Early Childhood Education and Life-cycle Health

Abstract

This paper forecasts the life-cycle treatment effects of a widely-emulated, high-quality, and intensive early childhood program on chronic diseases. Our forecasts combine non-experimental and experimental data from a long-term follow up during adulthood, which included health surveys and a full medical examination with blood and other physical tests. The program significantly reduced the prevalence of heart disease, stroke, cancer, and mortality across the life-cycle. Monetizing the benefits that arise from this program using quality-adjusted life years indicates that its health benefits are almost enough to offset all costs associated with program implementation (including the welfare costs of financing the program through taxation).

1. Introduction

Child poverty is a persistent problem in the United States.¹ Investing in comprehensive birth-to-five early childhood education is a potentially powerful and cost-effective way to mitigate the negative consequences of child poverty on child development and adult opportunity (Heckman, 2008). While the upfront costs of comprehensive early childhood education can be high, such investments have the potential to pay off in both the short and long run.

A large body of evidence documents that high-quality early childhood education boosts the skills of disadvantaged children.² However, much of this research is based on short-term followups to the interventions. Only a few studies analyze longer-term outcomes and they focus mainly on labor market and crime outcomes.³ This paper builds on recent work by García et al. (2018), who quantify the life-cycle benefits of high-quality early childhood education across multiple domains of human development. They estimate that every dollar spent on high-quality early childhood education targeted to disadvantaged children generates an economic return of 7.3 dollars (accounting for the welfare costs of financing the project through taxation).

This paper focuses on the health benefits of the program that they analyze. They demonstrated that a significant increase in quality-adjusted life years (QALYs) induced by the program, which, when appropriately valued, are nearly enough to offset all costs associated with program implementation (i.e., if the only benefit of the program had been the improvement in QALYs, the program would have almost paid for itself). For males, the increase in QALYs more than offsets all program costs, generating positive returns. For females, the increase in QALYs offsets nearly half of the program costs. This paper examines the risk-reducing impacts of interventions for specific chronic conditions over the life cycle. We investigate risk-reducing properties of high-quality early childhood education on six chronic conditions: cancer, lung disease, diabetes, heart disease, hypertension, and stroke.

We study the health outcomes from an influential pair of essentially identical early childhood programs conducted in North Carolina that targeted disadvantaged children. The Carolina Abecedarian Project (ABC) and the Carolina Approach to Responsive Education (CARE), henceforth ABC/CARE, were implemented as randomized control trials. Both programs were launched in the 1970s. The programs started early in life (at 8 weeks of life) and engaged participants until age 5. The program is a prototype for many programs planned or in place today.⁴ The original goal of the program was to boost cognition and promote schooling and attachment to society. Yet, it also boosted health.

Campbell et al. (2014) use the full adult medical sweep to document that randomly assigned treatment children in ABC had significantly lower prevalence of risk factors for cardiovascular and metabolic diseases in their mid-30s. Figure 1 summarizes their evidence. The findings in Campbell et al. (2014) suggest that early childhood education can have substantial benefits in later-life health. This paper conducts a rigorous forecasting analysis that allows us to simulate the effects of mid-life health outcome improvements on potential risk reductions in chronic diseases over the life-cycle.

Figure 1: ABC Health Effects at Mid-30s.

Note: This figure replicates the treatment-effect results in Campbell et al. (2014). Metabolic syndrome, obese, hypertension, and prehypertension are indicators. Chol2HDL/10 stands for LDL cholesterol and it is the “bad cholesterol” divided by 10, HDL-C/100 stands for HDL cholesterol and it is the “good cholesterol” divided by 100, Diastolic/100 and Systolic/100 stand for diastolic and systolic pressure divided by 100.

Our analysis is based on an adaptation of the Future Adult Model (FAM) developed in Goldman et al. (2015). FAM is a dynamic economic-demographic microsimulation model that projects the lifetime health and economic outcomes for individuals. FAM allows us to forecast the prevalence of chronic diseases for ABC/CARE individuals and understand the life-cycle trajectories of their health.⁵ We use auxiliary data to construct synthetic cohorts from non-experimental samples to estimate production functions of health outcomes. Many of the inputs to the production functions for health are affected by treatment and are measured in both experimental and non-experimental data. The inputs to our forecasts are the epidemiological health assessments in Figure 1. They are the “initial conditions” of our forecasts and serve as the basis for life-cycle treatment effects on chronic diseases. We forecast likely future outcomes of the experiment participants using our estimated production functions applied to non-experimental data with inputs and outputs suitably adjusted for cohort effects.

We show that ABC/CARE has substantial, life-cycle effects on cancer, heart disease, stroke, and mortality for both males and females. Across the life-cycle, treatment group females are less likely to have a stroke than their control group counterparts. By age 70, control group males are twice as likely to have a stroke as their treatment group counterparts. Similar results hold for heart disease, lung disease, and cancer. By age 50, a significant difference between the likelihood of dying due to any of these diseases emerges between treatment and control group participants, both male and female. For males after age 60, this difference grows substantially. At age 70, control group males are almost four times as likely to die as their treatment group counterparts. Results for women are less stark.

