The value of a year’s general education for reducing the symptoms of dementia

Abstract

We present a method for estimating the benefits of years of education for reducing dementia symptoms based on the cost savings that would accrue from continuing independent living rather than relying on formal or informal carers. Our method for estimating the benefits of education involves three steps: first taking a year of education and seeing how much this lowers dementia, second using this dementia reduction and estimating how much independent living is affected and third applying the change in caregiving costs associated with the independent living change. We apply our method for estimating education benefits to a National Alzheimer’s Coordinating Center sample of 17,239 participants at 32 US Alzheimer’s disease centres over the period September 2005 and May 2015.

I. Introduction

Dementia is a syndrome caused by a number of progressive illnesses that affect memory, thinking and the ability to perform everyday activities. In 2015, worldwide, there were 897 million people aged 60 and over and 5.2% of these had dementia. In North America, there were 147 million people over the age of 60 and 6.4% of these had dementia. In the high-income part of North America, the annual cost per person with dementia was estimated to be $56,218 (World Alzheimer Report 2015).

Given the prevalence and cost of this disease, it is important to carry out economic evaluations of interventions that can have an impact on dementia symptoms. Cost–benefit analysis, CBA, is the only way to carry out an evaluation that establishes whether an intervention is socially worthwhile or not (Brent 2014, 2006). To date, there is no cure for dementia, in which case the main CBA intervention candidates for evaluation are to delay its onset or mitigate the symptoms. The main aim here is to generate cost savings by delaying institutionalization (see e.g. the New York University Caregiver Intervention evaluated by Long et al. 2014). Cost savings is therefore a frequently used method to value the benefits of dementia interventions.

What is missing from the dementia CBA literature is an evaluation of an intervention that actually reduces dementia rather than just delaying costly institutionalization. While there are no existing ways to change brain pathology, changing the symptoms of dementia may be possible. One intervention that has been found in many studies to reduce dementia symptoms is general education in early life (World Alzheimer Report 2014). As there are no existing CBAs of the effects of early education from reducing the symptoms of dementia, this study attempts to help remedy this deficiency by presenting a method for estimating the monetary benefits of dementia reductions stemming from education.

Our contribution to the economic literature on the evaluation of education interventions is threefold: first, to provide a new health benefit category stemming from education’s impact on dementia symptoms and to add to the many other well-known categories of monetary benefits that education supplies; second, to present a method for estimating the magnitude for this new benefit category; and third, to supply estimates of this new benefit category based on a national data set. With estimates of the monetary benefits of dementia symptoms reduction made available here, there is something extra to compare with the monetary costs of education in order to carry out CBAs of particular education interventions (like high school dropout programmes). We discount the dementia benefits to ensure that they are comparable time wise when an earlier education intervention is likely to take place.

In the process of estimating the effect of years of education on dementia symptoms, we also make a contribution to the dementia literature by helping to settle the issue of whether education is causal or not in explaining dementia symptoms reductions. There are two competing hypotheses. One explanation (the ‘brain size hypothesis’) would suggest that education was not causal, while the other explanation (the ‘brain reserve hypothesis’) points to there being a causal link between years of education and dementia symptoms reductions. Our identification strategy allows us to distinguish the two hypotheses as we include proxies for brain size as controls in the estimation. In this way, we ensure that brain size is not in the error term and so cannot explain both education and dementia symptoms. We thereby obtain a valid test of the brain reserve hypothesis.

The article is structured as follows. We complete the introductory section with an explanation of the data source and how we measured dementia symptoms. In Section II, we examine the mechanisms by which education can causally affect dementia symptoms and explain how causality will be established in this study. In Section III, we explain the method for estimating the benefits of education for reducing dementia that we are proposing and implementing. As we shall see, this has three components and basically uses the standard cost-saving approach to value the benefits.

Section IV presents the estimation framework that will be used to estimate two of the components. Estimates of the third component will come from the literature. Section V gives the definitions for all the variables that appear in the regression equations and this is followed by the data summary for these variables. Section VI reports the estimation results. Section VII takes the results from the two regression equations that pertain to two of the components and combines them with the estimate of the third component coming from the literature to form the total benefit estimate. Section VIII contains the discussion, summary and conclusions.

The data source

The data we will be using to estimate the benefits of education for reducing dementia come from the National Alzheimer’s Coordinating Center (NACC). NACC has constructed a data set that has been fully operational since 2005. These data consist of demographic, clinical, diagnostic and neuropsychological information on participants with normal cognition, mild cognitive impairment and dementia at 32 US Alzheimer’s disease centres. The data set is fully explained elsewhere (Beekly et al. 2007). This study uses the initial visit data for 17,239 participants collected between September 2005 and May 2015.

