen, 2010; Classen & Thompson, 2016). Our analysis also estimates absolute mobility for children from the 25^th and 75^th percentile of parent health to be around the 47^th and 56^th percentiles, which closely matches estimates from Halliday et al. (2021) who find absolute mobility to be the 44^th and 57^th percentiles respectively. Fletcher and Jajtner (2020) though find absolute mobility to be a little more sticky in a sample of younger children²⁰ – with absolute mobility estimated at the 41^st and 62^nd percentiles respectively.

Results from our analysis suggest the environment, and not exclusively genetic factors, plays a role in determining the intergenerational transmission of health. Specifically, in this analysis health persistence decreases by approximately 33% in the adoptee sample relative to the biological parent-child pair sample. Thompson (2014) finds intergenerational persistence to decrease by approximately 20–30% for health conditions including asthma, chronic headaches and hay fever. A more recent study on the intergenerational transmission of Body Mass Index (BMI) however found an adoptee sample with an estimated elasticity of −0.008, which was not statistically significant, relative to a biological sample with elasticity of 0.202 (Classen & Thompson, 2016). Considering the estimates presented in this paper are concerned with overall health as measured by self-reported health status, it is unsurprising to find slope coefficients attenuated by 33% in the adoptee sample, between estimates from Thompson (2014) and Classen & Thompson (2016). Collectively the evidence suggests that while genetic factors likely play a non-negligible role in the persistence of health across generations, there is a rather sizable portion of intergenerational health persistence which appears to be related to environment factors.

Estimates regarding heterogeneity of intergenerational health mobility and persistence in many ways corroborate limited previous findings, but also uncover novel patterns. For example, children without health insurance or whose mother has less than a high school education are found to experience lower health rank, which is consistent with estimates in Halliday et al. (2021). Our analysis also extends stratifications of parent child characteristics finding children whose parents are unmarried also experience lower health rank relative to their more advantaged peers.

Our analysis only partially corroborates previous findings with respect to heterogeneity by race-ethnicity. Non-Hispanic Black parent-child pairs are typically found to experience disadvantages in intergenerational economic mobility (Chetty et al., 2018; Hertz, 2005; Mazumder, 2014). Early research in intergenerational health persistence, where health is defined by birth weight, finds mixed evidence with respect to race. A dichotomous indicator of low birth weight finds greater intergenerational persistence of health for Blacks relative to Whites, while a log transformation of continuous birth weight suggests less intergenerational persistence for Blacks relative to Whites (Currie & Moretti, 2007). Halliday et al. (2021) finds Black parent-child pairs experience less health persistence (rank slope coefficient is 0.13 relative to White rank slope coefficient of 0.243), but a gap in expected absolute health mobility among children whose parents are at the 25^th percentile of parent health around ten percentiles. That analysis also finds more downward health mobility for Black children whose parents are at the 75^th percentile of parent health, a gap of approximately 15 percentiles (see Table 4 below). Recent results from a sample with younger children also suggests a significant gap in absolute mobility for non-Hispanic Black and non-Hispanic White children of approximately 7 and 9 percentiles at the 25^th and 75^th percentiles respectively (Fletcher & Jajtner, 2020). Our estimates are similar to Halliday et al. (2021) with respect to relative mobility, or health persistence. However, we find little gap in expected absolute mobility for these groups as shown in Table 4. It is unclear what the source of this discrepancy is – whether it could be due to inclusion of relatively few Hispanic parent-child pairs in the Halliday et al. (2021) analysis, if health discrepancies have not manifested by the relatively early age at which Add Health participants are observed, cohort differences, or if there may be some other reason.

Table 4:

Comparison of race stratified results

	Add Health		PSID
	nH White	nH Black	White	Black
Rank Slope	0.200	0.144	0.243	0.130
E(rankc|rankp=25)	47.2	46.4	46.5	36.8
E(rankc|rankp=75)	57.2	53.6	58.7	43.3
Observations	5856	1966	4555	3139

Source:Authors’ calculations using Add Health and estimates from Halliday et al. (2021)

Notes:Parent-Child PSID results found in Halliday et al. (2021) Table 8, which partitions the sample by race only. “nH”: non-Hispanic.

