Technical Paper Series

Congressional Budget Office

Washington, DC

UNCERTAINTY ABOUT PROJECTIONS OF 

MEDICARE COST GROWTH

Julie Topoleski

Health and Human Resources Division

Congressional Budget Office

Washington, DC

julie.topoleski@cbo.gov

August 2004

2004-13

Technical papers in this series are preliminary and are circulated to stimulate discussion

and critical comment. These papers are not subject to CBO’s formal review and editing

processes. The analysis and conclusions expressed in them are those of the authors and

should not be interpreted as those of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series can be obtained at

www.cbo.gov/tech.cfm.
ABSTRACT

Over the next several decades, Medicare costs are going to increase significantly. 

Previous analysis has looked at the potential range of costs using a deterministic, scenario-based

analysis. This provides a range of potential outcomes but provides no information as to the

likelihood of these outcomes. The analysis here systematically considers the uncertainty inherent

in forecasting Medicare costs using a Monte Carlo approach that reflects both the uncertainty in

forecasting health costs and the uncertainty association with economic and demographic

projections. Within 100 years, the 90 percent confidence interval for Medicare costs as a percent

of GDP spans more than 30 percentage points
1

The author would like to thank John Sabelhaus and Michael Simpson of CBO’s Health and Human

Resources Division for their support and helpful comments.

2

See for example, Congressional Budget Office (2003) or Boards of Trustees (2004).

3

Lee and Miller (2002) follow a similar approach.

4Note that all costs are not net of premiums; that is, premiums have not been removed from the costs shown.

1

1. Introduction1

Previous studies of the long-run outlook for Medicare have characterized the range of

future costs by varying the rate of excess cost growth (the rate at which medicare costs per

beneficiary exceeds growth in GDP per capita) and extrapolating into the future.2 Although

history is a useful guide for telling us what average excess cost growth might be, it provides no

way of assigning probabilities to these high or low-cost paths. The approach used in this paper is

to explicitly model the probability distribution for excess cost growth as well as other

demographic and economic determinants of outlays. Stochastic simulation is then used to

directly measure the probability distribution of future Medicare costs.3

The Congressional Budget Office (CBO) (2003) estimates that, in 2030, Medicare will

account for between 5.7 and 11.5 percent of GDP.4 In 2050, that estimate rises to between 6.4

and more than 21 percent (2003). To put this in context, Medicare accounted for 2.6 percent of

GDP in 2003 (Boards of Trustees, 2004). These ranges are developed by varying the long run

excess cost growth rate. Under the intermediate cost scenario, a long run excess cost growth rate

of 1 percent is assumed; that is, Medicare costs per beneficiary are assumed to grow 1 percent

faster than GDP per capita. Under the low-cost scenario, Medicare costs are assumed to grow at

the same rate as GDP per capita, and under the high cost scenario, an excess cost growth rate of
5

See CBO (2003) for more details on the assumptions underlying these estimates.

6

See Boards of Trustees (2004) for more details.

2

2.5 percent is assumed.5 While this approach estimates a range of possible outcomes, it provides

no information as to the likelihood of those outcomes.

The Boards of Trustees of the Federal Hospital Insurance and Federal Supplementary

Medical Insurance Trust Funds (“Boards of Trustees”) follow a similar approach with its high,

low, and intermediate cost scenarios. Under each scenario, the complete set of inputs is varied

together. Those inputs include the change in GDP per capita, the average wage in covered

employment, the consumer price index, the real wage differential, the real interest rate, the total

fertility rate, mortality rates, and health care costs. In the low-cost scenario, all inputs move to

push the system toward lower costs. In the high cost scenario, the converse is true. Under the

intermediate assumptions, Medicare costs are estimated to be 7.0 percent of GDP by 2030, 10.0

percent in 2050, and 13.9 percent by 2080. 

