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Vol. 33, No. 4

ECONOMIC REVIEW

FEDERAL RESERVE BANK
OF CLEVELAND

1
http://clevelandfed.org/research/review/

ECONOMIC REVIEW
1997 Quarter 4
Vol. 33, No. 4

Generational Accounts for the
United States: An Update

by Jagadeesh Gokhale, Benjamin R. Page,
and John R. Sturrock
Although the generational stance of U.S. fiscal policy has improved considerably over the last two years, it remains substantially imbalanced and
is unsustainable. If living generations’ continue to be treated as they are
under current policy, future generations will have to pay almost half of their
lifetime labor incomes in net taxes to balance the government’s books. This
is more than 70 percent larger than the 28.6 percent today’s newborns are
slated to give up. In this article, the authors look at what it would take to
restore a generationally balanced fiscal policy. The possible solutions
include an immediate and permanent income tax hike of 20 percent, a 19
percent cut in transfer payments, or a 15 percent reduction in government
purchases. These measures may seem harsh, but waiting to act will make
the task even more difficult.

Does Intervention Explain the Forward
Discount Puzzle?

by William P. Osterberg
This article uses official 1985–91 intervention data to investigate the
impact of U.S. and German central-bank interventions on the forward discount puzzle for two exchange rates—the German mark/U.S. dollar and
the Japanese yen/U.S. dollar. Evidence on the importance of intervention is
strongest for the mark/dollar exchange rate. However, whereas Flood and
Rose (1996) found that the puzzle was stronger for floating than for fixed
exchange-rate regimes, this study finds it to be stronger during periods of
intervention than at other times. Thus, if intervention is associated with
fixed-rate regimes, the results reported here are inconsistent with those of
Flood and Rose.

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ISSN 0013-0281

Generational Accounts
for the United States:
An Update
by Jagadeesh Gokhale,
Benjamin R. Page, and
John R. Sturrock

Introduction
To pay for all the goods and services a government ever buys, someone of some generation
must pay at some time. If one generation pays
less, another must pay more. If the government
does not pay for what it purchases with current
taxes, it must raise them later—either to retire
the ensuing debt or to pay interest forever.
Sooner or later, someone pays.
This idea underlies the intertemporal government budget constraint, which states that
the present value of prospective government
purchases must be financed from the sum of
three sources: the current net wealth of government, the present value of the prospective net
taxes of current generations (people now
alive), and the present value of the prospective
net taxes of future generations (people not yet
born).1 Thus, the constraint reveals the way in
which government purchases involve a fiscal
burden that someone must bear.
For the prospective purchases implied by a
given fiscal policy, generational accounting estimates how much of that total burden will fall
on current versus future generations.2 The
analysis begins by calculating the present value
of prospective purchases for a given policy.

Jagadeesh Gokhale is an economic advisor at the Federal
Reserve Bank of Cleveland, and
Benjamin R. Page and John R.
Sturrock are economic analysts
at the Congressional Budget Office. The authors thank Robert
Kilpatrick and Laurence Kotlikoff
for helpful discussions. This article is reprinted, with additions,
from Generational Accounts
around the World. eds. Alan J.
Auerbach, Laurence J. Kotlikoff,
and Willi Leibfritz (Chicago: University of Chicago Press, forthcoming), by permission of the
publisher. Copyright 1998 by the
National Bureau of Economic
Research. All rights reserved.

The first source of financing (the government’s
current net wealth) is given. The second source
(the present value of current generations’ net
taxes) is obtained by estimating the per capita
net taxes that each living generation will pay
during its remaining lifetime, actuarially discounting the payments back to the present, and
summing over the discounted values to obtain
a generational account for each generation.3
Those respective generational accounts are
then added over everyone currently alive to
find their combined contribution to prospective
purchases. Having calculated the present value
of prospective purchases and the first two
sources of financing, the third source (the present value of unborn generations’ net taxes) can
be computed as a residual. This residual expresses the fiscal burden that must be placed
on unborn generations for the government to
remain solvent forever.
■ 1 Net taxes are taxes minus transfers.
■ 2 The technique of generational accounting was developed in
Auerbach, Gokhale, and Kotlikoff (1991). See also Auerbach, Gokhale,
and Kotlikoff (1994).
■ 3 An actuarial calculation allows for the fact that the current number of people in a generation will later be decreased by death or increased
by immigration.