The measure of dementia

Brain pathology (such as plaques on the outside of the neurons, or fibres on the inside of brain cells for Alzheimer’s disease, or lesions for vascular dementia) likely occurs many years before the onset of clinical dementia. This means that brain pathology is not a sufficient condition for a diagnosis of dementia. It may also not be a necessary condition as one can have cognitive impairment without the brain pathology. For this reason, it is important to employ a measure of dementia that focuses on cognitive functioning rather than pathology. The instrument that we will be using to measure dementia is the Clinical Dementia Rating (CDR) scale. The CDR is a well-accepted measure of dementia severity used globally based primarily on a neurological exam and informant reporting and this was administered to each NACC participant at each visit by a clinician. It is available in 14 languages and has been judged to be the best-evidenced dementia scale in a recent review (Olde Rickert et al. 2011). There are six domains in the CDR: memory, orientation, judgment and problem solving, community affairs, home and hobbies, and personal care. Each domain is assessed using a 0-3 interval. The CDR-SB (the CDR sum of boxes) is the aggregate score across all six domains and this has a range of 0–18.

II. Education and causality: the identification strategy

Our method for estimating the benefits of education mainly relies on an empirical, inverse relationship between education and the symptoms of dementia. Many different explanations of how and why education lowers dementia have been presented in the literature (World Alzheimer Report 2014). There are two main competing explanations. The first is called the brain size hypothesis. It suggests that education is a consequence of other factors and so would not be causal. Thus, it could be that people with a larger brain volume have more physical resources (neurons and synapses) that enable one to compensate for the underlying pathology of dementia and that people with larger brains are more likely to stay in education (Stern 2012).

The other explanations suggest a more causal mechanism. The brain reserve hypothesis involves education changing the structure and processing of the brain such that there are protective and compensating mechanisms making for greater resilience to the destructive pathologies of dementia (Stern 2012, op cit.). Linked to the brain reserve hypothesis is the ‘use it or lose it hypothesis’ whereby lifetime cognitive activity may be necessary to prevent cognitive decline. In this context, education would be causal if it provides motivation to pursue intellectual stimulation over one’s lifetime.

Given these two competing hypotheses, if we are to interpret our regression between years of education and symptoms of dementia as a causal reduction, we need to rule out the first, brain size explanation. Although we do not have data on brain size at birth in our data set, it turns out that brain size is hereditary. Part of the ENIGMA consortium working on the many mental effects of brain size was a team who established that brain size (and other brain patterns and connections) is more similar among family members than unrelated individuals (see Thompson et al. 2014). Since we have information in our data set on parental and sibling dementia associations with the clients in the AD clinics, our identification strategy will be to include these family dementia associations as controls to accompany years of education in our regression analysis. In this way, we remove from the error term any hereditary brain size effects that could determine both years of education and dementia symptoms. Even though there exist numerous studies providing robust evidence supporting the cognitive reserve hypothesis (reviewed in Sharp and Gatz 2011; Meng and Darcy 2012), it is important to eliminate the possibility that the brain size hypothesis was relevant to our data set.

Note that the use of hereditary variables for our controls is somewhat similar to that of Nguyen et al. (2016) who used a genetic risk score constructed from single nucleotide polymorphisms (SNPs) derived from DNA samples as an instrument variable (IV) for years of education. They were able to test whether the SNPs were good instruments for education. In our case, we are focusing on brain size as the genetic variable. Since we were not able to measure brain size, we use our hereditary measures simply as proxies for brain size. These hereditary measures cannot be used as instruments for years of education. This is because the whole purpose of including the hereditary variables is due to the fact that brain size is known to determine dementia, and so the hereditary proxies would violate the exclusion restriction necessary for a suitable IV. Nonetheless, it is reaffirming for our study that in the literature, genetic factors were also found to prove a causal link between education and dementia symptoms.

In addition, it is important to understand that our regression analysis automatically rules out any reverse causation between education and dementia. Years of education occur many years (anywhere from 40 to 60 years) prior to the observance of dementia symptoms and so years of education cannot, like weight loss (Dahl et al. 2008), be a consequence of dementia.

III. The method for estimating the benefits of education

The extent to which a person has dementia affects whether the person can live independently or requires assistance from a carer, either formally by paying for a helper or informally by relying on a family member. The cost of providing for the assistance, in terms of the payments made or the earnings foregone, is one measure of the benefits of not having any specific magnitude of dementia.

Because education will be shown to reduce the dementia symptoms, and by lowering dementia the caregiving costs are smaller, the benefits of education can be judged by the caregiving cost savings that it provides. Thus, our method for estimating the benefits of education involves three steps: first taking a year of education E and seeing how much this lowers dementia symptoms D, second using this dementia reduction and estimating how much independent living L is affected and third applying the change in caregiving costs C associated with the independent living change. That is, our method (formula) for estimating the benefits of education involves using the derivative of the savings in cost of dependent living with respect to a year of education and applying the chain rule:

$$\frac{\partial C}{\partial E}=\frac{\partial C}{\partial L}\frac{\partial L}{\partial D}\frac{\partial D}{\partial E}.$$ (1)

where $\frac{\partial C}{\partial E}$ is the cost-saving benefits per year of education, $\frac{\partial C}{\partial L}$ is the cost change per change in independent living, $\frac{\partial L}{\partial D}$ is the change in independent living per unit change in dementia and $\frac{\partial D}{\partial E}$ is the change in dementia per year of education.