In their 2004 report, the Boards of Trustees present a supplementary assessment of

uncertainty in Part B Medicare cost projections. Only uncertainty in Part B cost growth is

modeled stochastically, and other inputs remain deterministic. These results show that Part B

costs could vary substantially from the intermediate projections.6

It is this potential for reality to vary significantly from a set of deterministic forecasts that

makes stochastic analysis so useful. History is clearly a useful guide to what the future may look

like, but it tells us nothing about the likelihood of future outcomes. Any stochastic simulation

yields a scenario for which some chance exists that the set of exogenous inputs chosen will be
3

observed in the real world, and the likelihood of these outcomes will vary. Because the

probability distribution for each input is assumed to have a bell-shaped distribution where values

are likely to bunch around the expected value, repeated stochastic simulations will generate a

distribution of outcomes that also exhibits bunching. The model can be solved many times

making it possible to make inferences about the probability distributions of inputs and the

resulting outputs.

This analysis focuses on developing a time series model for excess cost growth. The

resulting time series equation, along with time series equations for other economic and

demographic inputs, is then used to explicitly model the probability distribution of inputs used to

forecast Medicare costs. The standard statistical tool for making inferences from historical data

is time-series analysis, which uses historical data to project both the future values of variables

and the variability around those future values. The resulting estimated equation (or set of

equations) is used to generate expected future values simply by solving it forward through time. 

Understanding excess cost growth and the likelihood of any given value is particularly

important given the relative magnitude of growth attributable to the aging of the population and

growth attributable to factors other than economic and demographic change. The portion of the

increase in Medicare costs attributable to excess cost growth is larger than the portion

attributable to the increasing number of Medicare beneficiaries and rising longevity (see Figure

1). This figure is derived deterministically using a long run excess cost growth rate of 1 percent. 

If 1 percent is too low, as has been the case historically, the relative importance of excess cost

growth would be even greater. Further, understanding the likelihood of a given set of outcomes

is an important advance in thinking about this issue.
7Data on national health expenditures are available from CMS at

http://www.cms.hhs.gov/statistics/nhe/default.asp.

4

This analysis shows that by 2100, Medicare costs as a percentage GDP could range from

7.9 percent up to 39.7 percent over a 90 percent confidence interval. This clearly is a large range

of possible outcomes, and it is based on an expected long run excess cost growth rate of 1

percent. It also assumes a continuation of current Medicare law and no change in the factors

influencing health care growth. The range of possible outcomes could be quite different if a long

run excess cost growth rate of 1 percent proves to be incorrect. This highlights the importance of

moving beyond the deterministic forecasts that researchers have typically produced to a

stochastic approach that allows the likelihood of a range of outcomes to be formally evaluated.

2. Trends in Excess Cost Growth

Following the Review of Assumptions and Methods of the Medicare Trustee’s Financial

Projections, the Centers for Medicare and Medicaid Services (CMS) adopted a long run excess

cost growth rate of 1 percent. This 1 percent figure is based on a careful analysis of growth in

real national health expenditures per capita relative to growth in real GDP per capita. National

health expenditures were chosen rather than Medicare costs alone because Medicare costs have

been more heavily impacted by policy changes over the period of analysis than have total

national health expenditures.7 

Starting with data similar to that used by the Technical Review Panel on the Medicare

Trustees Reports, the analysis presented in the Medicare Technical Panel Report is replicated and
8

See Chapter III of Review of Assumptions and Methods of the Medicare Trustees’ Financial Projections

(December 2000) for more detail. 

9

The Medicare technical panel elected not to make any adjustments for age and gender arguing that such

adjustments would not substantially affect the results.

10Data for total medical expenditures are used, and results are weighted using the person weight provided

with the data. Data for 1987 are adjusted using the algorithm provided in Zuvekas and Cohen (2002) to make the

1987 data comparable to the 2000 data.

11Data for infants in 1987 are dominated by a small number of extremely high cost patients.