Finally, generational accounting compares
all living generations on a lifetime basis by estimating the effective rate at which each pays net
taxes over its entire life—its lifetime net tax
rate. The method estimates past and prospective net taxes and labor income that each living
generation earns over its life. The lifetime net
tax rate is then stated as a percentage, namely,
the present value, at birth, of a generation’s lifetime net taxes as a share of the present value,
at birth, of its lifetime labor income.
As an illustrative device, generational accounting further supposes that future generations share the residual burden equally (with an
adjustment for economic growth). This implies
that males and females born in each future year
will face the same lifetime net tax rate. Thus,
the method compares all generations on the
same basis—the effective rate at which they
pay net taxes over their entire lives.
Generational accounts help us judge whether
fiscal policy is generationally balanced, that is,
whether future generations will pay, on average, the same lifetime net tax rate as current
newborns (people born in the base year). A
generationally balanced policy is sustainable,
meaning that it can be followed forever without
changing its scheduled effective rates for taxes,
transfers, and spending. Conversely, a policy is
imbalanced (or unsustainable) if it implies that
future generations must pay a different net tax
rate than current newborns.
An imbalance implies that to pay for prospective purchases, the scheduled rates of
effective net taxes must change—if not for current generations, then for future ones. If an
imbalance implies that the future rate will be
higher than the current rate, the rate must eventually rise. If the imbalance is large, then the
rate for some living or future generations will
have to increase substantially and may harm
their incentives to work, save, and invest.
Hence, a large generational imbalance points to
the potential for a weaker future economic performance. Conversely, if an imbalance implies
that the future rate will be lower than the current one, someone must pay less to keep the
government’s net wealth from growing so big
that government owns all of the nation’s assets.
Generational accounting can estimate the sizes
of policy changes that would restore sustainability and generational balance.
Section I reports generational accounts and
the associated lifetime net tax rates for the United States. The results suggest that U.S. fiscal policy is generationally imbalanced. If living generations pay net taxes as scheduled, future
generations will have to pay a lifetime net tax

rate far exceeding that of current newborns—
49.2 versus 28.6 percent, an arithmetic difference of 20.6 percentage points.
Ordinarily, generational accounting does not
estimate by age who benefits from prospective
purchases, only who pays for them with their
net taxes. In this study, however, we also calculate an alternative set of accounts that assign to
each living generation the benefit from its share
of government spending on education. The
recalculated accounts show a similar arithmetic
difference in lifetime net tax rates.
These results depend on a “reference” scenario for fiscal policy, the economy, and the
population. The reference policy used here
cuts the deficit, splitting the reduction evenly
between Medicare and discretionary spending
and balancing the budget in the years from
2002 through 2007. After that, however, it
allows the deficit to widen, reflecting an aging
population, slowing labor force growth, and
rising per capita medical costs. Through 2070,
the reference scenario depends on three factors: the federal tax and spending schedule,
the “no-feedback” economic projection of the
Congressional Budget Office (CBO), and the
Social Security Administration’s (SSA) intermediate population projection.4 Beyond 2070, the
reference scenario extends those fiscal, economic, and demographic projections by the
methods described below.
The reference scenario does not include the
recent budget reconciliation package (the Balanced Budget Act of 1997 and the Taxpayer Relief Act of 1997), because long-term projections
under that package are not yet available. Other
things equal, the results under the reference
scenario should roughly correspond to those
under the reconciliation package, since both
policies cut base spending on health care and
other (non–Social Security) programs in about
the same proportions. However, the most recent
budget projections yield more than just midterm budget balance; they show a small surplus
in 2002, which rises to about 0.7 percent of
GDP in 2007 (CBO [1997c]). Therefore, the current fiscal stance is likely to produce a smaller
generational imbalance than the one based on
the reference policy. Even so, in contrast to the
accounts reported earlier, the reference scenario
implies a sharp decline in the degree of generational imbalance.5

■ 4 See SSA (1997) and CBO (1997a, chapter 1, 1997b).
■ 5 The results here update those in Auerbach, Gokhale, and
Kotlikoff (1995).

