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papers

NUMBER 5

by Jagadeesh Gokhale and Kent Smetters

POLICY DISCUSSION PAPER

Fiscal and Generational Imbalances:
New Budget Measures for
New Budget Priorities

DECEMBER 2003

POLICY DISCUSSION PAPERS

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Fiscal and Generational Imbalances:
New Budget Measures for
New Budget Priorities
by Jagadeesh Gokhale and Kent Smetters
This paper describes the deﬁciencies of the measures used to calculate the federal budget,
make revenue and spending projections, and assess the sustainability of current ﬁscal policies.
The nature of the deﬁciencies hides the tremendous impact that Social Security and Medicare
commitments will have on the budget in the future, given the way the programs are structured
currently and the momentous demographic shift underway as the baby boom generation
approaches retirement age. This paper proposes two new simple measures that will enable
government ofﬁcials and the public to calculate more accurately the costs of maintaining
these programs into the relevant future. The measures provide a better understanding of the
costs involved, when they will be incurred, and by whom. The measures also provide a way
to meaningfully compare the various solutions that have been proposed for dealing with the
impending ﬁscal crisis that will be caused by Social Security and Medicare.
This article was also published as a monograph by the AEI Press, the publisher for the American
Enterprise Institute.

POLICY DISCUSSION PAPERS

Policy Discussion Papers are published by the Research Department of the Federal Reserve
Bank of Cleveland.To receive copies or to be placed on the mailing list, e-mail your request
to 4dsubscriptions@clev.frb.org or fax it to 216-579-3050. Please send your questions
comments, and suggestions to us at editor@clev.frb.org.

Jagadeesh Gokhale was an economic
advisor at the Federal Reserve Bank of
Cleveland when the research was done
on which this paper is based, as well as
a consultant to the U.S. Department of
Treasury from July to December 2002
and a visiting scholar at the American
Enterprise Institute in 2003. He will join
the Cato Institute in early 2004. Kent
Smetters was deputy assistant secretary
for economic policy at the U.S. Department
of Treasury from 2001 to 2002 and a
Treasury consultant from August 2002 to
February 2003. He is currently an assistant
professor at the University of Pennsylvania.
The authors thank Robert Anderson,
Michael Boskin, Robert Bramlett, Robert
Clark, Robert Dugger, Doug Holtz-Eakin,
Doug Elmendorf, William Gale, Howell
Jackson, Richard Jackson, Robert
Kilpatrick, Laurence Kotlikoff, Patrick
Locke, Peter Orszag, John Palmer, Tom
Saving, and participants in the conferences
at the Stanford Institute for Economic
Policy Research, Washington, D.C.,
May 8, 2003; the American Enterprise
Institute, Washington, D.C., May 9, 2003;
the Social Security Administration’s
Retirement Research Consortium, May
15, 2003; and the National Tax Association
meetings, Washington, D.C., May 29,
2003, for helpful comments on drafts of
this paper. The authors also thank the
White House Ofﬁce of Management and
Budget for providing long-range Budget
projections, Felicitie Bell of the Social
Security Administration for providing
long-range population projections and
demographic assumptions used for the
2002 Social Security Trustees report,
and Kevin Brennan and Pernille DortheHansen for excellent research assistance.
All opinions are those of the authors, and
not necessarily of the American Enterprise
Institute, the Federal Reserve Bank of
Cleveland, the Federal Reserve System,
or the U.S. Department of Treasury.

ISSN 1528-4344

Policy Discussion Papers are available on the Cleveland Fed’s site on the World Wide Web:
www.clevelandfed.org/Research.
Views stated in Policy Discussion Papers are those of the authors and not necessarily
those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal
Reserve System.

Materials may be reprinted,
provided that the source is
credited. Please send copies
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Table of Contents
Introduction ........................................................................................................................................1
The Fiscal Imbalance (FI) Measure .....................................................................................................3
The Generational Imbalance (GI) Measure.........................................................................................5
The Desirable Properties of a Fiscal Measure .....................................................................................7
The Bias in Policymaking Arising from Current Budget Accounting ................................................10
Estimates of Federal Fiscal and Generational Imbalances in the United States ................................11
Total Federal Fiscal Imbalance...................................................................................... 12
Social Security.............................................................................................................. 12
Medicare ...................................................................................................................... 14
The Rest of the Federal Government ........................................................................... 14
Evaluating the Size of Federal Fiscal Imbalance................................................................................15
Comparison with Official Estimates ............................................................................ 15
Comparison of FI with Present Values of Payroll, GDP, and Other Aggregates ............ 16
Sensitivity to Alternative Assumptions ......................................................................... 17
Conclusion ........................................................................................................................................20
Appendix A:The Fiscal and Generational Imbalance Measures ........................................................21
Derivation of the Infinite Horizon Fiscal Imbalance Measure ..................................... 21
Generational Imbalance............................................................................................... 22
Appendix B: Assumptions and Methods for Estimating Fiscal Imbalances for
Social Security, Medicare, and the Rest of the Federal Government .................................................24
Method for Extending the Social Security Administration’s Population Projections... 24
Method for Projecting Social Security Revenues and Benefits .................................... 24
Methodology for Projecting Medicare Revenues and Outlays..................................... 26
Estimating Fiscal Imbalance for the Rest of the Federal Government......................... 27
Distributing and Projecting Federal Outlays......................................................... 27
Distributing and Projecting Federal Revenues ..................................................... 27
Estimating Consumption Profiles by Age and Sex ................................................ 28
Appendix C: Methodology for Extending SSA’s Population Projections...........................................29
Population Projections................................................................................................. 29
Assumptions and Definitions ....................................................................................... 30
Appendix D: Methodology for Projecting Social Security Age–Sex Benefit Profiles .........................31
Additional Widow(er) Reductions at Ages 60–61 to Adjust Profiles for Advancing FRA .......31
Additional OASI Benefit Reductions at Ages 62–66 to Adjust Profiles for Advancing FRA....33
Appendix E: Calculating and Projecting Social Security Taxes and Benefits per Capita ...................35
Appendix F: Derivation of Age–Sex Profiles for Medicare Revenues and Outlays ............................36
References.........................................................................................................................................39

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Introduction
Traditional budget measures are becoming obsolete as federal budget priorities shift from providing
“brick and mortar” public goods toward delivering social insurance services.As the share of retirees
in the nation’s population balloons and human life spans continue to lengthen, Social Security and
Medicare transfers will increasingly dominate total federal outlays.Traditional annual cash-flow budget measures may have been sufficient when Congress could directly allocate almost all budgetary
resources via the annual appropriations process. During this century, however, federal spending will
be determined mostly by factors outside of short-term legislative control. Because the current structure of Social Security and Medicare involves long-term payment obligations, backward-looking or
short-term measures such as debt and deficits need to be complemented by long-term, forwardlooking ones that explicitly measure future payment obligations relative to the resources available
to meet them under current laws. Such measures are needed to assess how far the federal budget is
from fiscal sustainability, and the size of policy changes needed to achieve sustainability.
Many, if not most, analysts and policymakers use traditional fiscal measures such as debt held by
the public, deficit projections over limited (usually five- or ten-year) horizons, or seventy-five year
estimates of Social Security and Medicare financial shortfalls.1 Some budget analysts acknowledge
that short-term measures such as national debt and deficits are inadequate, as they significantly understate the financial shortfall that the federal government faces under today’s fiscal policies.2 As a
consequence, the degree to which current policy is unsustainable remains hidden from policymakers. In addition, we argue here, reliance on traditional measures introduces a policy bias favoring
current debt minimization at the expense of policies that are sounder from a long-term perspective. Even under seventy-five-year budget measures, we believe the federal fiscal shortfall would be
significantly understated, hindering objective fiscal policymaking. Nevertheless, official budgeting
agencies continue to promote such measures: The recently published Budget of the United States
Government, Fiscal Year 2004 (hereafter Budget) reports seventy-five-year “actuarial deficiency”
measures for Social Security and Medicare.
We propose that federal budget agencies such as the Office of Management and Budget and
the Congressional Budget Office should begin reporting a pair of measures on a regular basis to
track the true costs of current fiscal policy: Fiscal Imbalance (FI) and Generational Imbalance (GI).
The FI measure for the federal government is the current federal debt held by the public plus the
present value in today’s dollars of all projected federal non-interest spending, minus all projected
federal receipts.The FI measure indicates the amount in today’s dollars by which fiscal policy must
be changed in order to be sustainable: A sustainable fiscal policy requires FI to be zero.3 The GI
measure indicates how much of this imbalance is caused, in particular, by past and current generations.
The FI measure is similar to the standard perpetuity “open-group liability” concept that is sometimes used to analyze shortfalls in social insurance programs, while the GI measure is similar to the
standard “closed-group liability” concept. The FI measure is also sometimes called the “fiscal gap”
(see Auerbach, Gale, Orszag, and Potter 2003). We argue here that the FI and GI measures together
possess several desirable properties, the most important being that they render policy decisions
free of the aforementioned bias because they enable comparisons of alternative policies on a neu-

1. See Budget of the United States
Government, Fiscal Year 2004,
Analytical Perspectives, Chapter
3, “Stewardship.”
2. “Beyond Borrowing: Meeting
the Government’s Financial
Challenges in the 21st Century,”
Remarks of Under Secretary
of the Treasury Peter R. Fisher
to the Columbus Council on
World Affairs, Columbus, Ohio,
14 November 2002, available
at http://www.ustreas.gov/
press/releases/po3622.htm.
See also the related subsequent
article by Steven Cecchetti, “A
Forward Looking Fiscal Policy
Strategy,” Financial Times, 23
December 2002, available at
http://economics.sbs.ohiostate.
edu/cecchetti/pdf/cpi23.pdf. Also
see Howell Jackson (2002). For
an even more recent discussion, see the Federal Reserve
Board’s Semiannual Monetary
Policy Report to the Congress
Before the United States
Senate Committee on Banking,
Housing, and Urban Affairs,
11 February 2003, available at
http://www.federalreserve.gov/
boarddocs/hh/2003/ february/
testimony.htm.
3. This requirement assumes that
the economy is characterized by
“dynamic efﬁciency.” A dynamically inefﬁcient economy is one
with excessive capital relative to
the labor force—one where living
standards can be improved by
discarding capital. Abel, Mankiw,
Summers, and Zeckhauser
(1989) suggest that the U.S.
economy has been characterized
by dynamic efﬁciency since 1929.

tral footing.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

The Fiscal Imbalance associated with today’s federal fiscal policy is very large. Taking present
values as of fiscal-year-end 2002, and interpreting the policies in the FY 2004 federal Budget as “current policies,” the federal government’s total Fiscal Imbalance is $44.2 trillion. By “present value,” we
mean that all future spending and revenue not only are reduced for inflation but are additionally
discounted by the government’s (inflation-adjusted) long-term borrowing rate. For example, after
accounting for inflation, a dollar of revenue or outlay as of fiscal-year-end 2003 is only worth about
97 cents as of fiscal-year-end 2002; a dollar received or paid 100 years from now is worth only about
3 cents. This present-value calculation allows us to determine how much money the government
must come up with immediately to put fiscal policy on a sustainable course. Since the government
obviously does not have an extra $44.2 trillion today, it must make cuts or increase revenue in future
years that add up to $44.2 trillion in present value. Of course, for their discounted value to equal
$44.2 trillion in present value, the cumulative value of these policies will have to be substantially
more than $44.2 trillion. See the text box below for a discussion of the present value concept.
Of the current federal FI of $44.2 trillion, Social Security’s FI is about $7 trillion in present value.
Medicare’s FI is $36.6 trillion (for both Parts A and B), of which Part A (the Hospital Insurance
program) contributes $20.5 trillion and Part B (the Supplementary Medical Insurance program)
contributes $16.1 trillion.4 By contrast, the rest of the federal government’s FI is only $0.5 trillion,
which comprises a $4.6 trillion surplus in revenues minus obligations to Social Security, Medicare,
and publicly held debt of $5.1 trillion.

VIEWING GOVERNMENT OBLIGATIONS AND REVENUE IN “PRESENT VALUE”

As most investors know, a dollar received one year from today is not worth as
much as a dollar received today. The reason is that a dollar received today can
be invested, say in a bank account, to earn interest income over the year. This
same intuition holds for the government as well. A dollar received in revenue in
the future is not as valuable to the federal government as a dollar of revenue received today. The reason is that a dollar received today would allow the government to reduce its level of federal debt held by the public and, hence, reduce the
interest payments it must make to nongovernment entities. Similarly, it costs the
government more to pay a dollar today than paying a dollar next year, because
of larger borrowing costs.
The “present value” operation is a way of converting future dollars to current dollars. It not only adjusts for changes in inﬂation over time, it additionally “discounts”
(i.e., reduces) the value of future dollars in order to recognize that a future dollar is not worth as much as a dollar received or paid today. Naturally, dollars in
the distant future are discounted by more than dollars at a nearer date since the
government must pay more interest income to borrow money over many years.
The present value operation, therefore, allows us to consistently compare dollars
received or owed at different times by adjusting for the interest costs. Failing to
discount future dollars could potentially present a very misleading picture of the
government’s ﬁnancial position by ignoring borrowing costs.
While the government often uses the present value operation to compare different policy options, the ﬁve-year and ten-year budget tables reported by the Ofﬁce of Management and Budget (OMB) and the Congressional Budget Ofﬁce
(CBO) are not stated in the present-value form. Instead, when describing accumulated deﬁcits, the CBO and OMB use an ad-hoc approach to adjust for the
government’s borrowing costs: They include interest spending as part of the government’s outlay and then sum undiscounted values over different years. But this
approach facilitates attempts at “budget arbitrage” even within the short ﬁve-year
and ten-year budget windows. Bazelon and Smetters (1999) discuss how the
present value concept is used in the federal budget process.

4. As we explain later, consistent
with the Social Security and
Medicare Trustees, we assume
that health care per capita grows
one percentage point faster than
GDP per capita until 2080—a
very conservative assumption
relative to the past two decades.
Between 2080 and 2100, the
one percentage point differential
is gradually reduced to zero,
thereby assuming that health
care spending grows no faster
than GDP. Even with these very
cautious assumptions, very large
Medicare Fiscal Imbalances exist.