The cost-saving benefits of education will therefore be obtained as the product of three components. In our study, we use the NACC data set to provide estimates for two of them and use information in the literature to supply estimates of the remaining component.

IV. Estimation framework

Following the logic of the chain rule, we use a two-equation recursive framework whereby education will lower dementia symptoms and reducing dementia will decrease independent living costs.¹ The first estimation equation has dementia symptoms as the dependent variable and education as the independent variable, together with a set of controls, the vector Z. To allow for non-linearity, education will be expressed in log form. The regression equation is

$$D_i={\alpha }_0+{\alpha }_{1}ln{E}_i+{\alpha }_2{Z}_i+{\epsilon }_i.$$ (2)

where the αs are fixed coefficients and ε_i is the random error term. From estimating this equation, we obtain

$$\frac{\partial D}{\partial E}=\frac{{\alpha }_1}{E}.$$ (2a)

The second estimation equation has independent living as the dependent variable and dementia symptoms as the independent variable, again with the vector Z as controls. The equation can be thought of as a production function relating dementia symptoms as an input to independent living as an output. The regression equation is

$$L_i={\beta }_0+{\beta }_1{D}_i+{\beta }_2{Z}_i+{\upsilon }_i.$$ (3)

where the βs are fixed coefficients and υ_i is the random error term. From this equation, we derive

$$\frac{\partial L}{\partial D}={\beta }_1.$$ (3a)

The selection of the controls

As our identification strategy is to include Z variables that are hereditarily known to impact brain size, we will use family (parental and sibling) dementia variables as controls. Everyone inherits some form of a copy of the gene apolipoprotein E (APOE) from their parents (e2, e3, e4). Those who inherit APOEe4 from one parent have an increased risk of Alzheimer’s. Those who inherit APOEe4 from both parents have an even higher risk, but not a certainty.

For the non-hereditary Z variables, we will use demographic characteristics (age, age squared, race and gender) which although impacting the number of years of education are inherently exogenous. Other factors that are known to be associated with dementia symptoms, such as alcohol, smoking, depression, blood pressure and obesity, are omitted from the regressions. These life style variables are prone to result from dementia as well as be causes of dementia. We therefore exclude these life style variables to rule out any possible reverse causation.

V. The description of all the variables used in the study and the data summary

All the variables used in the two estimation equations are listed in Table 1 together with their definitions.

Table 1.

Definitions of all variables.

Variable	Description
Education	Subject’s years of education
CDR-SB	Total CDR score based on memory, orientation, judgement and problem solving, community affairs, home and hobbies, personal care, each of the six categories on a scale of 0-3
Age	Subjects age at initial visit
Age squared	Subjects age at initial visit squared
Male	Subject’s sex Male = 1; female = 0
APOE (1 copy)	Number of APOE (APOEe4) 1 copy 1 = 1 copy of e4 allele; 0 = no e4 allele copy or 2 e4 allele copies
APOE (2 copies)	Number of APOE (APOEe4) 2 copies 1 = 2 copies of e4 allele; 0 = no e4 allele copy or 1 e4 allele copy
Sibling	Sibling with dementia 1 = Has a sibling with dementia; 0 = no sibling with dementia
Independence living level	The subject’s level of independence 1 = Able to live independently 2 = Requires some assistance with complex activities 3 = Requires some assistance with basic activities 4 = Completely dependent
Race	NIH race definition 1 = White; 0 = non-white

CDR-SB: Clinical Dementia Rating sum of boxes; APOE: apolipoprotein E.

The log version for education is in natural logarithmic terms. The definitions come from NACC’s ‘Description of NACC Derived Variables to be Used in Data Analysis’ (August 2014) and NACC’s Uniform Data Set ‘Coding Guidebook for Initial Visit Packet’ (last modified January 14 2014).

The data set was screened to include only information on the initial visit, so each observation is for a separate individual. When there was no missing information, there were 17,341 observations. Actual sample sizes for the estimation equations were dependent on the number of missing observations.

Table 2 gives the data summary in terms of the number of observations, mean values, SDs and minimum and maximum values. We can see that on average subjects had 15 years of education and scored a 3 on the CDR-SB scale. The average age was 72 years. 38% of the sample was males, 81% was White, 35% had 1 copy of APOE e4, 7% had two copies and 63% lived completely independently (living level 1).

Table 2.

Descriptive statistics for all the variables.