Section II details the reasons for that decline, which occurred largely because per capita costs for medical programs have recently
grown more slowly than expected. Section III
reports the amounts by which generational
accounts change when we alter the assumptions for population growth, government
spending, and economic growth or discount
rates. Generational accounts move into or near
balance under some of these assumptions, but
remain imbalanced under most.
Section IV considers hypothetical policy
actions that achieve generational balance by
changing the reference policy’s schedule for
purchases or for the net taxes that living generations will pay. The required size of such a
change depends on whether it cuts prospective
purchases or raises prospective net taxes for
current generations. For instance, under the
reference assumptions, balance could now be
restored by proportional cuts of 15.4 percent in
purchases or 18.5 percent in transfers, or by an
increase of 8.9 percent in taxes. (The changes
differ because the programs involve different
initial dollar amounts and because the effects
of the changes depend on both how fast the
programs expand and which generations are
most affected.) Although we examine these
policies only as examples of the magnitude of
the imbalance, it is clear that the longer the
status quo persists, the more difficult it will be
to restore generational balance. Section V
concludes the paper.

I. The Generational
Stance of U.S.
Fiscal Policy

2070, it is assumed to be 1.2 percent per year
(its average annual growth rate for most of the
reference scenario), 3) aggregate taxes, transfers, and purchases through 2070 are given by
the reference projection; beyond 2070, they are
assumed to grow at a rate consistent with per
capita growth at the same rate as labor productivity, and 4) the population through 2070 is
the SSA’s intermediate projection; from 2070
through 2200, we extend that projection by assuming that fertility, mortality, and net immigration rates remain at their 2070 values; beyond
2200, we assume that the size and the age composition of the population remain fixed.
Under the reference policy and the assumptions mentioned earlier, PVGt equals $29.4 trillion, and NWGt (calculated as the algebraic sum
of past real government surpluses) amounts to
–$2.1 trillion. Loosely, NWGt is the negative of
net public debt, NDGt . PVLt equals $22.1 trillion, and PVFt is $9.4 trillion.8
It is PVFt , rather than NDGt , that more meaningfully reflects the fiscal burden that the reference policy imposes on future generations.
NDGt includes only the explicit legal obligations of U.S. governments, not their implicit
obligations. For example, the current debt
ignores the unfunded liabilities of Medicare,
Social Security, and government retirement programs. Outlays for these programs will accelerate in the future as the baby boom generations
retire and as the costs of health care programs
mount. In contrast to the debt, PVFt includes
all prospective government liabilities, implicit
as well as explicit. We calculate that PVFt is
more than four times as large as NDGt —$9.4
trillion versus $2.1 trillion.

Generational Accounts
Intertemporal Government
Budget Constraint

A generational account is the present value of
the per capita net taxes that a generation will

The intertemporal government budget constraint is expressed as
(1)

PVGt = NWGt + PVLt + PVFt ,

where PVGt is the present value of government
purchases, NWGt is the current value of government financial net wealth, PVLt is the total
present value of net taxes that living generations will pay over the rest of their lives, and
PVFt is the residual fiscal burden that future
generations must bear.6,7
To calculate these values for a base case, we
assume the following: 1) the real discount rate is
6 percent, 2) labor productivity growth through
2070 is given by the reference scenario; beyond