5

updated.8 The analysis is then repeated using a methodology that adjusts for the changing age

and sex composition of the population.9 These adjustments and the different methodology do not

substantially alter the general results, even though changes in per capita health expenditures vary

by age group from 1987 to 2000. Data from the Medical Expenditure Panel Survey (MEPS) for

2000 and the National Medical Expenditure Survey (NMES) for 1987 are used to calculate

average health expenditures by age group.10 Note that expenditures for children less than a year

old are omitted.11 The highest percentage change was for 30 to 39 year olds, and the smallest

was for the 13 to 18 year olds (see Figure 2).

Much research has been done to attribute the growth in health care costs to its underlying

components (see Weisbrod (1991), Newhouse (1992), Peden and Freeland (1995), and Jones

(2002)), and the general consensus is that the technological change is the primary contributing

factor. Jones quantifies the amount attributable to technology as 50 to 75 percent of the increase

in health expenditures as a percentage of GDP. Peden and Freeland attribute 70 percent of the

373 percent growth in real per capita medical spending from 1960 to 1993 to “two technologyinducing” variables: the level of insurance coverage and noncommercial medical research

spending. The current paper does not focus on the reasons for growth in health care costs and

instead concentrates on analyzing the growth itself.
12See Sabelhaus, Simpson, and Topoleski (2004) for a discussion of the impact of including time until death

in Medicare spending indices. The general conclusion is that the addition of time until death does not significantly

change forecast results.

6

To perform this analysis, excess cost growth needs to be backed out from total cost

growth and the trends need to be estimated. The ultimate goal is to develop an excess cost

growth series and associated probability distribution to forecast Medicare costs. Data on national

health expenditures are used rather than historical Medicare costs, which provides both a longer

time series for analysis and abstracts from policy changes that have significantly impacted

Medicare costs since its inception. 

For purposes of this paper, excess cost growth (xt) refers to any unexplained growth in

national health expenditures (Ht/Ht-1) after accounting for growth in per capita GDP (GDP/N) and

changes in the age and sex distribution in the population (specifically, growth in the population

by age and sex (nas) multiplied by an age-sex index ((as)). In other words, this is all growth not

accounted for by economic and demographic change. Specifically,

Excess cost growth is calculated for 1951 through 2002. 

To develop a complete set of indices ((as) for all age and sex groups, a data set containing

health expenditure data for all ages is needed. The spending indices used in this analysis are

calculated using the NMES for 1987 and the MEPS for 1996 through 2000.12 For each year,

average total medical expenditures are calculated for each age and sex group. To create the

index, the reference person is a 40-year-old male. For years prior to 1987, the age-sex profile is
13The volatility could be because of time series variation, but it also could be attributable to sampling

variation. MEPS documentation notes that MEPS expenditure estimates are especially sensitive to sampling

variation because of the “underlying skewed distribution of expenditures.” (Agency for Healthcare Research and

Quality, 2004)

14This is consistent with the approach taken for the Medicare Technical Panel Report although the text

accompanying their Table 4 indicates that they adjust for general price inflation using a chain-weighted GDP price

index.

7

assumed to equal that for 1987. Between 1996 and 2000, the indices exhibit a large amount of

volatility, and so rather than using each year of data separately, the indices are averaged across

years.13 Those averages are used for each year from 1996 through 2000 and for all years after

2000. For 1988 through 1995, the indices gradually move from the 1987 level to the average for

1996 to 2000.

The excess cost growth rates are largely consistent with the results presented in the

Medicare Technical Panel report for the gap between growth in real GDP per capita and growth

in real national health expenditures per capita even though the methodology is different. The

numbers presented are based on ten-year rolling averages, which is consistent with the approach

taken by the Medicare Technical Panel (see Table 1). Note that both real GDP and real national

health expenditures are deflated using a CPI index.14 To create per capita figures, these numbers

are divided by total population.