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Our estimate of today’s federal Fiscal Imbalance is more than ten times as large as today’s debt
held by the public that arose from past federal financial shortfalls.The reason is that FI also includes
prospective financial shortfalls. Hence, policy changes that eliminate only the debt held by the public would still leave the federal government far from being financially solvent. In particular, spending
must be reduced and/or taxes increased in order to put federal fiscal policy on a sustainable course.
Moreover, the FI grows by about $1.6 trillion per year to about $54 trillion by just 2008 unless corrective policies are implemented before then.This rapid annual increment is also about ten times as
large as the official annual deficit reported for fiscal year 2002.
How much must we cut federal spending or increase federal receipts to eliminate the current
$44.2 trillion FI? We estimate that an additional 16.6 percent of annual (uncapped) payrolls would
have to be taxed away forever beginning today to achieve long-term fiscal sustainability—implying a greater than doubling of the current payroll tax rate of 15.3 percent that is currently paid
in equal shares by employees and employers to the Social Security and Medicare systems. Alternatively, income tax revenues would have to be hiked permanently by another two-thirds beginning
immediately—increasing their share in gross domestic product (GDP) from 9.5 percent to 15.9
percent. Other (equally drastic) alternatives would be to cut Social Security and Medicare benefits
by 45 percent immediately and forever, or permanently eliminate all future federal discretionary
spending—although the latter policy still falls short by about $1.8 trillion. Moreover, the size of the
necessary corrective policies will grow larger the longer their adoption is postponed. For example,
waiting until just 2008 before initiating corrective policies would require a permanent increase in
wage taxes by 18.2 percentage points, rather than 16.6 percentage points if we began today.
Finally, this paper shows that the estimated Fiscal Imbalance remains large regardless of variations in underlying economic assumptions. Calculations under alternative growth and discount rate
assumptions suggest a low-side estimate of federal FI of $29 trillion and, under still quite conservative assumptions, a high-side estimate of $64 trillion.Although FI expressed in today’s dollars is fairly
sensitive to these economic assumptions, we argue below that this sensitivity only strengthens the
need to focus on FI rather than on traditional shorter-term fiscal measures. Furthermore, the ratios
of FI to the present value of GDP and future payrolls—and, consequently, estimates of tax hikes or
spending cuts required to restore fiscal sustainability—are less sensitive to alternative economic
assumptions because the denominators (GDP and the payroll base, respectively) are similarly sensitive to the underlying assumptions.As discussed below, although FI is smaller ($36.9 trillion) under
our low productivity growth rate assumption, it declines by less than the present value of payrolls.
Consequently, the wage-tax hike needed to eliminate FI is larger under the low productivity growth
rate assumption—18 percentage points compared to 16.6 percentage points under baseline assumptions. Under our high growth rate assumption, a 14.8 percentage point wage-tax increase
would be needed to eliminate FI.

The Fiscal Imbalance Measure
The federal government provides a myriad of public goods and services. Programs such as Social
Security and Medicare provide retirement and health security to American citizens and residents.
Other programs include national defense, homeland security, judicial and legislative operations, international diplomacy, transportation, energy, infrastructure development, education, and income
support for the needy.
3

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Whether these programs can continue to operate indefinitely at current service levels depends
upon the availability of resources to finance them. All federal purchases and debt-service payments
must be financed out of future federal revenues. Sources of federal revenue include tax receipts, net
income of public enterprises, fees, and other levies. Although the government can borrow money,
additional debt must also be serviced out of future tax receipts. Hence, current (net) debt held by
the public plus the government’s future non-interest spending must be balanced over time by its
future receipts.5
The government’s total fiscal policy may be considered balanced if today’s publicly held debt
plus the present value of projected non-interest spending is equal to the present value of projected
government receipts.The spending and revenue projections are made under today’s fiscal policies.
“Present values” mean that dollars paid or received throughout the future are discounted at the

5. Because outstanding debt held by
the public is included among the
obligations that must be ﬁnanced,
projected interest outlays are
excluded when calculating the
present value of projected spending to avoid double counting.

government’s long-term interest rate in order to reflect their true value today (see text box on page
2).A fiscal policy that is balanced can be sustained without changing either federal outlays or federal
revenues. Hence, the Fiscal Imbalance measure as of the end of year t is defined as:
(1)

FIt = PVEt – PVRt -- At.

This definition is simply understood as the excess of total expenditures over available resources
in present value. Here, PVEt stands for the present value of projected expenditures under current
policies at the end of period t. PVRt stands for the present value of projected receipts under current
policies, and At represents assets in hand at the end of period t.
The FI measure can be calculated for the entire federal government. It can also be calculated
separately for federal programs that are financed with dedicated revenues, such as Social Security
and Medicare. FI can also be calculated for the rest of the government, reflecting the government’s
spending obligations and tax resources outside of Social Security and Medicare.
When calculating FI for programs such as Social Security and Medicare, At is positive and equal
in value to the program’s respective trust fund, which reflects the excess of previous payroll contributions over spending by past and current generations. When calculating FI for the rest of government, however, the value of At is negative since it reflects monies owed to these trust funds as well
as the money owed to the public that is holding government debt. The level of debt held by the
public, in turn, reflects the excess of spending over revenue by past and current generations.
While the variable At reflects the excess of revenue over spending done by past and current
generations, the difference PVEt – PVRt shown in equation (1) reflects the contribution to FI from
all projected financial shortfalls and surpluses—those on account of living and future generations.
Hence, FI measures the aggregate financial shortfall from all generations—past, living, and future.
For the entire federal government’s policy to be sustainable, its FI must be zero.The government
cannot spend and owe more than it will receive as revenue in present value. In other words, while
the government can spend more than it collects in taxes on some generations, other generations
must eventually “pay the piper,” thereby returning the Fiscal Imbalance to zero.6 Similarly, FI’s for
programs such as Social Security and Medicare must equal zero if they are to continue without
changes to revenues or outlays. Hence, if the FI measured under current policies is positive, those
policies are unsustainable and policymakers will have to change them at some future point in time.

6. Geanakoplos, Mitchell, and
Zeldes (1998) discuss the implications of this type of zero-sum
constraint for analyzing Social
Security reform.

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The Generational Imbalance Measure
To be useful to policymakers, any proposed measure must be able to fully reflect the fiscal impact
of all possible policy changes.The FI measure alone, however, is not capable of doing so for all types
of policy changes. As is obvious from equation (1), any new policy that changes projected expenditures and revenues so that their increments are exactly equal in present value will produce offsetting increases in PVEt and/or PVRt, leaving FI unchanged. However, such FI-neutral policies could
nevertheless transfer net tax burdens from living to future generations. Therefore, we need a complementary measure to show such redistributions of fiscal burdens.
For example, suppose that Congress passes legislation to immediately reduce Social Security
payroll taxes but sharply increase payroll taxes in twenty years. If the revenue loss from the immediate tax reduction is equal in present value to the magnitude of the revenue gain in twenty years,
then the value of PVRt shown in equation (1) remains unchanged. As a result, Social Security’s FI
remains unchanged, as does the federal government’s total FI. But clearly such a policy would shift
substantial amounts of resources across generations.
As another example, suppose Congress creates a new Medicare benefit and finances it by
raising payroll taxes such that each year’s additional outlay is matched by additional revenue. By
construction, this policy has no impact on Medicare’s FI and, therefore, no impact on the federal
government’s total FI. The reason is that the values of PVEt and PVRt shown in equation (1) increase by the same amount after this policy change, thereby producing no change in the value of
their difference, PVEt − PVRt. Nevertheless, this policy could potentially shift a substantial amount
of resources away from future generations and toward current generations, similar to the previous
example. In particular, current retirees and workers about to retire at the time of the policy change
would gain from the new Medicare benefit, for which they will pay little or nothing.Younger workers and future generations, however, would be worse off because they will not fully recover the
value of their additional taxes via their own additional retirement benefit: The investment income
that they would lose on the resources now devoted to paying additional payroll taxes will not be
fully made up by their future benefits.7
To identify such fiscally induced redistributions, therefore, we need to augment the FI measure
with another measure. Because FI exclusively reflects the sustainability of a given policy, the com-

7. This result, again, assumes that
the economy is dynamically
efﬁcient. See note 3.

plementary measure should indicate how FI is distributed across population subgroups. Although
it is possible to complement FI with measures of its distribution across cohorts distinguished by
year-of-birth, gender, race, and so forth, we adopt a more modest approach and follow the standard
“closed-group liability” concept—showing the component of FI that arises due to past and living
generations. We call this measure Generational Imbalance, or GI. We define the GI measure as:
(2) GIt = PVELt – PVRLt − At.
PVELt represents the present value of projected outlays that will be paid to current generations.
PVRLt

represents the present value of projected tax revenues from the same generations. At, again,

represents the program’s current assets. Note that if the program has positive current assets, past
tax payments exceeded the program’s outlays to date. Therefore, GI captures the part of FI arising
from all transactions with past and living generations throughout their lifetimes.The projected contribution to FI by future generations simply equals the difference, FI minus GI.8

8. As shown in appendix A, the
measure for future generations,
FI-GI, can be further broken down
into projected net transfers to
each future birth cohort under
current policy. These estimates
are not reported in this paper,
but they are available from the
authors upon request.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Our proposed GI measure should not be confused with Generational Accounting—the measure
developed by Auerbach, Gokhale, and Kotlikoff (1991).9 Generational Accounting involves a hypothetical policy reform that restores FI to zero by increasing the net tax burden on unborn generations. Generational Accounting’s measure equals the difference in the net tax burdens per capita on

9. For the latest available estimates
of United States’ generational accounts, see Gokhale and Kotlikoff
(2001).

current newborns (not affected by the hypothetical reform) and future generations. Hence, Generational Accounting’s measure incorporates a hypothetical and sustainable policy. In contrast, the
FI and GI measures correspond to current law, making them more applicable as a budget concept.
One reason why the FI and GI measures are easy to understand is that they don’t incorporate any
hypothetical policy change.
Returning to the previous example, a new pay-as-you-go Medicare benefit would increase
Medicare’s imbalance on account of past and living generations (GI) and reduce the imbalance on
account of future generations (FI – GI) by the same amount, leaving the overall Fiscal Imbalance (FI)
unchanged (see text box below). In other words, past and living generations would receive a windfall that is directly offset by a reduction in the resources available to future generations. Medicare’s
FI does not capture this redistribution because it adds together the net Medicare transfers received
by all generations—past, living, and future—under current policies. This redistribution is, however,
indicated by the change in GI.
Note that the traditional focus on the publicly held debt would also not capture the redistributive impact of the Medicare policy described earlier: Outstanding debt remains unchanged for
any new outlay that is financed on a strictly pay-as-you-go basis, since the outlays in each year are
PAY-AS-YOU-GO PROGRAMS AND THE GENERATIONAL IMBALANCE MEASURE

Consider the following simple example: Divide each generation’s lifespan into two
parts—“work” and “retirement.” For simplicity, assume that both phases require the
same length of time; that there is no inﬂation; that the interest rate equals 3 percent;
and that productivity growth always equals zero.10 All generations are assumed to
live for exactly two periods. A new generation of workers of ﬁxed size is born in each
period. One period’s workers grow to be the next period’s retirees. Hence, one generation of workers and one generation of retirees are alive in any given period.
Now suppose that a new pay-as-you-go Medicare program conferring $100 beneﬁt
to retirees is introduced in period 1 and it is ﬁnanced by a payroll tax on period-1’s
workers of $100. The net value of this beneﬁt to period-1’s retirees is $100—equal
to the beneﬁt they receive in period 1. For workers in period 1, however, the value
of the new program equals the present value of next period’s Medicare beneﬁt—
$100/1.03 = $97.09—minus period-1’s payroll tax of $100. Hence, the net value
of this program for these workers is a loss of $2.91. It equals the present value
of the interest they could have earned in period 2 on their $100 payroll taxes—
$3/1.03 = $2.91. Hence, the GI corresponding to just this new Medicare policy
equals the sum of the net beneﬁts of those alive in period 1—that is, $100 − $2.91 =
$97.09. This GI will be in addition to any preexisting GI.
Now consider the impact of this Medicare policy on future generations. Workers in
period 2 also pay $100 when working and receive beneﬁts worth $100 when retired.
Hence, when the present value is taken as of period 2, they also lose $2.91. However, discounting this loss back to period 1 reduces it to $2.91/(1 + 0.03) = $2.83.
Similarly, workers in period 3 lose $2.91 when the present value is taken as of
period 3. But this loss equals $2.91/(1 + 0.03)2 = $2.74 as of period 1. As of
period 1, therefore, the present value loss to all future generations equals the sum:
[$2.91/(1 + 0.03) + $2.91/(1 + 0.03)2 + $2.91/(1 + 0.03)3 + …]. When taken over all
future generations, this sum equals exactly $97.09. This loss to all future generations
is exactly equal to GI—the gain to past and living generations in present value as of
period 1. Hence, FI is unchanged by this policy because the gain to past and current generations (GI) is exactly offset in present value by the loss to all future generations (FI – GI).

10. Incorporating productivity growth
makes the example complicated
but does not change its basic
message as long as this growth is
not so large as to imply dynamic
inefﬁciency (see note 3).

FEDERAL RESERVE BANK OF CLEVELAND

financed with taxes collected in that year. Note, however, that the level of publicly held debt would
increase for a lengthy amount of time in the previous example where taxes are decreased initially
and then increased after twenty years. Interestingly, both policies shift a large financial burden from
current generations to future generations. In fact, with only minor adjustments, it is possible to construct both policies so that identical burdens are shifted across generations.Yet the level of publicly
held debt increases in the tax cut example but not in the Medicare benefit example.This distinction
makes little sense economically—a point emphasized by Kotlikoff (2001).
So, while the Fiscal Imbalance measure properly captures many large unfunded payment obligations not included in traditional accountings of public debt, both measures fail to reveal the
resource transfers across generations that some policies can cause. The GI measure does, however,
capture the redistributive effect of all policies. Under the pay-as-you-go financed Medicare policy
described above, the GI measure increases even though FI does not change. Of course, this implies
that the imbalance on account of future generations decreases. Hence, FI and GI measures taken
together comprise a powerful analytical tool for policymakers, enabling more informed decisions.
In the future, policymakers must achieve two objectives simultaneously: First, they must reduce
the Fiscal Imbalance to zero by either increased taxes or reduced spending, or a combination of
both. This can be accomplished in a myriad of ways, each of which will affect the burden placed
on future generations differently. For example, lowering the growth of entitlement benefits—which
affects those about to retire—will be more beneficial to future generations than increasing, say,
payroll taxes—which leaves today’s older generations unaffected but negatively impacts today’s
workers and future generations. Hence, the second objective for policymakers is to choose a policy
that delivers the best trade-off in costs imposed on different generations. The GI measure offers
policymakers a parsimonious approach for analyzing this issue and choosing among different sustainable paths.
Identifying the GI component of FI is feasible for programs such as Social Security and Medicare,
where outlays can be easily attributed to different individuals. It cannot be easily identified, however,
for the rest of the federal government because the benefits of outlays (such as spending on national
defense or public infrastructure) cannot easily be allocated to different generations. For example,
much of the benefit from spending on education or national defense accrues to society in general
and, to some extent, to unborn generations. Only the revenue side of the rest-of-government’s budget may be so attributed.11 Hence, for the rest of the federal government, we can only report how
revenues can be distributed into the accounts of past and living generations.Although this does not
fully correspond to the GI measure, it is nevertheless useful to know the generational distribution
of the burden of paying for the rest-of-government’s outlays under current policies.