■ 6 The constraint includes all debt, taxes, transfers, and purchases
at every level of government. Unlike the National Income and Product
Accounts, generational accounting treats spending on medical, disability,
and retirement benefits for veterans and government workers as purchases
(payment for past services), rather than as transfers. For an explanation
of how generational accounts treat taxes, transfers, and purchases, see
Auerbach, Gokhale, and Kotlikoff (1991); for a description of how generational accounting implements the calculations, see the Appendix.
■ 7 NWGt excludes the value of tangible government assets, and
PVGt excludes the service flows of those assets. If NWGt included the
assets, PVGt would have to include the service flows. Because (in equilibrium) the assets and their service flows are equal in present value, their
inclusion would not affect the balance in equation (1).
■ 8 All dollar figures are reported in constant 1995 dollars. For
details about the calculations, see the Appendix.

T A B L E

Composition of Male
Generational Accounts under
Reference Assumptionsa
Tax Payments
Generation’s
Age in 1995

Net Tax
Payment

0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Future
generations d
Percent
difference

Transfer Receipts

Labor
Income

Capital
Income

Payroll

Other b

Social
Security c

Health

Other

77.4
95.7
119.5
149.1
182.2
196.2
196.8
189.0
171.2
139.2
93.7
37.5
–25.5
–77.7
–89.2
–87.9
–77.2
–68.3
–53.8

33.5
41.6
52.1
65.1
79.5
86.0
86.3
82.9
76.0
65.1
50.8
34.6
18.6
7.4
3.2
1.6
0.9
0.7
0.5

9.0
11.2
14.3
18.1
23.5
27.9
33.7
40.7
46.6
50.2
51.3
49.7
46.3
41.2
33.0
22.4
11.2
0.0
0.0

34.3
42.8
53.9
67.8
83.6
90.6
90.2
86.0
78.6
67.4
52.9
36.3
19.5
7.5
3.3
1.7
1.0
0.7
0.5

31.5
36.6
42.5
48.6
53.4
53.5
52.7
51.4
50.4
47.7
43.7
38.7
32.9
27.5
22.2
16.9
11.9
8.0
6.3

7.2
8.8
10.6
12.1
13.7
16.4
19.9
24.6
30.8
38.8
49.3
62.8
80.1
91.8
85.0
71.7
54.8
42.6
33.7

19.6
22.5
26.3
30.4
34.4
35.4
36.4
38.2
40.9
44.3
48.0
52.0
56.5
63.8
60.9
54.5
44.4
32.9
25.9

4.2
5.2
6.5
8.1
9.7
10.1
9.8
9.2
8.7
8.1
7.6
7.0
6.3
5.7
5.1
4.2
3.1
2.1
1.7

134.6

—

71.9

—

a. Present value in thousands of 1995 dollars.
b. Includes excise taxes, other indirect taxes, and property taxes.
c. Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds.
d. Generations born in 1996 and thereafter.
NOTE: The net tax payment represents a present value as of 1996. The percentage difference between the net tax payments of future
generations and current newborns is calculated after adjustment for economic growth (see text).
SOURCE: Authors’ calculations.

pay for the rest of its life under the assumed fiscal policy. (Generational accounting defines a
generation by sex and year of birth.) To obtain
each generation’s prospective per capita values
through 2070, generational accounting first distributes among the generations the reference
projections for aggregate taxes and transfers.
The distribution assumes that the current ratios
of per capita taxes and transfers by age and sex
remain fixed. For instance, in a given year, 50year-old women always pay 38 percent as
much in per capita payroll taxes as do 40-yearold men.9,10 Beyond 2070, generational accounting assumes that the per capita amount of
each type of tax or transfer by age or sex grows
at the same rate as labor productivity. The
resulting streams of per capita net taxes are
actuarially discounted to the base year in order
to calculate the generational account for each

living generation. (The base year in this case is
1995, the latest year for which we have the
ratios of per capita taxes and transfers by age
and sex.)
As tables 1 and 2 show, generational accounts follow a life-cycle pattern. Young generations at or near working age will pay a significant amount of taxes for several years long
before they retire and collect Social Security
■ 9 The ratios are estimated from official survey data. For details of
the procedure, see Auerbach, Gokhale, and Kotlikoff (1991); for a description of the respective ratios of per capita net payments by age and sex, see
CBO (1995), pp. 7–8.
■ 10 For Social Security and government retirement programs, the
generational accounts shown here reflect the way in which productivity
growth feeds gradually into benefits under current schedules. Thus, the
ratios of per capita benefits by age and sex for these programs need not
remain fixed. See CBO (1997b).