Variable	Number	Mean	SD	Minimum	Maximum
Education	17,239	14.93	3.51	0	28
Log education	17,203	2.67	0.30	0	3
CDR-SB	17,341	3.08	4.46	0	18
Age	17,341	72.28	10.75	18	104
Age squared	17,341	5339	1493	324	10,816
APOE (1 copy)	11,790	0.35	0.48	0	1
APOE (2 copies)	11,790	0.07	0.26	0	1
Sibling	17,117	0.18	0.38	0	1
Independence	17,299	1.56	0.85	1	4
Independence level 1	17,299	0.63	0.48	0	1
Independence level 2	17,299	0.22	0.41	0	1
Independence level 3	17,299	0.11	0.31	0	1
Independence level 4	17,299	0.04	0.20	0	1
Race	17,095	0.81	0.39	0	1

CDR-SB: Clinical Dementia Rating sum of boxes; APOE: apolipoprotein E.

VI. Estimation results

Estimating the effect of education on dementia

OLS was used to estimate Equation (2). The results using four alternative specifications, i.e. regression equations (1A)–(1D), are shown in Table 3. All variables reported were significant at the 1% level. Education has a coefficient of more than −3 in all the specifications.

Table 3.

Effect on CDR-SB of years of education using OLS (t-stats in parentheses).

	Equations with and without controls
Variable	Equation (1A)	Equation (1B)	Equation (1C)	Equation (1D)
Log education	−3.6090*** (10.33)	−3.1780*** (9.95)	−3.3186*** (10.28)	−3.1130*** (9.39)
Age		−0.1446** (2.52)	−0.1441** (2.51)	−0.1812*** (3.08)
Age squared		0.0016*** (3.53)	0.0016*** (3.51)	0.0019*** (4.03)
Male			0.6251*** (4.40)	0.6129*** (4.95)
APOE (1 copy)				1.9063*** (13.90)
APOE (2 copies)				3.4285*** (18.22)
Sibling				0.3179*** (3.64)
Constant	12.6910*** (12.58)	5.7525*** (5.33)	13.3562*** (6.15)	12.9161*** (6.33)
R2	0.0609	0.1048	0.1094	0.1793
Sample size	n = 17,203	n = 17,203	n = 17,203	n = 11,609

APOE: Apolipoprotein E.

Significance levels:

^*10%;

^**5%;

^***1%.

Cluster SEs for all coefficients based on the AD centre involved.

Equation (1A) just includes years of education. Education on its own accounts for about 6% of the variation in dementia. Equations (1B)–(1D) add the other variables as controls. Equations (1B) and (1C) just add the demographic variables age and gender (race was not significant). Age and age squared were both statistically significant supporting the idea that ageing has a progressive dementia effect. Together, the age variables raise the explanatory powers to 10%. Being male had a positive impact on dementia symptoms. This is unexpected, except for the fact that the average age in our sample was 72 years. Having an older sample negates the fact that females live longer and more likely to have dementia on this account. In any case, the additional explanatory power of including gender in the regressions was very small.

Equation (1D) then adds the hereditary factors as controls and this raises the R² considerably to 18%. Having a sibling with dementia has a small positive effect on dementia symptoms. However, inheriting 1 and 2 APOE e4 copies combined raised dementia symptoms by over 5 points on the CDR-SB scale. On its own, APOE (2 copies) had a coefficient that was larger (and opposite in sign) than for the education variable. Due to the importance of the hereditary factors in equation (1D), we can conclude that our identification strategy was successful in controlling for brain size and ensuring that years of education can have a causal interpretation. Since equation (1D) is identified, and has the most explanatory power, we will take the coefficient −3.1130 to be the best estimate of α₁ to use to value the benefits of education. It is also the most conservative estimate of those in Table 3.

Estimating the effect of changes in dementia on independent living

The dependent variable in the production function Equation (3) was the extent of independent living. In our analysis, there are four different degrees of living independence: the ability to live independently, requiring some assistance with complex situations, requiring some assistance with basic activities and being completely dependent. Because these four categories record differential orders of independent living, we use a four-category, ordered probit equation to predict how each of the four degrees of living independently is altered by a one-unit reduction in CDR-SB. Table 4 shows the marginal effects on the four living levels of changes in dementia symptoms together with the marginal effects for all the controls accompanying the CDR-SB variable.

Table 4.

Marginal effects on independence levels using ordered probit (z-scores in parentheses).

	Level of independence
Variable	Independence 1	Independence 2	Independence 3	Independence 4
CDR-SB	−0.0686*** (25.90)	0.0406*** (14.87)	0.0181*** (22.43)	0.0100*** (25.68)
Age	−0.0021*** (4.77)	0.0012*** (4.56)	0.0005*** (5.07)	0.0003*** (4.50)
Race	−0.0361*** (3.11)	0.0213*** (2.96)	0.0095*** (3.28)	0.0052*** (3.32)

CDR-SB: Clinical Dementia Rating sum of boxes.