We also extend knowledge on variation by race-ethnicity by providing comparable estimates specifically for Hispanic-Americans. Our estimates suggest Hispanic-Americans have very low health persistence (i.e. β₁=0.072) and greater downward health mobility relative to non-Hispanic Whites. Previous research finds children of Mexican-born mothers are less likely to have low birth weight compared to children of US-born mothers. This particular health advantage erodes in the subsequent generation as grandchildren of these same mothers face more similar probabilities of low birth weight (Giuntella, 2017). Literature also suggests Hispanic immigrants may be in better health relative to their US-born counterparts once SES is taken into account (Crimmins et al., 2007; Hamilton et al., 2015). However, this advantage is not necessarily reflected in later life disability. For example, foreign-born Hispanics in the U.S. have an increased incidence of Activities of Daily Living even after adjusting for SES, stress exposure and smoking habits (Boen & Hummer, 2019). With more than 20% of parents in this Add Health Hispanic subsample being born outside the U.S., future research should investigate the link between these two strains of literature.²¹

Another key contribution of this paper is uncovering novel patterns and significant heterogeneity in intergenerational health mobility and persistence based on schools and location. These results uncovering high geographic heterogeneity of intergenerational health relationships extend research finding geographic variation in intergenerational economic mobility (Chetty et al., 2014). Halliday et al. (2021) also find absolute health mobility to be lowest in the South, although limitations from PSID prevent a more granular analysis. Add Health schools located in the South though do not appear to have systematically differentiated health mobility or persistence. Generally, schools identified with low health persistence (i.e. high relative health mobility) also experience high absolute health mobility, although the correlation of these metrics is far from perfect.²² In extending previous research, this analysis finds areas with higher portions of single parents may experience less health persistence. We also find limited evidence that health persistence may be lower in areas with more inequality. These results are in contrast with local characteristics of economic mobility in Chetty et al. (2014) which finds more income inequality and higher portions of single mothers are associated with lower economic mobility (i.e. more persistence). We caution that further research in this direction with a larger sample is required. Our results simply suggest a correlational direction to relationships between health persistence or mobility with local characteristics. Statistical significance of these results furthermore must be caveated. We do not account for multiple hypotheses testing in the reported p-values. As many of the statistical associations are marginal to begin with, we elected to report coefficients and statistical significance without adjustment to provide guidance for future research on potentially fruitful avenues.

Overall, evidence from this analysis suggests there is wide dispersion in intergenerational health mobility and persistence in the U.S. that is correlated with parent or child characteristics and location. National health persistence using Add Health is found to be 0.170 (95% confidence interval: 0.137 – 0.204). Absolute mobility for children whose parents are at the 25^th (75^th) percentile of parent health is estimated to be 47.4 (55.9), meaning children are expected to reach approximately the 47^th and 56^th percentiles respectively conditional on parent health rank. Leveraging rich covariates on parent-child characteristics and the spatially clustered sampling design of Add Health reveals significant heterogeneity in intergenerational health mobility and persistence. For example, children with health insurance, from homes with married parents, or a mother with more than a High School credential tend to have higher expected health rank relative to their more disadvantaged peers. Areas with high proportions of minorities and single parents may experience less persistence while areas with high average maternal education have high persistence and absolute mobility. These findings represent an important step in better understanding how the health of one generation is related to another generation. While stratifications utilized in this analysis are clearly non-causal, it lends support to the notion that health is not predetermined, and that policies and the environment can potentially play a modifying role in the persistence of health to subsequent generations.

