Does Schooling Improve Cognitive Abilities at Older Ages? Causal Evidence From Nonparametric Bounds Open Access

Abstract

We revisit much-investigated relationships between schooling and health, focusing on schooling impacts on cognitive abilities at older ages using the Harmonized Cognition Assessment Protocol in the Health and Retirement Study (HRS) and a bounding approach that requires relatively weak assumptions. Our estimated upper bounds on the population average effects indicate potentially large causal effects of increasing schooling from primary to secondary. Yet, these upper bounds are smaller than many estimates from studies of causal schooling impacts on cognition using compulsory schooling laws. We also cannot rule out small and null effects at this margin. However, we find evidence for positive causal effects on cognition of increasing schooling from secondary to tertiary. We replicate findings from the HRS using data on older adults from the Midlife in United States Development Study Cognitive Project. We further explore possible mechanisms behind the schooling effect (e.g., health, socioeconomic status, occupation, and spousal schooling), finding suggestive evidence of effects through such mechanisms.

Introduction

Does schooling have a causal effect on cognition at older ages? This question is important for several reasons. First, cognitive health is a vital component of the overall health and well-being of older adults, who represent an increasing segment of the population because of population aging. In 2020, 17% of the U.S. population was aged 65 or older, compared with 5% of the population in 1920. The growth rate of the older population over this period is almost five times that of the total population (Caplan 2023). Lower cognitive functioning is associated with a poorer quality of life owing to difficulties in performing daily activities (Garrett et al. 2019), increased disabilities (Lee et al. 2005), and higher mortality risks (Batty et al. 2016). Understanding the causal effects of schooling on older age cognition can thus help determine whether investing in schooling will lead to health improvements for older adults.

Second, the causal effect of schooling on older adults’ cognition has important implications for tackling Alzheimer's disease and related dementia (ADRD), a pressing public health issue. In 2023, 6.7 million Americans were living with ADRD, and this figure is projected to reach 13.8 million by 2060 (Alzheimer's Association 2023). The health care costs of ADRD are forecast to increase from $345 billion in 2023 to $1 trillion in 2050 (Alzheimer's Association 2023). ADRD also imposes substantial costs on caregivers. In 2022, more than 11 million caregivers provided 17 billion hours of care worth $340 billion (Alzheimer's Association 2023). Although age is the largest risk factor for ADRD, schooling has been identified as a modifiable early-life intervention to tackle ADRD. The 2024 Lancet Commission on Dementia Prevention, Intervention, and Care estimated that 5% of dementia cases could be avoided by increased levels of basic schooling (Livingston et al. 2024), and research in the United States has found that increases in schooling attainment are significantly associated with declining dementia trends (Hudomiet et al. 2022).

One mechanism through which schooling can reduce dementia risks is improving cognitive abilities at older ages. Neuropsychological testing is widely used to determine whether individuals meet the criteria for dementia diagnoses. Higher schooling attainment is associated with better performance on cognition tests (Opdebeek et al. 2016); higher attainment is associated with a lower likelihood of being diagnosed with dementia according to existing thresholds and thus a later age at dementia onset. Small delays in age at onset can lead to large reductions in population disease burdens. For example, Brookmeyer et al. (1998) projected that a 2015 intervention to delay dementia onset by one year would reduce global cases in 2050 by 10% (12 million). Given the potentially large effect of schooling on overall dementia cases operating through the age at dementia onset, understanding whether schooling has a causal effect on the cognition of older individuals is vital for assessing future dementia trends, given that cohorts reaching older ages will have higher levels of schooling as a result of schooling expansion in the twentieth century.

Third, poor cognition and ADRD have important financial ramifications. Lower cognitive function at older ages is associated with less favorable financial outcomes. Banks and Oldfield (2007) found that low levels of numeracy were associated with lower levels of wealth and a lower probability of owning a private pension among individuals in the English Longitudinal Study of Ageing (ELSA). Using data from the U.S. Health and Retirement Study (HRS), Angrisani and Lee (2019) found that declines in household financial decision-makers’ cognition scores were associated with reductions in household wealth. Nicholas et al. (2021) found that individuals with ADRD were more likely to miss bill payments six years before diagnosis and develop subpar credit scores 2.5 years before diagnosis. Thus, policies to increase schooling attainment might improve the health and financial standing of older adults if schooling has a causal effect on cognition decades later in life at older ages.

Figure 1 illustrates mechanisms through which schooling could affect cognition at older ages. Schooling can improve older adults’ cognition by reducing age-related brain pathology (brain maintenance) and by building cognitive reserve (Stern et al. 2023). Schooling is hypothesized to protect the brain from age-related pathology, such as the white matter damage that accumulates in all older adults, thus aiding brain maintenance. Cognitive reserve refers to the brain's ability to maintain successful cognitive performance despite age-related brain changes. Cognitive stimulation that occurs during schooling is thought to build cognitive reserve. Schooling attainment is a marker of cognitive reserve, and higher schooling attainment is hypothesized to allow individuals to process and store information that allows for normal cognitive functioning despite brain aging (Stern 2002). Some empirical evidence found that schooling was associated with cognitive reserve but not brain maintenance (Zahodne et al. 2019).¹

Schooling might have indirect effects through socioeconomic status (SES) and health at middle and older ages. More schooling is associated with greater income, enabling the purchase of basic health-enhancing resources. Individuals with more schooling might be more likely to work in cognitively stimulating occupations or more frequently engage in cognitively stimulating activities (e.g., social/cultural clubs) that build cognitive reserve. Similarly, more schooling is associated with better self-reported health and lower likelihoods of depression and smoking, which are associated with better cognition. Another indirect channel is marriage. Highly schooled individuals tend to have highly schooled spouses, and spousal schooling is positively associated with cognition at older ages (Liu et al. 2024; Saenz et al. 2020; Xu 2020). Spousal schooling can influence cognition at older ages by promoting healthier behaviors and increasing household SES (income/wealth) and cognitive reserve through engagement in cognitively stimulating activities.