Significance levels:

^*10%;

^**5%;

^***1%.

Cluster SEs for all coefficients based on the AD centre involved.

Ordered probit based on 17,055 observations. The pseudo-R² for the regression equation was 0.4696.

In the ordered probit results given in Table 4, the 1, 2, 3 and 4 categories correspond to the independent living levels 1, 2, 3 and 4, respectively, as defined in Table 1. As expected, dementia symptoms reduce independent living and increase the three categories of dependent living. Independent living goes down by −0.0686; level 2 goes up by 0.0406, level 3 goes up by 0.0181 and level 4 rises by 0.0100. The controls in all four equations are the subject’s age and race (gender was insignificant). Both these controls lower the chances of independent living and increase the chances of dependent living. The explanatory power of the determinants of independent living levels estimates was very high as the ordered probit regression equation, from which the four independent living levels were derived, had a R² of 0.47.

The identification strategy for independent living was simply to rely on the fact that the demographic factors used as controls were both inherently exogenous and that the very high explanatory powers of the regression equation minimized the possibility that there would be an influential variable in the error term that was correlated with both independent living and the dementia symptoms.

VII. The three cost-saving components and total benefits

The change in dementia per year of education:∂D/∂E

Because education was entered in log form in Equation (2), the change in dementia per year of education was given in Equation (2a) by the slope of the regression equation divided by the number of years of education that had occurred, i.e. α₁/E_i. From Table 3 equation (1D), we see that the slope was −3.1130, which meant that for the first year, the effect was to reduce dementia by this amount, i.e. 3.1130/1 points. For year 2, the impact was −3.1130/2, which is a 1.5565 reduction in dementia, and so on for every number of years examined. For those who had the greatest number of years of education in our data set, which was 28 years, the reduction in dementia was only 0.1112 for the 28th year of education. The reductions in dementia for each of the 28 years of education are recorded as column (2) in Table 6. (Table 6 is discussed fully later.)

Table 6.

Cost savings benefits by year of education in 2010 dollars.

(1) Year of education	(2) Reduction in dementia	(3) Undiscounted yearly benefits	(4) Undiscounted total benefits	(5) Discounted yearly benefits	(6) Discounted total benefits
1	3.1130	45,319	45,319	8658	8658
2	1.5565	22,659	67,978	4459	13,116
3	1.0377	15,106	83,085	3062	16,178
4	0.7783	11,330	94,414	2365	18,543
5	0.6226	9064	103,478	1949	20,492
6	0.5188	7553	111,031	1673	22,164
7	0.4447	6474	117,506	1477	23,641
8	0.3891	5665	123,170	1331	24,972
9	0.3459	5035	128,206	1219	26,191
10	0.3113	4532	132,738	1130	27,320
11	0.2830	4120	136,858	1058	28,378
12	0.2594	3777	140,634	999	29,377
13	0.2395	3486	144,120	950	30,326
14	0.2224	3237	147,358	908	31,234
15	0.2075	3021	150,379	873	32,107
16	0.1946	2832	153,211	843	32,950
17	0.1831	2666	155,877	817	33,768
18	0.1729	2518	158,395	795	34,563
19	0.1638	2385	160,780	776	35,338
20	0.1557	2266	163,046	759	36,097
21	0.1482	2158	165,204	745	36,842
22	0.1415	2060	167,264	732	37,574
23	0.1354	1970	169,234	721	38,295
24	0.1297	1888	171,122	712	39,007
25	0.1245	1813	172,935	704	39,711
26	0.1197	1743	174,678	697	40,408
27	0.1153	1678	176,357	692	41,100
28	0.1112	1619	177,975	687	41,787

The change in independent living per unit change in dementia:∂L/∂D

The change in independent living per unit of change in dementia was given as β₁ by Equation (3a) derived from Equation (3). Since we have identified four different levels of independent living, β₁ will have four different estimates. These four estimates were given as part of the ordered probit results shown in Table 4. Table 5 extracts and displays these four estimates. Because we are analysing dementia reductions caused by education increases, the signs in Table 4 are reversed in Table 5 to acknowledge the fact that reductions in dementia will lead to increases in independent living and that, for the three dependent living levels 2-4, the costs will be reduced.

Table 5.

The effect of a change in dementia on levels of living independence.

Level of living independence	Effect of 1 unit fall in CDR-SB
(1) Able to live independently	+0.0686
(2) Requires some assistance with complex situations	−0.0406
(3) Requires some assistance with basic activities	−0.0181
(4) Completely dependent	−0.0100

CDR-SB: Clinical Dementia Rating sum of boxes.