Appendix

A.1. Tables of Main Results

Table A.1.1:

Intergenerational health persistence and mobility stratified by race-ethnicity

	Full Sample	nH White	nH Black	Hispanic
Beta	0.170	0.200	0.144	0.072
-- s.e.	0.017	0.017	0.041	0.033
-- lower limit	0.137	0.167	0.063	0.007
-- upper limit	0.204	0.233	0.225	0.137
E(rankc| rankp =25)	47.4	47.2	46.4	48.3
-- s.e.	0.85	0.94	1.41	2.19
-- lower limit	45.7	45.3	43.7	44.0
-- upper limit	49.1	49.0	49.2	52.6
E(rankc| rankp =75)	55.9	57.2	53.6	51.9
-- s.e.	0.71	0.71	1.92	2.09
-- lower limit	54.5	55.8	49.9	47.8
-- upper limit	57.4	58.6	57.4	56.0
N	10112	5856	1966	1658

Source:Authors’ calculations using Add Health

Notes:Table A.1.1 corresponds to Figure 1 in the text. Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c| rank_p =25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health (i.e. absolute upward health mobility), and E(rank_c| rank_p =75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute downward health mobility). Estimates are weighted and use the full Add Health sample. Standard errors (s.e.) are below the estimates, and lower and upper limits refer to the 95% confidence intervals.

Table A.1.2:

Intergenerational health persistence and mobility stratified by race-ethnicity, mothers vs. fathers and daughters vs. sons

	Mothers & All Children				Fathers & All Children
	Full Sample	nH White	nH Black	Hispanic	Full Sample	nH White	nH Black	Hispanic
Beta	0.161	0.177	0.150	0.086	0.137	0.167	0.102	0.056
-- s.e.	0.018	0.019	0.041	0.037	0.017	0.019	0.063	0.042
-- lower limit	0.125	0.139	0.070	0.013	0.103	0.130	−0.023	−0.028
-- upper limit	0.197	0.214	0.230	0.159	0.171	0.205	0.227	0.140
E(rankc| rankp =25)	48.0	48.2	46.8	48.4	48.8	48.6	47.6	48.7
-- s.e.	0.9	1.0	1.4	2.3	0.8	1.1	1.8	2.0
-- lower limit	46.2	46.3	44.0	43.9	47.1	46.5	44.1	44.7
-- upper limit	49.8	50.1	49.7	53.0	50.4	50.7	51.1	52.7
E(rankc| rankp =75)	56.0	57.1	54.3	52.7	55.7	57.0	52.7	51.5
-- s.e.	0.7	0.8	1.8	1.9	0.9	1.0	2.5	2.6
-- lower limit	54.6	55.5	50.7	48.9	53.8	55.1	47.7	46.3
-- upper limit	57.5	58.6	58.0	56.5	57.5	58.8	57.8	56.7
N	9909	5727	1938	1630	7731	4892	1095	1224
	All Parents & Daughters				All Parents & Sons
	Full Sample	nH White	nH Black	Hispanic	Full Sample	nH White	nH Black	Hispanic
Beta	0.184	0.206	0.192	0.122	0.156	0.190	0.118	0.009
-- s.e.	0.024	0.024	0.069	0.043	0.020	0.022	0.047	0.044
-- lower limit	0.137	0.159	0.056	0.037	0.116	0.146	0.025	−0.078
-- upper limit	0.231	0.253	0.329	0.206	0.196	0.234	0.211	0.097
E(rankc| rankp =25)	46.5	46.2	45.4	46.6	48.1	48.0	47.1	49.9
-- s.e.	1.1	1.2	2.2	2.8	1.0	1.3	1.8	2.5
-- lower limit	44.4	43.9	41.1	41.0	46.1	45.4	43.5	45.0
-- upper limit	48.7	48.6	49.7	52.2	50.2	50.5	50.8	54.8
E(rankc| rankp =75)	55.7	56.5	55.0	52.7	55.9	57.5	53.1	50.3
-- s.e.	1.1	1.0	3.4	3.3	0.9	1.0	2.4	2.9
-- lower limit	53.6	54.5	48.4	46.2	54.1	55.4	48.4	44.6
-- upper limit	57.8	58.5	61.7	59.1	57.8	59.5	57.7	56.1
N	5217	3011	1068	829	4895	2845	898	829

Source:Authors’ calculations using Add Health

Notes:Mothers typically report health status for fathers. Health ranks are sex-specific (i.e. daughter’s health is ranked among daughters and father’s health is ranked among fathers). Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c| rank_p =25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health (i.e. absolute upward health mobility), and E(rank_c| rank_p =75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute downward health mobility). Estimates are weighted and use the full Add Health sample. Standard errors (s.e.) are below the estimates, and lower and upper limits refer to the 95% confidence intervals.

