Theoretical Economics Letters, 2011, 1, 105-110
doi:10.4236/tel.[phone] Published Online November 2011 (http://www.SciRP.org/journal/tel)
U.S. National Healthcare Expenditures: Demonstration
and Explanation of Cubic Growth Dynamics
Jack E. Riggs1, Jeffrey C. Hobbs2, Gerald R. Hobbs3, Todd H. Riggs4
1Department of Neurology, West Virginia University, Morgantown, USA
2Departme n t of Finance , Banking and Insurance, Appalachian State University, Boone, USA
3Department of Stat i s t i c s, West Virginia University, Morgantown, USA
41st Aviation Traini n g Brigade, United St at es Army, Fort Rucker, USA
Received August 7, 2011; revised September 23 , 20 1 1; accepted September 30, 2011
Abstract
U.S. national healthcare expenditures (NHE) increased from under 28 billion dollars in 1960 to over 1.35
trillion dollars in 2000. This enormous growth threatens the sustainability of the provision of healthcare. By
definition, in any year, current NHE must equal population times consumer price index (CPI) times per cap-
ita CPI-adjusted constant dollar healthcare expenditures. Linear relationships were observed over time with
total population (r2 > 0.99), with CPI (r2 > 0.96), and with per capita CPI-adjusted dollar healthcare expendi-
tures (r2 > 0.98). The finding that those three factors were well described by linear equations suggests that
NHE growth should display cubic dynamics over time. NHE from 1960 through 2000 did display cubic
growth dynamics (r2 > 0.99). Moreover, actual NHE from 1960 through official U.S. government NHE pro-
jections in 2019 also displayed cubic growth dynamics (r2 > 0.99). This model explains why U.S. NHE has
displayed cubic growth dynamics and suggests that U.S. NHE will continue to display cubic growth dynam-
ics as long as increases in population, CPI, and per capita CPI-adjusted constant dollar healthcare expendi-
tures continue to increase reasonably linearly over time.
Keywords: Consumer Price Index, Cubic Dynamics, Economic Modeling, National Healthcare Expenditures,
Per Capita Healthcare Expenditures, Population, United States
1. Introduction
Rising national healthcare expenditures (NHE) are con-
sistently in the U.S. national political and economic spot-
light [1-4]. NHE increased nearly 50-fold in the U.S.
between 1960 and 2000, from under 28 billion dollars to
over 1.35 trillion dollars per year (Table 1). This enor-
mous growth in NHE threatens the sustainability of
healthcare for many Americans since employers cannot
afford the large ongoing increases in healthcare insur-
ance premiums for their employees, healthcare insurance
companies continuously seek to control their risk by ex-
cluding high risk patients and restricting covered benefits,
governments cannot afford to provide unlimited benefits
for its citizens by shifting the costs to future taxpayers,
and very few individuals can afford to pay for their own
healthcare should a significant injury or illness occur.
This enormous growth in healthcare expenditures seri-
ously undermines the sustainability of national discre-
tionary spending. A June 2010 Congressional Budget
Office report stated, “Because health care costs will ac-
count for a significant share of the federal budget under
current law, and the growth of those costs is a major
contributor to the long-term fiscal pressures facing the
country, policy options to restrain the growth of federal
spending on health care will continue to attract consid-
erable interest.” (http://www.cbo.gov/ftpdocs/115xx/doc
11579/06-30-LTBO.pdf).
Despite the impact and importance of rising NHE,
very little regarding the dynamics of this enormously
increasing and very important sector of the U.S. econ-
omy has been described [5]. By definition, in any given
year, current NHE must equal population times con-
sumer price index (CPI) times per capita CPI-adjusted
constant dollar healthcare expenditures. Trends in these
three factors must, therefore, influence total NHE. Trends
in population, consumer price index, and per capita
CPI-adjusted healthcare expenditures were explored to