The cost change per level change in independent living:∂C/∂L

The cost savings associated with each of the three effects of dementia on living independence shown in Table 5 depend on how much caregiving is required at each independence level and the cost of that care. Formal care can be defined as care obtained through an agency or provided by someone hired directly, whereas informal care can be defined by the carer being a relative or unpaid nonrelative with no agency affiliation. Based on a national longitudinal survey for 2010 (Hurd et al. 2013), it was estimated that for a year of formal care for dementia purchased in the marketplace, the cost was $28,501 (including total out-of-pocket spending, total Medicare spending, net formal home care and nursing home care). For informal care, there were two estimates. The estimate was $27,789 if the care was valued by replacement cost, which is the cost of equivalent care service if purchased on the market by a home health agency, and it was $13,188 if the care was valued at the foregone earnings of the unpaid carer.

On the basis of these 2010 estimates, we assume that any person who was living completely dependent in our study would require formal care and this would therefore cost $28,501. If someone requires some assistance with basic activities, then this would also equate with a serious lack of living independence and someone at the level of a formal care worker would be required. Their care can then be costed at the higher estimate for informal care given as $27,789. For someone requiring some assistance only for complex situations, their dementia care needs would not be so serious and the cost of their care could be valued at the lower estimate for informal care being $13,188. In the sensitivity analysis in Section VII, we provide alternative estimates of the costs of independent living that also may be plausible.

Total benefits of education:∂C/∂E

We assemble the three components that comprise our method for estimating the benefits of education from reducing dementia expressed in Equation (1) of Section II using the information given in Section VI. We will first present the results in undiscounted terms assuming that the benefits occur in the year when dementia is reduced. Then, we give the results in discounted terms allowing for the fact that the benefits occur many decades after the years of education have been completed.

Undiscounted benefits

The undiscounted yearly and total benefits are shown as columns (3) and (4) in Table 6. Our benefit method comprises three partial derivatives. The component in the benefit formula labelled ‘change in dementia per year of education’ corresponds to ∂D/∂E and this is shown as column (2) in Table 6. As explained in the estimation of the effect of education on dementia in Section VI, this derivative was estimated to vary by the year of education. As we can see, column (2) has the education effects declining over time.

The remaining two components of the benefits formula, ‘change in independent living per unit change in dementia’ and ‘cost change per change in independent living’, when multiplied together form the cost savings per unit of dementia decline, i.e. ∂C/∂D, which corresponds to ∂C/∂L times ∂L/∂D in Equation (1). This cost saving does not vary by year of education as it stems from the decline in living costs due to a unit reduction in dementia. This cost saving is a fixed amount per unit decline in dementia and amounts to $1323. Essentially, this cost savings per unit of dementia decline is a weighted average of the three levels of independent living that are reduced by dementia declining per year of education, as shown in Table 5 in Section VI, where the weights are given by the three cost estimates for each level of independent living that was presented Section VI.

To see specifically how this cost saving per unit of dementia estimate was obtained, consider the first level of dependent living that is reduced by a unit decline in dementia, which is level 2 in Table 5. This is shown to fall by 0.0406. Each year in level 2 living costs $13,188. As this is reduced by 0.0406 for each unit of dementia decline, the expected cost savings for level 2 living is 0.0406 times $13,188 which is $535. Similarly, level 3 living falls by 0.0181, and each year in living level 3 costs $27,789, making 0.0181 times $27,789, which is $503, as the expected cost savings for level 3 living. Finally, the expected cost savings for level 4 living is 0.010 times $28,501 or $285. Summing the three cost savings for each of the three levels produces the $1323 estimate of the yearly cost savings from a unit dementia decline. We assume that once dementia is diagnosed, non-independent living will last 11 years, which is the median life expediency for a person first diagnosed with dementia (Aneshensel, Pearlin, and Mullan et al. 1995). This makes the lifetime total $14,558 per unit of dementia.

The final step to obtain the benefits figure for a year of education is to recognize that the annual cost savings of ∂C/∂L is for a unit dementia decline, whereas a year of education provides a varied decline in dementia for all years, see column (2). Therefore, multiplying column (2) by $14,558 generates the benefits per year of education that is in column (3) of Table 6. The benefits range from $45,319 for the first year of education to $1619 for the 28th year of education.

Column (4) in Table 6 gives the total benefits, the cumulative cost savings for the current and all previous years of education. For someone completing high school with 12 years of education, the benefits are $140,634, and they are $153,211 for someone who has completed high school and then goes straight on to graduate college in 4 years.

Discounted benefits

The discounted yearly and total benefits are presented as the final two columns (5) and (6) in Table 6. For this discounting exercise, we use a time line that is contained in the age and education characteristics in our sample. The average age in the NACC data set is 72 years and the maximum number of years of education is 28. As we have previously assumed that the benefits of dementia reduction persist for a 11-year period, this makes year 62 the time when dementia will be assumed to start. We therefore use age 62 as the base year from which we discount backwards the benefits from the earlier 28 years of education.

The 28 years of education was assumed to take place consecutively after the first 5 years when the person will have been at home growing up. Age 6 is the starting date for education and the maximum ending date is age 33. Age 6 is 56 years earlier than age 62 and therefore requires 56 years of discounting. Age 33 is 29 years earlier than age 62 and had 29 years of discounting. The years between ages 6 and 33 were also discounted at the relevant number of years prior to age 62.