Looking instead at the annual variation in excess cost growth, the mean is slightly lower

than the ten-year rolling average at 3.1 percent (see Table 2). The median is higher at 3.2

percent. The minimum is actually negative at -4.0 percent. Clearly, excess cost growth is a

highly volatile measure. Annual changes in GDP and national health expenditures per capita

follow the same basic pattern as the ten-year rolling averages, but there is greater variation in 

the series.
15For more details, see O’Harra et al. (2004).

16For more details on other time series processes used in forecasting future Medicare costs, see

Congressional Budget Office, 2001.

8

The calculated excess cost growth rate is very sensitive to the years included in the

analysis (see Table 3). The excess cost growth rate has clearly accelerated in recent years, and so

when calculated through 2002 rather than through 1999, the last year of data available to the

Medicare Technical Panel, the averages are higher. Between 2000 and 2002, the average annual

excess cost growth rate exceeds 5 percent regardless of the calculation method.

This faster growth in health care costs is well documented. In fact, 2002 marked the sixth

consecutive year of faster growth in national health expenditures with expenditures growing 9.3

percent in 2002. The average from 1990 through 2000 was 6.5 percent (Sethi and Fronstin,

2004). By 2002, national health expenditures accounted for 14.9 percent of GDP. This is up

from 2000 levels of 13.3 percent, where it had hovered since 1993 (Levit et al., 2004). Levit et

al. note that this growth is largely driven by a rebound in the growth of hospital spending.

3. Estimating a Probability Distribution for Future Excess Cost Growth

The results presented in this paper are projected using a model that combines a stochasticdemographic model with a model designed to forecast overall government expenditures,

including Medicare costs.15 The goal of the stochastic macro-demographic model is to generate

values for the economic and demographic inputs to the budget forecasting model in a Monte

Carlo setting. The basic approach involves using standard time-series techniques applied to the

stochastic inputs as in Frees et al. (1997) and Chang and Cheng (2002).16 The demographic
17In the language of time series econometrics, a process is described in terms of it “AR” and “MA”

properties, with “AR” denoting how may lagged terms are included in the equation and “MA” denoting how long the

moving average is for the error terms. The simplest equation is an “AR(1)” which has only one lagged term and no

9

inputs are the rate of mortality improvement across detailed age and sex groups, the overall

fertility rate, and the level of immigration. The economic inputs for the budget model are real

wage growth, inflation, the unemployment rate, interest rates, and rates of disability incidence

and termination. The goal of the macro-demographic model is to create realistic stochastic

variation in the annual values for each input, including correlations between those variables. 

The stochastic macro-demographic model starts with Social Security Administration

(SSA) intermediate projections to set central tendencies for each of the economic and

demographic inputs. The SSA intermediate values are based on extrapolating historical averages

for (generally) stationary processes like wage and price growth rates, and in that sense is

consistent with the underlying time-series analysis used to build the macro-demographic model

used here. Most of the stochastic inputs are treated as independent time-series processes, though

inflation, unemployment, and interest rates are modeled together in a vector auto-regression

(VAR). In all cases, the specifications were chosen using standard time-series techniques (CBO,

2001). Note that while this all of the stochastic inputs are discussed here, the most important

when forecasting Medicare costs is excess cost growth.

Demographic Inputs

The three demographic models are all estimated using data from the Social Security

Administration (see Table 4). Mortality improvement is modeled as an auto regressive (AR(1))

process for each of 42 separate age-sex groups.17 The data are available back to 1900. Although
moving average. The most complicated process is an “ARMA(4,1),” meaning there are four lagged terms and a

single-period moving average of errors.

10

the equations are estimated separately, the rates of mortality improvement across age groups are

correlated because the vector of innovations is drawn from a multivariate normal distribution

estimated using the historical error terms, which are correlated. The overall fertility process is

characterized as an ARMA(4,1) model estimated on data back to 1917. Identifying a stationary

characterization for the fertility process is somewhat complicated by distinct breaks in the series

at various points in history, notably at the end of the baby boom. Experiments with an alternative

to the ARMA representation (a first-difference model) did change implied fertility dynamics, but

the effect on variability in system finances was modest (CBO, 2001). Finally, the immigration

process is also dominated by distinct breaks in the time-series at various points in history, but in

this case, because of changes in policy. Again, the ARMA(4,1) representation is most

appropriate for immigration.