T A B L E

Composition of Female
Generational Accounts under
Reference Assumptionsa
Tax Payments
Generation’s
Age in 1995

Net Tax
Payment

0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Future
generations d
Percent
difference

Transfer Receipts

Labor
Income

Capital
Income

Payroll

Otherb

Social
Security c

Health

Other

51.9
63.4
78.1
95.7
115.0
122.6
120.7
113.8
99.0
72.8
37.4
–5.2
–52.0
–91.2
–101.0
–101.0
–90.2
–73.5
–55.8

19.4
24.1
30.2
37.7
45.7
48.1
46.2
42.8
38.2
31.6
23.6
15.0
7.6
2.7
1.0
0.5
0.3
0.1
0.1

9.5
11.9
15.1
19.3
24.8
30.3
36.2
42.3
46.3
47.7
46.8
44.8
41.6
35.6
25.3
14.1
5.3
0.0
0.0

20.9
26.1
32.9
41.3
50.7
53.7
51.6
47.9
43.0
35.7
26.9
17.2
8.7
3.1
1.2
0.6
0.3
0.1
0.1

30.4
35.2
40.5
45.6
49.8
50.4
50.1
49.8
48.6
46.2
42.3
37.6
32.4
27.1
22.2
16.9
12.4
9.4
7.2

6.8
8.3
10.0
11.3
12.7
15.3
18.6
23.0
28.8
36.5
46.9
60.6
78.6
89.3
83.4
71.6
57.2
43.5
33.2

14.8
16.9
19.9
23.4
26.6
28.9
31.7
35.2
39.6
45.0
49.5
54.5
59.5
66.5
63.9
58.5
48.8
37.8
28.5

6.8
8.5
10.6
13.5
16.8
15.7
13.2
10.8
8.7
7.0
5.6
4.8
4.2
3.8
3.4
2.9
2.4
1.9
1.5

90.2

—

71.9

—

and Medicare benefits. Hence, their generational accounts are positive and high. By contrast, older generations in or near retirement
will pay low taxes and receive high transfers
for most of their remaining years. Thus, their
generational accounts are negative.
The generational accounts for women of any
age are lower (or more negative) than those for
men of the same age. On average, women pay
lower taxes because they are less likely to work
in the marketplace, and earn less when they
do. Moreover, they live longer and often receive payments as widows on their husbands’
accounts. Therefore, relative to their earnings,
they receive more in transfers, especially for
medical care and Social Security.

Generational accounts compare on the same
lifetime basis the net payments of current newborns (those born in 1995) and future generations (those born later). That is, the accounts
show the present value of per capita net taxes
that each group will pay over its entire life.
How do their accounts compare? Under the
reference policy, the generational account for
a 1995 newborn is $77,400 for a male and
$51,900 for a female. As mentioned earlier, the
residual burden on future generations is $9.4
trillion, but there is no way to know how they
would share that burden. To get around this
problem, generational accounting assumes that
future generations split the burden equally on
a growth-adjusted basis. As noted, this assumption amounts to specifying that males

T A B L E

Lifetime Net Tax Rates
under Reference Assumptionsa

Generation’s
Year of Birth

1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
1995
Future
generations b

Net
Tax Rate

Components of Net Tax
Gross
Transfer
Rate
Rate

23.9
27.5
29.6
31.3
32.5
33.4
33.3
32.4
30.8
29.3
28.6

28.0
33.4
36.4
38.4
40.3
43.0
44.1
44.3
43.0
42.1
41.7

4.0
6.0
6.7
7.1
7.8
9.5
10.8
11.9
12.2
12.8
13.1

49.2

—

a. Percent.
b. Generations born in 1996 and thereafter.
NOTE: Numbers may not sum because of rounding.
SOURCE: Authors’ calculations.

and females born in each future year will pay
combined lifetime net taxes at a uniform
rate.11 Given this assumption, the reference
policy implies that males born in 1996 will pay
an average of $134,600 (in present value as of
1996), while females will pay an average of
$90,200. These payments are larger than the
corresponding payments of current newborns,
indicating that the reference policy is out of
generational balance.