J. E. RIGGS ET AL.
106
determine if they might suggest or reveal a model ex-
plainin g the underly i ng growt h d y n amics of U.S . NH E.
2. Method & Model
2.1. Data Sources
Three public and readily available sources of data for the
years 1960 through 2000 were used in this analysis. Of-
ficial estimates of the total U.S. population for those
years (Table 1) were obtained fro m the U.S. Census Bu-
reau (www.census.gov). Official estimates of the U.S.
consumer price index (CPI) for those years (Table 1)
were obtained from the U.S. Department of Labor, Bu-
reau of Labor Statistics (www.bls.gov). Official esti-
mates of total U.S. NHE in current dollars fo r tho se years
(Table 1) were obtained from the U.S. Department of
Health and Human Services, Centers for Medicare &
Medicaid Services (www.cms.hhs.gov). Dividing the
annual total NHE by that year’s CPI gives the annual
NHE in CPI-adjusted dollars. Dividing the annual NHE in
CPI-adjusted dollars by the corresponding annual popula-
tion gives the annual per capita CPI-adjusted healthcare
expenditures. The relationship of annual population, CPI,
and per capita CPI-adjusted healthcare expenditures over
time, between 1960 a nd 20 00, was examined.
2.2. Model
Figure 1 illustrates the relationship between total U.S.
population and year. As shown, there is a strong linear
relationship between total U.S. population and year.
Linear regression between total population and year
yielded the following equation:
x
POP 2293408.2 X 181774463 (1)
where POPx is the total U.S. population in year X, and X
is the year, which varied from 0 for year 1960 to 40 for
year 2000. The r2 value for this linear regression was >
0.99. Thus, the total U.S. population increased by ap-
proximately 2293408 individuals per year between the
years 1960 and 2000. The least-squares estimate of the
parameters in the regression equation:
x
POP aX A (2)
is therefore, a is 2293408.2, and A is 181774463.
Figure 2 illustrates the relationship between CPI and
year. As shown, there is a reasonably linear relationship
between CPI and year. The linear regression between
CPI and year yielded the following equation:
x
CPI 0.040218641 X 0.0643875 (3)
where CPIx is the consumer price index in year X, and X
is the year, which varied from 0 for year 1960 to 40 for
year 2000. The r2 value for this linear regression was >
0.96. Thus, the CPI increased by approximately 0.0402
per year between the years 1960 and 2000. Since the
numbers in Equation 3 are constants, the following equa-
tion will be used:
x
CPI bX B

 (4)
where b is 0.040218641 , and B is 0.0643875.
Figure 3 illustrates the relationship between per cap ita
CPI-adjusted healthcare expenditures and year. As shown,
there is a near linear relationship between per capita
CPI-adjusted healthcare expenditures and year. Linear
regression between per capita CPI-adjusted healthcare
expenditures and year yielded the following equation:
x
PCNHE 60.181652 X 335.2974

 (5)
where PCNHEx is the per capita CPI-adjusted healthcare
expenditures in year X, and X is the year, which varied
from 0 for year 1960 to 40 for year 2000. The r2 value
for this linear regression was >0.98. Thus, per capita
150
200
250
300
0 1020304
Year
Population (Millions)
0
Figure 1. Total U.S. population for the years 1960 (year 0)
through 2000 (year 40) is displayed. The r2 value for the
linear regression performed on this data was >0.99.
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
0 10203040
Y
ear
Consumer Price Index
Figure 2. The consumer price index (CPI) for the years
1960 (year 0) through 2000 (year 40) is displayed. The r2
value for the linear regression performed on this data was >
0.96.

