Study population

Using anonymized extracts from examinations for military service in the Netherlands between 1962–1965, we followed 45,037 men selected from the national birth cohorts 1944–1947 [27]. These examinations are based on yearly listings of all Dutch male citizens aged around 18 years in the national population registers. The study was reviewed by the Institutional Review Board of the Columbia University Medical Center in New York, NY. The Board determined that studies on this study population do not meet the DHSS definition of ‘human subjects research’ and are exempt from IRB approval. In the Netherlands, the study does not need approval by Ethical Review Boards or by the National Data Protection Authority (College Bescherming Persoonsgegevens) as all study procedures are in compliance with Dutch privacy legislation and do not need the consent of the data subjects concerned or of their relatives. The study is based on population wide administrative records and not on patient records.

Examination records

The examination records contain detailed information on demographic and socio-economic status, including education, father’s occupation, birth order, religion, the place of birth, and a standardized psychometric test battery with several measures of intelligence.

The principal intelligence measure included is the Raven Progressive Matrices, a nonverbal untimed test that requires inductive reasoning about perceptual patterns [28]. Because the test does not depend on reading, writing, or language skills and is easily administered and interpreted it is widely used to test military conscripts across the world. We used separate tests for Arithmetic and Language performance. Scores for all tests were grouped in six levels from 1 (highest) to 6 (lowest). The test scores are highly correlated with Pearson’s r values in the range of .63 to .76.

The education system in the Netherlands is characterized by the nominal number of years of schooling and by two parallel streams in the educational system- general academic and vocational. Streaming choices are made at the end of primary school. Students in the vocational stream cannot directly enter university. Students with more than twelve years of education will nearly always be in the academic stream [29, 30].

Conscripts’ education was classified in four levels [31]: primary school (primary, six years of schooling); lower vocational education (eight years of schooling); lower secondary education (ten years of schooling); and intermediate or higher vocational or academic education (higher, twelve or more years of schooling). Because conscripts were age 18 at examination the highest education group includes men who had just started university.

Father’s occupation was classified into five categories: professional and managerial workers; clerical, self-employed and skilled workers; farmers; semi-skilled workers including operators, process workers and shop assistants; and laborers and miners. Fathers with unknown occupations were classified separately.

Birth order was recorded as reported by the examinee.

Place of birth was categorized in four urbanization levels distinguishing rural communities (rural communities with 20% or more farming population), urbanized rural communities (rural communities with less than 20% farming population), towns (townships and cities with less than 100,000 inhabitants), and cities with populations of 100,000 or more.

Self-reported religion was classified as Roman Catholic, Protestant (Dutch Reformed or Calvinist), other or none.

Follow-up

As described elsewhere [27] we traced all examinees through population register records and national death records to ascertain vital status. Follow-up was until January 1, 2011, by which time the oldest men born in 1944 had reached the age of 66 years. We identified 45,037 men for tracing at age 18, and ascertained vital status for 41,096 (91.2%) as per January 1, 2011. Among this group, 35,157 (85.5%) were alive and 5,939 (14.5%) had died. For 1,316 (2.9%), only a partial follow-up was possible due to emigrations or other reasons, and for 2,625 (5.8%) no follow-up was possible because of missing data. For this study, we excluded partly institutionalized conscripts who had attended special schools for the illiterate, handicapped, deaf-mute, or mentally retarded, and conscripts who had not completed schooling through 12 years. After exclusion of these 2,614 conscripts, 39,798 men remain for analysis.

Our study is based on military examination records for men born in the Netherlands in the years 1944–1947 which were originally sampled to the study of the relation between prenatal famine exposure and mortality [27]. For that reason, men born in the Western Netherlands in 1944–1945 were over-represented. In this population, there was no relation however between famine conditions around birth and either mental performance [32] or education at age 18 [27]. The study population appears suitable therefore to obtain unbiased estimates of the relation between cognitive ability, education, and mortality.

Data description

Selected demographic and socio-economic characteristics at the time of medical examinations are given in Table 1. Education level is strongly related to father’s occupation; men with the highest education tend to have fathers in the professional or managerial occupations. First-born conscripts also tend to have higher levels of education. In Table 2, intelligence test scores obtained by three instruments are presented by level of education. Again, men with the highest education tend to do best on all psychometric tests.