The Desirable Properties of a Fiscal Measure
As we outline in table 1, the FI and GI fiscal measures have several desirable characteristics that other fiscal measures do not. We discuss these properties in this section.
The first desirable property of a proper fiscal measure is that it should be forward-looking.
Under current budget accounting, many analysts and policymakers (as well as the general public)
tend to focus on annual deficits and the level of debt held by the public.12 For years, policymakers
and public-interest groups have debated how to control deficits and debt. These measures, however, substantially understate the true magnitude of the fiscal shortfall that the federal government

11. Note that we can only estimate
the direct and immediate
incidence of taxes on different
generations but not the ultimate
incidence that includes the
distorting effects that taxes have
on work-effort and consumptionsaving decisions. Bohn (1992)
discusses this type of difﬁculty in
more detail.
12. To be sure, alternative concepts
of debt do exist in Budget
reports—gross debt, debt subject
to ceiling, debt held in trust funds,
and debt held by the public. But
these measures suffer from the
same problems as the debt held
by the public that we identify
here. We focus our attention on
debt held by the public because
it is the most meaningful concept
for measuring overall federal
indebtedness.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

faces. Specifically, the large future obligations associated with Social Security and Medicare are not
reported in standard budget documents, which focus primarily on the effect that current policies
have on current fiscal flows. Adopting new forward-looking budget measures would reveal a very
different and more accurate picture of the federal government’s financial status, as well as the size
and nature of needed policy adjustments. Indeed, as the results below suggest, even if we could immediately pay off the entire $3.5 trillion of outstanding debt, federal spending would nevertheless
have to be reduced and/or revenues increased by about $41 trillion in present value to make the
system sustainable in the long run.
A second desirable feature of a proper fiscal measure is that it should include all future years.
That is, it should be calculated in perpetuity. Several agencies have been regularly reporting other
forward-looking measures. For example, the Social Security and Medicare Trustees’ measure of
“actuarial balance” incorporates those programs’ assets and seventy-five-year-ahead projections of
revenues and outlays. Normal cash flow budget reporting covers a span of only five or ten future
years. However, the most recent Budget also reports seventy-five-year present-value “actuarial deficiencies” for Social Security and Medicare based on information included in the Trustees Reports
and prepared by the same actuaries.
As is well known, however, such measures do not completely account for those programs’ fiscal
imbalances because of the arbitrary truncation of the projection horizon at seventy-five years. As
the seventy-five-year projection window moves forward over time, the cumulative inclusion of an
additional year’s deficit or surplus will impart instability to such measures even if the underlying
revenue and outlay projections remain unchanged. If deficits (or surpluses) beyond the seventy-fifth
year are especially large and growing, measures based on seventy-five-year-ahead projections will
severely understate the true magnitude of the program’s Fiscal Imbalance by two-thirds or more.
As shown later, this occurs even though each dollar beyond seventy-five years is heavily discounted
and, hence, receives a considerably smaller weight in present-value calculation.13 Moreover, seventyfive-year measures preserve some of current policy bias in favor of short-term fixes. That would be
true, for example, if the costs of a future reform fall within the seventy-five-year window while some
of its benefits fall outside it.
Indeed, the bias created by the seventy-five-year measure was the key reason why the maximum
size of the personal accounts was limited to a $1,000 annual contribution (indexed over time with
wages) in model 2 of the president’s Social Security Commission. Whereas today’s Social Security
TABLE 1

PROPERTIES OF ALTERNATIVE FISCAL MEASURES
Various Budget Measures

Properties of budget measures

Uniﬁed
annual
deﬁcit

Debt held
by the
public

Forward looking

75-year
actuarial
deﬁcit

Generational
accounting

Accrued
obligation
measures

FI and GI
composite
measure

Calculated in perpetuity
Comprehensive

Based on current policy

Correctly indicates impact of
all policies
Easy to communicate

13. Before 1965, Social Security’s
Trustees calculated that
program’s ﬁnancial imbalance
in perpetuity. However, because
Social Security beneﬁts were
not indexed to prices, the
perpetuity estimates incorporated
“level-cost” beneﬁts over time.
Imbalance estimates based
on level costs were not heavily
inﬂuenced by the truncation of the
projection horizon to seventy-ﬁve
years. Indeed, the 1965 Advisory
Council on Social Security
noted that truncation reduced the
projected shortfall by less than
3 percent. Not surprisingly, the
1965 Advisory Council concluded:
“It serves no useful purpose to
present estimates as if they had
validity in perpetuity.” However,
Social Security’s chief actuary at
the time agreed that including all
future years was the appropriate
choice, at least in theory. (See
the Oral History Interview by
Robert Myers available at
http://www.ssa.gov/history/
myersorl.html.) Today, however,
retirement beneﬁts are indexed
for price inﬂation. Moreover,
Social Security beneﬁt formulae
take into account real wage
growth over beneﬁciaries’ working
lifetimes. Therefore, the practical
motivation for truncating the
projection horizon to seventy-ﬁve
years no longer exists. Indeed,
such truncation under-estimates
Social Security’s long-term
imbalance by two-thirds.

FEDERAL RESERVE BANK OF CLEVELAND

benefit formula allows for growth in the real (inflation-adjusted) value of successive retiree cohorts’
benefits, model 2 proposes eliminating such growth. As a result, the purchasing power of Social
Security benefits received by later-retiring cohorts would remain the same (rather than increase)
relative to that of earlier retiring cohorts.
Social Security’s scheduled outlays, therefore, would decrease over time. However, much of the
cost saving from such a change falls outside of the seventy-five-year window and, therefore, is not
captured by the seventy-five-year estimate. Had model 2 been analyzed using the FI and GI measures
suggested here, the commissioners would have had the flexibility to recommend larger personal
accounts.14
A third desirable feature of a fiscal measure is that it be complete—that is, it should encompass
the entire government’s operations. Otherwise, the measures would be subject to manipulation—
“budget arbitrage”—by reshuffling revenues and outlays among programs. This issue has been
particularly important in recent Social Security reform discussions where some plans recommend
using general revenues to shoulder some of the burden of future shortfalls. These transfers are not
indicated by the traditional seventy-five-year measures that focus only on Social Security and Medicare, creating the illusion of free money.
A fourth desirable property is that the measure should be based on current fiscal policy. For a
proposed measure to be useful for policymaking, it must characterize today’s fiscal policy. That is,
it should incorporate projected revenues and outlays based on the continuation of current policy,
revealing how far current policy is from being sustainable.15 The measure should not incorporate
hypothetical policies.16
For example, a Social Security “shutdown” liability measure based on “accrual accounting” is one
potential alternative to the GI measure proposed here.17 Like the GI measure, accrual accounting
attempts to measure the unfunded financial obligations arising because of current and past generations. The accrual concept considers a hypothetical reform in which current participants are
effectively bought out of the Social Security system based on their previous contributions, thereby
allowing Social Security to be shut down. However, many current participants would actually be
better off if they left the Social Security system, because it represents a bad deal for them. Indeed,
they would be willing to pay to leave the system. Hence, accrual accounting overestimates the true
burden imposed by current and past generations associated with the continuation of Social Security
(see Smetters and Walliser, forthcoming). Accrual accounting must also rely on some fairly arbitrary
rules for determining a person’s benefit when he or she has a limited work history. Finally, accrual
accounting deviates from current law by treating past contributions as obligations of the United
States government—that is, as benefits “owed” rather than as a description of scheduled benefits
corresponding to current policy.18 The accrual concept makes sense for a private corporation that
cannot assume that it will be in business in future years and, therefore, cannot include future expected pension contributions into its analysis. The concept appears less appealing for describing
the federal government’s finances.
Fifth, the measure should also correctly reflect the impact of all policy changes. This condition
has two complementary components: First, the measure should not change when policy changes
are actuarially neutral for all generations.That is, if a policy alters future taxes, benefits, or outlays in
a way that leaves all generations’ resources unaffected in present value, the measure should remain
unchanged. Second, it must accurately reflect all actuarially non-neutral policies. As noted in the

14. As we explain in the next section,
the creation of personal accounts
alone does not affect FI or GI
when the new personal accounts
are actuarially fair. However,
the personal accounts in model
2 were constructed to be more
than actuarially fair. The personal
accounts in model 2, therefore,
would cost the government more
resources in present value in the
form of diverted payroll taxes than
they would save the government
in the form of smaller future
outlays, a point emphasized by
Diamond and Orszag (2002). As
a result, the personal accounts
alone would increase Social
Security’s FI. However, taken as
whole, model 2 would substantially reduce Social Security’s
FI and, in particular, could have
accommodated much larger
personal accounts.
15. In some cases—such as discretionary outlays subject to annual
appropriations—it is uncertain
what “current policy” entails for
the long term. For example, under
the Budget Enforcement Act of
1990, discretionary appropriations were temporarily subject
to statutory limits with no clear
principle guiding their evolution
after the limits expired. In such
circumstances, our proposed
measure would adopt a convention consistent with longer-term
historical experience: Long-term
outlay/revenue growth will occur in
tandem with overall economic growth
after such temporary rules expire.
16. An example of a measure based
on such a hypothetical policy
is the concept of generational
balance developed in Auerbach,
Gokhale, and Kotlikoff (1991),
and discussed brieﬂy above. This
measure distributes a component
of the overall ﬁscal burden equally
across all futureborn cohorts. See
the critique by Diamond (1996). Also, see
Liu, Rettenmaier, and Saving (2002).
17. Accrual accounting for Social
Security has been analyzed
by Jackson (2002). See also
the Federal Reserve Board’s
Semiannual Monetary Policy
Report to the Congress Before
the United States Senate
Committee on Banking, Housing,
and Urban Affairs, 11 February 2003.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

previous section, the measure should correctly reflect the size and direction of intergenerational
redistributions engineered via pay-as-you-go policies.19
Finally, the sixth desirable feature is that the measure should be conceptually straightforward
and possess properties that are easy to communicate. One advantage of the FI measure is that,

18. In Flemming v. Nestor 363 U.S. 603
(1960), the Supreme Court made it
clear that Social Security beneﬁts
are subject to the discretion of
policymakers.

under given budget projections, it grows over time at the rate of interest—just like a corpus of debt.
Hence, a change in the measure from one year to the next can be broken down into the amounts
due to accumulated interest, policy changes, differences in economic outcomes relative to projections, and updates to economic assumptions used in making budget projections.The GI measure is
also simple: It equals the amount of FI due to current and past generations. However, other complementary measures could also be used, including ones that describe imbalances by narrowly defined
birth cohorts, gender, race, and so on.

The Bias in Policymaking Arising from Current Budget Accounting
The previous section emphasized that focusing exclusively on backward-looking or short-term fiscal measures—such as publicly held debt—substantially understates the true magnitude of the federal government’s fiscal shortfall.This section discusses the biases that such an understatement can
introduce into policymaking, in particular with regard to our choices among ways of financing programs such as Social Security and Medicare.

19. The desirable features mentioned
here imply that the measure
will be invariant to accounting
conventions adopted in describing
different transactions between the
government and private entities
(Kotlikoff 2001). The FI and GI
measures proposed here are
both invariant to the choice of
accounting labels. For example, if
Social Security taxes and beneﬁts
were relabeled as “borrowing” and
“repayment,” the size of FI for the
entire federal government would
remain unchanged. However,
this labeling change would result
in Social Security’s FI being
reclassiﬁed as a part of debt held
by the public.

Currently, these programs are financed mostly on a pay-as-you-go basis, whereby workers’ payroll taxes are immediately used up to pay retiree benefits. Individual Social Security taxes are not
saved to pay for the contributors’ future benefits.To be sure, Social Security and Medicare both have
trust funds that reflect past payroll tax revenue and other receipts in excess of past benefit payments. But their size is very small in comparison to the programs’ future obligations. Moreover, the
trust funds represent an obligation on the rest-of-federal-government account.20
An alternative system would give individuals the option to invest some of their payroll taxes
in personal accounts that they would own and control. Suppose, in exchange for this option, a
person’s Social Security benefit is reduced one dollar in present value for each payroll tax dollar
that the person is allowed to invest in his or her personal account.The retirement benefits of those
who participate in such a system would consist of reduced traditional Social Security benefits plus
income derived from their personal account assets. But to pay current retiree benefits, the federal government would have to borrow an additional dollar for each dollar invested in a personal
account rather than paid to the government as payroll taxes.This would drive up annual deficits and
public debt. Under traditional accounting, therefore, this reform does not look favorable.
However, the level of publicly held debt is just one component of the government’s true fiscal
imbalance. Another component includes the present value of Social Security’s future scheduled
benefits that are not currently tracked in official federal Budget reports. Under this reform, future
Social Security obligations would decrease by the same amount as the increase in the debt; the
government’s true fiscal imbalance, therefore, would remain unchanged. In other words, current
discussions about Social Security reform start from a biased position, since even a neutral reform
looks bad under the current focus on public debt. Including the present value of future Social Security benefits into the current Budget would remove this bias.
Now suppose, for example, that future Social Security benefits were reduced by a little more
than one dollar for each dollar of payroll that a person invests into a personal account.This example
10

20. Whether previous trust fund
surpluses have reduced the debt
held by the public or produced
higher levels of spending,
however, is an area of active
research. See Schieber and
Shoven (1999), Diamond (2003),
and Smetters (2003).

FEDERAL RESERVE BANK OF CLEVELAND

is very similar to model 1 of the president’s Social Security Commission, where future benefits were
discounted by 50 basis points above the government’s borrowing rate. Many people might choose
this plan in order to have more control over their retirement resources.This reform would increase
publicly held debt over the short term because the government would need to borrow additional
resources to meet current benefit obligations, but the government’s true long-term fiscal imbalance
would actually decline, because the increase in debt would be less than the reduction in present
value of future Social Security benefits. Nonetheless, policymakers would not favor such a plan if
debt were the only measure used for judging the government’s fiscal position.
The traditional focus on publicly held debt, therefore, creates a bias in decision-making against
potential reforms to Social Security and Medicare that could reduce the government’s fiscal imbalance. This bias is especially problematic given the large existing imbalances. A more complete
accounting, which explicitly recognizes the future net obligations of Social Security and Medicare
as well as the rest of the government, would reduce this bias.