Table A.1.3:

Intergenerational health persistence for biological and adopted children

	Full Sample	nH White	nH Black	Hispanic
Biological	0.173	0.210	0.111	0.105
-- s.e.	0.008	0.011	0.019	0.021
-- N	14569	8235	3024	2432
Adopted	0.115	0.121	0.021	0.283
-- s.e.	0.035	0.042	0.092	0.112
-- N	845	565	135	79
-- p-value: Biological vs. Adopted	0.11	0.03	0.34	0.14

Source:Authors’ calculations using Add Health

Notes:Adopted children are identified if either parent is not a biological parent. Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence).

Table A.1.4:

Distribution of school-stratified estimates of intergenerational health persistence and mobility

	Rank Slope	E(rankc|rankp=25)	E(rankc|rankp=75)
Minimum	−0.201	26.34	20.56
10th	−0.043	35.89	43.13
25th	0.043	41.00	48.66
50th	0.161	46.92	54.86
75th	0.261	53.37	60.63
90th	0.341	59.11	63.69
Maximum	0.489	76.49	76.68

Source:Authors’ calculations using Add Health

Notes:Table A.1.4 corresponds to Figure 2 in the text. Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c|rank_p = 25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p = 75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). Estimates are not weighted, but use only children identified in the Core sample to produce school-specific results.

Table A.1.5:

Distribution of local characteristics

	N	Mean	s.d.
West	131	0.214	0.412
Midwest	131	0.221	0.417
Northeast	131	0.153	0.361
South	131	0.412	0.494
Rural	131	0.145	0.353
Suburban	131	0.550	0.499
Urban	131	0.305	0.462
% nH Black ^	131	21.9	27.6
% Hispanic ^	131	13.1	18.8
% Other Race-ethnicity ^	131	5.3	8.5
Median Income ($1,000s 1990 dollars) ^	131	29.6	8.1
σ Income ($1,000s 1990 dollars) ^	131	29.4	5.5
Average Mother’s Education ^	131	13.2	0.9
% Single Parents ^	131	11.5	3.4
Hospital Beds (per 100,000) ^	131	456.1	257.4
School PTA	129	0.91	0.28
Health Ed. Requirement	131	0.80	0.40

Source:Authors’ calculations using Add Health

Notes:Mean represents the average of each characteristic over N schools in the sample. “s.d.” is the standard deviation among the N school’s characteristic.

^{^}represents covariates that are standardized to mean zero, standard deviation one.

Table A.1.6:

Correlates of intergenerational health persistence and mobility (with urbanicity controls)

		Rank Slope	E(rankc|rankp=25)	E(rankc|rankp=75)
	Full Sample Estimates	0.170	47.4	55.9
1	South (ref. not South)	0.029	0.232	1.702
		(0.026)	(1.616)	(1.546)
2	West (ref. South)	−0.068*	−0.537	−3.951+
		(0.034)	(2.107)	(2.038)
	Midwest	0.013	−2.910	−2.269
		(0.034)	(2.072)	(2.004)
	Northeast	−0.029	3.004	1.569
		(0.038)	(2.356)	(2.279)
3	Rural (ref. Urban)	0.052	−4.096	−1.503
		(0.041)	(2.522)	(2.440)
	Suburban	0.038	−1.535	0.377
		(0.029)	(1.772)	(1.714)
4	% non-Hispanic Black	−0.029*	−0.978	−2.449**
		(0.014)	(0.872)	(0.818)
	% Hispanic	−0.010	−0.900	−1.424
		(0.016)	(1.011)	(0.948)
	% Other race-ethnicity	−0.009	0.738	0.301
		(0.015)	(0.935)	(0.877)
5	Median Income	0.013	−1.228	−0.582
		(0.028)	(1.755)	(1.702)
	σ Income	−0.033	1.611	−0.064
		(0.026)	(1.610)	(1.561)
6	Average mother’s education	0.027*	1.700*	3.069***
		(0.013)	(0.809)	(0.747)
7	% Single Parents	−0.030*	0.099	−1.415+
		(0.013)	(0.840)	(0.803)
8	Hospital Beds	−0.013	1.431+	0.804
		(0.014)	(0.828)	(0.808)
9	School PTA	−0.092+	3.287	−1.312
		(0.047)	(2.903)	(2.825)
10	Health Ed. Requirement	0.008	2.854	3.274
		(0.046)	(2.822)	(2.725)
11	% Smokers	−0.005	−0.600	−0.828
		(0.018)	(1.116)	(1.041)