Alternatively, associations between schooling and cognition at older ages might reflect the influence of earlier abilities or other unobserved confounders (e.g., genetics and family background) that are correlated with schooling and older age cognition rather than causal relationships. Studies using schooling reforms as natural experiments have found evidence of a causal effect of schooling on cognition at ages 19–20 (Brinch and Galloway 2012; Lager et al. 2017; Xiao et al. 2017), suggesting that early-life cognition could be a confounding factor. Hence, it is important to determine whether the relationship between schooling and older age cognition is causal.

The literature on the causal effects of schooling on cognition at older ages is surprisingly sparse. Some studies using changes in compulsory schooling laws to identify exogenous variation in schooling attainment (e.g., Banks and Mazzonna 2012; Glymour et al. 2008; Gorman 2023; Schneeweis et al. 2014) have found protective effects on immediate and delayed memory, with estimates showing that an extra grade of schooling improved immediate and delayed memory scores by 0.08–0.50 standard deviations (SD). However, findings for other cognitive domains are mixed.

Despite some advantages of estimates based on compulsory schooling laws, such estimates also have shortcomings. First, they capture the effects only for individuals whose schooling is causally increased by such laws rather than effects for the general population. Second, they mostly represent the effects of increasing schooling from primary to secondary education and are not directly informative about the effects of schooling elsewhere in the educational distribution. Third, causal inference relies on the relatively strong assumption that school reforms affect cognition only through their effect on schooling (the exclusion restriction), which might not always hold (e.g., Avendano et al. 2020).

We provide new evidence on the causal effect of schooling on cognition at older ages using the Harmonized Cognition Assessment Protocol (HCAP) in the HRS. We use a nonparametric partial-identification approach (Manski and Pepper 2000), which provides bounds on the causal effect using relatively weak and arguably credible assumptions. Specifically, we assume that (1) there is positive selection into schooling such that individuals with higher schooling attainment have, on average, higher latent cognition; and (2) more schooling does not worsen cognitive abilities. We then employ the mother's schooling attainment as a monotone instrumental variable (IV)—a variable that is assumed to have a weakly increasing mean relationship with potential outcomes—to help tighten the bounds under these assumptions.

Our approach has several attractive features. First, it provides bounds on the population average treatment effect (ATE) instead of the average effect for a subpopulation, such as those for whom compulsory schooling laws are binding. Second, it allows for arbitrary correlations between schooling and unobserved factors that can affect cognition. Third, it allows us to look at dose–response relations between schooling and cognition by providing bounds on the effect of increasing schooling at different parts of the educational distribution (e.g., going from being a high school dropout to a high school graduate or from being a high school graduate to a college graduate). Obtaining credentials (a high school diploma or a college degree) might have important effects on cognition because credentials likely have large effects on midlife conditions, such as income and occupation. Nonlinear effects of schooling have been observed for other health outcomes, including mortality (Montez et al. 2012).

We find that completing secondary schooling has potentially large effects, with estimated bounds indicating that an extra grade of schooling increases immediate and delayed memory by a maximum of 0.18 SD when increasing schooling from primary to secondary. This estimated upper bound is smaller than many estimates from studies using compulsory schooling laws. We also cannot rule out small and null effects at this margin. We obtain tighter bounds that indicate a statistically significant positive causal effect of increasing schooling from secondary to tertiary. An extra grade of schooling increases immediate and delayed memory scores by 0.03–0.10 SD when transitioning from being a high school graduate to a college graduate. Statistically positive effects are also found for several other cognitive domains. We find suggestive evidence that this effect could work through better health at older ages, lower probabilities of being in poverty, higher probabilities of working in managerial and professional occupations (which likely involve cognitive stimulation), and having more schooled spouses.

We view our estimates as providing important new and complementary evidence about the plausible magnitude of the causal effect under relatively weak assumptions. By using a completely different research design, our study contributes by triangulating evidence and increasing confidence that the relationship between schooling and cognition at older ages is causal. Although we do not point-identify the causal effect, Mullahy et al. (2021) argued that partial identification should be more prevalent in public health and clinical research and that public health recommendations and policies should be based on ranges of plausible effects rather than point estimates. Finally, we replicate the findings from the HRS in a sample of older adults from the Midlife in United States Development Study Cognitive Project. This replication provides additional confidence in our results and highlights the value of using partial identification in different datasets to assess external validity.

Previous Studies

Most studies have used schooling variation arising from changes in compulsory schooling laws within IV and fuzzy regression discontinuity (RDD) designs.²Glymour et al. (2008) predicted grades of schooling in the 1980 U.S. Census 5% sample using compulsory schooling laws between 1907 and 1961. Predicted grades of schooling were then employed as an independent predictor of cognition in the HRS. Banks and Mazzonna (2012) used the ELSA and the 1947 increase in the minimum school-leaving age from 14 to 15 with a fuzzy RDD. Both studies found large effects of schooling on memory. An extra grade of schooling was associated with 0.34- and 0.50-SD increases in memory in the HRS and the ELSA, respectively. Glymour et al. (2008) found no effect of schooling on mental status. Banks and Mazzonna (2012) found that schooling improved executive functioning for men but not for women. Employing the 1972 increase in the minimum school-leaving age from 15 to 16 in the United Kingdom and using the Understanding Society dataset, Gorman (2023) found that an additional grade of schooling increased memory scores by 0.42 SD. She also found positive but imprecise effects on verbal fluency. Exploiting compulsory schooling laws across Europe, Schneeweis et al. (2014) found that an extra grade of schooling increased immediate and delayed memory by 0.08 and 0.09 SD, respectively, for older adults in the Survey of Health, Ageing and Retirement in Europe. They found no causal effects of schooling on verbal fluency, numeracy, and orientation to date.