Estimates of Federal Fiscal and Generational Imbalances in the United States
This section reports estimates of total Fiscal Imbalance and, where appropriate, the Generational
Imbalance for the federal government under the assumption that the Budget’s policies represent
“current policies.”This so-called policy-inclusive treatment of the federal Budget is consistent with
how the Budget is usually presented. The calculations are based on long-term Budget projections
(through the year 2080) provided by the Office of Management and Budget (OMB) and, naturally, incorporate OMB’s economic assumptions, including a real GDP per capita growth rate of 1.7 percent
per year after ten years (that is, after projected short-run cyclical effects have elapsed).21 We use a
real discount rate of 3.6 percent per year, corresponding to the average yield on thirty-year Treasury
bonds during the past several years.
As demonstrated later, the most important assumption is the future growth rate in real healthcare (Medicare and Medicaid) outlays per capita. Consistent with the Medicare Trustees, our baseline assumes that real health-care outlays per capita will grow at an annual rate that is 1 percentage
point faster than the growth rate in GDP per capita until 2080.22 Between 2080 and 2100, that differential is gradually reduced to zero, so that health-care outlays grow as a share of GDP only because
of population aging after 2100. These assumptions are considerably more conservative relative to
historical experience. Indeed, between 1980 and 2001, health-care expenditures have grown by 2.3
percentage points faster per year than GDP.23
Constructing the GI measures for Social Security and Medicare as well as extending OMB’s projections beyond 2080 required detailed work using micro-data sets. In particular, we constructed
eight age–sex profiles using various micro-data sets corresponding to every tax category (labor, payroll, capital, estate, excise, customs duties, gift taxes, and miscellaneous receipts). Moreover, eighteen
other age–sex profiles were constructed corresponding to each of the major outlay programs that
targets specific population subgroups (Social Security, Medicare, Medicaid, federal civilian retirement, veterans’ benefits, SSI,WIC, etc.). Outlay programs whose benefits are more diffused throughout the population (national defense, justice, international affairs, etc.) were distributed equally
across population in year of spending. This equal distribution does not represent an “allocation
of benefit” to specific generations. Rather, it is an intermediate step used for projecting aggregate
discretionary outlays beyond OMB’s projection horizon of 2080. The projection method assumes

21. This rate of real GDP growth per
capita is obtained by deﬂating
projected nominal GDP per capita
by the projected Consumer Price
Index (CPI) rather than by the
GDP deﬂator. This procedure
implies that all constant dollar
values reﬂect the opportunity cost
in consumption units. In addition,
because the CPI is known to
contain an upward bias, the FI
and GI estimates reported here
are likely to err on the low side.
22. See the Medicare Trustees,
assumptions on the growth in
healthcare outlays, available at
http://www.cms.gov/publications/
trusteesreport/ 2003/tabid1.asp.
23. This calculation is based on
the Centers for Medicare and
Medicaid Services’ estimates of
national health-care expenditures
(see http://www.cms.hhs.gov/
statistics/nhe/historical/t1.asp).
Hefﬂer et al. (2003) provide
a more detailed breakdown
by period. They show that
during 1966–1988, real national
health expenditures grew at an
annual average rate of 6.3 percent,
whereas the chain-weighted GDP
index grew at 5.4 percent—a
difference of 0.9 percent. During
1989–1993, the numbers were
6.3 percent and 3.2 percent,
respectively; and during
1994–2000 they were 3.8 percent
and 1.8 percent, respectively.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

that public goods and services per capita grow at the same rate as GDP per capita beyond 2080—
1.7 percent per year.
These age–sex profiles were then used to decompose the OMB numbers by generation before
2080 and then to extend OMB’s numbers beyond 2080 using demographic projections relevant for
those years.The age–sex profiles also allow us to break down the revenue side of the rest-of-government finances by generation. The profiles must be indexed by age, since the amount and type of
taxes paid vary by age.The profiles must also vary by gender because women are projected to live
longer than men and, therefore, pay different levels of taxes and receive different levels of benefits.
Even though we do not break down our final results by gender, incorporating gender into the underlying calculations improves the accuracy of our estimates. See the appendixes for details.
FI calculations are reported beginning with fiscal-year-end 2002. However, to show the evolution
of FI and GI under current policies and projections, they are recalculated each year through fiscal
year 2008. Present values are calculated using projected interest rates on long-term Treasury securities (also provided by OMB).The appendixes provide detailed descriptions of the methods used in
extending OMB’s Budget projections.

Total Federal Fiscal Imbalance
Table 2 comprehensively documents total federal FI, its sources by program, and its breakdown into
the GI attributable to past and living generations. The first three panels show FI and GI measures
for Social Security, Medicare Part A, and Medicare Part B. In each of these panels, the GI measure is
subdivided into the present value of prospective payments and receipts by living generations and
the trust fund that includes the net contributions from past transactions.The last row in each panel
shows the residual—FI minus GI—which indicates the contribution to FI on account of future generations. Panel 4 of table 2 shows the FI measure for the rest of the federal government—that is, for
non-Social Security and non-Medicare transactions. As mentioned earlier, the GI measure is not calculated for the rest of the federal government because outlays cannot be easily distributed across
generations. Instead, only prospective revenues are subdivided into those that living and future generations are projected to pay under current fiscal policy.
Total FI for the federal government as of fiscal-year-end 2002 equals $44.2 trillion (table 2, last
row). The Social Security program contributes $7 trillion. Medicare contributes $36.6 trillion—the
largest share by far. The rest-of-federal-government’s contribution is relatively small—only $0.5 trillion.Appendix A shows that the total fiscal imbalance grows at the rate of interest if no policy action
is taken to reduce it. This relationship implies that if future projected revenues and outlays remain
unchanged, the imbalance will quickly grow larger over time. By 2008, for example, it will have
grown to $54 trillion.

Social Security
Social Security’s FI of $7 trillion equals the present value of projected Social Security benefits plus
administrative costs minus the present value of projected payroll taxes, federal employer payments,
income taxes on Social Security benefits, and minus the initial balances in the Social Security trust
fund. It is broken down into the GI of $8.8 trillion and the residual, FI minus GI, of minus $1.7 trillion.
Social Security’s imbalance is caused by past and living generations. In particular, as of 2002, past
and living generations are projected to receive $8.8 trillion more in benefits than they will contribute in payroll taxes (using the present value of both benefits and taxes). In contrast, future genera12

FEDERAL RESERVE BANK OF CLEVELAND

tions are projected to pay $1.7 trillion more in taxes than they will receive in benefits. Hence, under
current tax and benefit rules, future generations are projected to reduce Social Security’s imbalance
by $1.7 trillion, but not by enough to restore the Social Security program to a sustainable system in
the presence of the $8.8 trillion liability “overhang” left over from current and past participants. 24
For Social Security to fully return to balance, living and future generations must collectively receive
fewer benefits and/or pay more taxes by $7 trillion in present value. For example, if only future generations were required to carry the full burden of eliminating Social Security’s FI, they would need
to pay an additional $7 trillion in taxes or receive equivalently lower benefits. As another example,
suppose that living generations were required to cover half of Social Security’s imbalance in the
form of lower benefits or higher taxes while future generations were required to cover the remainTABLE 2

FISCAL AND GENERATIONAL IMBALANCES IN SOCIAL SECURITY, MEDICARE, AND THE
REST OF THE FEDERAL GOVERNMENT
(present values in billions of constant 2002 dollars; ﬁscal year-end)
2002

2003

2004

2005

2006

2007

2008

7,022

7,204

7,436

7,692

7,967

8,258

8,569

Imbalance on account of past and living
generations (GI)

8,771

8,943

9,171

9,424

9,694

9,981

10,289

Future net beneﬁts of living generationsa

10,100

10,398

10,762

11,166

11,593

12,043

12,518

Trust fund

−1,329

−1,455

−1,591

−1,742

−1,899

−2,062

−2,230

−1,749

−1,739

−1,736

−1,732

−1,727

−1,723

−1,720

20,497

21,071

21,764

22,513

23,285

24,091

24,939

Imbalance on account of past and living
generations (GI)

8,526

8,867

9,265

9,696

10,136

10,600

11,088

Future net beneﬁts of living generationsa

8,755

9,118

9,537

9,991

10,459

10,949

11,464

1. Fiscal Imbalance (FI) in Social Security

Imbalance on account of future
generationsb,c
2. Fiscal Imbalance (FI) in Medicare Part A

Trust fund

−229

−250

−271

−295

−323

−350

−377

11,972

12,204

12,499

12,817

13,148

13,491

13,851

16,145

16,519

16,978

17,479

18,009

18,562

19,144

Imbalance on account of past and living
generations (GI)

6,633

6,853

7,109

7,392

7,693

8,011

8,343

Future net beneﬁts of living generationsa

6,671

6,881

7,140

7,423

7,728

8,046

8,381

−39

−28

−32

−35

−36

−38

9,513

9,666

9,869

10,087

10,315

10,552

10,801

36,643

37,590

38,742

39,992

41,293

42,653

44,084

550

676

753

864

1,005

1,153

1,310

Imbalance on account of future
generationsb,c
3. Fiscal Imbalance (FI) in Medicare Part B

Trust fund
Imbalance on account of future
generationsb,c
Fiscal Imbalance (FI) in Medicare (Parts
A and B)
4. Fiscal Imbalance (FI) in the rest of the
federal government
Future outlays

80,676

81,701

83,161

84,780

86,503

88,307

90,202

−85,263

−86,552

−88,295

−90,103

−91,985

−93,917

−95,938

Living generations

−32,596

−33,273

−34,141

−34,997

−35,885

−36,781

−37,698

Future generations

−52,667

−53,278

−54,154

−55,106

−56,100

−57,136

−58,240

−4,587

−4,851

−5,134

−5,323

−5,482

−5,609

−5,736

Obligations to Social Security and Medicare
trust funds

1,597

1,734

1,894

2,069

2,256

2,448

2,644

Debt held by the public

3,540

3,793

3,993

4,119

4,231

4,314

4,402

44,214

45,470

46,930

48,548

50,265

52,064

53,962

Future revenues

Excess future outlays over revenues

Total federal Fiscal Imbalance (FI)

24. Geanakoplos, Mitchell, and
Zeldes (1998) show that most
of Social Security’s overhang
stems from past generations
receiving substantially more in
beneﬁts than they paid in taxes. In
particular, under our calculations,
if the amounts of Social Security
beneﬁts received by past and
current generations were equal in
present value to the beneﬁts that
they received and are projected
to receive in the future, the size
of the trust fund would be $10.1
trillion in 2002, thereby reducing
Social Security’s GI to zero. In
this case, we would say that
Social Security was “fully funded.”
The actual value of the trust fund,
however, is only $1.3 trillion.
Most of the $8.7 trillion difference
stems from past generations
receiving more in beneﬁts than
they paid in taxes.

SOURCE: Authors’ calculations.
NOTE: Positive items increase the Fiscal Imbalance.
a. Those born ﬁfteen years ago and earlier. In 2002, for example, this category includes people born before 1988.
b. Those born fourteen years ago and later. In 2002, for example, this category includes people born during 1988 and later.
c. Calculated as FI minus GI.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

der. In that case, the imbalance on account of past and living generations would decline to approximately $5.2 trillion in 2002, while the imbalance on account of future generations would be minus
$5.2 trillion.Thus, some generations must receive less or pay more in order to return Social Security
to sustainability. Regardless of which policy is chosen, creating balance in Social Security (that is, a
zero Social Security FI) requires that the Generational Imbalance (GI) caused by past and current
generations be exactly offset by the imbalance on account of future generations (FI minus GI).

Medicare
Medicare’s FI is $36.6 trillion—more than five times as large as Social Security’s imbalance. This
number reflects the projected faster growth of Medicare outlays per capita, in addition to the
aging of the U.S. population through the next century. The Medicare program has two parts—Part
A (Hospital Insurance) and Part B (Supplementary Medical Insurance). Unlike Medicare Part A,
which is financed out of dedicated payroll taxes, Part B is partially financed out of premiums paid
by those who choose to participate. Premiums cover roughly 25 percent of Part B’s annual outlay.
The remaining 75 percent is financed through transfers from the general fund (rest-of-government
account) to Medicare Part B’s trust fund. The transfers are made several times each year, based on
estimated outlays through the following year. Consistent with the view of the Social Security and
Medicare Trustees, we follow the convention of not counting these transfers as a dedicated resource for Medicare Part B.25 This choice reflects the principle of associating FI with the program
that incurs the outlays. Hence, Medicare Part B’s FI is calculated as the present value of projected
spending minus the present value of projected premium receipts.26 Table 2 shows the breakdown
of Medicare’s FI arising from Parts A and B. It shows that Part A contributes $20.5 trillion, or about
56 percent of Medicare’s total FI. At $16.1 trillion, Medicare Part B’s FI is about 80 percent as large
as that of Medicare Part A.
In sharp contrast to Social Security, a majority of Medicare’s FI arises from future generations (FI
minus GI) rather than from past and current generations (GI). For example, the GI for Medicare Part
A is only $8.5 trillion, whereas the residual (FI minus GI) contributes $12 trillion to Medicare Part
A’s total imbalance of $20.5 trillion. The contributions of past, current, and future generations to
Medicare Part B’s aggregate Fiscal Imbalance show a similar pattern. The reason for future generations’ significantly larger contribution is the rapid projected growth in Medicare outlays per capita
during the next several decades. As with Social Security, some current or future generations must
receive less or pay more for Medicare to become fiscally sustainable.

The Rest of the Federal Government
Table 2 shows that the rest of the federal government’s FI is $550 billion. Under current projections,
the present value of the rest-of-federal-government’s projected receipts exceeds its non–Social
Security and non-Medicare outlays by $4.6 trillion. However, the Treasury securities held by the
Social Security and Medicare trust funds, and counted among those programs’ dedicated resources,
must be entered as a liability on the rest-of-government’s account.This liability plus debt held by the
public exceeds the prospective surplus of rest-of-government receipts over outlays by $0.5 trillion.
Out of the present value of all prospective receipts of $85 trillion, past and living generations are
projected to contribute only $32.6 trillion, or about 37 percent. Future generations contribute the
remainder—$52.7 trillion. OMB revenue estimates include a secular rise in revenues relative to GDP
that could arise from the taxation of withdrawals from assets in tax-deferred savings accounts—as
14

25. For example, see chart E in the
Trustees’ Summary of the 2003
Annual Reports available at http:
//www.ssa.gov/OACT/TRSUM/
trsummary. html.
26. If, alternatively, general
revenue transfers were treated as
dedicated revenue to Part B, they
would appear as an outlay in the
rest of the Budget and, therefore,
have no effect on the federal
government’s total FI. To be sure,
the exact placement of Part B’s
revenue in the table is open to
interpretation. However, we follow
the Social Security and Medicare
Trustees’ lead by not representing
this revenue as “free” to the
Medicare program.