Economic Inputs

Three of the four economic variables (inflation, unemployment, and the interest rate gap)

passed the test for inclusion in a vector auto-regression (VAR). The VAR model uses two

annual lags for each of the three variables and is estimated using data from Bureau of Labor

Statistics (BLS) and the Social Security Administration for the period 1954-1999. 

Unemployment rates are transformed using a log-odds ratio prior to estimation so the predicted

values are constrained to the zero-one range in all cases. Total factor productivity is a white
11

noise process. The standard deviation of the innovations is computed using data for 1950

through 2000.

The last two inputs to the long-term budget model are Social Security disability incidence

and termination. Finding reasonable equations for variation in disability incidence and

termination rates is made difficult because consistent data only exist back to 1975, and is further

complicated because of changes in policy (stated and implicit) with respect to eligibility for the

program. The problem is similar to the fertility model; there are clear breaks in the data that are

(ex post) explainable, but it is not clear how to use that information when predicting future

variability. Because there is no clear signal from the data, both models are specified as simple

AR(1) processes. 

Medicare Excess Cost Growth

The variation is excess cost growth is also estimated using an AR(1) process such that 

xt = 2.123 + 0.367xt-1 + ,t

 (0.577) (0.126)

where xt is excess cost growth and ,t represents the random variable that describes the annual

random shocks to excess cost growth. Standard errors are in parentheses. The standard deviation

of the annual random shocks is 3.044. The p-value for the Dickey-Fuller test is 0.0002,

indicating the rejection of the presence of a unit root. The results of the Ljung-Box test for white

noise of the residuals indicate that there is no autocorrelation of the residuals.

A Monte Carlo simulation procedure is used to produce those probability distributions for

future outcomes. The procedure involves making repeated random draws from values for annual
12

shocks, and the values for these annual shocks are entered into a time series equation, which

generates a time path for excess cost growth. By repeating this process many times, inferences

can be drawn about the probability distribution of future outcomes. In the case of excess cost

growth, an expected value of 1 percent is assumed as opposed to using the expected value from

the historical series. This assumption is consistent with the intermediate projections of the

Boards of Trustees and consistent with previous CBO studies. In constructing the distribution of

excess cost growth rates, a calculated deviation is added to this assumed expected value.

This process results in excess cost growth rates that vary quite considerably around the

long term assumed mean of 1 percent (see Figure 3). The 90 percent uncertainty bands for the

projection of excess cost growth cover a range of between -5 percent to over 6 percent annually. 

The range for average values narrow considerably to 2.5 percentage points in total. Note that

average uncertainty bands show the 90 percent confidence range for the average of 2004 through

a given year; the annual uncertainty bands show the 90 percent confidence interval for a given

year. The figure shows results for aggregate excess cost growth, while the forecasting model

uses category-specific excess cost growth rates. In the long run, however, all excess cost growth

rates are assumed equal.

The forecast is shown as aggregate Medicare costs as a percentage of GDP, but

underlying this aggregate forecast is a set of category-specific cost forecasts. Each category of

costs, which include inpatient hospital, outpatient hospital, skilled nursing facilities, home health

services, hospice care, physicians and other Medicare Part B services, and prescription drugs, has

its own excess cost growth rate. For each category of costs, excess cost growth rates are

calculated separately for the early years of the forecast. In the long run, assumed excess cost
13

growth rates for each category are 1 percent. As described above, this is consistent with the

assumption made by the CMS actuaries. Between the short and long run, the excess cost growth

rates slowly phase in to the long term rates. The same time series equation is used to develop a

distribution for each excess cost growth rate, however. Lack of data on a category-specific basis

prevented the estimation of separate time series equations for each excess cost growth rate. The

same stochastic draw is used to predict each excess cost growth series in each year.

