THE VALUE OF LIFE AND THE RISE IN
HEALTH SPENDING*
ROBERT E. HALL AND CHARLES I. JONES
Over the past half century, Americans spent a rising share of total economic
resources on health and enjoyed substantially longer lives as a result. Debate on
health policy often focuses on limiting the growth of health spending. We inves-
tigate an issue central to this debate: Is the growth of health spending a rational
response to changing economic conditions—notably the growth of income per
person? We develop a model based on standard economic assumptions and argue
that this is indeed the case. Standard preferences—of the kind used widely in
economics to study consumption, asset pricing, and labor supply—imply that
health spending is a superior good with an income elasticity well above one. As
people get richer and consumption rises, the marginal utility of consumption falls
rapidly. Spending on health to extend life allows individuals to purchase addi-
tional periods of utility. The marginal utility of life extension does not decline. As
a result, the optimal composition of total spending shifts toward health, and the
health share grows along with income. In projections based on the quantitative
analysis of our model, the optimal health share of spending seems likely to exceed
30 percent by the middle of the century.
I. INTRODUCTION
The United States devotes a rising share of its total resources
to health care. The share was 5.2 percent in 1950, 9.4 percent in
1975, and 15.4 percent in 2000. Over the same period, health has
improved. Life expectancy at birth was 68.2 years in 1950, 72.6
years in 1975, and 76.9 years in 2000.
Why has this health share been rising, and what is the likely
time path of the health share for the rest of the century? We
present a framework for answering these questions. In the model,
the key decision is the division of total resources between health
care and nonhealth consumption. Utility depends on quantity of
life—life expectancy—and quality of life— consumption. People
value health spending because it allows them to live longer and to
enjoy better lives.
* We are grateful to David Cutler, Amy Finkelstein, Victor Fuchs, Alan
Garber, Michael Grossman, Emmett Keeler, Ron Lee, Joseph Newhouse, Tomas
Philipson, David Romer, Robert Topel, the editors and referees, and participants
at numerous seminars and NBER meetings for helpful comments. Jones thanks
the Center for Economic Demography and Aging at Berkeley for financial support.
Matlab programs that generate the numerical results in this paper are available
at Jones’s website. Contact information for the authors follows. Robert E. Hall:
rehall@stanford.edu, http://stanford.edu/
⬃
rehall. Charles I. Jones: chad@econ.
berkeley.edu, http://www.econ.berkeley.edu/
⬃
chad
© 2007 by the President and Fellows of Harvard College and the Massachusetts Institute of
Technology.
The Quarterly Journal of Economics, February 2007
39
In our approach, standard preferences— of the kind econo-
mists use to study issues ranging from consumption to asset
pricing to labor supply—are able to explain the rising share of
health spending. As consumption increases, the marginal utility
of consumption falls quickly. In contrast, extending life does not
run into the same kind of diminishing returns. As we get older
and richer, which is more valuable: a third car, yet another
television, more clothing— or an extra year of life? There are
diminishing returns to consumption in any given period and a key
way we increase our lifetime utility is by adding extra periods of
life.
Standard preferences imply that health is a superior good
with an income elasticity well above one. As people grow richer,
consumption rises but they devote an increasing share of re-
sources to health care. Our quantitative analysis suggests these
effects can be large: projections in our model typically lead to
health shares that exceed 30 percent of GDP by the middle of the
century.
Many of the important questions related to health involve the
institutional arrangements that govern its financing— especially
Medicare and employer-provided health insurance. One approach
would be to introduce these institutions into our model and to
examine the allocation of resources that results. We take an
alternative approach. We examine the allocation of resources that
maximizes social welfare in our model. We abstract from the
complicated institutions that shape spending in the United
States and ask a more basic question: from a social welfare
standpoint, how much should the nation spend on health care,
and what is the time path of optimal health spending?
The recent health literature has emphasized the importance
of technological change as an explanation for the rising health
share—for example, see Newhouse [1992]. According to this ex-
planation, the invention of new and expensive medical technolo-
gies causes health spending to rise over time. Although the de-
velopment of new technologies unquestionably plays a role in the
rise of health spending, the technological explanation is incom-
plete for at least two reasons.
First, expensive health technologies do not need to be used
just because they are invented. Although distortions in health
insurance in the United States might result in overuse of expen-
sive new technologies, health shares of GDP have risen in virtu-
ally every advanced country in the world, despite wide variation
40 QUARTERLY JOURNAL OF ECONOMICS
in systems for allocating health care [Jones 2003]. We investigate
whether the social payoff associated with the use of new technol-
ogies is in line with the cost. Second, the invention of the new
technologies is itself endogenous: Why is the United States in-
vesting so much in order to invent these expensive technologies?