FEDERAL RESERVE BANK OF CLEVELAND

recently claimed by Boskin (2003)—or real bracket creep, or an increase in the number of taxpayers subject to the Alternative Minimum Tax.27
Under the convention adopted here of not counting general revenue financing of Medicare
Part B as a resource dedicated to that program, an overwhelming majority—98.8 percent—of total
federal FI arises from Social Security and Medicare.

27. When asset growth in taxdeferred plans is evaluated on a
risk-adjusted basis, however, tax
deferral costs the government
money.

Evaluating the Size of Federal Fiscal Imbalance
Comparison with Official Estimates
The FI estimate shown in table 2 dwarfs the traditional measure of fiscal indebtedness—debt held
by the public—by more than a factor of ten.The Budget acknowledges the inadequacy of traditional
budget measures as indicators of the government’s long-term financial solvency. For example,
“A traditional balance sheet with its focus on past transactions can only show so much
information. For the government, it is important to anticipate what future budgetary
requirements might flow from future transactions. Even very long-run Budget projections
can be useful in sounding warnings about potential problems despite their uncertainty.
Federal responsibilities extend well beyond the next five or ten years, and problems that
may be small in that time frame can become much larger if allowed to grow.” [Budget]
Nevertheless, the Budget’s summary tables do not include complementary indicators of the
federal government’s fiscal position.28 Rather, the Budget devotes a separate chapter to report
the prospective shortfalls in Social Security and Medicare only. An analysis of these estimates is
presented in the Analytical Perspectives volume of the Budget.These estimates, however, are based
on the economic assumptions of the Social Security and Medicare Trustees, which differ from the
economic assumptions that OMB uses in preparing the forecasts that appear elsewhere in the Bud-

28. These comments also
apply equally to other Budget
reporting agencies such as the
Congressional Budget Ofﬁce,
Joint Tax Committee, and others
that employ short-term reporting
horizons.

get. Moreover, the Social Security and Medicare calculations reported in the Budget are limited to
a projection horizon of seventy-five years and do not include the administration’s own new policy
recommendations, in contrast to the “policy-inclusive” nature of the rest of the Budget. Social Security’s “long-term deficiency” is reported as $3.4 trillion and Medicare’s is $13 trillion. Both estimates
include the programs’ trust funds balances as resources dedicated for those programs. Because of
the truncated projection horizon (and the non-policy-inclusive nature of the Social Security and
Medicare projections), these estimates understate considerably the true magnitude of fiscal imbalance embedded in the Budget’s policies.
More recently, the 2003 Social Security and Medicare Trustees’ report shows seventy-five-year as
well as infinite-horizon shortfall estimates for that program.The Trustees also reported Social Security’s closed-group liability, which is constructed in the same way as the GI concept in this paper.
The Trustees’ seventy-five-year shortfall estimate closely approximates the figures reported in the
Budget.Their infinite horizon estimate is $10.5 trillion—larger than that reported here. We suspect
that this difference is primarily due to the higher discount rate that we use—a rate consistent with
OMB’s projection of interest rates on long-term Treasury debt. Medicare’s Trustees, however, do not
provide an infinite-horizon estimate of Medicare’s fiscal imbalance. The estimate of Medicare’s FI
that we report is almost three times as large as the seventy-five-year number reported in the Budget.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Our estimate, however, also includes the policy proposals contained in the FY 2004 Budget, including the president’s original prescription drug plan.
This paper does not endorse the use of an FI measure calculated over just seventy-five years.
However, for comparison with the estimates in the Budget and in the Trustees’ report (both of
which are based on the Trustees’ economic assumptions and exclude the Budget’s newest policy
proposals), table 3 shows seventy-five-year estimates of FI based on policy-inclusive OMB projections and OMB’s own economic assumptions that it uses in the rest of the Budget. Our estimate of
the seventy-five-year FI for Social Security is only $1.6 trillion, compared to $3.4 trillion that was
reported in the Budget. The difference primarily stems from the higher assumed rate of productivity growth under the OMB assumptions that we use. Higher productivity growth increases payroll
tax receipts over the short and medium term and increases Social Security benefit outlays over the
long term. Also OMB’s long-term real discount rate—3.6 percent per year—is about 60 basis points
higher than that used by the Social Security Trustees.The cumulative effect over a seventy-five-year
projection window is to make our seventy-five-year estimate of Social Security’s FI smaller than that
reported in the Budget.
By contrast, table 3 shows that our seventy-five-year $15.1 trillion estimate of Medicare’s FI (using
OMB assumptions) is larger than the $13 trillion value reported in the Budget. Because of the higher
discount rate under OMB’s assumptions, our estimate would have been much lower than the Budget’s estimate if we had also excluded the Budget’s newest policy proposals.29 However, the impact
of new Medicare proposals in the Budget, including the original prescription drug plan, more than
offset the effect of using a higher discount rate. In general, we conclude that our estimate for Social
Security’s FI is more conservative than official estimates. Medicare’s FI would also be smaller but for
the impact of new Medicare policies proposed in the Budget.

Comparison of FI with Present Values of Payroll, GDP, and Other Aggregates
Another way to assess the magnitude of total federal FI is to compare it to the present value of future
GDP or future payrolls.Table 4 shows that as of the end of fiscal year 2002, total FI equaled 6.5 percent
of the present value of all future GDP and about 16.6 percent of the present value of future capped
payrolls. So, for example, restoring a balanced fiscal policy could, in theory, be accomplished with
an immediate and permanent wage tax increase of 16.6 percentage points. If we instead choose to
eliminate FI by increasing federal income taxes, those revenues would have to be increased by another two-thirds.Alternatively, table 4 shows that future Social Security and Medicare outlays would
have to be permanently lowered by 45 percent or non–Social Security and non-Medicare outlays
would have to be cut by 54.8 percent immediately and forever. Alternatively, eliminating the entire
TABLE 3

SEVENTY-FIVE-YEAR FISCAL IMBALANCES
(Present values in billions of constant 2002 dollars; ﬁscal year-end)

75-year Fiscal Imbalance—U.S. federal government
Social Security
Medicare
Rest of federal government

SOURCE: Authors’ calculations.

2002

2003

2004

2005

2006

2007

2008

16,315

17,101

17,943

18,889

19,900

20,966

22,097

1,596

1,689

1,804

1,932

2,072

2,224

2,389

15,080

15,676

16,631

17,102

17,868

18,672

19,518

–360

–264

–222

–145

–41

190

29. OMB did not provide projections
excluding the administration’s
latest Budget proposals.

FEDERAL RESERVE BANK OF CLEVELAND

federal discretionary budget immediately and permanently would still fall about $1.8 trillion short
of achieving fiscal sustainability. Such tax hikes or spending cuts would obviously be devastating to
the economy. However, the alternative of waiting to make the adjustment is worse:Waiting until just
2008 to introduce corrective policies would require an immediate and permanent wage tax hike
of 18.2 percentage points rather than 16.6 percentage points, or a 73.7 percent increase in income
tax revenues instead of 68.5 percent. If the entire adjustment were made by cutting non–Social
Security and non-Medicare outlays, they would have to be reduced by 59.8 percent in 2008 instead
of 54.8 percent today.

Sensitivity to Alternative Assumptions
Federal revenue and outlay projections—and, hence, the values of FI and GI—obviously depend on
the underlying assumptions. This section reports the sensitivity of FI to variations in three key underlying parameters: the government’s long-term annual discount rate (r); the annual growth rate of
GDP per capita (g); and the differential (h) between the annual growth rate of outlays on Medicare
and Medicaid per capita and g.The differential, h, however, only exists until 2080. Between 2080 and
2100, the annual growth rate of outlays on Medicare and Medicaid per capita is gradually reduced to
g so that the differential, h, becomes zero, where it remains after 2100.As a result, health-care outlays
per capita (distinguished by age and sex) grow no faster than GDP after 2100.These projections of

TABLE 4

TOTAL FISCAL IMBALANCE AS A SHARE OF PRESENT VALUES OF
PAYROLL, GDP, AND VARIOUS OUTLAYS
(Present values in billions of constant 2002 dollars; ﬁscal year-end)

2002

2003

2004

2005

2006

2007

2008

Total Fiscal Imbalance (FI)

44,214

45,470

46,930

48,548

50,265

52,064

53,962

PV payroll base

265,646

272,027

275,398

280,161

285,399

290,918

296,641

16.6

16.7

17.0

17.3

17.6

17.9

18.2

64,564

65,593

66,995

68,474

70,005

71,561

73,181

Total FI as a percent of PV of income
taxes

68.5

69.3

70.1

70.9

71.8

72.8

73.7

PV of payroll taxes plus taxes on Social
Security beneﬁts

47,038

47,655

48,517

49,456

50,451

51,482

52,565

94.0

95.4

96.7

98.2

99.6

101.1

102.7

PV of discretionary outlays

42,458

42,884

43,533

44,260

45,045

45,875

46,752

Total FI as a percent of PV of
discretionary outlays

104.1*

106.0*

107.8*

109.7*

111.6*

113.5*

115.4*

PV of Social Security and Medicare
outlays

97,666

99,675

102,234

105,022

107,959

111,017

114,232

PV of FI as a percent of Social
Security and Medicare outlays

45.3

45.6

45.9

46.2

46.6

46.9

47.2

PV of Non-Social Security and nonMedicare outlays

80,676

81,701

83,161

84,780

86,503

88,307

90,202

54.8

55.7

56.4

57.3

58.1

59.0

59.8

682,156

699,070

708,187

720,896

734,861

749,573

764,811

6.5

6.6

6.7

6.8

6.9

7.1

Total FI as a percent of PV of payroll
PV of income taxes

Total FI as a percent of payroll
taxes plus taxes on Social Security
beneﬁts

Total FI as a percent of non-Social
Security and Non-Medicare outlays
PV of GDP
Total FI as a percent of PV of GDP

SOURCE: Authors’ calculations.
* The number exceeds 100, implying that eliminating all discretionary spending immediately and forever would be sufﬁcient to
achieve a sustainable ﬁscal policy (i.e., FI = 0).

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

entitlement outlay growth cause the share of Medicare and Social Security spending in GDP to rise
from 7.6 percent in 2002 to 13.1 percent by 2080. Under the baseline set of assumptions corresponding to results presented earlier, r=3.6, g=1.7, h =1 percent.We now consider two alternative values—
low and high—for each parameter.The low and high values for r are 3.3 and 3.9 percent; those for g
are 1.2 and 2.2 percent; and those for h are 0.5 and 1.5 percent.30
Table 5 shows that the FI for fiscal-year-end 2002 is quite sensitive to the discount rate assumption: FI is estimated to be $34.6 trillion under the high discount rate assumption (r = 3.9 percent),
whereas it is $58.6 trillion when the assumed discount rate is low (r = 3.3 percent).31 The high
sensitivity of FI to the different values of r is not surprising. Notice, for example, that the baseline
total FI is almost three times larger than the truncated seventy-five-year estimate (see tables 2 and
3), suggesting that annual imbalances are projected to grow considerably beyond the seventy-fifth
year.This high projected growth of annual imbalances in the distant future causes the FI to be very
sensitive to variations in the assumed discount rate.
To understand the sensitivity of FI to the discount rate, consider, for example, two different time
series of annual imbalances. Assume that both series are initially equal in present value at a given
discount rate. By the process of compound interest, a change in the discount rate alters the discount
factor applicable to values further in time by more than those nearer in time. Hence, between these
two time series, the one that exhibits growing annual imbalances will be more sensitive to discount
rate changes than the one that is stable over time. Therefore, the high sensitivity of FI to changes
in the discount rate indicates that projected annual financial shortfalls continue to grow over time.
Hence, the sensitivity of FI only confirms the inappropriateness of using short-term fiscal measures or
measures based on an arbitrarily truncated projection to assess the extent of policy unsustainability.
Turning now to the productivity growth rate assumption, g, table 5 also shows that the total
FI is $55.9 trillion under the high growth rate assumption (g = 2.2 percent). Social Security’s FI
increases from $7 trillion under baseline assumptions to $12 trillion under the high growth rate
assumption.32 Medicare’s FI increases from $36.6 trillion to $66.1 trillion because greater productivity growth also occurs in the Medicare sector (that is, the differential, h, is unchanged). However,
TABLE 5

SENSITIVITY OF FISCAL IMBALANCE (2002) TO DISCOUNT RATE AND
GROWTH ASSUMPTIONS
(Present values in billions of constant 2002 dollars; ﬁscal year-end)

Baseline
assumptions

Total Fiscal Imbalance—U.S.
federal government
Social Security
Medicare
Rest of federal government

Health-care
outlay growth per
capita

High

Low

High

Low

High

Low

34,564

58,608

55,892

36,908

63,930

29,450

7,022

5,025

9,978

11,975

4,933

7,022

36,643

28,910

47,962

66,071

23,194

50,035

26,644

550

629

668

–22,153

8,781

6,874

–4,215

Present value of excess of
outlays over receipts

–4,587

–4,508

–4,470

–27,290

3,644

1,737

–9,352

Liability to Social Security
and Medicare

1,597

Debt held by the public

3,540

SOURCE: Authors’ calculations.

44,214

Discount rate

GDP growth per
capita

30. An increase in g does not
necessarily have the same impact
as an equal decline in r because
higher growth does not necessarily imply higher outlays in every
category. For example, higher
growth is likely to result in lower
social welfare outlays. Hence, we
show below the sensitivity of FI
estimates to variations in r and g
separately.
31. We consider the sensitivity of
each parameter relative to the
baseline set of parameters.
Future work could extend this
analysis by considering
different parameter combinations
together with the probability of
each combination in order to
create a distribution of possible
outcomes.
32. The increase in Social Security’s
FI seems counterintuitive at
ﬁrst glance, because faster
future productivity growth does
not affect the real value of
existing retirees’ beneﬁts. Rather,
payroll tax revenues increase
immediately, but beneﬁts rise only
gradually as faster wage growth
(stemming from the assumed
faster productivity growth) is
incorporated in calculating future
retirees’ beneﬁts. To understand
why Social Security’s FI
increases in value, suppose that
in response to faster productivity growth, the payroll tax base,
payroll tax revenues, and outlays
doubled. The imbalance between
outlays and revenues would
also double. However, if, more
realistically, outlay increases
were delayed by a few years,
the imbalance would increase to
less than twice its original size.
We discuss below how the total
FI changes relative to payroll tax
base and other measures as we
change the underlying economic
assumptions.