A key assumption for causal inferences in these studies is the exclusion restriction—that school reforms affect cognition only through their effect on schooling—which could be violated in certain contexts. For example, using the 1972 schooling reform in the United Kingdom, Avendano et al. (2020) found that education did not improve mental health for individuals in their mid-50s and that compulsory schooling laws might affect later life mental health through channels other than increased schooling.³ They argued and provided descriptive evidence that the reform forced young people who wanted to enter the labor market to continue their education instead. These young people might have been negatively affected by being forced to stay in school in a stressful academic environment where they were less likely to succeed than their peers. Courtin et al. (2019) also found that France's 1959 increase in the minimum school-leaving age from 14 to 16 increased depressive symptoms for women in their 60s. These findings imply that Gorman's (2023) results based on the 1972 reform and other results from studies that utilize compulsory schooling laws for identification might be biased because compulsory schooling laws might have directly led to worse mental health, potentially affecting cognition (e.g., Donovan et al. 2017; Nafilyan et al. 2021). Hence, mental health is another channel through which compulsory schooling laws could affect cognition later in life, which would violate the exclusion restriction. This assumption could also be violated if compulsory schooling laws are correlated with school quality, which can affect cognition independently of schooling level. Stephens and Yang (2014) showed that estimates of the effect of schooling on wages, unemployment, divorce, and occupation in the United States using compulsory schooling laws as instruments became insignificant and, in many instances, wrong-signed when they controlled for school quality.

In the presence of heterogeneous effects, IV and fuzzy RDD methods identify a local average treatment effect (LATE) for individuals whose treatment is affected by the instrument (“compliers”). That is, these methods estimate the average effect of increasing schooling on cognition only for individuals who increased their schooling because of the compulsory schooling laws (i.e., those whose schooling would have been lower in the absence of such laws). Previous IV and fuzzy RDD studies are thus not directly informative about the population ATE or about schooling effects at the upper parts of the schooling distribution (e.g., college education) because compliers are generally in the lower part of the schooling distribution (Clark and Royer 2013).⁴

In sum, the current evidence suggests that there likely is a causal relationship between schooling and memory, but findings for other cognitive domains are mixed. Point identification of causal effects, though, rests on strong assumptions; the effects identified pertain to specific subpopulations and usually lower parts of the schooling distribution. In contrast, our approach employs relatively weak assumptions to provide bounds on the population ATE of increasing schooling at different parts of the schooling distribution.

Econometric Framework

Let $Yi(t1)$ and $Yi(t2)$ be two potential outcomes: the values of the outcome (older age cognition) that individual $i$ would obtain as a function of two different treatment or schooling levels (e.g., high school graduation, $t2$⁠, and less than high school, $t1$⁠). We are interested in the population ATE of increasing schooling attainment from less than high school (⁠$t1)$ to high school graduation (⁠$t2)$ on cognition test scores, defined as follows:

Estimation of the ATE is complicated because the potential outcome $Y(t2)$ is unobserved for individuals with schooling level different from $t2$⁠, and $Y(t1)$ is unobserved for individuals with schooling level different from $t1$⁠. Letting S denote realized schooling and using the law of iterated expectations, we write the expected potential outcome $E[Y(t2)]$ as follows:

The data identify the sample analogs of all the right-side quantities except the counterfactuals $E[Y(t2) | S<t2]$ and $E[Y(t2) | S>t2]$—that is, the average cognition under high school graduation $(t2)$ for individuals with realized schooling (⁠$S)$ of, respectively, less than high school and more than high school. A similar equation applies to $E[Y(t1)].$ The bounding approach we employ consists of making assumptions to bound each of the counterfactuals in the expressions for $E[Y(t2)]$ and $E[Y(t1)]$ to then bound the ATE $Δ(t1,t2)$⁠. The assumptions are outlined here and illustrated in Figure 2; for further details, see the online appendix, section A.

• Assumption 1: Bounded Support. This assumption exploits that the measures of cognition employed have minimum (⁠$Ymin$⁠) and maximum (⁠$Ymax$⁠) values, which are used in place of the counterfactuals (Figure 2, panel a) to obtain a lower and upper bound on each $E[Y(t2)]$ and $E[Y(t1)]$⁠.

• Assumption 2: Monotone Treatment Selection (MTS). MTS states that individuals with higher schooling attainment, on average, have weakly higher potential outcomes at every schooling level, $t$⁠. For example, when comparing high school graduates with high school dropouts, the MTS assumption requires that the average potential cognition score at any schooling level (e.g., less than high school, some college, college graduation) of high school graduates is higher than that of high school dropouts.

Although the MTS assumption is untestable (because counterfactual outcomes are unobserved), it is plausible in our application. Economic models of human capital posit that individuals with higher innate ability have more schooling (Ben-Porath 1967) and that polygenic scores for education and cognition (which can be interpreted as measures of innate ability) predict cognition at older ages (Fletcher et al. 2021; Herd and Sicinski 2022), indicating that higher innate ability is likely related to better cognition at older ages. Given that individuals with higher innate ability are more likely to have more schooling and better cognition at older ages, it is plausible that, on average, individuals with higher schooling attainment have higher potential cognition at all schooling levels.⁵ More generally, MTS captures the notion that relative to individuals who self-select into lower schooling levels, individuals who self-select into higher schooling levels are more likely to have pretreatment characteristics that make them more likely to have better average potential older age cognition at any given schooling level because of, for instance, (on average) higher innate ability, better health inputs, and better family background.

