Going from Bad to Worse: Adaptation to Poor Health, Health Spending, Longevity, and the Value of Life

TL;DR: This paper sets up a a life cycle model in which individuals are subject to physiological aging, calibrate it with data from gerontology, and compare behavior and outcomes of adapting and non-adapting individuals.

Abstract: Aging humans adapt to their worsening state of health and old people are usually happier than estimated by young individuals. In this paper we investigate how adaptation to a deteriorating state of health affects health spending, life expectancy, and the value of life. We set up a a life cycle model in which individuals are subject to physiological aging, calibrate it with data from gerontology, and compare behavior and outcomes of adapting and non-adapting individuals. While adaptation generally increases the value of life (by about 2 to 5 percent), its impact on health behavior and longevity depends crucially on whether individuals are aware of their adaptive behavior.

Summary

1. Introduction

• From the gerontological viewpoint, the human life cycle can be characterized as the continuous deterioration of physiological fitness.
• The authors set up a life cycle model of human aging, in which deliberate health investments reduce the speed of aging and thus the age of death, calibrate the model with gerontological data, and compare behavior and outcomes for adapting and non-adapting individuals.
• The authors explain the economic intuition behind these results.
• Most importantly, health capital is a latent variable, unknown to doctors and medical scientists, a fact that confounds any serious calibration of the model.

2. The Basic Model

• Consider an individual who derives utility from consumption and from being in good health.
• Additionally, the optimal solution fulfils the terminal condition H(T ) = 0 and the solution for sophisticated types fulfils the terminal condition λ.
• The table shows for naive and sophisticated types the deviation of the solution from non-adaptive types in percent.
• Results are shown for discounted life time health expenditure, the length of life, and the value of life.
• Naive types spend 12 percent more on health and live almost one percent longer than non-adaptive types while sophisticated types spend 28 percent less on health and their live expectancy declines by more than 2 percent.

3. Model Extensions

• The authors next consider robustness of results with respect to extending the model to uncertain survival.
• This approach implies that individuals assess their health and its implications for survival correctly, the only potential mistake that they make regards life time utility due to failed anticipation of adaptation to deteriorating health.
• All other parameters are kept from the simple model.

4. Conclusion

• Life expectancy, and the value of life.the authors.
• While the health behavior of naive and sophisticated types differs drastically and has significant impact on their life expectancy, the authors find, perhaps surprisingly, only small differences for the experienced value of life.
• Both naive and sophisticated types experience an about two percent higher VOL compared to non-adapting types (for which the VOL at age 20 is estimated to be $ 6.5 million).
• Under the assumption that the retirement decision is, among other things, determined by the subjectively perceived health status, the authors would expect that adaptation to poor health leads to later retirement for sophisticated agents but not necessarily for naive agents who may actually aim at an early retirement.

Figures

Table 3: Results: Life Cycle Savings

Figure 1: Health Adaptation: Benchmark Run

Figure 3: Health-Dependent Survival and Survival by Age

Figure 4: Health Adaptation: Savings

Figure 2: Adjustment after Bad Health Shock at Age 20

Table 1: Sensitivity Analysis

Table 4: Results: Life Cycle Savings & Uncertain Survival

Table 2: Results: Uncertain Survival

Full text

Schünemann, Johannes; Strulik, Holger; Trimborn, Timo
Working Paper
Going from bad to worse: Adaptation to poor health,
health spending, longevity, and the value of life
cege Discussion Papers, No. 268
Provided in Cooperation with:
Georg August University of Göttingen, cege - Center for European, Governance and Economic
Development Research
Suggested Citation: Schünemann, Johannes; Strulik, Holger; Trimborn, Timo (2015) : Going
from bad to worse: Adaptation to poor health, health spending, longevity, and the value of life,
cege Discussion Papers, No. 268, University of Göttingen, Center for European, Governance
and Economic Development Research (cege), Göttingen
This Version is available at:
http://hdl.handle.net/10419/123284
Standard-Nutzungsbedingungen:
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen
Zwecken und zum Privatgebrauch gespeichert und kopiert werden.
Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle
Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich
machen, vertreiben oder anderweitig nutzen.
Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen
(insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten,
gelten abweichend von diesen Nutzungsbedingungen die in der dort
genannten Lizenz gewährten Nutzungsrechte.
Terms of use:
Documents in EconStor may be saved and copied for your
personal and scholarly purposes.
You are not to copy documents for public or commercial
purposes, to exhibit the documents publicly, to make them
publicly available on the internet, or to distribute or otherwise
use the documents in public.
If the documents have been made available under an Open
Content Licence (especially Creative Commons Licences), you
may exercise further usage rights as specified in the indicated
licence.

ISSN: 1439-2305
Number 268 – November 2015
GOING FROM BAD TO WORSE:
ADAPTATION TO POOR HEALTH,
HEALTH SPENDING, LONGEVITY, AND
THE VALUE OF LIFE
Johannes Schünemann
Holger Strulik
Timo Trimborn