With the time line set, all that remains to be explained is the discount rate that was chosen to carry out the discounting. The discount rate used most often in the healthcare evaluation field is 3% – see Brent (2014). In large part, this is due to the influential study by Gold et al. (1996) that recommended 3% coming from a panel of experts that were assembled to give guidelines for how health economic evaluations should be standardized in practice. This rate was based on the social time preference rate and estimated by the observed, net of inflation, interest rate on long-term government securities in the United States. 3% is also very close to the 3.5% estimate by Moore et al. (2004) who used the Ramsey Rule as its underpinnings for the United States. So, we used 3% as our discount rate for discounting education benefits.

The discount factor for year 1’s benefits (which occur at age 6) for 56 years of discounting at 3% is 0.1910. Multiplying the $45,319 benefits of year 1 by 0.1910 produces the $8658 figure that appears as the first entry in column (5) forming the present value for the education benefits for that year. All other entries were calculated in a similar fashion by multiplying the amounts in column (3) by the appropriate discount factor. Thus, the year 28 discounted benefits of $687 were obtained by multiplying $1619 by the 0.4243 discount factor (from 33 years of discounting at 3%). The discounted yearly benefits range from $8658 to $687. The discounted cumulative benefits in column (6) vary between $8658 and $41,787. Someone completing high school with 12 years of education has discounted benefits of $29,377 and they are $32,950 from graduating college in 4 years straight after high school.

The sensitivity analysis

The benefits figures given in Table 6 are considered to be the best estimates. However, it is useful to see the extent to which they are sensitive to the particular underlying assumptions on which they are constructed. We will provide two alternative estimates of the effect of education on the dementia symptoms, and two alternative estimates of the costs associated with independent living that any reduction in dementia symptoms can be thought to generate. The alternative estimates of the total discounted benefits by years of education are presented in Table 7. For ease of comparison, the best estimates in column (6) of Table 6 are repeated as column (2) of Table 7.

Table 7.

Discounted total benefits by year of education in 2010 dollars.

(1) Year of education	(2) Best estimates	(3) Lower bound estimates	(4) Upper bound estimates	(5) Full sample estimates	(6) Linear estimates
1	8658	6425	10,890	9229	744
2	13,116	9734	16,449	13,982	1510
3	16,178	12,006	20,350	17,246	2299
4	18,543	13,761	23,325	19,767	3111
5	20,492	15,208	25,776	21,845	3948
6	22,164	16,449	27,880	23,628	4810
7	23,641	17,545	29,738	25,202	5698
8	24,972	18,533	31,412	26,621	6613
9	26,191	19,437	32,945	27,920	7555
10	27,320	20,275	34,366	29,124	8525
11	28,378	21,060	35,696	30,252	9525
12	29,377	21,802	36,952	31,316	10,554
13	30,326	22,506	38,147	32,329	11,615
14	31,234	23,180	39,289	33,297	12,707
15	32,107	23,828	40,387	34,227	13,832
16	32,950	24,454	41,448	35,126	14,990
17	33,768	25,060	42,475	35,997	16,183
18	34,563	25,650	43,475	36,845	17,413
19	35,338	26,226	44,451	37,672	18,679
20	36,097	26,789	45,406	38,481	19,983
21	36,842	27,342	46,343	39,275	21,326
22	37,574	27,885	47,263	40,055	22,709
23	38,295	28,420	48,171	40,824	24,134
24	39,007	28,949	49,066	41,583	25,602
25	39,711	29,471	49,952	42,333	27,114
26	40,408	29,989	50,829	43,076	28,671
27	41,100	30,502	51,699	43,814	30,275
28	41,787	31,011	52,563	44,546	31,927

The sensitivity analysis begins with the results of providing alternative estimates associated with independent living than those given in Section VI. Instead of the expected values of costs taken from Hurd et al., we can use the lower and upper bound values that come from the 95% confidence interval attached to their expected values. The lower bound values replaced $28,501, $27,789 and $13,188 with $20,881, $21,112 and $9636, respectively; and the upper bound values were $36,122, $34,466 and $16,740. The lower bound results are shown in column (2) and the upper bound results are in column (3). They differ from the best estimates by around $2000 from 1 year of education, but this increases to over $10,000 from 28 years of education.

The results in columns (1)–(3) are all predicated on the 3.1130 reduction in the CDR coming from equation (1D) of Table 3. Note that in order to estimate equation (1D), it was necessary to exclude over 5000 observations due to missing values for the hereditary variables.

If the original sample size were used, and the hereditary variables were excluded instead, the reduction in the CDR would be based on the 3.3186 figure found in equation (1C) of Table 3. The resulting benefits are shown in column (5) of Table 7 where they are listed as the full sample estimates. They only differ slightly from the best estimates, so the results are not sensitive to varying the sample size.