The outline of the paper is as follows. Section 2 describes the ABC/CARE program and the data collected on its participants. Section 3 discusses our adaption of the FAM model that allows us to forecast life-cycle chronic diseases for ABC/CARE participants. Section 4 reports and discusses our findings. Section 5 concludes. This paper presents the essential components of our forecasts and results and the information that is basic to understanding them.

2. ABC/CARE Program and Data Description

ABC/CARE is a randomized early childhood intervention with longitudinal follow-up data from birth until adulthood. Data on cognitive skills, socio-emotional skills, family environment, and self-reported health of control and treatment group children were collected annually during the duration of the program and periodically until participants reached their mid-30s. ABC/CARE is a widely emulated early childhood program. Despite larger sample sizes and multi-site designs in other randomized programs, few have longitudinal data on health outcomes until adulthood (Elango et al., 2016). Long-term outcomes are especially important for health since many chronic conditions manifest later in life after years of sustained behavior.

The goal of the Carolina Abecedarian Project (ABC) and Carolina Approach to Responsive Education (CARE), ABC/CARE, was to prepare children for school socially, cognitively, and academically by promoting language and cognitive development in center-based care. There was no focus on adult health yet we find important impacts on it. The interactive curriculum provided an educational environment with small student-staff ratio and small-group learning. The program also provided nutritious meals and medical checkups for participants.

ABC and CARE recruited four and two cohorts, respectively, of disadvantaged children born in Chapel Hill, North Carolina between 1972 and 1980. Potential participants were referred to researchers by local social service agencies and hospitals at the beginning of the mother’s last trimester of pregnancy. Eligibility was based on a High Risk Index⁶ developed by the Frank Porter Graham Center (FPG) at the University of North Carolina at Chapel Hill. Eligible mothers were 20 years old on average, 74% of fathers were absent, and 94% of the sample was African-American.

The final ABC sample consisted of 114 subjects, with 58 in the treatment group and 56 in the control group. CARE consisted of 65 families, with 25 in a family education treatment group, 23 in the control group, and 17 in a center-based childcare treatment group. Six and five subjects attrited from the ABC and CARE samples respectively. The problem of attrition is addressed in García et al. (2018), and their methods are applied in this paper.

Children were randomized into treatment and control groups using child pairs matched on family background. All subjects received diapers and formula for the first six months, and treatment group subjects received additional daily health screenings. From the ages of 0 to 5, treatment group subjects received cognitive and social stimulation for eight hours a day in center-based care.⁷ Even though CARE subjects also received home visits from the ages of 0 to 5, this component was shown to have very weak estimated effects (Campbell et al., 2014). Thus, we justify merging the treatment groups of ABC and CARE in light of previous analyses. A detailed description of ABC/CARE and the data sample considered for analysis can be found in Appendix A of García et al. (2018).

Follow-up data collection of ABC/CARE subjects occurred at ages 12, 15, 21, and 30. Various education, employment, health, crime, and family structure measures were collected through both administrative and self-reported channels. Additionally, data from a full-medical sweep of participants in their mid-30s is also available. Our analysis leverages on this data.

We use all characteristics of the non-attrited 88 ABC/CARE subjects at age 30 as inputs for the Future Adult Model (FAM) described in Appendix G of García et al. (2018) to project the subjects’ states of health until death. We exclude five outlier subjects (four females and one male) with mid-30s BMI greater than 50 in the final analysis, leaving a total 83 ABC/CARE subjects. The life-cycle projections are used to estimate the treatment effects on cancer, lung disease, diabetes, heart disease, hypertension, stroke, and mortality.

3. Forecasting Chronic Diseases for ABC/CARE

We first formally state the Future America Model, the model that we use for forecasting. We then apply it.

3.1. Notation and Model Development

Let $\mathcal{M}$ denote a set of possible health states, some of which can be absorbing. Transition times are ages of measurement. Let $\mathcal{A}:=[0,\dots ,\overline{A}]$ index ages, where $\overline{A}$ is the last age that we forecast. We define $h_{a,m,m^{\prime }}$ as the probability of transitioning from state m to state mˊ at age $a\in \mathcal{A}$, where $m,m^{\prime }\in \mathcal{M}$. We drop individual subscripts to avoid notational clutter.

We denote a transition from m to mˊ at age a by $D_{a,m,m^{\prime }}=1$. If this transition does not occur, $D_{a,m,m^{\prime }}=0$. We let ${\tilde{D}}_{a,m}$ be the indicator of occupancy of state m at age a. ${\tilde{D}}_{a,m}$ is a generic entry in the the vector of age-a state occupancy indicators denoted by ${\tilde{D}}_{a.}$. ${\tilde{D}}_0$ denotes the vector of initial state-occupancy conditions.

Instead of estimating a full competing risks model, we simplify a complex reality of multiple health states and general state dependence. We model individual health states.