J. E. RIGGS ET AL.
107
Table 1. United States national healthcare expenditures (NHE) in millions of dollars, population, consumer price index (CPI),
and cubic modeled NHE in millions of dollars for the years 1960-2000.
Year NHE Population CPI Modeled NHE
1960 27,534 180,671,158 0.296 3924
1961 29,370 183,691,481 0.299 7615
1962 32,053 186,537,737 0.302 12,298
1963 34,910 189,241,798 0.306 18,008
1964 38,694 191,888,791 0.310 24,777
1965 42,173 194,302,963 0.315 32,639
1966 46,430 196,560,338 0.324 41,626
1967 52,062 198,712,056 0.334 51,774
1968 59,012 200,706,052 0.348 63,114
1969 66,396 202,676,946 0.367 75,680
1970 74,894 205,052,174 0.388 89,505
1971 83,265 207,660,677 0.405 104,623
1972 92,974 209,896,021 0.418 121,067
1973 103,034 211,908,788 0.444 138,870
1974 116,809 213,853,928 0.493 158,066
1975 133,124 215,973,199 0.538 178,688
1976 152,478 218,035,164 0.569 200,769
1977 172,826 220,239,425 0.606 224,342
1978 194,126 222,584,545 0.652 249,441
1979 219,940 225,055,487 0.726 276,099
1980 253,373 227,224,681 0.824 304,349
1981 293,592 229,465,714 0.909 334,226
1982 330,743 231,664,458 0.965 365,761
1983 364,676 233,791,994 0.996 398,988
1984 401,599 235,824,902 1.039 433,941
1985 430,284 237,923,795 1.076 470,653
1986 471,265 240,132,887 1.096 509,158
1987 512,973 242,288,918 1.136 549,487
1988 574,043 244,498,982 1.183 591,676
1989 638,794 246,819,230 1.240 635,757
1990 714,127 249,464,396 1.307 681,763
1991 781,608 252,153,092 1.362 729,728
1992 849,039 255,029,699 1.403 77,968
1993 912,485 257,783,000 1.445 831,667
1994 962,061 260,327,021 1.482 885,708
1995 1,016,271 262,803,276 1.524 941,841
1996 1,068,526 265228572 1.569 1,000,100
1997 1,124,915 267,784,000 1.605 1,060,517
1998 1,190,059 270,248,003 1.630 1,123,125
1999 1,265,158 272,690,813 1.666 1,187,959
2000 1,353,187 274,951,554 1.722 1,255,052

J. E. RIGGS ET AL.
108
0
500
1000
1500
2000
2500
3000
3500
0 102030
Year
Per Capita CPI-Adjusted
National Health Expenditures
(Constant Dollars)
40
Figure 3. Per capita CPI-adjusted constant dollar U.S.
healthcare expenditures for the years 1960 (year 0) through
2000 (year 40) is displayed. The r2 value for the linear re-
gression performed on this data was > 0.98.
CPI-adjusted healthcare expenditures increased by ap-
proximately $60.18 per year between the years 1960 and
2000. Since the numbers in Equation (5) are constants,
the following equation can be used:
x
PCNHE cX C (6)
where c is 60.18 1652, and C is 335.2974.
For any given year, the following relationship is valid:


 
xxx
NHE POPCPIPCNHE x

(7)
where NHEx is national healthcare expenditures in cur-
rent dollars in year X, POPx is the total U.S. population
in year X, CPIx is the consumer price index in year X,
and PCNHEx is the per capita CPI-adjusted healthcare
expenditures in year X. Substitutin g the linear regression
derived equations for POPx, CPIx, and PCNHEx into
Equation (7) yield s:

x
NHEaX AbX BcX C (8)
Multiplying out the terms in Equation (8) yields the fol-
lowing equation:


32
x
N
HE abcX Abc aBc abCX
ABc AbC aBCX ABC

 
(9)
Equation (9) suggests that NHE should be described
by a cubic function over time as long as POP, CPI, and
PCNHE are reasonably described by linear equations.
Accordingly, a cubic polynomial fit of national health-
care expenditures (Table 1) over time was performed.
That analysis demonstrated that NHE between 1960 and
2000 conformed to a cubic function, and the r2 value of
that fit was >0.99.
Equation (7) was used to model or predict annual val-
ues of NHE for each year from 1960 to 2000 by calcu-
lating the product of the derived Equations (1), (3), and
(5). These values are also shown in Table 1. Figure 4
displays a plot of actual and modeled NHE from 1960 to
2000. This cubic model of NHE growth, based on the
product of the three derived linear equations from 1960
to 2000 data, correlated very well with actual NHE from
1960 to 2000, with an r2 v alue of that fit >0.99.
Since this model predicts that NHE growth should
display cubic dynamics, combined actual (1960 to 2008)
and official U.S. government predictions (2009 to 2019)
of NHE (www.cms.hhs.gov) were plotted in Figure 5. A
cubic polynomial fit of national healthcare expenditures
over that time period was performed. That analysis dem-
onstrated that actual and projected NHE between 1960
and 2019 also conformed to a cubic function, and the r2
value of that fit was >0.99.
3. Discussion
A model of NHE based on the fact that in any year, cur-
rent NHE must equal population times CPI times per
capita CPI-adjusted constant dollar healthcare expendi-
tures (Equation 7) was developed and analyzed. Equation
7 is a truism; that is, Equation 7 can be algebraically
Figure 4. Actual (square s) and modeled (solid line) national
health expenditures (in current millions of dollars) for year
0 (1960) through year 40 (2000).
Figure 5. Actual (1960 to 2008) and projected (2009 to 2019)
(squares) and best cubic fit (solid line) national health ex-
penditures (in current millions of dollars) for year 0 (1960)
through year 59 (2019).