Using this approach rather than one where the assumed long run excess cost rate is fixed

allows a probability distribution of outcomes to be calculated. It also allows excess cost growth

to vary annually (around a predetermined mean). Looking back historically, excess cost growth

has been a highly variable series. Using this approach, some of that variability is allowed 

to continue.

4. Stochastic Analysis of Future Medicare Outlays

Looking at a 90 percent confidence interval based on the results from one thousand

Monte Carlo simulations, Medicare costs range from 5.6 percent of GDP at the fifth percentile to

16.3 percent at the ninety-fifth percentile in 2050. As the years progress, this range increases,

and so by 2075, this range has increased to 6.7 percent of GDP at the fifth percentile and 24.9

percent at the ninety-fifth. By 2100, this range has increases still further to between 7.9 percent

and 39.7 percent. The range of possible outcomes widens significantly as the forecast period gets

longer (see Figure 4). The median is also shown in the figure, and this closely mirrors the results

of a deterministic simulation. Even at the median, Medicare costs as a percentage of GDP

exceed 20 percent within 100 years. 
14

These stochastic projections assume that a 1 percent excess cost growth rate is the most

likely future outcome, and so they should be viewed with that in mind. Should actual future

excess cost growth differ from that 1 percent, the distribution would shift. Using this

assumption, the range of possible outcomes is narrower than CBO predicts in 2050.

These projections assume a continuation of current Medicare policy and no change in the

factors driving health care costs. A substantial rise in Medicare costs as a share of GDP could

induce changes in the policy environment or in the factors that drive health care costs. The

chances of this occurring are clearly asymmetric. If Medicare costs were to increase gradually,

changes in the health care environment would be less likely. Health care costs increasing to a

much larger share of GDP may trigger changes to the extent that the increase forced reduced

consumption of other goods and services. Estimates of the behavioral response to large increases

in health care spending are beyond the scope of this paper.

5. Conclusion

Medicare costs as a percentage of GDP are expected to increase significantly as the baby

boom generation ages. Health care costs under current law are expected to continue to grow

more quickly than GDP, as the number of Medicare beneficiaries grows with the impending

retirement of the baby boomers. Uncertainty is inherent in any long term forecast. This paper

treats the uncertainty in the long term growth of health costs systematically, in addition to the

systematic treatment of uncertainty in other economic and demographic inputs. Specifically,

fertility, mortality, and GDP all vary stochastically and feed directly into the calculation of
15

Medicare costs. This analysis shows the uncertainty associated with projections of Medicare

costs as a percentage of GDP.
16

REFERENCES

Agency of Health Care Research and Quality, Center for Financing, Access and Cost Trends. 

MEPS HC-059G: 2001 Office-Based Medical Provider Visits. Rockville, MD: Agency

for Healthcare Research and Quality, January 2004.

Boards of Trustees, Federal Hospital Insurance and Federal Supplementary Medical Insurance

Trust Funds. 2004 Annual Report of the Boards of Trustees of the Federal Hospital

Insurance and Federal Supplementary Insurance Trust Funds. Washington, DC: US

Government Printing Office. March 2004.

Chang, S. And H. Cheng. “Pension Valuation Under Uncertainties: Implementation of a

Stochastic and Dynamic Monitoring System.” Journal of Risk and Insurance 69(2),

2002. pp. 171-192.

Congressional Budget Office. The Long Term Budget Outlook. Washington, DC: Congressional

Budget Office, 2003.

Congressional Budget Office. Uncertainty in Social Security’s Long Term Finances: A

Stochastic Analysis. Washington, DC: Congressional Budget Office, 2001.

Frees, Edward W. “Summary of Social Security Administration Projections of the OASDI

System. Working paper for the 1999 Technical Panel on Assumptions and Methods. 