Panel b of Figure 2 shows that under the MTS assumption, the observed mean cognition for those with schooling $t2$(⁠$E[Y(t2) | S=t2]$⁠)—for example, high school completion—can be used as an upper bound (respectively, lower bound) for the mean potential cognition under high school completion for those with realized schooling less than (more than) a high school education, as $E[Y(t2) | S<t2]≤E[Y(t2) | S=t2]$$≤E[Y(t2) | S>t2]$⁠.

• Assumption 3: Monotone Treatment Response (MTR). MTR assumes that more schooling does not decrease cognitive ability at older ages for any individual—that is, for two schooling levels $t1$ and $t2$ with $t2>t1$⁠, $Yi(t2)≥Yi(t1)$⁠. MTR is thus an assumption about the (weak) ranking of the potential outcomes for the same individual: it compares potential cognition under high school graduation with potential cognition under less than high school graduation for the same individual. By contrast, the MTS assumption compares means of the same potential outcome (e.g., cognition under high school graduation) for two different subpopulations defined by their observed levels of schooling (e.g., high school graduates vs. high school dropouts).

The MTR assumption is stronger than the MTS assumption because it must hold for each individual rather than on average. The MTR assumption will be violated if more schooling leads to worse cognitive performance for some individuals. One could argue that more schooling might worsen mental health for individuals who work in stressful jobs or for individuals forced to stay in school by compulsory schooling laws and that such deterioration in mental health could lead to worse cognition. The MTR assumption does not rule out such negative channels. Instead, it assumes that the positive channels linking schooling to cognition dominate. For example, the negative impacts of poor mental health on cognition are outweighed by the positive impacts of schooling on brain maintenance, cognitive reserve, assortative mating, and midlife health and SES conditions.

Some theoretical models suggest that the MTR assumption holds. In Grossman's (1972) model of health production, schooling directly increases health production by increasing the marginal productivity of health inputs or behaviors (productive efficiency) and by enhancing individuals’ abilities to acquire and process health information (allocative efficiency). Cognition at older ages is a component of overall health, which is increased through schooling's effect on affecting productive and allocative efficiency. The MTR assumption is also consistent with theories of cognitive reserve (Stern 2002).⁶

Panel c of Figure 2 illustrates how MTR tightens bounds on $E[Y(t2)]$⁠. Intuitively, for the counterfactual $E[Y(t2) | S=t1]$ (e.g., mean cognition under high school for those with no high school), MTR provides the lower bound $E[Y(t1) | S=t1]$ (mean observed cognition for those with no high school) because more schooling cannot decrease potential cognition, implying $E[Y(t2) | S=t1]≥E[Y(t1) | S=t1]$⁠. Panel d shows how tighter bounds on $E[Y(t2)]$ can be obtained by combining the MTS and MTR assumptions. Manski and Pepper (2000) showed that a testable implication of the combined MTS and MTR (i.e., MTS+MTR) assumptions is that observed mean cognition scores are weakly increasing in schooling attainment. This testable implication will fail if the assumptions are not satisfied in the data, providing a check on them.

• Assumption 4: Monotone Instrumental Variable (MIV). Each of the bounds under the previous assumptions can be narrowed by using an MIV, a variable with a monotone (weakly increasing or weakly decreasing) mean relationship with the potential outcomes, $Y(t)$⁠. We use mothers’ schooling attainment as the MIV, thus assuming that individuals’ mean potential cognition at older ages weakly increases (i.e., does not strictly decrease) with their mothers’ schooling levels. Mothers’ schooling attainment is a natural MIV, given that studies have shown that higher parental schooling and, more generally, childhood SES are associated with better cognition at older ages (for a review, see Greenfield and Moorman 2019).

The MIV assumption is weaker than the exclusion restriction requiring that mothers’ schooling affects children's older age cognition only through effects on children's schooling. The exclusion restriction is unlikely to be satisfied because mothers’ schooling can affect children's older age cognition through many other channels. Mothers with more schooling might have children with higher innate abilities who obtain higher schooling levels and have better older age cognition. More schooled mothers might also provide better nutrition to their children or more cognitively stimulating home environments that affect neurocognitive development (Hackman and Farah 2009). These channels are allowed by the MIV assumption and help to justify its plausibility. This assumption does not require the MIV (mothers’ schooling) to have causal effects on outcomes (children's older age cognition).⁷

For mothers’ schooling, the MIV assumption implies that if we take two subsamples where individuals counterfactually have the same level of schooling but two different levels of mothers’ schooling (e.g., mothers are high school dropouts and mothers are high school graduates), mean potential cognition (⁠$E[Y(t)]$⁠) will be weakly higher for the sample whose mothers have the higher schooling attainment. This inequality holds weakly, so it also allows for such means to be equal. The inequality is also assumed to hold for all schooling levels, $t$⁠, and it does not need to hold for every individual in the two subsamples because the MIV assumption refers to average (rather than individual) potential outcomes. Lastly, the MIV assumption is untestable because counterfactual outcomes are unobserved.

To illustrate how the MIV narrows bounds, consider using the MIV along with the MTS+MTR bounds. We can divide the sample into bins defined by the values of mothers’ schooling and compute the MTS+MTR bounds within each bin. We then obtain MTS+MTR+MIV bounds on $E[Y(t2)]$ by taking the weighted average over all the conditional-on-MIV bounds, resulting in bounds that are (weakly) narrower than we would obtain without using the MIV.