Lifetime Net
Tax Rates
So far, it has been legitimate to compare directly
only the generational accounts of current newborns and future generations. These accounts
give each group’s net payment over its entire
life. Other generations, however, are at varying
stages of their life cycles. Thus, their accounts
are not directly comparable because their net
payments are stated only over their remaining
lives. For instance, the generational account of a
40-year-old man is higher than that of a 50-yearold man, because the 40-year-old has 10 more
years of taxes to pay and is 10 years farther
from receiving Social Security and Medicare
benefits. But the accounts cannot say whether
the 40-year-old paid net taxes in the past at the

same effective rate as the 50-year-old when he
was 40. Nor do the accounts state how a 60year-old woman’s current negative account
compares with her past net taxes.
To compare everyone on the same basis,
generational accounting calculates the effective
rate at which each generation pays net taxes
over its entire life—its lifetime net tax rate. The
method first estimates each generation’s past
net taxes (in addition to its prospective net
taxes) to find its per capita lifetime net taxes.
Those per capita net taxes are then discounted
to the year in which the generation was born in
order to find its generational account at birth.
Similarly, the procedure estimates each generation’s per capita lifetime labor income and finds
its present value at birth. The generational account at birth is then divided by the present
value at birth of per capita lifetime labor income to yield the generation’s lifetime net tax
rate.12 A lifetime net tax rate compares all generations on the same basis—the effective share
of labor income that its members will pay in
net taxes over their entire lives.
As table 3 shows, the lifetime net tax rate
for successive generations has both risen and
fallen over the century. It started at 23.9 percent
for people born in 1900, climbed to 33.4 percent for those born in 1950, then fell to 28.6
percent for those born in 1995.13 The rise in
the rate for successive generations through
1950 coincided with a similar increase in the
share of output devoted to government purchases. The decline in the rate for successive
generations since 1950 stems mostly from three
factors: longer life expectancies, a decline in
the effective rate of excise taxes, and—most
■ 11 See the Appendix for details. The calculation assumes that
labor productivity (and hence, eventually, per capita income) grows each
year at rate g. In that case, an equal growth-adjusted share of the burden
means that the per capita net payment of each future generation is (1 + g )
times that of its immediate predecessor. If males born in 1996 pay $Y
each, then males born in 1997 pay $Y (1 + g ) each, males born in 1998
pay $Y (1 + g ) 2 each, and so forth. (Generational accounting gives those
per capita net payments in present value as of the generation’s birth year.)
Similarly, if females born in 1996 pay $X each, then females born in 1997
pay $X (1 + g ) each, and so on. This procedure amounts to assuming that
all future males pay lifetime net taxes at a uniform rate: Their lifetime net
taxes grow generation by generation at the same rate as their lifetime
incomes. Future females also pay lifetime net taxes at a uniform rate, but it
is lower than the rate for males.
■ 12 For a discussion of the reasons that generational accounting
uses lifetime income from labor, rather than from both capital and labor,
see the Appendix.
■ 13 These rates are ratios of population-weighted net taxes to
population-weighted labor incomes.