What supplies the biggest contrast with the best estimates comes from replacing the log of education with a linear specification. Instead of a year of education having a declining effect on dementia symptoms as shown in column (2) of Table 6, ranging from 3.1130 to 0.1112, a linear specification would have a constant annual CDR reduction of 0.2674. The linear education specification produces the estimates of benefits that are given in column (6) of Table 7. The difference that assuming a diminishing marginal productivity effect that we have incorporated in our main model, over assuming a constant rate of education effect, depends very much on the number of years of education that one is considering. The linear specification would indicate estimates that were less than 10% of the benefits that 1 year of education would provide under a log specification; though this would rise to 76% if someone had 28 years of education.

VIII. Summary and conclusions

Education is known to provide many kinds of benefits. From the individual perspective, it is an investment in human capital which leads to increases in lifetime earnings (Becker, 1993). From the social perspective, there are also gains to others whose productivity is raised when an educated person enters the workforce (Weil 2009). An educated mother produces health benefits for her offspring (Gakidou, Cowling, and Lozano 2010). Staying in school helps reduce crime and incarceration (Heckman et al. 2010) and re-incarceration (Brent and Maschi, forthcoming). The capacity for education to reduce dementia must be added to this list and constitute a further category of monetarized benefits to assign to providing education for all.

In this study, we provided a method for evaluating the benefits of lowering dementia. It was estimated that the first year of education produced $8658 worth of discounted benefits and it averaged $2448 per year over the 12 years one needs to complete high school. These benefits are expressed in 2010 dollar terms. In the sensitivity analysis, we showed that alternative plausible estimates also provided sizeable benefits.

The method we presented provided a minimum best estimate of benefits. We focused just on the cost savings in terms of living arrangements that lowering dementia produces. This excludes any benefits to carers whose health often suffers by looking after dementia patients (Zarit and Talley, 2013). Although education has been shown to not increase life expectancy of those with reduced dementia symptoms (Paradise, Cooper, and Livingston, 2009), the quality of life of those with lowered dementia symptoms is enhanced and this is also a benefit that needs to be added to the cost-saving benefits estimated in this study.

For education to be a viable intervention to provide benefits via reduced dementia symptoms, it is necessary that it be causal. Alternative mechanisms have been suggested. If brain reserve is to be the mechanism, then we can be sure that education has caused the benefits. If other mechanisms are in play, whereby, say, brain size and not brain functioning is involved, then education causality could be in question. However, in so far as brain size runs in the family, the fact that we were able to control for family dementia as a cause of individual dementia means that brain size is not likely to be the causal link in our study. So our analysis supports the brain reserve hypothesis.

What our study also helps to understand is what constitutes a high ‘dose’ of education. For someone undertaking 28 years of education, which was the largest number in our sample, the maximum reduction in the CDR-SB was 12.23 points out of a total score of 18. This is a very large contribution. However, there are diseconomies of scale from years of education. Exactly a quarter of the maximum reduction can be achieved from just 1 year of education and just over a half from 4 years of education. Experiencing 16 years of education by going to college, as opposed to just the 12 years leading to high school completion, further increased the CDR-SB by 0.86. Consequently, the discounted cost-saving benefits of education were $8658 for 1 year of education, they were $29,377 for 12 years, they were $32,950 for 16 years and they were $41,787 for 28 years of education. If one did not assume diseconomies of scale, the 1-year benefit of education would be only $744. But, over 28 years of schooling, the total discounted benefits would still be considerable at $31,927, which would be 76% of the best estimate.

The benefits of years of education from reducing the symptoms of dementia that we estimated related to education that took place independently of any given policy intervention, other than for universal compulsory high-school education. Thus, the estimates were for education choices that were previously undertaken. But, the benefits estimated here can also be used in part to carry out a CBA of a particular current education intervention, for example, a dropout prevention programme. In this context, costs need to be included together with the benefit estimates that we have supplied in this article. Our benefit estimates relate to just the contribution of education to reducing dementia symptoms and can be added to all the other benefit categories that education is known to generate.

As an illustration, consider the Check & Connect dropout prevention programme. Tyler and Lofstrom (2009) report a study where the dropout rate for the programme by the end of the ninth-grade was 9% compared to 30% without the programme, a 21% increase in the probability of completing the year. From Table 6, we see that for year 9, the discounted benefits were $1219 (they would be nearly as high at $942 with the linear education estimate), which makes the benefits of the Check and Connect programme in terms of reducing dementia symptoms $256. The cost of the programme was about $1400 per student. One could not justify the programme on the basis of the estimated dementia benefits alone. But 18% of the costs would be covered just by the dementia benefits, which would probably be the least of all the benefit categories of a school dropout prevention programme (see e.g. the CBA of the Perry Preschool Program, Heckman et al., 2010).