The probability of occupying state $m\in \mathcal{M}$ at age a ∈ A is assumed to be generated by an index threshold-crossing model:

$$I_{a,m}=1\left({\tilde{D}}_0\ge 0\right){\Omega }_m+1\left({\tilde{D}}_{a-1}\ge 0\right){\Lambda }_m+W_a{\beta }_m+B{\alpha }_m+{\tau }_{a,m}+{\epsilon }_{a,m},$$ (1)

where ${\tilde{D}}_{a,m}=1\left(I_{a,m}\ge 0\right),1\left({\tilde{D}}_0\right)$ is a vector of indicators of mutually exclusive initial conditions with associated coefficients Ω_m, $1\left({\tilde{D}}_{a-1}\ge 0\right)$ is a vector of mutually exclusive health conditions in the previous period with associated coefficients Λ_m, W_a denotes variables that can be affected by treatment with associated coefficients β_m, B is the vector of eligibility conditions with associated coefficients α_m, τ_a,m is a function of age,⁸ and ε_a,m is a serially uncorrelated shock which is assumed to be uncorrelated with all of the right-hand side observables. In practice, when analyzing discrete outcomes, we assume that it is a unit normal random variable.

Instead of modeling initial conditions, we directly condition on them in Equation (1). The assumption of uncorrelatedess of ε_a,m across ages, health states, and subjects together with normality allows us to perform separate estimation of the coefficients characterizing Equation (1) for each $m\in \mathcal{M}$ using maximum likelihood. We estimate [Ω_m, Λ_m, β_m, α_m, τ_a,m] for each $m\in \mathcal{M}$. Despite these simplifications, FAM performs well in fitting population means of the outcomes that we analyze (see Tysinger et al., 2015).

The probability of occupying discrete states is generated in FAM using Equation (1). When simulating the model to forecast the health outcomes for the ABC/CARE subjects, we use their observed age-30 conditions as initial conditions ${\tilde{D}}_0$. Most of these initial conditions relate to health, but we also include initial conditions related to economic status. The vector ${\tilde{D}}_0$ can be affected by treatment. We follow the simulation algorithm described below and modify when appropriate to account for discrete states.

This model easily accommodates absorbing states. An absorbing state is a state $m\in \mathcal{M}$ such that once a subject occupies that state he/she never leaves it. Thus, $m\in \mathcal{M}$ > is an absorbing state if ${\tilde{D}}_{a,m}=1$ implies that ${\tilde{D}}_{a^{\prime },m}=1\forall a^{\prime }\in \mathcal{A}$ with aˊ ≥ a. Once an individual reaches an absorbing stage his/her model in Equation (1) is no longer used to generate transitions. An obvious example of an absorbing state is death.

Ordered and unordered outcomes are also easily accommodated using standard methods in discrete choice. An example of the former is the level of psychological distress (e.g., low, medium, high). An example of the latter is labor force status (e.g., labor force status is categorized as out of labor force, unemployed, working part time, or working full time).

We also model continuous outcomes so that I_a,m is observed and the variables in ${\tilde{D}}_a$ are replaced by observed counterparts. An example of a continuous outcome is body-mass index (BMI). We can also modify the model to accommodate mixed discrete/continuous variables.

Estimation of the inputs affecting health outcomes is performed separately. The economic outcomes that we include are labor income, for which we use the forecast discussed in García et al. (2018), as well as labor force participation, relationship status, and childbearing models generated in FAM to account for the socioeconomic disadvantage of participants.

Tables 1 to 3 list the variables determining each of the states and health and economic outcomes that we consider.⁹ For each of the outcomes we list: (1) the outcome itself; (2) the variable type—e.g., absorbing state, binary outcome, continuous outcome; (3) initial health state occupancies and other outcomes— ${\tilde{D}}_0$ in Equation (1); (4) lagged health-state occupancies— ${\tilde{D}}_{a-1}$ in Equation (1); (5) and (6) other health and economic outcomes used to determine the outcome of interest—W_a in Equation (1); and (7) background variables—B in Equation (1). From this information, the reader can read off the type of outcome being modelled, its classification, as well as determinants and their categorization according to Equation (1). The outcomes that help predict each other are based on research and advice of clinicians and other medical professionals, as explained and justified in Goldman et al. (2015).

Table 1:

Determinants of Equation (1) for Different Outcomes

(1)	(2)	(3)	(4)	(5)	(6)	(7)
		${\tilde{D}}_0$	${\tilde{D}}_{a-1}$	Wa	Wa	B
Outcome	Variable Type	Initial Conditions	Other States	Health Outcomes	Economic Outcomes	Demographics
Heart Disease	Absorbing	Childhood Economic Environment	Hypertension	Smoking		Race
		Education	Diabetes	BMI		Ethnicity
		Asthma		Physical Activity		Age Gender
Hypertension	Absorbing	Childhood Economic Environment	Diabetes	Smoking		Race
		Education		BMI		Ethnicity
				Physical Activity		Age Gender
Stroke	Absorbing	Childhood Economic Environment	Heart Disease	Smoking		Race
		Education	Hypertension	BMI		Ethnicity
			Diabetes	Physical Activity		Age
			Cancer			Gender
Lung Disease	Absorbing	Childhood Economic Environment		Smoking		Race
		Education		BMI		Ethnicity
		Asthma		Physical Activity		Age Gender
Diabetes	Absorbing	Childhood Economic Environment		Smoking		Race
		Education		BMI		Ethnicity
				Physical Activity		Age Gender
Cancer	Absorbing	Childhood Economic Environment		Smoking		Race
		Education		BMI		Ethnicity
				Physical Activity		Age Gender
Mortality	Absorbing	Education	Heart Disease	Smoking		Race
			Hypertension	Binge Drinking		Ethnicity
			Stroke			Age
			Lung Disease			Gender
			Diabetes
			Cancer
			Functional Status
Functional Status	Ordered	Childhood Economic Environment	Heart Disease	Smoking		Race
		Education	Hypertension	BMI		Ethnicity
			Stroke	Physical Activity		Age
			Lung Disease	Functional Status		Gender
			Diabetes
			Cancer
Smoking	Binary	Childhood Economic Environment	Heart Disease	BMI		Race
		Education	Lung Disease	Binge Drinking		Ethnicity
			Diabetes	Physical Activity		Age
				Psychological Distress		Gender

Note: This table provides details on the empirical specification of Equation (1) for the different outcomes that we consider.