FEDERAL RESERVE BANK OF CLEVELAND

for the rest of government, faster productivity growth also brings in more general revenue and
reduces the outlays on Medicaid, unemployment compensation, and various welfare programs.As a
result, the rest-of-federal-government’s FI shifts from $0.5 trillion under the baseline to minus $22.2
trillion. Nevertheless, across all government programs, the net effect of higher productivity is to
increase total FI relative to its value under baseline assumptions.
Conversely, lower assumed productivity growth (g = 1.2 percent) reduces Social Security and
Medicare’s imbalances, but increases the imbalance on account of the rest of the federal government.The resulting total FI is $36.9 trillion, which is smaller than the $44.2 trillion baseline value.
The impact on FI of alternatively assuming higher- and lower-than-baseline growth rates in
federal health-care spending is more substantial. Under the high-h assumption (h = 1.5 percent),
FI is $63.9 trillion, whereas it comes in at just $29.5 trillion under the low-h assumption (h = 0.5
percent).33 Under the high-h assumption, annual health-care costs per capita are assumed to grow
at 1.5 percentage points above the annual GDP per capita growth rate until 2080—an assumption
that is actually quite plausible when compared with experience during the previous two decades
when, as noted earlier, we witnessed an annual differential of 2.3 percentage points. Under the lowh assumption, however, health-care costs are assumed to grow at just 0.5 percentage point above
GDP, an assumption that strikes us as fairly unlikely. In both cases, between 2080 and 2100, the differential is reduced to zero where it stays forever—an assumption that is clearly conservative by
historical standards.

33. Notice that Medicare’s FI is
actually larger under the high-g
assumption relative to the high-h
assumption even though the
assumed growth rate of future
health, g plus h, is identical under
both assumptions. The reason
is that we follow OMB rules and
begin the high-g assumption in
2003 while starting the high-h
assumption in 2014.

The ratio of FI to the present values of payroll and GDP, however, exhibits greater stability than
the present value constant 2002 dollar amounts in response to changes in the various parameter
values because the denominator—the present value of future payrolls or GDP—changes in the
same direction as total FI. In other words, while the dollar value of the Fiscal Imbalance is sensitive
to the underlying assumptions, the size of the tax rate increase or percent decrease in spending
required to achieve sustainability is much less sensitive.
Table 6 shows that under baseline assumptions, the total FI is 16.6 percent of the present value
of the (uncapped) payroll tax base as of fiscal-year-end 2002. Under high and low productivity
growth assumptions, it is 14.8 and 18 percent, respectively. Recall that, as reported earlier, the total
FI is larger in present-value dollar terms under the high productivity growth assumption. In contrast,
it is actually smaller as a share of the present value of future payrolls relative to the baseline. The
reason is that FI grows proportionally less than the payroll base because of larger rest-of-government receipts and smaller outlay growth for some expenditure categories.
Under the high and low health-care growth assumptions, the variation in the ratio of FI to the
present value of payrolls is wider—between 24.1 and 11.1 percent, respectively.This variation is not
so surprising given the 100 basis point difference per year between our high- and low-cost healthTABLE 6

SENSITIVITY OF TOTAL FISCAL IMBALANCE (FISCAL-YEAR-END 2002) AS
A SHARE OF THE PRESENT VALUE OF PAYROLL
Policy
baseline

High

Discount rate

16.6

15.0

18.8

Productivity growth per capita

16.6

14.8

18.0

Health-care outlay growth per capita

16.6

24.1

11.1

Low

SOURCE: Authors’ calculations.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

care growth rate assumptions, which produces a large compounded difference over time. These
numbers show that an immediate and permanent 11.1 percentage point tax increase on all wages is
needed to return U.S. fiscal policy system to sustainability even under very optimistic assumptions
about growth in health-care costs per capita.

Conclusion
The federal government’s spending priorities are set to change over the coming decades as the
baby boom generation retires: future federal outlays will predominantly consist of social insurance
payments. In such a budget environment, traditional measures such as debt held by the public, fiveor ten-year-ahead cash-flow deficit projections, and longer-term but truncated summary measures
have limited usefulness for policymaking. Indeed, continuing to focus on such measures is likely to
sustain a policy bias that favors short-term debt reduction over policies that would be beneficial
in addressing the nation’s true longer-term fiscal imbalance. To evaluate and compare all available
policy alternatives on a neutral footing, we need to introduce new fiscal measures as part of our fiscal vocabulary.
The FI and GI measures proposed here possess several desirable properties. The main effect of
adopting them would be to place the debate on entitlement reform on a neutral basis. These measures would provide policymakers with a powerful tool for analyzing the long-term financial health
of the federal government:The FI measure informs us about the extent of the federal government’s
long-term insolvency, and the GI measure provides a metric for choosing among alternative sustainable policies to strike an acceptable balance between the costs imposed on different generations.
The GI measure could also be augmented with other, more detailed measures of the impact of fiscal
policies across population subgroups.
Based on OMB’s policy-inclusive budget projections, the federal government’s long-term Fiscal
Imbalance is $44.2 trillion as of fiscal-year-end 2002.This is the amount of resources in present value
that the government must produce, either by cutting spending or increasing revenues, in order to
put the nation’s fiscal policies on a sustainable path.This value is more than ten times as large as the
size of debt currently held by the public; it is also several times larger than similar values published
elsewhere under a seventy-five-year projection horizon. To fully eliminate the existing FI, wage
taxes, for example, would have to be increased by 16.6 percentage points forever. Eliminating all
discretionary spending immediately and forever would fall short by $1.8 trillion.
To be sure, the dollar value of the FI is sensitive to underlying growth and discount rate assumptions. But this occurs because of the rapid growth in projected financial shortfalls—which only
reinforces the case for reporting the perpetuity FI measure rather than a truncated seventy-five-year
measure.The ratio of the FI to the tax base or GDP—and, hence, the size of alternative fiscal reforms
to achieve solvency—is much less sensitive to changes in these economic assumptions since the
tax base and GDP tend to respond in the same direction as FI.
We remain optimistic about the potential for further reform in federal Budget accounting. Positive changes have already occurred in the official reporting of the long-term financial status of Social
Security and Medicare: The Social Security Trustees have adopted the FI and GI measures for that
program along with other changes including stochastic analysis.We hope that the Trustees will soon
begin officially reporting these measures for Medicare, and that CBO and OMB will begin reporting
these measures for the rest of the federal government as well.
20

FEDERAL RESERVE BANK OF CLEVELAND

Appendix A:The Fiscal and Generational Imbalance Measures
Derivation of the Infinite Horizon Fiscal Imbalance Measure
The derivations refer to any program with dedicated resources such as Social Security and Medicare. Subtract the actuarial present value of the program’s projected revenues and the inherited
value of the program’s assets from the actuarial present value of projected outlays [see equation 1
in the text]. If present values are calculated in perpetuity, the residual represents the Fiscal Imbalance (FI) measure:
∞

b+∆

(A1) FI0 = Σ

Rt[ Σ (βxb,t – τxb,t )p b,t ] – Γ-1 R-1,
x

b=–∆ t=max(0,b) x=m,f

where βxb,t represents period-t outlays per capita and τxb,t represents period-t taxes per capita on
x

persons of sex x ( = m or f ) born in period b, both in inflation adjusted terms, and p b,t represents
the population in period t of such individuals. The discount factor R equals 1/(1+r), where r is the
per-period real interest rate and Γ-1 denotes the trust fund inherited in period 0 (its value at the end
of period t = –1). The necessary condition for the program to be actuarially solvent in perpetuity
(but not necessarily solvent in each period if trust fund borrowing is prohibited) is FI0 ≤ 0.
How this measure changes over time under given projections of benefits, outlays, and demographics can be seen by decomposing the first term into two parts—the current deficit and the
present value of future deficits. Doing so yields:
0

(A2) FI0 = Σ

(βxb,0 – τxb,0 )p b,0
x

b=−∆ x=m,f

∞

b+∆

+R Σ

Rt-1[ Σ (βxb,t – τxb,t )p b,t ] – Γ−1 R–1.
x

b=–∆+1 t=max(1,b)

x=m,f

Manipulate equation (A2)—add and subtract Γ0 and use the relation
0

(A3) Γ0 = Γ-1 R–1 – Σ

Σ (βxb,0 – τxb,0 )p b,0
x

b=–∆ x=m,f

to get
∞

(A4) FI0 = R

{ Σ

FI1.

b+∆

Rt–1 [ Σ (βxb,t – τxb,t )p b,t ] – Γ-1 R-1}

b=–∆+1 t=max(1,b)

x=m,f

Thus, under given tax and benefit projections, the time series of FI grows at the rate of interest.
If FI0= 0, equation (A4) implies that all terms in the FIt time series equal 0. Hence, this measure
exhibits a knife-edge characteristic: Absent changes in projections and policy, if the government
program being considered is just actuarially solvent initially, it stays so through time. However, if FI
is non-zero initially, the imbalance grows larger over time at a rate equal to the rate of interest.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Generational Imbalance (GI)
The right-hand-side of equation (A1) can be broken down in another way—according to cohortspecific present values of benefits net of payroll taxes. This is done by distinguishing between the
cohort of those alive today (which includes those born ∆ periods ago through period-0 newborns)
and the cohort of past generations (those no longer alive). The inherited assets of the program encompass the excess of past payments by both groups.This measure is calculated as the present value of benefits received by those currently alive minus the present value of their taxes and minus
the inherited trust fund:
b+∆

(A5)

FI0 = { Σ

Σ Rt [ Σ (βxb,t – τxb,t )p b,t] – Γ-1 R-1}
x

b=−∆ t=0

x=m,f

∞

b+∆

b=1

t=b

+ Σ

Σ Rt [ Σ (βxb,t – τxb,t )p b,t],
x

x=m,f

where the term in curly brackets is GI0. Expanding this term into current flows and the present value of future flows, and expanding the second term into the present values of benefits minus taxes
of those born in period 1 and those born in periods 2 and later, we get,
0

(A6)

FI0 = Σ

b=–∆

(βxb,0 – τxb,0 )p b,0
x

x=m,f

b+∆

+R Σ

Σ Rt-1[ Σ (βxb,t – τxb,t )p b,t] – Γ-1 R-1
x

b=–∆+1 t=1

x=m,f

1+∆

+ R Σ Rt-1 [ Σ (βx1,t – τx1,t )px1,t]
x=m,f

t=1

∞

b+∆

+Σ

Σ Rt [ Σ (βxb,t – τxb,t )p b,t].
x

b=2 t=b

x=m,f

Manipulate equation (A6) as earlier [add and subtract Γ0 and use equation (A3)] to get

b+∆

FI0 = R { Σ

(A7)

Σ Rt–1 [ Σ (βxb,t – τxb,t )p b,t ] – Γ0 R–1}
x

b=–∆+1 t=1

x=m,f

∞ b+∆

+ R Σ Σ Rt-1 [ Σ (βxb,t – τxb,t )p b,t].
x

b=2 t=b

x=m,f

Hence, the relationship between the GI terms [the terms in curly brackets in equations (A5) and
(A7)] can be expressed as

(A8) GI0 = R

1+∆

GI1 – R Σ Rt–1 [ Σ (βx1,t – τx1,t )p 1,t ].
t=1

x=m,f

Rearranging,
(A9) R

GI1 – GI0 = R

NT1

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or
(A9a)

NT1 = GI1 – (GI0 / R),
b+∆

where NTb stands for Σ Rt-b[ Σ (βxb,t – τxb,t )p b,t ]—the net transfer to the cohort born in period
x

t=b

x=m,f

b. Equation (A9) says that the difference between GI0 and the discounted value of GI1 is equal to
the discounted net transfer to the generation born in period 1. Rewriting equation (A9) after shifting the time index ahead by one period yields
(A10)

GI2 – GI1 = R

NT2 .

Hence, it is easy to deduce that
(A11)

GIn – GI0 = Σ Rs
s=1

NTs .

In general, the difference between appropriately discounted GI measures equals the total net transfer to cohorts born in the intervening time periods.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Appendix B: Assumptions and Methods for Estimating Fiscal Imbalances for
Social Security, Medicare, and the Rest of the Federal Budget
The assumptions and methods used to estimate the measures of fiscal imbalance presented in this
paper were first developed in connection with generational accounting. They have been updated
and integrated with OMB’s budget projections to compute the fiscal imbalance measures reported
here. The techniques described below are used to estimate how federal program benefits are distributed and, for the period beyond OMB’s projection horizon, to project the growth of total federal
outlays and receipts.

Method of Extending the Social Security Administration’s Population Projections
Population projections are extended beyond the last year for which the Social Security Administration (SSA) provides projections (the year 2080). SSA’s terminal-year fertility, immigration, and mortality assumptions are used.The following method is employed in extending the projections:
First, the population of newborns for 2081 is obtained by applying the terminal-year female
fertility rates by age to the population of females in 2080. The resulting births are split into male
and female newborns applying the historical norm of male births to total births. This ratio equals
0.5122. Next, the 2080 population of individuals aged 0 year through 99 years is aged by one year
to obtain the 2081 population aged 1 through 99 and the addition to the 100-and-older population.
This process involves applying age-sex mortality rates and immigration counts to the 2080 population. The SSA procedure assumes that immigration remains constant in absolute terms after about
two decades.
The survival probabilities, mortality rates and immigration counts through 2080 are those under
SSA’s intermediate assumptions. Mortality rates for years after 2080 are estimated using SSA’s projection methodology. This methodology adjusts each future year’s mortality rates by age and sex
according to a cause-of-death-specific rate of decline in the death rate weighted by the number of
deaths by cause of death. The annual decline in mortality rates by cause of death is assumed to be
constant.
Finally, the evolution of the age 100-plus population is estimated.The survival rate for “100-yearolds” is computed as follows: The “100-year-old” population is the sum of those aged 100 and more.
As a first approximation, it is assumed their population is divided between ages 100 through 119,
in the same proportion as their cumulative survival probabilities to particular ages within that interval conditional on having survived to age 100. The fraction of 100-year-olds that survive equals
1 minus the product of their population proportions between age 101 and 119 and mortality rates
applicable at these ages. The procedure detailed here is applied repeatedly to derive each successive year’s population projection beyond 2080—for as long as needed. A more precise description
of this procedure is given in appendix C.