Bounds on the ATE$Δ(t1,t2)$⁠. Let $LBAE[Y(t)]$ and $UBAE[Y(t)]$ denote, respectively, the lower and upper bounds for the mean potential outcome at schooling level $t$ under the different assumptions $A$ ={NA, MTS, MTR, MTS+MTR, MTS+MTR+MIV}, where NA denotes the “no assumptions” bounds using only Assumption 1. Bounds on the ATE of increasing schooling from $t1$ to $t2$ for a given set of assumptions are calculated as follows:

Bounds on the ATE for other schooling margins (e.g., increasing schooling from high school graduation to some college or from high school to college graduation) are computed analogously. Note that under the MTR assumption, the lower bound on $Δ(t1,t2)$ is never below zero because the MTR rules out the possibility that more schooling worsens cognitive abilities.

Estimation and Inference. We estimate all bounds by plugging in sample analogs for the expectations and probabilities in the corresponding bounds’ expressions provided in the online appendix (section A). Inference is undertaken by constructing confidence intervals that cover the true value of the population ATE with a specified probability. Estimation and inference for bounds using the MIV assumption are nonstandard, requiring us to address biases arising from taking minima and maxima (intersections) over several candidate bounds. We address these issues by applying Chernozhukov et al.’s (2013) method to obtain all the estimated bounds and confidence intervals, including those not using the MIV assumption. Section A of the online appendix provides further details. We implement the methods using the user-written STATA command mpclr (Germinario et al. 2021).

Data

The HRS is a U.S. nationally representative longitudinal survey of individuals older than 50 and their spouses that started in 1992. The initial HRS cohort consisted of persons born in 1931–1941 and their spouses of any age. A second study, Asset and Health Dynamics Among the Oldest, was fielded the next year to capture an older birth cohort, those born in 1890–1923. In 1998, the two studies were merged, and two new cohorts were enrolled to make the sample fully representative of the older U.S. population: (1) the Children of the Depression, born in 1924–1930; and (2) the War Babies, born in 1942–1947. The HRS now employs a steady-state design, replenishing the sample every six years with younger cohorts to continue making it fully representative of the population older than 50.

Schooling Attainment

We obtain the schooling attainment of HRS participants and their mothers from the RAND HRS dataset (version V1), which is measured as 0–17 grades of schooling. We discretize participants’ schooling attainment into high school dropout (<12), high school graduation (12), some college education (13–15), and college graduation (≥16). We discretize mothers’ schooling into high school dropout, high school graduate, and more than high school.

Cognition Measures

Cognition measures come from the HCAP, which was initiated in 2016. Participants were selected to be part of the HCAP if they were aged 65 or older and had completed the 2016 interview. Although the HRS includes spouses/couples, the HCAP does not include spousal/couple pairs. Of those eligible for HCAP, the HRS randomly selected one half of the uncoupled respondents and one respondent from each coupled household.

The HCAP consisted of a respondent interview and an informant interview. In the respondent interview, participants completed comprehensive, in-person neuropsychological assessments (see the online appendix, section B, for test descriptions) that took roughly one hour. Immediately afterward, an individual nominated by each HRS respondent completed an informant interview in another room, answering questions about the respondent's functioning and changes in abilities over the last 10 years. Of the eligible 4,425 participants, 3,496 completed the HCAP interview. For 149 cases, the HRS respondents were unable to complete interviews, and only the informant interviews were conducted.

Table C2 (online appendix) shows the order in which the cognitive tests were taken, the cognitive domains assessed, the number of observations, and the number of missing observations. The number of missing observations is low for most cognition tests (<50; 2% of HCAP respondents) but is higher for some tests (e.g., letter cancellation has 150 observations imputed). Because the HRS imputed missing cognition scores, we do not lose data as a result of missing cognition scores in our analysis.

To aid comparisons with the literature, we primarily focus on composite scores for immediate and delayed memories constructed by summing up the scores on the HRS Telephone Interview for Cognitive Status (TICS), three trials of the Consortium to Establish a Registry for Alzheimer's Disease (CERAD) word list–immediate, three trials of the CERAD word list–delayed, CERAD constructional praxis–delayed, story recall–immediate, and story recall–delayed tests. The other cognition outcomes we examine are scores on the Mini-Mental State Examination (MMSE, a measure of global cognition), recognition memory (sum of scores on CERAD word list recognition and story recall recognition), verbal fluency (animal naming test), executive function (Raven's progressive matrices test), attention/speed (sum of scores on backward counting and letter cancellation tests), and visuospatial ability (CERAD constructional praxis–immediate).

Results

Descriptive Statistics

Summary statistics for our analytic sample of 3,072 are shown in Table 1, column 1. From the full HCAP sample of 3,496 observations, we lose 149 observations for which no respondent interview was conducted. We then drop respondents with missing data on schooling (4 observations), mothers’ schooling (269 observations), and race (2 observations). The average age is 76 years (range = 65–102 years), 61% are female, and 73% are non-Hispanic White. Mothers’ schooling is concentrated at the lower end of the schooling distribution. More than half (54%) of individuals had mothers who never graduated from high school, and 32% of individuals had mothers who graduated from high school. Only 14% of individuals had mothers with more than a high school education. The average number of schooling grades for HCAP participants is 12.92; 18% were high school dropouts, and 25% were college graduates.