Table 3:

Determinants of Equation (1) for Different Outcomes, Continued

(1)	(2)	(3)	(4)	(5)	(6)	(7)
		${\tilde{D}}_0$	${\tilde{D}}_{a-1}$	Wa	Wa	B
Outcome	Variable Type	Initial Conditions	Other States	Health Outcomes	Economic Outcomes	Demographics
Labor Force Participation	Unordered Categorical	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
		Environment, Education	Hypertension	BMI	Disability Insurance Claiming	Ethnicity
			Stroke	Functional Status	Social Security Claiming	Age
			Lung Disease		Supplemental Security Income Claiming	Gender
			Diabetes		Earnings
			Cancer		Marital Status
Full-time Employment	Binary	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
		Environment, Education	Hypertension	BMI	Disability Insurance Claiming	Ethnicity
			Stroke	Functional Status	Social Security Claiming	Age
			Lung Disease		Supplemental Security Income Claiming	Gender
			Diabetes		Earnings	Marital Status
			Cancer
Disability Insurance	Binary	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
Claiming		Environment, Education	Hypertension	Functional Status	Disability Insurance Claiming	Ethnicity
			Stroke		Earnings	Age
			Lung Disease			Gender
			Diabetes
			Cancer
Social Security	Absorbing	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
Claiming		Environment, Education	Hypertension	Functional Status	Disability Insurance Claiming	Ethnicity
			Stroke		Earnings	Age
			Lung Disease		Marital Status	Gender
			Diabetes
			Cancer
Supplemental Security	Binary	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
Income Claiming		Environment, Education	Hypertension	Functional Status	Disability Insurance Claiming	Ethnicity
			Stroke		Social Security Claiming	Age
			Lung Disease		Supplemental Security Income Claiming	Gender
			Diabetes		Earnings
			Cancer		Marital Status
Health Insurance Type	Unordered Categorical	Childhood Economic	Heart Disease	Smoking	Labor Force Participation	Race
		Environment, Education	Hypertension	Functional Status	Disability Insurance Claiming	Ethnicity
			Stroke		Social Security Claiming	Age
			Lung Disease		Earnings	Gender
			Diabetes		Marital Status
			Cancer		Health Insurance Type
Nursing Home Residency	Binary	Education	Heart Disease	Functional Status	Nursing Home Residency	Race
			Hypertension		Widowhood	Ethnicity
			Stroke			Gender
			Lung Disease			Age
			Diabetes
			Cancer

Note: This table provides details on the empirical specification of Equation (1) for the different outcomes that we consider.

3.2. Simulating the Model

We estimate the models in Equation (1). With these models in hand, we simulate the future health trajectories of ABC/CARE subjects by initializing it with their initial conditions. To match the biennial structure of the PSID data used to estimate the models, the simulation proceeds in two-year increments.¹⁰

Among the ABC/CARE subjects simulated in FAM, the years of completion of the age-30 interview range from 2003 to 2009. FAM’s two-year time step only allows the simulation of even or odd years. For this reason, we run the simulation twice—once for the ABC/CARE subjects entering in odd years and again for the ABC/CARE subjects entering in even years.

The simulation model takes as inputs assumptions regarding the normal retirement age, future improvements in mortality, and real medical cost growth. The normal retirement age is assumed to be 67 for all ABC/CARE subjects, as in García et al. (2018).

The FAM mortality model represents mortality rates in 2009. The estimated mortality probabilities are reduced in simulated future years to represent improvements in mortality from sources such as medical innovation that are not included in the model. There are different adjustment factors for populations under and over the age of 65. The mortality reduction factors are taken from the intermediate cost mortality projections in the 2013 Social Security Trustee’s Report.

3.3. Data Sources for Estimation and Simulation

FAM uses data from ABC/CARE surveys to set the initial state of the cohort. The state-occupancy model parameters are estimated using the 1997 to 2013 waves of the Panel Study of Income Dynamics (PSID). We restrict the PSID to heads of households aged 25 and older because these subjects respond to the richest set of questions. We supplement the PSID with data from the Health and Retirement Study (HRS) to estimate nursing home and mortality models. We use the National Health and Nutrition Examination Survey (NHANES) to interpolate measured BMI from self-reported BMI of ABC/CARE subjects. Table 4 describes the data sources in more detail.