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Table 1. Population characteristics at age 18 years by level of education.

https://doi.org/10.1371/journal.pone.0141200.t001

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Table 2. Intelligence scores at age 18 years by level of education.

https://doi.org/10.1371/journal.pone.0141200.t002

Statistical analysis

We seek to evaluate the impact of education on life expectancy accounting for intelligence and other individual factors that influence both the education choice and mortality. A common characteristic of survival data, including time to death, is that not all individuals experience the event of interest during the observation period. Such right censoring makes inference based on means unreliable. Another characteristic is dynamic selection: those still alive at age 18 may not be a random selection of the original population of births. We therefore use the (mortality) hazard, or the force of mortality, as this effectively deals with these data characteristics. A common approach would be to ignore the impact of intelligence and estimate a proportional hazard model for the mortality rate including the education level as one of the explanatory variables that proportionally changes the mortality rate. However, it is very likely that not only the scale of the mortality hazard but also the shape is affected by education. It is also plausible that the effect of other individual factors differs by education level. However, it is very likely that not only the scale of the mortality hazard but also the shape is affected by education. It is also plausible that the effect of other individual factors differs by education level. For example, having a father with a professional occupation is likely to have a larger impact for men with only primary education than for men with higher education. We therefore start our analyses with separate proportional Gompertz models, that is separate by education level. We choose a Gompertz mortality rate [33–35], which assumes an exponential increase in the mortality by age, because this is known to provide accurate mortality hazards for middle aged individuals [36].

The difference in the implied life expectancy for these separate Gompertz models will only provide the educational gains in life expectancy accounting for observed individual differences by education. Individual intelligence seems an important factor influencing both the education choice and mortality and ignoring it would bias the results. However, intelligence is also heavily affected by parental background and by the education attained up till age 18 [37]. Another issue is that standard IQ-test are only a proxy of intelligence, or cognitive ability. This precludes the simple addition of intelligence as measured by IQ-test(s) into the Gompertz hazards. We therefore formulated a structural model to account for the interdependence of intelligence and education and their joint influence on mortality [26], extending the structural equation model of Conti and Heckman [24, 25] to a Gompertz proportional hazard model. The model allows for potential interdependencies between educational choice, intelligence and mortality. We assume that individuals base their schooling decision on expected utility maximizing and that the individual utility of each education level attained depends on the income earned and perceived health. This implies that the decision to continue schooling and, to attain a higher education level depend on expected income and (potentially) also on perceived health gains. The model consists of three parts: (i) the education choice, (ii) potential mortality hazards and (iii) a measurement system for latent intelligence. Fig 1 shows the structure of the model.

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Fig 1. Schematic depiction of the structural equation model.

Latent intelligence θ influences the utility, D*, of an individual choosing a particular education level, D. It also influences directly the (potential) mortality hazard λ^(k), for each education level D = k. The value of three measured IQ-tests, M₁, M₂ and M₃ all depend on the latent intelligence.

https://doi.org/10.1371/journal.pone.0141200.g001

The education choice is based on maximizing the expected future utility. Let denote the (latent) utility of an individual choosing a particular education level. We assume that the educational choice is endogenous and that selection into schooling is fully accounted for by the observed individual characteristics and their latent cognitive ability. Define the indicator of education, D, taking the value k if the individual has attained education level k (1, …, 4): D = k if ζ_k−1 < D* ≤ ζ_k with D* = γ′ X + α_D θ + ν_D, the underlying latent utility of choosing a particular education level, which is continuous and depends linearly on the (vector of) observed characteristics X and latent intelligence θ and where ζ₀ = −∞ and ζ₄ = ∞. We assume that ν_D is normally distributed and assume an ordered probit model for the educational choice. Therefore the probability that an individual has attained education level k Pr(D = k) is given by (1) with Φ(⋅) as the standard normal cumulative density. Once the individual has decided his education level, future mortality is potentially causally related to this decision.

The second part of the structural model comprises the potential mortality hazards. These hazards are potential because each individual’s mortality is only observed for the actual education level and not for potential alternatives in education level. For each education level we choose a Gompertz mortality rate. Let t be the age of the individual, with the potential hazard for education level k depending on the (vector of) observed characteristics X and latent intelligence θ. The shape of the hazard is captured by a_k and the scale of the hazard by β_k0. The effect of latent intelligence on the mortality hazard is captured by α_k. The corresponding potential survival rates are (2) (3) The Gompertz survival models for each of the four education levels include birth order, place of birth, religion, and father’s occupation as relevant control covariates related to survival and the impact of the latent intelligence. These models have a proportional hazard conditional on the latent intelligence. This is similar to including a (log-normal) frailty into the proportional hazard model [38].

The model is closed by three measurement equations linking the intelligence scores with the latent cognitive ability and the (vector of) observed individual characteristics. Because for each IQ test, q = 1, 2, 3, the continuous score is only observed in six ordered IQ classes, an ordered probit is assumed for each test with where ν_Mq is normally distributed and M_q = m if ϑ_qm−1 < M* ≤ ϑ_qm. The probability to observe an individual in one of the IQ-classes is given by (4)

An important feature of mortality outcomes is that some individuals are still alive at the end of the observation period and are right censored. Another feature of our data is that all men were about 18 years old at the start of the observation period at the time of military examination. We therefore condition on survival through the age at military examination. With the distribution assumptions on the educational choice, the latent mortality hazards and the measurement system the likelihood function is defined. We use a maximum likelihood estimation method to estimate all the parameters of the model. Details of the estimation procedure are presented in the Supporting Information. For the structural model, we jointly estimate the parameters of the education choice, the Gompertz-hazards and the measurement equations. We also estimate separate Gompertz proportional hazard models, in which we ignore the dependence on latent cognitive ability. From the estimated parameters the implied survival function can be calculated for each individual, given his observed characteristics X based on Eq (3). The results from the separate Gompertz proportional hazard models are used to decompose the educational gain into a selection on observed factors and on the latent intelligence.