By focusing explicitly on the social value of extending life and how
this value changes over time, we shed light on these questions.
We begin by documenting the facts about aggregate health
spending and life expectancy, the two key variables in our model.
We then present a simple stylized model that makes some strong
assumptions but that delivers our basic results. From this foun-
dation, we consider a richer and more realistic framework and
develop a full dynamic model of health spending. The remainder
of the paper estimates the parameters of the model and discusses
a number of projections of future health spending derived from
the model.
Our research is closely related to a number of empirical and
theoretical papers. Our work is a theoretical counterpart to the
recent empirical arguments of David Cutler and others that high
levels and growth rates of health spending may be economically
justified [Cutler et al. 1998; Cutler and McClellan 2001; Cutler
2004]. On the theoretical side, our approach is closest in spirit to
Grossman [1972] and Ehrlich and Chuma [1990], who consider
the optimal choice of consumption and health spending in the
presence of a quality-quantity tradeoff. Our work is also related
to a large literature on the value of life and the willingness of
people to pay to reduce mortality risk. Classic references include
Schelling [1968] and Usher [1973]. Arthur [1981], Shepard and
Zeckhauser [1984], Murphy and Topel [2003], and Ehrlich and
Yin [2004] are more recent examples that include simulations of
the willingness to pay to reduce mortality risk and calculations of
the value of life. Nordhaus [2003] and Becker, Philipson, and
Soares [2005] conclude that increases in longevity have been
roughly as important to welfare as increases in nonhealth con-
sumption, both for the United States and for the world as a whole.
Barro and Barro [1996] develop a model in which health invest-
ments reduce the depreciation rate of schooling and health capi-
tal; health spending as a fraction of income can then rise through
standard transition dynamics.
We build on this literature in two ways. First and foremost,
the focus of our paper is on understanding the determinants of
the aggregate health share. The existing theoretical literature
41THE VALUE OF LIFE AND THE RISE IN HEALTH SPENDING
generally focuses on individual-level spending and willingness to
pay to reduce mortality. Second, we consider a broader class of
preferences for longevity and consumption. Many earlier papers
specialize for their numerical results to constant relative risk
aversion utility, with an elasticity of marginal utility between
zero and one. This restriction occurs because these papers do not
consider a constant term in flow utility. As we show later, careful
attention to the constant is crucial for understanding the rising
health share. In particular, when a constant is included, a stan-
dard utility function with an elasticity of marginal utility well
above one is admissible. This property is the key to the rising
health share in the model.
II. BASIC FACTS
We will be concerned with the allocation of total resources to
health and other uses. We believe that the most appropriate
measure of total resources is consumption plus government pur-
chases of goods and services. That is, we treat investment and net
imports as intermediate products. Similarly, we measure spend-
ing on health as the delivery of health services to the public and
do not include investment in medical facilities. Thus we differ
conceptually (but hardly at all quantitatively) from other mea-
sures that include investment in both the numerator and denom-
inator. When we speak of consumption of goods and services, we
include government purchases of nonhealth goods and services.
Figure I shows the fraction of total spending devoted to
health care, according to the U.S. National Income and Product
Accounts. The numerator is consumption of health services plus
government purchases of health services and the denominator is
consumption plus total government purchases of goods and ser-
vices. The fraction has a sharp upward trend, but growth is
irregular. In particular, the fraction grew rapidly in the early
1990s and flattened in the late 1990s. Not shown in the figure is
the resumption of growth after 2000.
Figure II shows life expectancy at birth for the United States.
Following the tradition in demography, this life expectancy mea-
sure is not expected remaining years of life (which depends on
unknown future mortality rates), but is life expectancy for a
hypothetical individual who faces the cross-section of mortality
rates from a given year. Life expectancy has grown about 1.7
years per decade. It shows no sign of slowing over the fifty years
42 QUARTERLY JOURNAL OF ECONOMICS
reported in the figure. In the first half of the 20th century,
however, life expectancy grew at about twice this rate, so a longer
times series would show some curvature.
III. BASIC MODEL
We begin with a model based on the simple but unrealistic
assumption that mortality is the same in all age groups. We also
assume that preferences are unchanging over time, and income
and productivity are constant. This model sets the stage for our
full model, in which we incorporate age-specific mortality and
productivity growth. As we will show in Section IV, the stark
assumptions we make in this section lead the full dynamic model
to collapse to the simple static problem considered here.
The economy consists of a collection of people of different
FIGURE I
The Health Share in the United States
Note: The numerator of the health share is consumption of health services plus
government purchases of health services and the denominator is consumption
plus total government purchases of goods and services. For further information on
sources, see Section V.
43THE VALUE OF LIFE AND THE RISE IN HEALTH SPENDING