Table 4:

Summary of Data Sources

	ABC/CARE	PSID	HRS	NHANES
Ages used	0–34	25+	50+	30–40
Years used	- -	1997–2013	1998–2012	2002–2010
Longitudinal	✓	✓	✓
Time Intervals of Data Collection	Ages 0–8, 12, 15, 21, 30, 34	Biennial	Biennial	Annual
Demographic Outcomes	✓	✓		✓
Economic Outcomes	✓	✓	✓
Health Outcomes	✓	✓	✓	✓
Health Behaviors	✓	✓	✓
Health Expenditures	✓		✓
Family Outcomes	✓	✓
Includes Institutionalized Individuals		✓
Models	Initializing all models	Health	Mortality, widowhood, nursing home residency	BMI

Note: This table compares the main features of the auxiliary datasets used in simulating life-cycle health outcomes of ABC/CARE subjects. We restrict the PSID to heads of households aged 25 and older because these subjects respond to the richest set of questions. The data do not follow individuals in nursing homes or other long-term care facilities, so we supplement the PSID with the HRS when estimating mortality models. For the HRS, we use all cohorts in the dataset created by RAND, version O. The NHANES includes both self-reported height and weight as well as physical measures of BMI, which is why it is employed for interpolating physical measures from self-reported measures.

3.3.1. Variable Construction and Imputations

Some of the initializing variables are not available for all ABC/CARE subjects at the required ages for FAM and are imputed using the data sources in Table 4. The imputations made are described in Table 5. For each simulation repetition, the value for each imputed variable is randomly drawn from the probability distribution of each subject.

Table 5:

Imputation of Model Inputs

Input	Subjects with Missing Data	Models Requiring Input	Variables Used to Impute	Method Used to Impute
Mother’s Education Level	CARE subjects	Marital status and childbearing	Race, ethnicity, education, disease conditions, employment status, presence of a health-related work limitation, and a self-report of whether or not the subject was “poor” as a child	Ordered probit model is constructed using PSID data of subjects age 30 and 31 born between 1945 and 1981.
Socioeconomic Status of Parents	All subjects	Numerous models		Assume all subjects were “poor” given program eligibility.
Race	All subjects	All models		Assume no participants are Hispanic or Latino.1
Smoking and Employment Status	1 subject	Health states, marital status, childbearing, DI and SSI benefits, health insurance category		Multinomial logit model to estimate joint probability of each comibnation of smoking and employment amongst unemployed PSID subjects age 25 to 35.
Binge Drinking	1 subject	Mortality, smoking		Binary probit model using PSID data of subjects age 25 to 35.
BMI	All subjects	Health states, functional status, employment, and smoking	Self-reported height and weight at age 30 (CARE) or age 34 (BMI)	Covariate values from PSID age 30–34 data in 2002–2013 are used to impute measured BMI values for PSID respondents using estimated models based on NHANES and the method in Courtemanche et al. (2015). PSID is then used to estimate a model mapping imputed measured BMI at ages 33–40 to self-reported BMI at ages 30–32. This imputation is applied to ABC/CARE subjects with a health interview at least one year after their age 30 interview.
Activities of Daily Living (ADLs) and Instrumental Activities of Daily Living (IADLs)	All subjects	Benefits claiming, mortality, employment status, insurance category, and nursing home residency	If the subject has a physical or nervous condition that keeps them from working	Ordered Probit model estimated on PSID respondents aged 25 to 35.
DI and SSI benefits	All subjects	Employment status, insurance category, and Medicare enrollment	Single question asking about receipt of any kind of benefits	Multinomial logit model to estimate the joint probability of each combination of DI and SSI claiming using PSID respondents age 25 to 35 on benefits.

¹Census data on Hispanics in North Carolina were not available for 1970 and 1980, but Hispanic migration into this state is more recent than in other regions, and as late as 1990, only 2% of the North Carolina poor were Hispanic (Johnson, 2003)

Note: This table summarizes the models estimated in order to impute necessary outcomes in the FAM Model. ADLs include walking, dressing, eating, bathing or showering, getting in and out of bed or a chair, and using the toilet, including getting to the toilet. IADLS include preparing meals; shopping for toiletries and medicine; managing money; using the phone; doing heavy housework; and doing light housework or housecleaning.

3.4. Specification Tests for the First-order Markov Assumption

The FAM model assumes a vector first-order Markov process governing transitions with a variable state space depending on the analyzed outcome. In Equation (1), only ${\tilde{D}}_{a-1}$ and the initial state value enter the model. For heart disease, hypertension, and stroke, we compare the fit of Equation (1) with the following second-order model:

$$\begin{array}{l}{I}_{a,m}=1\left({\tilde{D}}_0\ge 0\right){\Omega }_m+1\left({\tilde{D}}_{a-1}\ge 0\right){\Lambda }_m+\left({\tilde{D}}_{a-2}\ge 0\right){\tilde{\Lambda }}_m\\ +W_a{\beta }_m+B{\alpha }_m+{\tau }_{a,m}+{\epsilon }_{a,m}.\end{array}$$ (2)

We use a likelihood ratio test to test the null hypothesis ${\tilde{\Lambda }}_m=0$ in Equation (2). Table 6 show the results from these tests. For the health states analyzed, we do not reject the null hypothesis. We do not perform these tests for lung disease, cancer, and diabetes because sample limitations do not give us ${\tilde{D}}_{a-2}$ for these diseases.