December 1999.

Jones, Charles I. “Why Have Health Care Expenditures as a Share of GDP Risen So Much.” 

NBER Working Paper 9325. Cambridge, MA. November 2002.

Lee, Ronald and Timothy Miller. “An Approach to Forecasting Health Expenditures, with

Application to the U.S. Medicare System.” Health Services Research. Vol. 37. No. 5,

October 2002.

Levit, Katharine, Cynthia Smith, Cathy Cowan, Art Sensenig, Aaron Caitlin, and the Health

Accounts Team. “Trends: Health Spending Rebound Continues in 2002; Once again,

hospital spending drives total health spending upward.” Health Affairs. Vol. 23. No. 1,

January/February 2004.

Newhouse, Joseph P. “Medical Care Costs: How Much Welfare Loss?” Journal of Economic

Perspectives. Vol. 6. No. 3. Summer 1992. pp. 3-21.

O’Harra, Josh, John Sabelhaus, and Michael Simpson. Overview of the Congressional Budget

Office Long-Term (CBOLT) Policy Simulation Model. Washington, DC: Congressional

Budget Office, Technical Paper 2004-1, 2004.
17

Peden, Edgar A. and Mark S. Freeland. “A historical Analysis of Medical Spending Growth,

1960-1993.” Health Affairs. Summer 1995. pp. 235-247.

Sabelhaus, John, Michael Simpson, and Julie Topoleski. “Incorporating Longevity Effects into

Long-Term Medicare Projections.” Washington, DC: Congressional Budget Office,

Technical Paper 2004-2, 2004.

Sethi, Rachel Christensen and Paul Fronstin. “National Health Spending Rose 9.3 Percent in

2002; Sixth Consecutive Year of Faster Growth.” EBRI Notes. Vol. 25, No. 3 March

2004.

Technical Review Panel on the Medicare Trustees Reports. Review of Assumptions and Methods

of the Medicare Trustees’ Financial Projections. December 2000.

Weisbrod, Burton A. “The Health Care Quadrilemma: An Essay on Technological Change,

Insurance, Quality of Care, and Cost Containment.” Journal of Economic Literature.

Vol. 29, No. 2 (June 1991), 523-552.

Zuvekas, Samuel H. And Joel W. Cohen. “A Guide to Comparing Health Care Expenditures in

the 1996 MEPS to the 1987 NMES.” Inquiry 39: 76-86. Spring 2002.
18

Table 1

Summary Statistics for Trends in National Health Expenditures and GDP, 1951-2002

Based on Ten-Year Rolling Averages

Real NHE Per

Capita

Real GDP Per

Capita

NHEGDPExcess Cost

Growth

Average 4.5% 1.8% 2.7% 3.4

Median 4.4 1.6 2.9 2.9

25th Percentile 3.7 1.3 2.5 2.5

10th Percentile 3.1 1.1 1.9 2.0

Minimum 2.6 0.4 1.0 1.7

NOTE: Column (1) less column (2) may not equal column (3) as the median and other statistics

are selected separately in each case. Excess cost growth is adjusted for age and sex.

Table 2

Summary Statistics for Trends in National Health Expenditures and GDP, 1951-2002

Annual Changes

Real NHE Per

Capita

Real GDP Per

Capita

NHE-GDP Excess Cost

Growth

Average 4.3% 1.8% 2.5% 3.1%

Median 4.2 2.0 2.3 3.2

25th Percentile 3.0 0.4 0.6 0.7

10th Percentile 1.8 -2.2 -0.8 -1.1

Minimum 0.2 -5.0 -4.4 -4.0

NOTE: Column (1) less column (2) may not equal column (3) as the median and other statistics

are selected separately in each case. Excess cost growth is adjusted for age and sex.
19