Method for Projecting Social Security Revenues and Benefits
Social Security’s payroll tax revenues are distributed by age and sex using age-sex relative profiles of
payroll tax payments obtained from the CPS (March 2001). The profile is constructed after imposing a taxable earnings limit on survey respondent’s wages, salaries, and self-employment earnings.
These age sex profiles are used to distribute OMB’s projected payroll tax revenues plus revenue

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from taxation of benefits as separate age-sex profiles are not available to distribute these two categories of revenue separately. For years beyond OMB’s terminal projection year, per-capita payroll tax
payments are incremented at the rate of GDP growth per capita—1.7 percent per year.
Social Security benefit rules in effect today are not static. Current rules schedule a gradual increase in the normal or full retirement age (FRA) beginning in 2003 that has already begun to affect
the benefits of some individuals who have decided to retire and collect benefits early. The already
scheduled increases in FRA will not be completed until the third decade of this century. Because of
the scheduled increase in FRA, the latest available age-sex Social Security benefit profile cannot be
applied to distribute projected Social Security benefits during the next few decades.The profile applicable to the year 2000 must be adjusted to take into account the projected reduction in benefits
of those who begin to collect benefits prior to attaining their applicable FRA.A detailed adjustment
procedure is developed to estimate changes in age-sex profile for future years.The adjustment procedure uses data published by the Social Security Administration in its Annual Statistical Supplement
to the Social Security Bulletin. That publication reports the number or retirees by age and sex and
the average benefits received by age and sex for several different types of Social Security benefits.
Data from years 2000 and 2001 is used to estimate the fraction of new retiree, widow(er), and
dependent beneficiaries at each age and by sex—the types of benefits that are subject to reduction
for collection at ages earlier than the applicable FRA. New beneficiaries at each age and sex are
calculated as the number of beneficiaries in the second year minus those in the same beneficiary
cohort in the previous year (who are one year younger) and minus those among the same cohort
who have died within the year.
In addition, data from 2001 is used to estimate age-sex profiles of average retirement, widow(er)
and dependent benefits relative to other benefits—those not subject to reduction for early collection (such as mother and father benefits and benefits for dependents who care for children etc.).
In addition the fraction of the population at each age and sex who collected benefits in 2001 has
been calculated. These frequencies of benefit collection, fraction of new beneficiaries, and average
benefits at each age and sex are combined with Social Security’s benefit reduction formulae for
early collection of retirement, widower, and dependents’ benefits to estimate the changes in age-sex
profiles in each successive year.The calculations indicate that the transition from the currently prevailing relative benefit profile to those that will prevail once the higher FRA has been fully phased
in (by 2023) will be completed within a few decades thereafter. Hence, the procedure to adjust
relative profiles for increasing FRA is carried forward until the year 2080. Appendix D documents
the precise adjustment procedure for each type of benefit that is subject to an early retirement
reduction.
All the benefit data are from 2000 and 2001. Estimating the relative decline in benefits at all ages
and by sex in future years does not yield the per capita benefit levels at each age and sex in those
future years. Each future year’s age-sex Social Security benefit profile is derived from data from 2000
and 2001 and is normalized by dividing every value by that applicable to a forty-year-old male in
that year.This yields the desired relative profiles of benefits by age and sex.To calculate benefits per
capita, these relative profiles are used to distribute the projected Social Security benefits applicable
to corresponding years in the future.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Take, for example, the calculation of per capita benefits for 2030. The sum over the product of
year 2030’s projected population and relative profile values by age and sex yields the number of
units into which 2030’s projected aggregate benefit must be divided to yield the per-capita benefit
of a forty-year-old male. The product of this per-capita value with other age-sex relative benefit values yields the per-capita benefits at those age sex values for 2030. This calculation is implemented
for each year for which OMB projections are available to obtain benefits per capita at each age and
sex in these years.
The profile of benefits per-capita by age and sex calculated for OMB’s terminal projection year
is multiplied by a growth factor to obtain successive years’ benefit levels. The growth rate applied
equals 1.7 percent—OMB’s real GDP growth per capita in the terminal year. This procedure is detailed in appendix E.

Methodology for Projecting Medicare Revenues and Outlays
Medicare Part A revenues are distributed by age and sex according to relative wages by age and
sex.Average wages by age and sex are estimated from the Current Population Survey’s (CPS) March
2001 supplement that contains data for the year 2000. Relative wage profiles by age and sex are
obtained by normalizing average wages by age and sex to those of forty-year-old males.The relative
profile for distributing Medicare Part B premiums is the distribution by age and sex of Medicare benefit recipiency relative to the total population by age and sex—also estimated from the CPS.
The relative profile of Medicare (Parts A and B) outlays is constructed using SSA’s population
projections and coefficients of relative Medicare expenditures in Lee, Skinner, and McClellan (1999).
Lee, Skinner, and McClellan provide estimates of Medicare benefits received by age and sex. Separate estimates are provided for those who survive for at least one year after the current year (“survivors”) and on those who die within the year (“decedents”).The profiles of benefits by age and sex
normalized to those of a sixty-five-year-old male survivor are constructed from these data.
Medicare Part A and B outlays for those aged sixty-five and older are modeled as the sum of
average outlays times the number of individuals in the two survivorship categories mentioned
above: SSA’s population projections are used to determine the number of individuals in these two
categories at all ages and for both sexes in every future year. Projected Medicare expenditures on
the elderly through OMB’s terminal projection year are distributed across their populations in these
years using the aforementioned relative benefit profiles.
For those aged sixty-four and younger (mostly disabled individuals and eligible survivors), benefits per capita are calculated by distributing their share of Medicare outlays according to their relative benefit profiles by age and sex. These average benefits by age and sex are also obtained from
Lee, McClellan, and Skinner (1999).
The shares of Medicare expenditures on the young and the elderly are obtained by applying to
projected total Medicare outlays the projected share of expenditures on those aged sixty-four and
younger. This share is provided by the Congressional Budget Office (CBO) through 2070 and is extrapolated through 2080 according to its trend between 2061 and 2070.
For years beyond OMB’s terminal projection year, the terminal year’s per capita benefits are extended by applying two growth factors.The first factor equals an assumed growth rate of per-capita
Medicare benefits at a rate equal to the rate of labor productivity growth—1.7 percent per year.

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The second factor is designed to capture the impact of projected mortality—specifically, changes
through time in the number of retirees by age and sex that are projected to die within one year
relative to those projected to survive for more than a year.The precise details of the procedure are
documented in appendix F.

Estimating Fiscal Imbalance for the Rest of the Federal Government
The fiscal imbalance measure for the “rest of federal government” used OMB projections extended
beyond their terminal year using the procedure described below.
Distributing and Projecting Federal Outlays

For those years where outlay projections are available, outlays are distributed by age and sex across
the populations alive in corresponding years.The SSA’s extended population projections are used in
doing so (see the section describing the method for extending SSA’s population projections).
The method for distributing federal outlays distinguishes between two types: Outlays that are
not intended to benefit a specific subset of the population and those that are. The first category
includes items such as national defense, the administration of justice, international affairs, etc. Such
items are distributed equally across the entire population in corresponding years for which aggregate projections are available.
Yet other federal outlays provide direct payments to individuals—by way of income support,
educational subsidies, child-care benefits, health and retirement benefits, etc. These outlays are distributed by age and sex according to age-sex relative profiles constructed from micro-data sources
that are publicly available—such as Survey of Income and Program Participation, the Current
Population Survey, the Panel Survey of Income Dynamics, etc. Outlay aggregates distributed in this
manner include federal civilian retirement, federal employee life insurance, railroad retirement, veterans’ benefits, D.C. pension fund, supplemental security income, workers’ compensation, military
retirement, unemployment compensation, general assistance, Women, Infants and Children, food
stamps, Medicaid, child care, coal miners’ benefits, earned income credit, and child tax credit outlays.
Federal outlay aggregates by category are distributed by age and sex for years 2003-80—the years
for which projected aggregate outlays are available. Beyond 2080, outlays per capita by age and sex
are projected by applying a per-capita growth rate to each age-sex value and summed across the
projected populations for future years.
Distributing and Projecting Federal Revenues

The method for distributing federal revenue aggregates is similar to that of distributing federal outlays. OMB projections are used through the terminal year of those projections. The projections are
extended beyond that year using the following procedures. In general, age-sex relative profiles are
estimated from micro-data surveys (the Current Population Survey, the Survey of Consumer Finances, and the Consumer Expenditure Survey). In each case, weighted averages are calculated for each
item and the age-sex profiles are smoothed using age-centered moving averages.
Relative profiles and population projections are used to distribute OMB’s projected revenue aggregates. Beyond the terminal year of those projections, tax payments per capita are obtained by applying a per-capita growth factor to the OMB terminal year per capita amounts and summed across
age and sex after weighting with the corresponding year’s population for each age-sex category.

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Through OMB’s terminal projection year, total income taxes are divided between those falling
on labor income and those on capital income.The division is done according to the estimated share
of labor income in net national income averaged over the years 1990-2001. Labor income taxes are
distributed using the age-sex wage profile obtained from the CPS for the year 2001, and modified
by the age-sex relative profile of average tax rates, also estimated from the CPS. Similarly the sum
of capital income taxes and corporate taxes is distributed according to a relative profile of wealth
holdings by age and sex estimated from the Survey of Consumer Finances.The wealth profile is also
modified by the CPS-derived relative profile of average tax-rates by age and sex.
Social insurance contributions on account of railroad retirement and federal civilian retirement
are distributed using age-sex relative profiles estimated from the CPS. Employer-paid unemployment
insurance taxes are distributed according to the CPS relative wage profile. Excise taxes and customs
duties are distributed according to the relative age-sex distribution of consumption estimated from
the Consumer Expenditure Survey (see next section for a description).
Estate and gift taxes are distributed by age and sex according to the SCF wealth profile modified by the probability of death by age and sex in each future year. Age and sex specific projected
mortality rates are used for each future year to implement the modification. This modification of
wealth holdings by age and sex yields the relative age-sex profile of decedent’s wealth. Finally, the
category of ‘miscellaneous receipts’ is distributed equally across the population through OMB’s
terminal projection year.
Estimating Consumption Proﬁles by Age and Sex

The Consumer Expenditure Survey consists of two components, a quarterly Interview Survey and a
weekly Diary Survey, each with its own questionnaire and sample. For the most part, these two surveys cover different expenditure items, but there is some overlap. An internal procedure provided
by the Bureau of Labor Statistics is used to generate a unique list of expenditures.This procedure is
adjusted to allocate expenditure items between male and female household members, and between
adults and children defined as members aged sixteen through eighteen. Because these profiles are
to be used to distribute excise and customs taxes, no expenditures are allocated to children aged
fifteen or younger.

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Appendix C: Methodology for Extending SSA’s Population Projections
Population Projections
Population projections are extended beyond SSA’s projection horizon (the year 2080) using SSA’s
terminal-year fertility, immigration, and mortality assumptions. The following methodology is used
to extend the projections.
x

Let p b,t stand for the year-t population of individuals of sex x (= m, f) born in period b (b =
x

t,…t−100).Values of p b,t , t=2002…2080, are provided by SSA. Each year’s value of p b,t for “100-yearolds” (b = t−100) includes the population of those who are aged 100 or more.
To extend the population projections to t = 2081, we first obtain the population of newborns.
This is done by applying the terminal-year female age-specific fertility rates fa to the population of
f

females, pb,2080 , b = 0…100. The resulting births are split into male and female newborns applying
m
t,t

the historical norm of male newborns to total newborns α = p

m
t,t

/( p

+ pt,t ) = 0.5122.This yields

the populations of newborn males and females in 2081:
(C1)

m
2081,2081

·Σ

2080

= α

pb,2080

f2080-b

b=1980

and
(C2)

p 2081,2081 = (1 — α)

·Σ

2080

f2080-b

b=1980

pb,2080 .

Next, the 2081 population of individuals older than newborns is obtained by applying mortality
rates by age and sex, δxa,t, a = 0,...100; x = m,f and SSA’s terminal immigration rates by age and sex,
βxa, a = 0,...100, to the previous year’s population.Thus,
(C3)

p b,2081 = (1 + βx

)

2080-b

(1 + δx

2080-b,2081

)

p b,2080,

x = m, f; b = 1981,…2080.
The mortality rates δxa,t, a = 0,...100; x = m,f for t > 2080 are projected using SSA’s mortality rates
by age, sex, and cause of death. Mortality rates are assumed to decline at SSA’s cause-of-death-specific
annual rates of decline by age and sex.
The survival rate for “100-year-olds” is computed as follows: The “100-year-old” population is the
sum of those aged 100 and more. As a first approximation, it is assumed their population is divided
between ages 100 through 119, in the same proportion as their cumulative survival probabilities to
particular ages within that interval conditional on having survived to age 100. Hence, it is assumed
that there are 1/S 100-year-olds, (1−δ100)/S 101-year-olds, (1−δ100)* (1−δ101)/S 102-year-olds, etc.,
where S is the sum of terms 1, (1−δ100), (1−δ100) (1−δ101), …etc. The fraction of 100-year-olds that
survive is, of course, (1−δ100). Hence (1−δ100)/S 100-year-olds survive; (1−δ100) (1−δ101)/S 101-yearolds survive;…etc. Hence the survival probability of the “100-year-old” group is the sum of such
terms:

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NUMBER 5, DECEMBER 2003

119

(C4)

a=100

π (1−δs)

s=100
119

1+ Σ

π (1−δs )

a=100 s=100

The values of δxa, a = 0,…100 are taken from SSA’s sex-specific mortality table for 2080.
This procedure [equations (C1) through (C4)] is applied successively to generate population
projections through the year 3500.

Assumptions and Definitions
Fertility.Terminal-year female fertility by age is assumed to remain constant. Newborns are split by
sex using the rule of 105 males per 205 births.
Immigration: Levels of legal and illegal immigration are assumed to remain constant.
Mortality:Weighted average of SSA’s terminal year mortality rates by cause of death. Mortality rates
are assumed to decline at SSA’s terminal constant annual rates of decline by cause of death.

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Appendix D: Methodology for Projecting
Social Security Age-Sex Benefit Profiles
Current Social Security benefit eligibility rules specify prospective increases in the full retirement
age (FRA)—the age of eligibility to unreduced benefits.This implies that age-sex benefit profiles derived from past data on the distribution of benefits per capita are not appropriate for distributing
future projected benefit outlays by age and sex. This appendix describes the adjustments made to
retirement, widow(er) and dependent benefit profiles based on the Social Security Administration’s
published data on average benefits and number of beneficiaries for 1999 and 2000.

Additional Widow(er) Reductions at Ages 60–61 to Adjust Profiles for Advancing FRA
βa,t =

Ba,t = βwa,t pwa,t + β0a,t p0a,t
Pa,t

Pa,t

βa,t = Social Security benefits per capita for people aged a in period t

Ba,t = total Social Security benefits for people aged a in period t

Pa,t = total population of beneficiaries aged a in period t

βwa,t = average widow(er) benefits for beneficiaries aged a in period t

β0a,t = average “other” [non-widow(er)] benefits for beneficiaries aged a in period t

pwa,t = population of widow(er) beneficiaries aged a in period t

p0a,t = population of “other” beneficiaries aged a in period t
The Annual Statistical Supplement (ASS) contains data on benefits by type of benefit, age, and sex.
Using data for t−1 = 1999 and t = 2000, compute widow(er) benefits for new beneficiaries aged a
in period t, βw,a,Nt , as

βw,a,Nt =

βwa,t pwa,t – βwa-1,t-1 pwa-1,t-1 (1–δa,t-1 )
pwa,t – pwa,t-1 (1 – δa,t-1 )

Here, δa,t refers to the mortality probability of those aged a in period t. ASS includes information
for calculating average (across beneficiaries) of other [non-widow(er)] benefits, β0a,t . This provides
N
the ratio βw,a,Nt / β0a,t = bw,
a ; a = 60, 61. Using data on the population of beneficiaries by benefit–type,

age, sex, and SSA-provided data on total population in t–1 and t,

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NUMBER 5, DECEMBER 2003

Compute ratios
pwa,t / Pa,t = πwa and p0a,t / Pa,t = π0a for a = 60, 61
Compute

ηwa = Min{0, [pwa,t – pwa-1,t-1 (1 – δa,t-1)]/ pwa,t }—the fraction of widow(er) beneficiaries that are
new, for a = 60, 61

For t > 2000 and a = 60, 61
1.