Table 6:

Tests Comparing First-Order and Second Markov Processes for Disease State-Occupancy Specifications

Disease	LR Statistic	Degrees of Freedom	p-value
Heart Disease	2.18	2	0.71
Hypertension	0.05	1	0.83
Stroke	3.94	4	0.14

Note: This table presents likelihood ratios contrasting the models in Equations (1) and (2) by testing the null hypothesis $H_0:{\tilde{\Lambda }}_{a,m}=0$. The variables included in the right-hand-side of each model are in Tables 1 to 3.

3.5. Inference

We study the life-cycle trajectories after age 30 for six chronic diseases and provide treatment effects for them. This produces hundreds of age-wise treatment effects across diseases. Summarizing these effects in an interpretable way is challenging. We draw on García et al. (2018) and construct combining functions that, within disease categories, count the proportion of treatment effects that are same-signed. We generate standard errors for these counts.

Formally, consider a block of outcomes ${\mathcal{J}}_{\mathcal{l}},\mathcal{l}\in \{1,\dots ,L\}$, with cardinality C_ℓ and associated treatment effects ${\Delta }_1,\dots ,{\Delta }_{C_{\mathcal{l}}}$. In our case, a block of outcomes is prevalence of diabetes between ages 30 and 40, 30 and 50, 30 and 60, and 30 and 70. For each of these blocks, we observe the prevalence of diabetes for each age. We construct similar blocks with the rest of the chronic diseases.

Treatment effects, Δ_j, can be either beneficial or detrimental. The interpretation placed on the sign of the combining function is evident from the context. The count of positive-valued treatment effects within block ${\mathcal{J}}_{\mathcal{l}}$ is:

$$D_{\mathcal{l}}=\sum _{j=1}^{C_{\mathcal{l}}}1\left({\Delta }_j>0\right).$$ (3)

We use the proportion of outcomes with Δ_ℓ > 0 as our combining function: D_ℓ/C_ℓ. Under the null hypothesis of no treatment effect for the block of outcomes indexed by ${\mathcal{J}}_{\mathcal{l}}$, and assuming the validity of asymptotic approximations, the mean of D_ℓ/C_ℓ is centered at $\frac{1}{2}$. ¹¹ We compute the fraction D_ℓ/C_ℓ and the corresponding bootstrapped empirical distribution to obtain a p-value. The bootstrap procedure accounts for dependence in unobservables across outcomes (within blocks) in a general way.

4. Empirical Results

We plot the life-cycle trajectories of probabilities of incidence of mortality and disease by 5-year bins from age 30 to 75 for cancer, lung disease, diabetes, heart disease, hypertension, and stroke. Disease incidence is defined as diagnosis or death in order to account for disease-free survival. We perform inference—at ages 40, 50, 60, and 70—on combining functions for the various chronic diseases. The combining functions are the proportion of years starting at age 30 exhibiting a positive treatment effect within each chronic disease. For example, at age 40, the combining function for lung disease is the proportion of years with a positive treatment effect on this chronic disease between ages 30 and 40. We calculate one-sided p-values using 1,000 bootstrap simulations of the FAM under the null hypothesis that D_ℓ/C_ℓ is equal to 50%. If one were to plot the trajectories for all 1,000 simulations, the p-value is the percentage of simulations where the majority of the control group trajectory is above that of the treatment group. This choice of inference emphasizes persistent treatment effects over the life-cycle that are consistent across simulations as opposed to treatment effect magnitudes. Note that life-cycle trajectories are plotted by 5-year bins while inference is performed using blocks of annual data. This can lead to slight discrepancies between the actual D_ℓ/C_ℓ and expected D_ℓ/C_ℓ based on the smoothed plot. We also display bootstrapped standard errors for the 5-year bins.

The combining functions are statistically significant at standard levels for heart disease, stroke, cancer, and mortality over most of the life-cycle for both genders. Females also have statistically significant combining functions for diabetes up to age 50. Diabetes is the only condition with adversely signed and statistically significant combining functions for males. One explanation for this is that treatment-group males work more and make more money across the life cycle as documented in García et al. (2018). These additional resources lead them to behaviors that trigger diabetes (e.g., worst diet). Despite the increase in these behaviors, the program has a positive effect in non-diabetic cardiovascular conditions that are mediated by the health improvements at mid-30s, as the several epidemiological assessments in Figure 1 show. The patterns of the health trajectories explain the mechanisms behind the QALYs in Table 7.

Table 7:

Net Present Value of Health Gains (2014 USD)

	Pooled	Females	Males
NPV of QALYs	87,181	42,102	106,218

Note: This table presents net present value (NPV) estimates of the gain in QALYs from treatment as calculated in García et al. (2018). Total cost of the program per child is $92,570 (2014 USD). More detailed analysis can be found in García et al. (2018).

We now describe the life-cycle trajectory for each chronic condition. Cancer shows significant combining functions for males up to age 70 and over the entire life-cycle for females in Figure 2. Female control and treatment incidence rates converge at age 35, after which treatment group incidence rates remain slightly lower than that of the control group. Near-zero p-values at all ages indicate a similar trend across all bootstraps. Treatment-group males exhibit a lower incidence rate than control-group males until age 58. There is a second crossover just after age 65, and both groups converge at age 75. These early- to mid-life treatment effects are consistent across simulations as combining functions are significant until age 60. Since age is one of the biggest risk factors for cancer, it is unsurprising that the combining function becomes insignificant at the end of the life-cycle.