Columns 2–5 provide summary statistics by gender and race. Although men have higher schooling attainment than women, they do not outperform women in all cognitive domains. On average, women score higher on the MMSE, immediate and delayed memory, and recognition memory; and on average, men perform better than women on verbal fluency, attention/speed, executive function, and visuospatial tests. Non-Hispanic White and non-Hispanic Black individuals have higher schooling attainment than Hispanic individuals. Average cognition scores on all domains are higher for non-Hispanic White individuals than for non-Hispanic Black and Hispanic individuals.

Average cognition scores by schooling attainment are shown in Table C3 (online appendix). Cognition scores increase with schooling attainment, consistent with the testable implication of the MTS+MTR assumptions. Finally, at equivalent levels of schooling, the average score on our composite measure of immediate and delayed memory is higher for women than men. For example, among high school dropouts, average immediate and delayed memory scores are 38.98 for women and 34.80 for men; comparative scores among college graduates are 58.96 for women and 53.71 for men. These findings are consistent with descriptive evidence from Angrisani et al. (2020) showing that the effect of the gender schooling gap is negligible on cognition tests that do not require numeracy or literacy.

Results for Immediate and Delayed Memory

Row A of Table 2 displays the results for increasing schooling from high school dropout to high school graduate. The ordinary least-squares (OLS) estimate (column 2) indicates that the memory score is, on average, 9.3 points higher for high school graduates than for high school dropouts. This figure represents an average effect of 0.58 SD relative to that for high school dropouts (the control group). Columns 3–7 show the estimated bounds and 95% confidence intervals under different sets of assumptions. The no assumptions bounds are wide, indicating that the true average causal effect of completing secondary schooling could lower memory scores by up to 71.80 points and improve scores by up to 74.44 points. Adding the MTS assumption—that individuals with higher schooling attainment have, on average, higher potential cognition—substantially reduces the estimated upper bound. Completing secondary schooling under the MTS assumption (column 4) increases memory scores by a maximum of 34.47 points. The MTS bounds are still wide and include zero. Adding the MTR assumption by itself (column 5) restricts the lower bound mechanically to zero because MTR rules out the possibility that schooling worsens cognition. The MTS+MTR assumptions (column 6) provide considerably tighter bounds compared to previous bounds. Completing secondary schooling, at worst, has no effect and, at most, increases the memory score by 12.92 points, representing a maximum effect of 0.81 SD relative to the control. To tighten the MTS+MTR bounds, we use mothers’ schooling as an MIV with three bins (high school dropout, high school graduate, more than high school). Adding the MIV to the MTS+MTR assumptions slightly reduces the estimated upper bound to 11.48 points (0.72 SD) in column 7.⁸

How does the range of causal effects for completing secondary schooling under the MTS+MTR+MIV assumptions compare with IV and fuzzy RDD estimates from studies using compulsory schooling laws? First, note that our bounds are on the population ATE of completing secondary schooling and are not directly comparable to prior IV and fuzzy RDD estimates. These latter estimates also capture effects at the lower part of the schooling distribution. However, they estimate a LATE for individuals who continued their schooling because of compulsory schooling laws (the compliers), which might differ from the effect for individuals who would have remained in school regardless of the compulsory schooling laws (Clark and Royer 2013) and thus from the population ATE. The bounds indicate a potentially substantial effect of completing secondary schooling, at 0.72 SD, implying that an additional grade of schooling increases memory scores by a maximum of 0.18 SD, given a four-grade difference in schooling between high school graduates and dropouts. Our estimated upper bound is thus substantially smaller than estimates of an extra grade of schooling for the United States (0.34 SD; Glymour et al. 2008) and the United Kingdom (0.42–0.50 SD; Banks and Mazzonna 2012; Gorman 2023) but possibly larger than the IV estimates identified for Europe (0.08–0.09 SD; Schneeweis et al. 2014). The fact that the IV estimate for the United States in Glymour et al. (2008) is above our estimated upper bound could be interpreted as reflecting treatment effect heterogeneity. Because compulsory schooling laws are most likely to affect the schooling levels of individuals who would otherwise have relatively low schooling (Card 1999), a larger average effect for the compliers than for the population would be consistent with these individuals having higher marginal returns to additional years of secondary schooling in terms of cognition at older ages relative to the overall population. Similar reasoning has been used in the context of estimating the effect of schooling on earnings. Card (1999) noted possible differences in the returns to education as a potentially important reason why IV estimates of this effect based on compulsory schooling laws tend to exceed corresponding OLS estimates. Finally, note that our bounds include the OLS estimates, and prior IV estimates are larger than OLS estimates.⁹

Row B of Table 2 shows results for increasing schooling from high school graduation to some college education. Under the MTS+MTR+MIV assumptions, going from high school to some college education increases memory scores by 0–4.10 points (0–0.24 SD). The MTS+MTR+MIV bounds in row C show that going from some college education to college graduation increases memory scores by 0–5.26 points (0.32 SD). Note that the estimated upper bounds under the MTS+MTR+MIV assumptions at both of these schooling margins are much smaller than those from high school completion.

Row D of Table 2 provides results for increasing schooling from high school to college graduation. Here, we obtain fairly tight bounds under the MTS+MTR+MIV assumptions. Increasing schooling from secondary to tertiary increases the average memory score by 1.87–6.74 points (0.11–0.39 SD).¹⁰ The estimated bounds exclude zero and the OLS estimate (9.64), as does the 95% confidence interval, which implies that the true effect is 1.14–7.75 points (0.07–0.45 SD). Given a difference of four grades of schooling between college and high school graduation, the estimated bounds (95% confidence interval) imply that an additional grade of schooling increases memory scores by 0.03–0.10 (0.02–0.11 SD).