T A B L E

Composition of Male
Generational Accounts under
Reference Assumptions:
Benefits of Education Spending
Distributed by Age and Sexa
Net Tax
Payment

0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Future
generationsd

25.7
33.1
71.4
120.1
172.7
193.3
195.1
187.8
170.4
138.7
93.6
37.3
–25.6
–77.7
–89.2
–87.9
–77.3
–68.3
–53.8

33.5
41.6
52.1
65.1
79.5
86.0
86.3
82.9
76.0
65.1
50.8
34.6
18.6
7.4
3.2
1.6
0.9
0.7
0.5

9.0
11.2
14.3
18.1
23.5
27.9
33.7
40.7
46.6
50.2
51.3
49.7
46.3
41.2
33.0
22.4
11.2
0.0
0.0

114.3

—

340.3

—

Percent
difference

Labor
Income

Tax Payments
Capital
Income
Payroll

Generation’s
Age in 1995

Transfer Receipts
Other b

Social
Security c

Health

Education

Other

34.3
42.8
53.9
67.8
83.6
90.6
90.2
86.0
78.6
67.4
52.9
36.3
19.5
7.5
3.3
1.7
1.0
0.7
0.5

31.5
36.6
42.5
48.6
53.4
53.5
52.7
51.4
50.4
47.7
43.7
38.7
32.9
27.5
22.2
16.9
11.9
8.0
6.3

7.2
8.8
10.6
12.1
13.7
16.4
19.9
24.6
30.8
38.8
49.3
62.8
80.1
91.8
85.0
71.7
54.8
42.6
33.7

19.6
22.5
26.3
30.4
34.4
35.4
36.4
38.2
40.9
44.3
48.0
52.0
56.5
63.8
60.9
54.5
44.4
32.9
25.9

51.7
62.6
48.1
28.9
9.5
2.9
1.7
1.2
0.7
0.5
0.2
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0

4.2
5.2
6.5
8.1
9.7
10.1
9.8
9.2
8.7
8.1
7.6
7.0
6.3
5.7
5.1
4.2
3.1
2.1
1.7

—

important—the rapid growth in per capita
health care and Social Security transfers that
began in the 1960s.14
The results shown in table 3 indicate that
the reference policy is unsustainable. Either
prospective purchases must fall or the effective schedule at which people pay net taxes
must rise—if not for current generations, then
for future ones. If current generations pay net
taxes as scheduled by the reference policy,
current newborns will pay lifetime net taxes of
28.6 percent, and future generations will pay
49.2 percent.15
We can use these lifetime net tax rates to
quantify the notion of generational imbalance.
The degree of such imbalance is given as a percentage, namely, the arithmetic difference in the
lifetime net tax rates of future generations and

current newborns as a fraction of the lifetime
net tax rate of current newborns. Thus, the
degree of imbalance under the reference scenario is 72 percent (the difference between
49.2 and 28.6 as a percentage of 28.6). A degree
of zero indicates generational balance, while a

■ 14 Excise taxes affect a generational account at birth more than do
other taxes. Generational accounting prorates excise taxes among all family members, including children. Therefore, a decline in the excise tax
lowers the estimated taxes that a child pays early in life. An earlier payment has a higher present value at birth than does the same payment at a
later time. Hence, a cut in the excise tax lowers lifetime net tax rates by
more than does a cut in another tax that reduces current revenue by the
same amount.
■ 15 These figures do not represent a forecast. They project only
what would happen if the reference policy applied to current generations
for the rest of their lives.

T A B L E

Composition of Female
Generational Accounts under
Reference Assumptions:
Benefits of Education Spending
Distributed by Age and Sexa
Tax Payments
Generation’s
Age in 1995

Net Tax
Payment

0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Future
generationsd
Percent
difference

Labor
Income

Capital
Income

Payroll

0.1
0.8
29.9
66.8
105.5
119.7
119.0
112.6
98.3
72.2
37.3
–5.3
–52.1
–91.2
–101.1
–101.0
–90.2
–73.6
–55.8

19.4
24.1
30.2
37.7
45.7
48.1
46.2
42.8
38.2
31.6
23.6
15.0
7.6
2.7
1.0
0.5
0.3
0.1
0.1