Figure 2: Life-cycle Trajectories of Cancer by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. Combining functions are highly significant across the life-cycle across both genders.

Lung disease does not exhibit any significant combining functions in Figure 3, though lifecycle patterns differ noticeably by gender. Female treatment and control trajectories closely follow one another with (insignificant) combining functions that fall on either side of 50%. However, after age 35, incidence rates for treatment-group males is lower than that of control-group males by 15% to 20% throughout the life-cycle. Despite insignificant combining functions for males, the trajectories in Figure 3 show that the profiles for both the treatment and control groups are precisely estimated. A main input that enters into our forecast of this chronic disease is smoking behavior. In the control group, 89% report to have smoked during the last year in the mid-30s interview. In the treatment group, the analogous figure is 72%. The treatment-control difference is statistically significant at the 10% level.

Figure 3: Life-cycle Trajectories of Lung Disease by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. There are no significant combining functions for lung disease.

Diabetes displays significant combining functions for females up to age 50 and adversely significant combining functions for males over the life-cycle in Figure 4. Treatment group females have lower incidence of diabetes from age 30 to 45, after which the female treatment trajectory remains marginally higher than that of control. Significant combining functions at ages 40 and 50 become insignificant at ages 60 and 70. Thus, there are consistent early life-cycle treatment effects for females across simulations.

Figure 4: Life-cycle Trajectories of Diabetes by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. There are highly significant combining functions up to age 50 for females. Note that diabetes is the only condition where there are adversely significant combining functions for males.

For males, diabetes is the only disease for which treatment has adverse effects throughout the life-cycle. The male treatment group has diabetes incidence rates that are slightly higher than that of the control group until a cross-over after age 65. A mechanism mediating this result is that males in the treatment group are significantly more likely to be employed and make more labor income across the entire life cycle,¹² which makes them abler and more likely to consume unhealthy diets. Data on diet was only collected when individuals were in their 20s. With this measure, we find that males in the treatment group consume junk food 2.7 times per week on average, while the average for control-group males is 1.9. There are no treatment-control differences in consumption of vegetables or fruit. Dietary differences predispose men in the treatment group to have higher prevalence of diabetes across the life cycle.¹³ Beneficial effects eventually emerge because males improve on several other health conditions as a consequence of treatment. Since combining functions at age 70 consider treatment effects from ages 30 to 70, the end-of-life cross-over is only partially reflected.

Heart disease exhibits highly significant combining functions up to age 60 for females and over the entire life-cycle for males in Figure 5. Treatment group females have consistently lower incidence rates until age 50, after which their incidence rates are slightly higher than that of control. Combining functions are significant until age 60. Treatment-group males have lower incidence rates than the control group over the life-cycle, and by a wider margin than females. Though male incidence rates converge at age 65, treatment group rates plateau at 50% while control group rates continue to increase. Combining functions equal 100% for all ages and have high significance, indicating consistent trajectories across bootstraps.

Figure 5: Life-cycle Trajectories of Heart Disease by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. Combining functions are highly significant except for females at age 70.

There are no statistically significant treatment effects for hypertension. The entire sample is diagnosed by age 65 in Figure 6, which is likely a predisposition of the individuals in the sample to contract this disease which the treatment fails to prevent. Treatment group females have slightly higher incidence rates until age 50, after which control group females have much higher incidence rates until age 65. There are perversely significant combining functions at ages 40 and 50. They become insignificant beyond age 60. There is a similar trend for males: treatment-group males have marginally higher incidence rates until age 40, after which control-group males have much higher incidence rates before convergence at age 65. There is an adversely significant combining function at age 40, but the estimates are statistically insignificant for the remainder of the life-cycle. Therefore, the difference in the incidence of hypertension is insignificant in the long-run. This can be attributed to nearly the entire sample contracting hypertension by age 65. This is unsurprising given that African-Americans have the highest rates of hypertension globally, with estimated rates of 45.0% and 46.3% for adult African-American males and females, respectively, in 2011 to 2014 (Benjamin et al., 2017).

Figure 6: Life-cycle Trajectories of Hypertension by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. Even though there are adversely significant combining functions for hypertension, they become insignifcant beyond ages 60 and and 50 for females and males, respectively.

Stroke displays significant combining functions over the entire life-cycle for both genders in Figure 7. Treatment group females have slightly lower incidence rates than control group females throughout the entire life-cycle, in both the main simulation and all bootstrap simulations. All combining functions are 100% and p-values are zero. Similarly, treatment-group males have consistently lower incidence rates than the control group. There are no cases of male stroke until age 40, after which treatment-group males have much lower incidence rates until age 65. However, age 50 and 60 combining functions have large p-values, implying larger mid-life variation in male stroke projection. The male treatment group rate plateaus at 30% by age 65, while that of the male control group increases past 50%. The age-70 combining function becomes significant.

Figure 7: Life-cycle Trajectories of Stroke by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who either have the disease or die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual contracts the disease or dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect as well as standard errors. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation, which we also use to calculate standard errors. Combining functions are highly significant throughout the life-cycle for females, and at the beginning and end of the life-cycle for males.