109 J. E. RIGGS ET AL.
simplified to state that for any given year, NHE must
equal NHE. However, the point of this model was to
separate NHE into three distinct components; population,
CPI, and per capita CPI-adjusted constant dollar health-
care expenditures. There is no a priori reason why each
of these three components should increase linearly over
time as was demonstrated in this analysis. Since popu-
lation, CPI, and per capita CPI-adjusted constant dollar
healthcare expenditures did increase reasonably linearly
over time between 1960 and 2000, this model suggested
that NHE growth should display cubic growth dynamics.
Indeed, NHE growth did display cubic dynamics from
1960 to 2000. Moreover, actual and projected NHE
growth from 1960 to 2019 also displayed cubic dynamics.
This analysis also suggests that future U.S. NHE growth
will remain cubic as long as increases in population, CPI,
and per capita CPI-adjusted constant dollar healthcare
expenditures remain reasonably linear over time. Cubic
growth is important to distinguish from exponential
growth.
Although explaining the cubic growth of U.S. NHE,
this model does not accurately predict future NHE. We
performed multiple analyses to determine whether
knowing that NHE increases cubically over time would
allow accurate prediction of future NHE. For example,
determining the cubic equation that best fit NHE’s from
1960 to 1980 does not allow an accurate prediction of
NHE in 1990. The reason for this failure to accurately
predict is that each new data point of population, CPI,
and per capita CPI-adjusted constant dollar healthcare
expenditures does alter th e corresponding linear equation
slightly. The slightly altered linear equations will still
accommodate all prior data points and produce a well-
fitted cubic function d escribing their product of previous
years’ NHE. However, when the three slightly altered
linear equations are multiplied together, their product
will not accurately predict future NHE due to the com-
pounding of errors. This dichotomy of hypotheses or
models, those that accommodate and explain past data
while failing to predict future data, is well-recognized in
science [6-10]. A classic example of this dichotomy is
Darwin’s theory of evolution by natural selection. Dar-
win’s theory explains the appearance and extinction of
past species, but can not predict the future course of
evolution [8]. Although unable to predict future NHE,
appreciation of the cubic dynamics describing NHE may
provide healthcare policy makers an improved frame-
work upon which to assess and monitor the impact of
healthcare policy changes.
Orszag and Ellis [11] suggested that “our country’s
financial health will in fact be determined by the growth
rate of per capita health care costs.” In this model of U.S.
NHE growth used to predict cubic dynamics, one might
assume that population growth and CPI growth were
relatively outside the influence of the U.S. healthcare
system. The remaining factor, constant dollar per capita
healthcare expenses, is consistent with the assertion
made by Orszag and Ellis [11]. While inflation adjusted
total per capita healthcare expenses have increased over
time [12], some public sector (Medicare) per capita
healthcare expenses have been claimed to have actually
declined [13]. Nevertheless, the impact of escalating
health care spending on the U.S. economy will continue
to be debated [14-16].
4. Conclusions
Rising healthcare costs impacts all sectors of the U.S.
economy and is eroding the sustainability of U.S federal
discretionary spending. Indeed, increasing healthcare
costs are not exclusively a U.S. economic problem; es-
calating healthcare costs are a global problem. While this
analysis does not attempt to show how to decrease the
rate of healthcare cost growth, it does suggest that infla-
tion-adjusted per capita healthcare costs is perhaps the
best measure to track and monitor NHE growth. More-
over, this analysis suggests that healthcare policy chan-
ges that merely shift the cost of healthcare expenses will
have little impact on NHE growth.
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