Source:Authors’ calculations using Add Health

Notes:Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations (i.e. health persistence). E(rank_c|rank_p=25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p=75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). All models control for regional fixed effects and urbanicity except estimates for just the South (row 1). Standard errors in parentheses,

^**p<0.01,

^*p<0.05,

⁺p<0.1

A.2. The IHA Slope

Halliday et al. (2018) develop a measure of intergenerational health persistence measure that is analogous to the Intergenerational Elasticity of Income (IGE) – the Intergenerational Health Association (IHA). Using HALex adjusted self-reported health²³ the authors estimate an Ordinary Least Squares (OLS) regression of parent health on child health as in equation 1, with β₁ measuring the IHA.

$$SRH{S}_c={\beta }_0+{\beta }_{1}SRH{S}_p+\sum {\beta }_z{C}_z+\epsilon$$ (1)

Halliday et al. (2020) however find the IHA to higher when using a nonlinear model relative to the linear OLS model applied in Halliday et al. (2018). The key assumption of linearity however appears to hold when using ranks of HALex adjusted self-reported health status (Halliday et al. 2020).

Our main analysis therefore adopts a rank-based methodology to examine heterogeneity in intergenerational health persistence and mobility. For completeness however, we briefly include results based on the IHA developed in Halliday et al. (2018). This sample estimates an IHA slope of 0.086 (95% CI 0.066 – 0.105) as seen in Table A.2.1. However, due to limitations in Add Health detailed in the background and discussion of the main paper, it is expected that this national estimate is attenuated. Although the IHA slope presents some challenges with estimation, patterns observed with the Rank slope appear mostly stable. The point estimates for non-Hispanic black parent-child pairs health persistence is smaller than the non-Hispanic white subpopulation and Hispanics appear to have the least health persistence.

Table A.2.1:

Intergenerational health persistence stratified by race

	Full Sample	nH White	nH Black	Hispanic
IHA Slope	0.086	0.102	0.071	0.049
-- s.e.	0.010	0.013	0.023	0.014
-- lower limit	0.066	0.077	0.027	0.021
-- upper limit	0.105	0.126	0.116	0.077
Rank Slope (Beta)	0.170	0.200	0.144	0.072
-- s.e.	0.017	0.017	0.041	0.033
-- lower limit	0.137	0.167	0.063	0.007
-- upper limit	0.204	0.233	0.225	0.137

Source:Authors’ calculations using Add Health

Notes:Table A.2.1 extends Table A.1.1 by including IHA slope estimates. IHA slope is the β₁ coefficient using HALex adjusted self-reported health in both generations. Rank slope is the β₁ coefficient using HALex adjusted self-reported health ranks in both generations. Estimates are weighted and use the full Add Health sample (sample sizes in Table A.1.1). Standard errors (s.e.) are below the estimates, and lower and upper limits refer to the 95% confidence intervals.

School-specific health persistence estimates using the IHA slope also exhibit a wide range of estimates as shown in Figure A.2.1 below. As discussed in greater detail in the following section (Appendix A.3), school-specific IHA slope estimates of persistence are likely noisy estimates, and there is reason to believe that these estimates may be no better than a random assignment of parent-child pairs to arbitrary schools.

Figure A.2.1.

School-stratified estimates of IHA slope

Source: Authors’ calculations using Add Health

Notes: IHA slope is the β₁ coefficient using HALex adjusted self-reported health in both generations. Estimates are not weighted, but use only children identified in the core sample to produce school-specific results. Solid red lines represent the full (national) estimates, while dashed red lines indicate perfect mobility (i.e. β₁ = 0). Black dots/line represent school-specific estimates. Vertical lines are the corresponding 95% confidence intervals for school estimates.