Table 3

Excess Cost Growth: Average Annual Growth Rates for Selected Time Periods

Real NHE per

capita

Real GDP per

capita

NHE-GDP Excess Cost

Growth

1951-2002 4.4% 1.7% 2.6% 3.1%

1960-2002 4.5 1.8 2.6 3.4

1970-2002 3.9 1.5 2.4 3.5

1980-2002 3.9 1.5 2.5 4.3

1990-2002 3.1 1.3 1.8 4.3

2000-2002 5.6 0.0 5.6 5.9

NOTE: Excess cost growth is adjusted for age and sex.
20

Table 4

Equations in Stochastic Macro-Demographic Model

Variable Description of Stochastic Process

Mortality

Improvement

Separate AR(1) equations for each of 21 age and 2 sex groups estimated

using SSA data for 1900-1995. Model draws correlated errors across 42

groups using multi-variate normal distribution.

Fertility ARMA(4,1) equation for overall fertility rate estimated using SSA data for

1917 through 1997.

Immigration ARMA(4,1) equation for total immigration estimated using SSA data for

1901 through 1995.

Unemployment VAR model with two lags each on unemployment, inflation, and real

interest gap estimated using BLS and SSA data for 1954 through 1999.

Inflation 

(CPI-W)

VAR model with two lags each on unemployment, inflation, and real

interest gap estimated using BLS and SSA data for1954 through 1999.

Total Factor

Productivity

A white noise process; standard deviation of innovations is computed

using data for 1950 though 2000.

Interest Rate

Gap

VAR model with two lags each on unemployment, inflation, and real

interest gap estimated using BLS and SSA data for 1954 through 1999.

DI Incidence AR(1) model for overall DI incidence rate estimated using SSA data for

1975 through 1999.

DI Termination AR(1) model for overall DI termination rate estimated using SSA data for

1975 through 1999.

In the language of time series econometrics, a process is described in terms of it “AR” and “MA”

properties, with “AR” denoting how may lagged terms are included in the equation and “MA”

denoting how long the moving average is for the error terms. The simplest equation is an

“AR(1)” which has only one lagged term and no moving average. The most complicated process

is an “ARMA(4,1),” meaning there are four lagged terms and a single-period moving average of

errors.
21

Figure 1 

Effects of Aging and Excess Cost Growth

02468

10121416

2004 2009 2014 2019 2024 2029 2034 2039 2044 2049 2054 2059 2064 2069 

Calendar Year

Percentage of GDPEffects of Aging Population Per Capita Growth in Excess of GDP Grow

Total

SOURCE: Author’s calculations 
22

Figure 2

Percentage Change in Per Capita Health Care Expenditures, 1987 to 2000

0%

10%20%30%40%50%60%70%80%90%

1 to 4 5 to 12 13 to 18 19 to 29 30 to 39 40 to 49 50 to 59 60 to 64 65 to 69 70 to 75 76 to 

$2,107

$798

$733

$1,066

$1,054

$1,643 $2,180

$3,101

$3,753 $5,012

$5,57

SOURCE: Author’s calculations NOTE: Compares data from 1987 NMES that have been adjusted to be comparable to later MEPS data (see Zuv2002). Numbers above bars are 2000 average expenditures. 
23

Figure 3 

Uncertainty Bands for Medicare Excess Cost Growth

-10

-5

05

101520

1961 1971 1981 1991 2001 2011 2021 2031 2041 2051 2061 2071 2081 209

Excess Cost Growth Rate

Actual Projected

Annual

Average

Average

Annual

SOURCE: Author’s calculations. NOTE: Annual uncertainty bands show the 90 percent confidence range for a given year. Average uncertainty bpercent confidence range for the average of 2004 through a given year. The center line shows deterministic exce
24

Figure 4 

Medicare Costs as a Percentage of GDP

05

10152025303540

2004200920142019202420292034203920442049205420592064206920742079208420892094209921

Percentage of GDP

90th Percentile

10th Percen

70th Percentile

30th Percentile

Median

SOURCE: Author’s calculations.