At the individual level, the main questions relate to the difference in life expectancy after age 18 and to the difference in expected years lived between ages 18 and 66 (the minimum and maximum observed age) comparing two adjacent educational levels. For the calculation of the life expectancy we assume that the estimated Gompertz hazards hold throughout adult life starting at age 18 and extending beyond the highest observed age of 66. For the calculation of the expected years lived we only focus on the interval of observed ages. Both measures can be obtained by integrating the difference in survival, S^(k+1)(t) − S^(k)(t), over the relevant age interval [38], where S^(k+1)(t) denotes the survival time up to age t for an individual with education (D = k + 1), and S^(k)(t) is the survival time up to age t for those with education (D = k), for k = 1, …, 3. As we only observe the mortality of an individual for his chosen education level and not for the counterfactual higher or lower education level, we can only calculate the expected life-expectancy and expected years lived averaged over all (relevant) individuals. It is important to note that the relevant distribution of the observed characteristics and the latent cognitive ability differ by education level. Except for the lowest and the highest education level we can for each education level calculate estimates of three average life-expectancy/expected years lived: (i) using the distribution of the characteristics for the adjacent lower education level, (ii) using the distribution of the characteristics for the particular education level, and (iii) using the distribution of the characteristics for the adjacent higher education level.

To obtain the average gain in life expectancy we first calculate the average survival gain. The gain in survival at age t when the educational level improves from level k to k + 1 with k = 1, 2, 3; referring to primary, lower vocational, lower secondary, and higher education is: (5) where X are the included covariates and θ is the value of the latent intelligence. We integrate over the joint distribution of the covariates and the latent intelligence given education level k (the lowest of the two adjacent education levels) F_{X,θ∣D = k}(x, c) to obtain the average treatment effect on the untreated (ATU). This treatment effect provides the average educational gain for the lower educated if they had obtained a higher education level. When interested in the effect of increasing the education level the average treatment on the untreated is the most relevant measure from a policy perspective, as it provides the educational gains for the population whose education level can be increased. Other treatment effects, such as the average treatment effect and the average treatment effect on the treated, take a less relevant reference population (respectively, the whole population and the population who has already attained a higher education).

The integrals described above cannot be solved analytically as the dimension of the covariates X is too large. The comparison of the survival functions also involves the counterfactual of surviving at another education level. Therefore simulations are needed to approximate the survival differences. This is explained in more detail in the Supporting Information methodological S1 Appendix.

Our interest is not limited to estimating gains in life expectancy associated with moving up one education level. We also want to decompose the observed difference in life expectancy into treatment effects and selection effects. The latter comprise effects from differences in observed characteristics and from differences in the unobserved intelligence. A limitation is that all observations are limited to the ages 18–66 years. The implied differences in expected years lived between ages 18 and 66 are therefore only shown by education level.

The standard (non-parametric) estimator of the survival function is the product-limit estimator proposed by Kaplan and Meier [39], with d_i is the number of deaths at age t_i and Y_i is the number of individuals who are at risk of dying at age t_i. The surface under the Kaplan-Meier provides the (non-parametric) estimate of the expected years lived of the individuals in the sample over the observed age interval [38]. We calculate the Kaplan-Meier survival function and the implied expected years lived between ages 18 and 66 for each education level. The Kaplan-Meier estimate of the survival function does not account for any observed factors that influence the survival, except for the education level. The unconditional differences in expected years lived based on the Kaplan-Meier estimates therefore provide the total educational effect on the expected years lived, which is the sum of the educational gain and a selection effect. The selection effect of education is the gain in expected years lived by individuals selecting themselves into different education levels. This gain is caused by the fact that individuals with different education levels also differ in other aspects that influence their survival. We can decompose the unconditional differences in expected years lived based on the Kaplan-Meier curves into the educational gain from Eq (5) and a residual, which is a selection effect on the basis of cognitive ability and the other observable factors. Mathematically, (6) where represents the unconditional differences in expected years lived from 18 to 66 from the Kaplan-Meier survival curve, is the treatment effect in Eq (5) from the structural model and represents the selection effect on the basis of observable characteristics X and cognitive ability θ, all when the educational level improves from level k to k + 1. Note that this selection effect is the combination of actual selection bias and selection based on perceived gains of higher education. The selection effect, , can be further decomposed into a selection on observables, selection effect observed, and a selection on latent intelligence, selection effect intelligence (7) where (8) is the gain in expected years lived based on the estimated separate Gompertz proportional hazard models, i.e. the models that ignore the influence of intelligence on the mortality. We integrate over the joint distribution of the covariates given education level k F_{X∣D = k}(x).

All model estimations were carried out using STATA statistical software version 12. All the simulations to calculate the educational gains were obtained using R version 2.15.