A.3. Falsification exercise of noise in school-specific estimates

Figure 2 highlights the observation that there is significant heterogeneity of intergenerational health mobility and persistence by school. However, the large confidence intervals around each of these individual estimates reflects that many of these schools are small and the estimates are subject to sampling variation. Recall that, for each school, a random sample of the students are selected for the Core sample that we use to estimate our intergenerational health measures, so we anticipate that the school level results are not biased but are noisy. In order to test whether estimates are able to capture the underlying signal apart from the sampling noise in the data, we explore a randomization exercise.

Briefly, we randomly allocate the set of students in our data to the set of schools and re-estimate the main school-level health persistence and mobility measures. We repeat this exercise one thousand times in order to construct a distribution of effect estimates that we then compare to our estimates using the true school assignments.

To provide more details: Although parent-child pairs are randomly assigned to schools, the school retains its size (or number of observations) for each iteration. For the purposes of this appendix, we refer to data obtained from this falsification exercise as the “false data”. While pure random assignment should produce deviations from the mean, we posit that there should be more variation in the true data relative to the false data. Visually in Figure 2, we hypothesize that the area between the curve produced by sequentially ordering schools based on their health mobility or persistence estimates (i.e. the black line of dots) and average health mobility or persistence (i.e. the red solid line) should be greater in the true data relative to the false data if the estimates from the true data differ from sampling variation. We calculate this area as a single value representing the absolute value of deviations from the estimated sample mean over all 131 schools. This value is calculated for each replication (and the true data) and each health mobility or persistence measure as in equation A.3.1. M_i is the school-specific estimated persistence or mobility measure from either the true data or one of the 1,000 replications while $\widehat{\mu }$ is the pooled sample mean of the measure in Add Health data.

$$\text{Mean Deviation }=\sum _i\left|\left(M_i-\widehat{\mu }\right)\right|$$ (A.3.1)

The figure below (Figure A.3.1) shows that variation from the true data exceeds variation from false data with 95% confidence in all intergenerational measures. When considering absolute mobility (both conditional on parent rank at the 25^th and 75^th percentile), the calculated mean deviation for the true data is far outside any estimate produced in the false data replication. For example, the largest mean deviation for absolute mobility conditional on parents in the 25^th or 75^th percentile is 844.743 and 753.77 respectively as shown in Table A.3.1. The true data’s mean deviation in these metrics however exceeds 900 units. Health persistence, or relative mobility, also passes this falsification test, although less persuasively. The true data’s mean deviation measures 15.723, which lies outside the 95% empirical distribution of replications. There are however a handful of false data replications that do exceed the mean deviation in the true data. Therefore, these three measures appear to be highlighting school-specific variation that is not due to chance²⁴.

Figure A.3.1:

Mean deviations for one thousand replications and the true data

Source: Authors’ calculations using Add Health

Notes: Rank slope is the β₁ coefficient using HALex adjusted health ranks in both generations (i.e. health persistence). E(rank_c|rank_p=25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p=75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility). Plots for each metric are a kernel density plot of mean deviations for one thousand replications. The mean of all random estimates is shown with the solid red line and corresponding 95% confidence interval (i.e. middle 95% of replications) is represented by the dashed lines. Add Health estimates from true data are shown by the red dot.

Table A.3.1:

True data mean deviation relative to false data replications

	Rank Slope	E(rankc|rankp=25)	E(rankc|rankp=75)
True Data	15.905	951.265	904.332
Replications	1000	1000	1000
-- minimum	11.109	521.298	491.109
-- bottom 2.5%	11.777	571.405	540.276
-- top 2.5%	15.345	754.890	690.100
-- maximum	16.669	805.971	742.094

Source:Authors’ calculations using Add Health

Notes:Rank slope is the β₁ coefficient using HALex adjusted health ranks in both generations (i.e. health persistence). E(rank_c|rank_p=25) is the expected health rank for a child conditional on his/her parent observed at the 25^th percentile of parent health, and E(rank_c|rank_p=75) is the expected health rank for children whose parent(s) are observed at the 75^th percentile of parent health (i.e. absolute health mobility).