Obtain the profile for other benefits in t = 2001 by growing the t = 2000 benefits: The growth
factor used equals SSA’s real-wage growth assumption: β0a,t = β0a,t-1 (1 + γ).

Use the ratio bw,a,Nt defined above to obtain βw,a,Nt —average widow(er) benefits that would
have resulted in the absence of the scheduled additional early widower reduction at age a for
new widow(er)s at that age.

The average (real) benefits of those who are already receiving widower benefits and those
receiving other benefits are assumed to remain at the previous year’s level.

Average benefits per capita in t = 2001 are given by

βa,t =

βwa-1,t-1 (1 – ηwa )πwa Pa,t + β0a,t bw,aN θwa ηwa πwa Pa,t
Pa,t

β0a,t π0a Pa,t
Pa,t

= βwa-1,t-1 (1 – ηwa )πwa + β0a,t

[bw,aN θwa ηwa πwa + π0a ].

Here, the first term represents widower benefits at age a for those who received such benefits
prior to year t. Of course, at a = 60 this term is zero because ηwa =1. The second term imputes reduced widow(er) benefits for those who begin claiming such benefits in year t. In this term, the
factor is θwa is the additional widow(er) reduction to be imposed on new beneficiaries because
of advancing FRA.This factor is computed as the ratio of a) the widow(er) reduction including additional months of early benefit receipts to b) the reduction excluding additional early months of
benefit receipt. For example, let U be the unreduced benefit α and a the original reduction factor
for early claimants. Then, the reduced benefit in the absence of advancing FRA would be Uα (estimated as β0a,t

bw,aN in the second term above). If δ (<α) represents the new reduction factor

(including additional months of early benefit receipt because of advancing FRA), the new reduced
benefit is Uδ. To get the latter from the former we compute Uδ = Uα×(δ/α) = Uαθ.
Widow(er) Benefit Reduction at age a is computed as product of the monthly reduction
amount times the number of months prior to FRA that widow(er) benefit will be collected—age a
through FRA. The monthly reduction amount equals 28.5 percent divided by the number of possible months of early retirement—from age sixty through FRA.

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Retirement Benefit Reduction at age a equals 0.0056 percent times the number of months prior
to FRA.
Husband’s and Wife’s Benefit Reduction at age a equals 0.0069 percent times the number of
months prior to FRA.
Finally, retain the value βwa,t = πwa [βwa-1,t-1 (1 – ηwa ) + β0a,t bw,aN θwa ηwa ] for the next period’s calculations.

Additional OASI Benefit Reductions—Ages 62–66 to Adjust Profiles for Advancing FRA
βa,t =

r pr + βs ps + βw pw + β0 p0
βwa,t = βa,t
a,t
a,t a,t
a,t
a,t
a,t a,t

pa,t

r = average retirement benefits per capita for people aged a in period t
βa,t

s = average husbands/wives benefits per capita for people aged a in period t
βa,t

βwa,t = average widow(er) benefits per capita for people aged a in period t

β0a,t = average other [non-retirees, non-spouses, non-widow(er)s] benefits per capita for people aged a in period t

r = population of those receiving retirement benefit aged a in period t
pa,t

s = population of those receiving husbands/wives benefit recipients aged a in period t
pa,t

pwa,t = population of those receiving widow(er) benefits aged a in period t

p0a,t= population of those receiving other [non-retirees, non-spousal, non-widow(er)] benefits
aged a in period t
Set t = 2000
Use benefits by type, age, and sex to compute ratios bar,N , bas,N , and bw,aN for ages a = 62, 100 in the
manner described above.
Again, using ASS beneficiary data and SSA’s population projections compute
•

ratios πar , πas , and πwa for a = 62, 100

•

ηar , ηas , and ηwa —fractions of new beneficiaries at a = 62, 100 (as defined earlier).
For t > 2000 and a = 62...100

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Obtain the profile for other benefits in t = 2001 by growing the t = 2000 benefits: The growth
factor used equals SSA’s real-wage growth assumption: β0a,t = β0a,t-1 (1 – γ).

r, N , βs, N , and βw, N , respecUse the ratios bar,N , bas,N , and bw,aN defined above to obtain βa,
t
a, t
a, t

tively—average benefits for new beneficiaries that would have resulted in the absence of the
scheduled additional early retiree, spousal, and widow(er) reductions at age sixty-two.
3.

Average benefits per capita in 2001 are given by

βa,t =

r
βa-1,t-1
(1 – ηar )πar Pa,t + β0a,t bar,N θar ηar πar Pa,t

Pa,t

s
+ βa-1,t-1
(1 – ηas )πas Pa,t + β0a,t bas,N θas ηas πas Pa,t

Pa,t
+ βwa-1,t-1(1 – ηwa )πwa Pa,t + β0a,t bw,aN θwa ηwa πwaPa,t
Pa,t
+ β0a,t π0aPa,t
Pa,t
r
s
= βa-1,t-1
(1 – ηar )πar + βa-1,t-1
(1 – ηas ) πas

+βwa-1,t-1(1 – ηwa )πwa + β0a,t

[bar,N θar ηar πar ]

+ [bas,N θas ηas πas + bw,aN θwa ηwa πwa + π0a ].
Here, θar , θas , and θwa are additional retiree, spousal, and widow(er) reductions, respectively, imposed because of advancing FRA. See earlier discussion for details.
In each period and for each age, average benefits by type are calculated and stored for carrying
forward into the next period’s calculations:
r = πr [βr
r
0
r,N r r
βa,t
a a-1,t-1(1 – ηa ) + β a,t ba θa ηa ]

s = πs [βs
s
0
s,N s s
βa,t
a a-1,t-1(1 – ηa ) + β a,t ba θa ηa ]

βwa,t = πwa [βwa-1,t-1(1 – ηwa ) + β0a,t bw,aN θwa ηwa ].

FEDERAL RESERVE BANK OF CLEVELAND

Appendix E: Calculating and Projecting Social Security Taxes and
Benefits per Capita
Let ρxb,t stand for the average amount of Social Security benefits received in period t by persons of
sex x born in period b relative to the average benefit received by forty-year-old males in period t (for
whom b = −40).That is, ρxb,t , b = −∆,…0; x = (m,f), is the relative profile of Social Security benefits
for those alive in period t. Similarly, let λxb,t , b = −∆,…0; x = (m,f), represent the relative profile of
payroll (OASDI) taxes. The values of ρxb,t are calculated from data on average benefits and number
of recipients for each type of OASDI benefit by age and sex reported in the Annual Statistical Supplement for year 2000 published by the Social Security Administration. Values of λxb,t are obtained
from the Current Population Survey for the latest available year 2001—containing data pertaining
to the year 2000.
Let Bt represent the total amount of Social Security outlays in the base year (t = 2002). The average benefit paid to male forty-year-olds equals
(E1) βm-40,t =

Σ ρxb,t pxb,t

b=–∆ x=m,f

Finally average Social Security benefits by age and sex in year t are calculated as

(E2) Bxb,t = βm-40,t

·ρ

x
b,t

b = −∆,…0, x = (m,f).

An analogous procedure is used to calculate λxb,t , b = −∆,…0, x = (m,f).
The relative profiles of Social Security benefits and payroll taxes are used to obtain per-capita
benefits and taxes using this procedure for each year in Social Security’s projection horizon of
seventy-five years. The base-year relative profile for payroll taxes is used for each year. The relative
profile of Social Security benefits is adjusted, however, to account for the scheduled increase in the
full retirement age (FRA) over the next two decades. The method for adjusting each year’s relative
Social Security profile is detailed in appendix C.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

Appendix F: Derivation of Age-Sex Profiles for
Medicare Revenues and Outlays
The relative age-sex profile of Medicare Part A revenues is the same as that used for OASDI revenues
in the base year—the taxable-ceiling-limited wage profile by age and sex normalized to its value for
forty-year-old males. This profile was estimated from the Current Population Survey (March 2001)
supplement containing data on wages and salaries for the year 2000.
The relative profile of Medicare Part A outlays is constructed using SSA’s population projections
and coefficients of relative Medicare expenditures in Lee, Skinner, and McClellan (1999). Lee, Skinner, and McClellan provide estimates by age and sex of Medicare outlays on those who survive for
at least one year after the current year (“survivors”) and on those who die within the year (“decedents”).The profiles of outlays by age and sex relative to outlays on a sixty-five-year-old male survivors constructed from these data is shown in table F1. In the following description, these relative
values are denoted by εxa, where a denotes age (a=65,…100) and x denotes sex (x = m, f).
For people aged a of sex x alive in year t, total Medicare Part A (HI) outlays are modeled as the
sum of average outlays, mxa,t,c, times the number of individuals, pxa,t,c, in two survivorship categories,
c: Those who will survive for at least one more year and those who will not.
Let the year-t populations of those aged a and of sex x belonging to the two survivorship categories be denoted by pxa,t,1+ and pxa,t,0, respectively. Using SSA’s population projections (and abstracting from complications introduced by immigration) one can determine the number of individuals
in the two categories at all ages for both sexes in future years t:
(F1) pxa,t,1+ = pxa,t+1
pxa,t,0 =

pxa,t –

pxa,t,1+

}

for a = 65,…98; x = m, f

For the populations aged ninety-nine and one hundred in all future years, it is assumed that the ratio of survivors to decedents equals that calculated for age ninety-eight. As mentioned earlier, total
Medicare Part A expenditures on people aged a and of sex x in year t, Mxa,t , can be expressed as:
(F2) Mxa,t = mxa,t,1+ pxa,t,1+ + mxa,t,0 pxa,t,0.

TABLE F1 RELATIVE PROFILES OF ANNUAL MEDICARE OUTLAYS FOR SURVIVORS BEYOND
ONE YEAR AND DECEDENTS WITHIN ONE YEAR

Age

Male
survivors

Female
survivors

Male
decedents

Female
decedents

65–69

1.0000

0.9092

6.2971

7.4775

70–74

1.2902

1.1761

6.3186

7.3520

75–79

1.5740

1.4552

6.3009

6.5755

80–84

1.8552

1.7495

5.6441

5.3562

85–89

2.0228

1.9616

5.1568

4.6760

90–94

1.8701

1.9345

4.1032

3.4136

95–100

1.8701

1.9345

4.1032

3.4136

SOURCE: Lee, McClellan, and Skinner, “Distributional Effects of Medicare,” Tax Policy and the
Economy, August 1999.

FEDERAL RESERVE BANK OF CLEVELAND

Noting that mxa,t,c /mm65,t,1+ = εxa,t,c represents the relative outlay for people in year t aged a of sex
x and belonging to survivorship category c, we can rewrite equation (F2) as
(F3) Mxa,t =

mm65,t,1+

[εxa,t,1+ pxa,t,1+ + εxa,t,0 pxa,t,0].

Summing over all ages and both sexes in year t, we obtain total Medicare Part A outlays for people
sixty-five and older in year t as
100

(F4) M65+,t = mm65,t,1+

·Σ

Σ [εxa,t,1+ pxa,t,1+ + εxa,t,0 pxa,t,0].

a=65 x=m,f

Equation (F4) can be solved to obtain the average expenditure on sixty-five-year-old male-survivors in year t as
M65+,t

(F5) mm65,t,1+

100

Σ Σ [εxa,t,1+ pxa,t,1+ + εxa,t,0 pxa,t,0]

a=65 x=m,f

Finally, expenditures per capita on individuals aged a and of sex x in year t are calculated from
equation (F3)—
(F6)

mxa,t

mm65,t,1+

[εxa,t,1+ pxa,t,1+ + εxa,t,0 pxa,t,0]

pxa,t

Medicare Part A expenditures on the elderly in future years t are obtained by applying to projected total Medicare Part A outlays the projected share of expenditures on those aged sixty-four
and younger.The projected share of outlays on young individuals through 2070 was obtained from
the Congressional Budget Office.These projections were extended through 2080 using the trend in
the share between 2061 and 2070 (see figure F1).
For those aged sixty-four and younger (young spouses and survivors eligible for Medicare benefits), benefits per capita are calculated by distributing their share of Medicare outlays according
to their relative benefit profiles by age and sex. Table F2 shows the relative benefit profile values
obtained from by Lee, McClellan, and Skinner (1999).
For years beyond 2080, year-2080’s per capita benefits are extrapolated by applying two growth
factors. The first factor equals an assumed growth rate of per-capita Medicare benefits, gh, due to
non-demographic factors such as larger demand and greater intensity of use of medical services
due to economic growth.The second factor is designed to capture the impact of projected mortality—specifically, changes through time in the number of retirees by age and sex that are projected

TABLE F2 RELATIVE MEDICARE BENEFIT PROFILES FOR INDIVIDUALS AGED 0–64
Age

Male

Female

0–35

0.1391

0.1101

36–45

1.0000

0.7420

46–55

1.4522

1.1159

56–60

1.8957

1.7855

61–64

3.9942

3.7855

SOURCE: Lee, McClellan, and Skinner, “Distributional Effects of Medicare,” Tax Policy and the
Economy, August 1999.

POLICY DISCUSSION PAPERS

NUMBER 5, DECEMBER 2003

to die within one year relative to those projected to survive for more than a year.This factor, gxd , is
calculated separately for both sexes as
100

(F7)

(1/pxa,t+1)

gxd =

·Σ

(1/pxa,t)

a=65
100

[εxa,t+1,1+ pxa,t+1,1+ + εxa,t+1,0 pxa,t+1,0]

[εxa,t,1+ pxa,t,1+

a=65

εxa,t,0 pxa,t,0]

Given year t’s benefits per capita by age and sex, year t+1’s benefits per capita are calculated as
(F8) mxa,t+1

= mxa,t+1 (1 + gxd )(1 + gh ).

FIGURE F1

PROJECTED SHARE OF MEDICARE (PART A) OUTLAYS ON THOSE AGED 0–64

Percent
14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0
2001

2011

2021

2031

2041
Year

Source: Congressional Budget Ofﬁce and authors’ projections.

2051

2061

2071

FEDERAL RESERVE BANK OF CLEVELAND

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