There are highly significant combining functions for mortality across the entire life-cycle for both genders (see Figure 8). There are no deaths until age 50 and 45 for females and males, respectively. The female treatment group has a slightly lower mortality rate than the control group over the remainder of the life-cycle. On the other hand, male mortality rates diverge over time between treatment and control. Control males are nearly four times more likely to be dead than treatment males by age 75. All combining functions are 100% and have high significance, indicating similar mortality trajectories across bootstrap simulations. Mortality is an informative indicator of the aggregate effect on all of the health conditions. Prevalence of each chronic disease increases the risk of mortality and the strength and precision of the treatment-control difference across the life cycle, as well as the gender difference in the treatment effects, summarizes the results in this section.

Figure 8: Life-cycle Trajectories of Mortality by Gender and Treatment Group.

Note: The figures plot the proportion of treatment and control subjects who die over the life-cycle by 5-year bins. The individual-level 5-year bin takes the value 1 if an individual dies in any year during the 5-year window, and 0 otherwise. The profile in the figure plots the treatment and control averages of the individual-level bins. We display the fraction of years from age 30 to ages 40, 50, 60, and 70 with a positive treatment effect. One-sided p-values are calculated with a null hypothesis of 50% using 1000 bootstraps of the microsimulation. All combining functions are highly significant regardless of gender.

The life-cycle trajectories of chronic health conditions can be summarized and monetized using quality-adjusted life years (QALYs). A QALY reweighs a year of life accounting for the burden of disease. Suppose one assigns a value of $150,000 (2014 USD) to each year of life. A QALY of $150,000 denotes the value of a year of life in the absence of disease (perfect health). The value of a QALY for an individual in a given year is smaller than $150,000 when there is disease, as worse health conditions imply a lower quality of life. QALY becomes zero at death.¹⁴ Table 7 presents the net present value of treatment gains in QALYs based on life-cycle health trajectories. Adjusted to 2014 USD, the program cost per child is $92,570 (2014 USD). Health benefits alone for treatment-group males, which total $106,218 (2014 USD), exceed the cost of the entire program and generate positive returns. In this dimension alone, female health gains pay for nearly half of the program cost. Overall, the pooled sample gains an average of $87,181 (2014 USD) from health benefits due to program participation. This estimate does not account for benefits arising in other domains including education, crime, and labor outcomes. The gain from QALYs is consistent with the results presented in this paper. We find persistent life-cycle treatment effects for the majority of chronic conditions in both genders. However, the magnitude of treatment effects is larger for males in multiple disease outcomes across the life-cycle.

5. Conclusion

This paper uses the Future America Model to forecast the life-cycle treatment effects of a widely-emulated, high-quality, and intensive early childhood program on chronic diseases. Our forecasts combine experimental and non-experimental data. In the experiment, there are substantial treatment effects on indicators of overall health when the participants are in their mid-30s. These treatment effects are the initial conditions of the life-cycle forecasts. Our results indicate significant, life-cycle treatment effects for heart disease, stroke, cancer, and mortality over the entire life-cycle across both genders.

As noted in Elango et al. (2016), the mediating mechanisms of these results are enhanced cognitive and personality skills which generated more self control and awareness of health risk. Since the net present value of the quality-adjusted life years that the program generates is $87,181 and the total cost of the program per child is $92,570, the value that arises from monetizing health conditions is almost enough to offset all of the costs associated with program implementation (including the welfare costs of financing the program through taxation). Reductions in the prevalence of chronic diseases across the life-cycle mediate this result. A program designated to enhance the cognitive and social and emotional skills of disadvantaged children turns out to have large effects on life-cycle health.

Table 2:

Determinants of Equation (1) for Different Outcomes, Continued

(1)	(2)	(3)	(4)	(5)	(6)	(7)
		${\tilde{D}}_0$	${\tilde{D}}_{a-1}$	Wa	Wa	B
Outcome	Variable Type	Initial Conditions	Other States	Health Outcomes	Economic Outcomes	Demographics
BMI	Continuous	Childhood Economic Environment		BMI	Marital Status	Race
		Education				Ethnicity
						Age
						Gender
Binge Drinking	Binary	Childhood Economic Environment	Marital Status	Binge Drinking		Race
		Education				Ethnicity
						Age
						Gender
Physical Activity	Binary	Childhood Economic Environment	Marital Status	Physical Activity		Race
		Education				Ethnicity
						Age
						Gender
Psychological Distress	Ordered	Childhood Economic Environment	Heart Disease	Smoking		Race
		Education	Hypertension	BMI		Ethnicity
			Stroke	Physical Activity		Age
			Lung Disease	Psychological Distress		Gender
			Diabetes	Functional Status
			Cancer
Childbearing	Ordered	Mother’s Education	Cancer	Marital Status	Labor Force Participation	Race
		Education			Number of Children	Ethnicity
						Age
						Gender
Paternity	Ordered	Mother’s Education			Labor Force Participation	Race
		Education			Marital Status	Ethnicity
					Number of Children	Age
Marital Status	Binary	Mother’s Education			Labor Force Participation	Race
		Education			Earnings	Ethnicity
					Marital Status	Age
					Number of Children	Gender
Partner Mortality	Binary	Education				Race
						Ethnicity
						Age
						Gender

Note: This table provides details on the empirical specification of Equation (1) for the different outcomes that we consider.