The return to education in terms of wealth and health

TL;DR: In this article, the authors investigated the extent to which the education gradient can be explained by fully rational and efficient behavior of all social strata and proposed a life-cycle model in which the loss of body functionality, which eventually leads to death, can be accelerated by unhealthy behavior and delayed through health expenditure.

Abstract: This study presents a new view on the association between education and longevity. In contrast to the earlier literature, which focused on inefficient health behavior of the less educated, we investigate the extent to which the education gradient can be explained by fully rational and efficient behavior of all social strata. Specifically, we consider a life-cycle model in which the loss of body functionality, which eventually leads to death, can be accelerated by unhealthy behavior and delayed through health expenditure. Individuals are heterogeneous with respect to their return to education. The proposed theory rationalizes why individuals equipped with a higher return to education chose more education as well as a healthier lifestyle. When calibrated for the average male US citizen, the model motivates about 50% percent of the observable education gradient by idiosyncratic returns to education, with causality running from education to longevity. The theory also explains why compulsory schooling has comparatively small effects on longevity and why the gradient gets larger over time through improvements in medical technology.

Summary

1. Introduction

• Better educated individuals are, on average, healthier and live longer than less educated people.
• It shows that the optimal life style is governed by conditions for (i) optimal expenditure on health and unhealthy goods, (ii) optimal aging (the evolution of the expenditure profiles with age), (iii) optimal length of schooling, (iv) optimal financial management, and (v) optimal time of death.

2. Model Setup

• Consider a young adult at the end of the compulsory schooling period.
• At each age t, the person experiences utility from consumption of health-neutral goods c(t) and unhealthy goods u(t).
• The feature that health-neutral and unhealthy consumption enter utility additively is harmless for the calibration since the desire for unhealthy consumption is counterbalanced by the restraint from the potential of the good to damage health.
• The authors allow for aggregate productivity growth such that the wage per unit of human capital grows at rate gw, which is taken as given by the individual.
• In order to utilize the findings of Mitnitski and Rockwood for the present work, I begin with differentiating the frailty law with respect to age, Ḋ (t) = µ (D (t)− E).6 Following Dalgaard and Strulik (2014), the authors assume that the factor E, which slows down exponential aging, can be increased by deliberate health expenditures.

6 In order to see that a larger autonomous component E implies less deficits at any given age, notice that the

• If individuals’ investment in health influences E, then one may wonder if the ”frailty law” should still work empirically, as E then is expected to exhibit individual-level variation.
• It should; but the cross-section estimate for E should be interpreted as the average level in the sample in question (see Zellner, 1969).
• The parameter δ controls for the feedback of age on general human capital.
• The parameters α1, α2, and δ are conceptualized as being job specific.
• While some cognitive skills and motor skills start deteriorating around the age of 30 or even earlier, so called crystallized abilities, i.e. the ability to use knowledge and experience, remain relatively stable until most of adulthood and start declining after the age of 60, or even later.

3. Solution

• Conceptually, however, it is hard to imagine why human capital should start to decline when individuals have “too much experience”.
• 3. Optimal Aging. (13) These Euler equations show how optimal expenditure evolves through life.
• The expenditure profile for health is also influenced by the curvature of the health investment function: a smaller γ implies a lower growth rate of health expenditure.
• Inserting the respective values leads to condition (8), in which gw denotes the growth rate of the wage per unit of human capital, w(t) = w̄ exp(gwt).
• This means that any causality behind the education gradient runs from increasing education to increasing health and longevity.

4. Calibration

• The initial age is set to 16 years, corresponding to model-age zero, because individuals below roughly the age of 16 are not subject to increasing morbidity (Arking, 2006) and are presumably not well described by the law of increasing frailty.
• In the following, I estimate parameter values for the average US American person.
• Preston et al. (2010) estimate that smoking takes away 2.5 years of life-expectancy of 50 year old US males.

5. Results

• 1. The Return to Education in Terms of Wealth and Health, and the Value of Life.
• They show the outcome of the original experiment when the price of unhealthy goods is 2 (instead of 1).
• Better educated people display, at any given age, better health status, i.e. fewer health deficits, in line with the evidence provided by Harttgen et al. (2013).
• Before w investigate other potential drivers of the education gradient, it is worthwhile to note that two seemingly natural candidates are already excluded by theory, namely the time preference rate, ρ, and income for given education, that is w̄.
• As shown in the final row of Table 1, an increase of productivity growth from 1.0 to 1.84 percent per year triggers one more year of education and, subsequently, behavioral changes, that enable a person to live about 1.7 years longer.

In all cases the experiment increases θ from 0.14 to 0.15. All other parameters from benchmark case (Figure 1).

• During the education period, the Reference American accumulates debt of about $ 150,000.
• Higher education has somewhat less impact on health behavior but the health gradient widens a bit because the less educated spend relatively more on unhealthy goods when demand is less price elastic.
• Case 8 considers the adjustment via higher A.
• These numerical experiments rationalize why the compulsory education gradient is large only when average education is low.
• The solid line shows the predicted longevity for the Reference American (endowed with a θ of 0.14, i.e. a return of education of 6.8 percent at 13.5 years of education).

6. Conclusion

• This study has proposed a new view on the education gradient.
• It has assumed away any explanation based on attitudes, non-cognitive skills, and allocative or productive inefficiency of the uneducated.
• It predicts that a person whose return to education (cognitive and non-cognitive skills) motivate one more year of education, spends more on health and less on unhealthy behavior such that the person lives about half a year longer.
• The theory motivates an almost linear education gradient, in line with the empirical observation (Cutler and Lleras-Muney, 2010).
• But since these skills are malleable at younger ages (see e.g. Heckman, 2006), the present study also highlights the importance of childhood development for later in life.

Figures

Figure 5: Longevity Gain: Exogenous Education

Figure 4: Health Inequality and the Return to Education

Table 1: The Education Gradient: Alternative Mechanisms

Table 2: The Education Gradient: Robustness Checks

Figure 6: Medical Technological Progress and the Health Gradient

Figure 2: The Return to Education in Terms of Wealth, Health, and the Value of Life

Figure 1: Optimal Life Cycle Trajectories: Basic Run

Figure 3: Education, Health, and Health Behavior

Frequently asked questions

Q1. What are the contributions in "The return to education in terms of wealth and health" ?

This study presents a new view on the association between education and longevity. In contrast to the earlier literature, which focused on inefficient health behavior of the less educated, the authors investigate the extent to which the education gradient can be explained by fully rational and efficient behavior of all social strata. Specifically, the authors consider a life-cycle model in which the loss of body functionality, which eventually leads to death, can be accelerated by unhealthy behavior and delayed through health expenditure.