Going from Bad to Worse: Adaptation to Poor Health,
Health Spending, Longevity, and the Value of Life
∗
Johannes Sch¨unemann
†
, Holger Strulik
‡
and Timo Trimborn
§
November 2015.
Abstract. Aging humans adapt to their worsening state of health and old pe opl e
are usually happier than estimated by young individuals. In this paper we investi-
gate how adaptati on to a deteriorating state of health affects health spending, life
expectancy, and the value of life. We set up a a life cycle model in which individu -
als are subject to physiological aging, calibrate it with data from gerontology, and
compare behavior and outcomes of adapti ng and non-adapting individuals. While
adaptation generally increases the value of life (by about 2 to 5 percent), it s impact
on health behavior and longevity depends crucially on whether individuals are aware
of the ir adaptive behavior.
Keywords: Health, Adaption, Aging, Longevity, Health Care Demand.
JEL: D 91, J17, J26, I12.
∗
We would like to thank Carl-Johan Da lg a a rd , Volker Grossmann, Casper Hansen, Kla u s Prettner, and
Asger Wing en d e r for discussion and helpful comments.
†
University of Goettingen, Department of Economics, Platz der Goettinger Sieben 3, 37073 Goettingen,
Germany; email:
‡
University of Goettingen, Department of Economics, Platz der Goettinger Sieben 3, 37073 Goettingen,
Germany; email: holger.strulik@wiwi. u n i- g oettingen.de.
§
University of Goettingen, Department of Economics, Platz der Goettinger Sieben 3, 37073 Goettingen,
Germany; email:

1. Introduction
From the gerontological viewpoint, the hum an life cycle can be characterized as the continu ous
deterioration of physiological fitness. Most human functions and capabilit i es are in decline
from early adulthood onwards (Case and Deaton, 2005; Skirbekk, 2004; Nai r, 2005). Human
aging, u nd er st ood as “t he intrinsic, cumulative, progressive, and deleterious loss of function that
eventually culminates in death” (Arking, 2006), has a deep foundation in evolutionary biology
(Fries, 1980; Gavrilov and Gavrilova, 1991; Robson and Kaplan, 2007) and, at the current state
of medical technology, it can at best be delayed, but not avoided. So it seems to be fortunate
that aging humans are capable to adapt to this sad state of affair s. However, at closer inspection,
doubts may arise. Couldn’t it be that quick adaptation to worsening health induces us to invest
less in health maintenance and repair and thus to live a shorter and perhaps overall unhap pi e r
life than we could without adaptation?
Assessing the impact of adap tat i on on health beh avior, longevity, and happiness with the
means of lab or field e xperiments, i s potentially hard if not impossible because of the missing
counterfactual. With the help of economic theory and the design of an appropriate computa-
tional experiment an assessment is r el at ively straightforward. In this paper we p r opose such a
computational experime nt. We set up a life cycle model of human aging, in which del i berate
health investments reduce the spee d of aging and thus the age of death, c ali b rat e the model
with gerontological data, and compare behavior and outcomes for adapting and non-adapting
individuals. We distinguish between individuals who are aware of their adaptive behavior (so
called sophi st i cat ed types) and those who are not (naive types). Thi s labeling of types follows
Strotz (1955), see also Rabin (1998). We find, pe rh ap s surprisingly, that naive adaptation is
conducive to a healthier and longer l i fe . Sophisticated types, on the other hand, spend less on
health and live shorter than otherwise identical non-adapting types. We use these results and
compute the implied value of life. We find , again perhaps surprisingly, that both naive and
sophisticated types experience about the same value of life and that bot h types experience a
significantly higher value of life t h an non-adapting types. We explain the econ omi c intuition
behind these results.
Since the seminal study of Brickman e t al. (1978), comparing happin ess of paraplegics and
lottery winners, t h e medical and economics literatu re has provided ample evidence that humans
adapt to health problems an d rate their happiness or quality of li fe much higher than predicted
1

by unaffected person s anticipating negative health events (e.g. Wu, 2001; Albrecht and Devlieger,
1999; Riis et al., 2005). T hi s seems to be true for (mild) nuisances like acne (Baron et al. 2003)
as well as for severe disability (Oswald and Powdthavee, 2008). Adaptati on after a severe health
shock is gradual and perhaps complete. Oswald and Powdthavee (2008) estimate approximately
30 percent ( 50 percent) hedonic adaptation 3 years after the on se t of severe ( m odest) disability
and they could not reject the hypothesis of complete adaptation after 6 years. Using a very
large German panel of individuals observed from 1984 t o 2006, Pagan-Rodri gu ez (2010) finds
also gradual adaptation to disability and cannot reject the hypothesis of complete adaptation
after 7 years.
The observations that healthy persons under es t im at e the happiness of sick persons an d that
sick persons believe they would be happier if they had n ever been sick (Boyd et al., 1990; Riis et
al., 2005) indicates that people are not fully aware of there adaptive behavior. It indicates naive
rather than sophisticated adaptation. The available evidence suggests also that adaptation to
bad healt h is “genuine” and not driven by an overoptimistic assessment of one’s health and
survival probabilit ie s (Wu, 2001) and that the mi s pr ed i ct i on of healt hy people of their adaptive
capabilities is har d to explain by focussing illusion (Ubel et al., 2001; Baron et al., 2003).
While most studies focus on adaptation after severe health s hocks, we are here mostly (but
not exclusively) interested in th e gradual and progressive decl i ne of health that comes with age.
While many stu di e s document that aggregate measures of happiness or wellbeing do not dec li n e
(by much) over the life cycle (e.g. Costa et al., 1987; Die ne r and Suh, 1998; Deaton, 2007),
a particular interesting study in the present context is provided by Lacey et al. (2006) who
asked 30 and 70 years old persons to rate their own happiness as well as t o estimate happiness of
average 30 and 70 years old persons. They found that both, young and old individuals, estimated
happiness of the young group to be higher while actually it was the other way round. The authors
conclude that people displ ay a “remarkable inab il i ty to recognize their own adaptation”.
The model that we set up below in order to discuss the effects of adaptation to deteriorat-
ing health is particularly suitable f or this purpose since it is based on the notion of aging as
progressive health deficit accumulation. It is easy to see that the alternative paradigm, the
Grossman (1972) model, is less suitable. It is based on health capital accumulation and the
assumption that health capital depreciates at a given (potential age-specific) rate d(t) such that
individuals with health capital H(t) lose health d(t)H(t) through health depreciation. It t hus
2