We also obtain informative bounds under the MTS+MTR+MIV assumptions for increasing schooling from primary to tertiary in row E of Table 2. The bounds indicate that the average causal effect is 3.43–16.30 points (0.22–1.02 SD). The 95% confidence interval excludes the OLS estimate (18.91) and zero, implying a statistically significant average memory effect of at least 0.22 SDs.

Figure 3 gives MTS+MTR+MIV bounds by gender and race at the different schooling margins. Across both gender and race, the effects of completing high school are potentially large: estimated upper bounds are 0.77 SD for men, 0.80 SD for women, 0.65 SD for non-Hispanic White individuals, 0.63 SD for non-Hispanic Black individuals, and 0.90 SD for Hispanic individuals. These bounds are also consistent with moderate, small, and null effects. In general, it is difficult to draw strong conclusions regarding effect heterogeneity because the bounds overlap such that there are no statistically significant differences by gender and race. Regarding differences between college and high school graduates, non-Hispanic White individuals have the narrowest bounds (0.09–0.34 SD). In contrast, non-Hispanic Black and Hispanic individuals have wider bounds, and the confidence intervals include zero. Finally, increasing schooling from primary to tertiary statistically significantly increases average memory scores across all genders and races.

Results for Other Cognitive Domains

We focus on results from increasing schooling from primary to secondary (for comparisons with studies using compulsory schooling laws) and from secondary to tertiary (to test whether the informative bounds for memory replicate).¹¹ The results for completing secondary schooling, shown in panel a of Figure 4, indicate that the causal effects could be zero, small, or potentially large. The literature has found mixed results for cognitive domains other than memory, and given the width of the bounds, we cannot make strong comparisons with previous studies. For example, the estimated upper bounds indicate that completing secondary schooling increases verbal fluency scores by a maximum of 0.67 SD, implying that an additional grade of schooling increases verbal fluency by a maximum of 0.17 SD. This estimate is larger than the IV estimate in Gorman (2023), who found that an extra grade of schooling increased verbal fluency by 0.05 SD, an effect that was imprecisely estimated. The bounds Schneeweis et al. (2014) documented excluded IV estimates for verbal fluency, which were negative and statistically insignificant.

Panel b of Figure 4 shows results for increasing schooling from secondary to tertiary. All the bounds statistically exclude zero (marginally for recognition memory and visuospatial ability), implying statistically significant average effects of increasing schooling from secondary to tertiary on these cognitive measures. The tightest bounds are obtained for the MMSE. Transitioning from high school to college graduate increases MMSE scores by 0.08–0.27 SD. The width of the bounds is similar for verbal fluency, executive function, and attention/speed, indicating average causal effects of roughly 0.05–0.40 SD. All the bounds and 95% confidence intervals (except for MMSE and recognition memory) exclude the OLS estimates. These results highlight the potential role that increasing schooling from secondary to tertiary can have in improving cognitive abilities at older ages.

Gender- and race-specific bounds under the MTS+MTR+MIV assumptions are shown in Figure 5. The figure shows no statistically significant differences. However, it provides some suggestive evidence of racial differences for attention/speed, where we can statistically rule out null effects only for non-Hispanic Black individuals (with bounds indicating effects of 0.26–0.47 SD). The effects of increasing schooling at other parts of the schooling distribution by gender and race are shown in Figures C1–C4 (online appendix). Again, we find no statistically significant gender or race differences.

Possible Mechanisms

In this section, we investigate effects of schooling on possible pathways through which schooling can affect older age cognition. Panel A in Table 3 presents MTS+MTR+MIV bounds on the effects of increasing schooling for HCAP respondents on the probability of poor/fair self-reported health, body mass index (BMI), depressive symptoms measured by the Center for Epidemiologic Studies Depression Scale (CES-D; scale = 0–8), the probability of reporting ever having smoked, the probability of reporting ever diagnosed with high blood pressure, and the probability of reporting not engaging in vigorous exercise in the 2016 HRS survey. Because schooling is negatively correlated with these measures, we employ nonpositive versions of the MTS and MTR assumptions and assume that mothers’ schooling has a weakly decreasing relationship with the mean potential outcomes of these measures.¹² Estimated bounds show that college graduates are 2.1–11.4 percentage points less likely to be in poor/fair health and 2.1–5.9 percentage points less likely to have ever smoked relative to high school graduates. The CES-D score is also 0.012–0.34 points lower for college graduates than for high school graduates. Although the estimated bounds exclude null effects, the 95% confidence intervals do not. The results thus provide suggestive evidence that the effects of increasing schooling from secondary to tertiary on older age cognition could operate partly through better health at older ages.

Panel B, column 1, reports the effects of schooling on the probability of the respondent's household being in poverty in the last calendar year. Going from high school to college graduate reduces the probability of being in poverty by 1.3–5.7 percentage points, and the 95% confidence interval marginally excludes zero. We use information on the occupation code for the job with the longest tenure from the RAND HRS 2016 wave to create a dummy variable for having worked in managerial/professional occupations the longest. Managerial/professional occupations are likely to be cognitively stimulating, which enhances cognitive reserves and protects against cognitive decline. Increasing schooling from secondary to tertiary statistically significantly increases the probability of having the longest tenure in managerial/professional occupations by 2.2–9 percentage points (column 2) and the probability of having spouses who graduated from college by 6.2–28.4 percentage points (column 3). Overall, these results suggest that the effects of increasing schooling from secondary to tertiary education on cognition could work through the channels shown in panel B.

Robustness Checks

We conduct two robustness checks. First, our main analysis uses grades of schooling to group respondents and their mothers into educational groups. Here, we investigate whether bounds would be narrower when using respondents’ grades of schooling as the treatment and mother's grades of schooling (with three bins) as the MIV. Results are shown in Table C7 (online appendix). Our main findings on the effects of increasing schooling from high school to college graduation are robust to this alternative coding scheme. We find that increasing schooling from 12 to 16 grades increases immediate and delayed memory scores by 0.14–0.27 SD, memory recognition by 0.04–0.17 SD, MMSE by 0.10–0.23 SD, verbal fluency by 0.10–0.34 SD, executive function by 0.25–0.33 SD, attention/speed by 0.24–0.30 SD, and visuospatial ability by 0.10–0.34 SD. With this coding scheme, we cannot statistically exclude null effects for MMSE, recognition memory, verbal fluency, and visuospatial ability. By contrast, in Figure 4, all the 95% confidence intervals exclude zero (marginally for recognition memory and visuospatial abilities).

Second, we examine the robustness of the estimated bounds to attrition in the HRS through inverse probability weighting. We first perform a logit regression on the probability of being in the HRS 2016 survey as a function of birth year, gender, schooling, mother's schooling, self-reported health, mental health (CES-D score), cognition scores, and BMI.¹³ We average self-reported health, BMI, CES-D, and cognition scores from the first observed wave through the last observed wave (not including 2016). We impute covariates with missing values (mainly mother's schooling) with the sample mean and control for this with missingness dummy variables. We then use the inverse of the predicted probabilities to weight the observations when computing the OLS estimates and estimated bounds. The results, shown in Table C8 (online appendix), are similar to our main findings.

Replication in the Midlife in United States Development Study (MIDUS)

For external validity, we examine schooling effects on cognition for a sample of older adults in the MIDUS, a national sample of 7,108 adults aged 25–74 who were first interviewed in 1995–1996. Nine years later, the second wave (MIDUS 2) included data from roughly 75% (N = 4,963) of the original respondents. We use the MIDUS 2 Cognitive Project in which 4,512 participants took the Brief Test of Adult Cognition by Telephone (BTACT). The BTACT included measures of memory (immediate and delayed recall of 15 words), inductive reasoning (number series; completing a pattern in a series of five numbers), verbal fluency (the number of words produced from the category of animals in 60 seconds, as in the HRS), processing speed (backward counting, as in the HRS), and working memory (backward digit span; the highest span achieved in repeating strings of digits in reverse order). Despite its brevity, the BTACT is a reliable and valid measure of cognition (Lachman et al. 2014).

We restrict our analysis to 1,016 individuals aged 65 or older with data on schooling and mothers’ schooling. Summary statistics are shown in Table C9 (online appendix). The average age and proportion of women in the MIDUS and the distribution of mothers’ schooling are similar to those in the HRS. Average grades of schooling are higher in the MIDUS (13.79) than in the HRS (12.92), reflecting the higher proportion of White individuals in the MIDUS than in the HRS (95% vs. 73%). The average number of grades of schooling of White individuals in our HRS analytic sample (13.49) is similar to that in the MIDUS.

Figure C5 (online appendix) presents a comparison of results for increasing schooling from primary to secondary and from secondary to tertiary (full results are in Table C10, online appendix). Similar to the HRS, the MIDUS bounds show that the average causal effect of completing secondary schooling could be zero, small, equal to OLS estimates, or potentially larger (but, at most, roughly 0.50–0.55 SD, depending on the specific measure). The OLS estimates and the width of the bounds are quite similar, especially for immediate and delayed memory. In the MIDUS, estimated bounds for increasing schooling from secondary to tertiary on immediate and delayed memory are tight (0.10–0.17 SD), but the 95% confidence interval is much wider (0–0.32 SD). Similarly, the bounds for verbal fluency and attention/speed do not statistically exclude zero, whereas they do in the HRS. In both datasets, all the estimated upper bounds are smaller than the OLS estimates.¹⁴

Summary

Does schooling have a causal effect on cognition at older ages? The evidence for this important question is surprisingly limited, given the growing number of ADRD cases, the recognition of schooling as the largest nonbiological life cycle intervention for ADRD, and the many associations documented without attempting to provide causal estimates between schooling and various dimensions of aging. We contribute to the literature by employing a partial-identification approach to determine a range of plausible values for the population average causal effect of schooling on cognition in the HRS under weak assumptions. We find that the average causal effect of increasing schooling from primary to secondary levels on immediate and delayed memory could be zero, small, or potentially large but no more than 0.72 SD. The estimated upper bound implies that an additional grade of schooling increases memory scores by a maximum of 0.18 SD. This estimate is substantially smaller than documented in studies using compulsory schooling laws for identification, where estimates represent a LATE only for those who increase their schooling because of these laws. We also reach similar conclusions for global cognition, verbal fluency, executive function, recognition memory, and visuospatial ability. We further provide new evidence of important effects of schooling on older age cognition at other parts of the schooling distribution. This evidence is critical because the previous literature using compulsory schooling laws for identification obtained LATE estimates for secondary school completion, and the effects might differ at other points of the schooling distribution. We obtain a fairly narrow range of estimated average causal effects of increasing schooling from secondary to tertiary on all cognitive domains. Moreover, these estimated bounds statistically rule out zero effects for all the cognitive domains (marginally for recognition memory and visuospatial ability). For example, the extra grade of schooling achieved by transitioning from high school to college graduation increases average immediate and delayed memory by 0.03–0.10 SD. Finally, we find suggestive evidence that these effects might work through having higher probabilities of working in cognitively stimulating (managerial/professional) occupations and having more schooled spouses, higher SES, and better health at older ages. Thus, our analyses lead to a more nuanced and extended understanding of the impacts of different schooling levels on cognition at older ages in the United States.

Acknowledgments

We thank Giuseppe Germinario for excellent research assistance.

Notes

References