9.5
11.9
15.1
19.3
24.8
30.3
36.2
42.3
46.3
47.7
46.8
44.8
41.6
35.6
25.3
14.1
5.3
0.0
0.0

0.3

—

328.3

—

Transfer Receipts
Other b

Social
Security c

Health

Education

Other

20.9
26.1
32.9
41.3
50.7
53.7
51.6
47.9
43.0
35.7
26.9
17.2
8.7
3.1
1.2
0.6
0.3
0.1
0.1

30.4
35.2
40.5
45.6
49.8
50.4
50.1
49.8
48.6
46.2
42.3
37.6
32.4
27.1
22.2
16.9
12.4
9.4
7.2

6.8
8.3
10.0
11.3
12.7
15.3
18.6
23.0
28.8
36.5
46.9
60.6
78.6
89.3
83.4
71.6
57.2
43.5
33.2

14.8
16.9
19.9
23.4
26.6
28.9
31.7
35.2
39.6
45.0
49.5
54.5
59.5
66.5
63.9
58.5
48.8
37.8
28.5

51.8
62.6
48.2
28.9
9.5
3.0
1.7
1.2
0.8
0.6
0.2
0.2
0.1
0.0
0.0
0.0
0.0
0.0
0.0

6.8
8.5
10.6
13.5
16.8
15.7
13.2
10.8
8.7
7.0
5.6
4.8
4.2
3.8
3.4
2.9
2.4
1.9
1.5

—

negative degree indicates an imbalance in favor
of the future.

The Benefits of
Government Spending
on Education by
Age and Sex
How would this outcome differ if the accounts
assigned, by age, the benefits that living generations receive from government purchases? It is
impossible to assign the benefits from many
purchases, such as those for defense or administration, because they generate public services
that apply equally to everyone.16 Arguably,
however, we can estimate by age the per capita
benefits from one category of purchases—education spending (now about one-fifth of total

government purchases). Below, we recalculate
the generational accounts by treating all prospective government spending for education as
a transfer rather than a purchase, then distributing that spending by age.17
The recalculation substantially lowers the
lifetime net taxes of those under age 25 (see
tables 4 and 5), since they receive most of the
benefits from such spending. The recalculated
generational account for males born in 1995 is
■ 16 Beyond 2070 (the end of the reference projection), generational
accounting prorates each year’s per capita cost of such purchases to everyone alive in that year. However, the method is used only to estimate total
prospective purchases, not to try to assign the benefits of those purchases
by age.
■ 17 Data used in the calculation are from the U.S. Department of
Education (1997).

F I G U R E

Comparison of Projected Budget
Aggregates: GA1993 Versus GA1995

a. Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds.
b. Excludes property taxes.
SOURCES: Congressional Budget Office; Office of Management and Budget; and authors’ calculations.

T A B L E

II. The Recent
Improvement in the
Generational Stance
of U.S. Fiscal Policy

Generational Accounts, 1993
Versus 1995: Cumulative Impact
of Updating Demographic and
Fiscal Projections

In the past two years, the generational stance of

Lifetime Net Tax Ratesa
Newborns

1993 accounts

Future
Generationsb

Percent
Difference

34.2

84.4

147.1

Freeze 1993
policy for two years

34.1

87.4

156.0

Update population
projections

33.6

85.3

154.1

Transfers
Social Securityc
Medicare and Medicaid
Other

34.6
36.9
37.7

76.4
46.9
44.5

121.2
27.1
18.1

Government purchases
Federal
State and local

37.7
37.7

46.0
21.5

22.0
–42.9

Government wealth

37.7

20.8

–44.8

33.6
31.1

32.5
40.5

–3.2
30.5

29.1
28.7

46.7
49.3

60.4
71.9

Fiscal projections

Taxes
Income d
Payroll
Excise and
other indirect
Property and other
Projected labor income
1995 accounts

28.6

49.2

71.9

28.6

49.2

71.9

a. Percent.
b. Generations born in 1996 and thereafter.
c. Federal Old-Age and Survivors Insurance and Disability Insurance Trust
Funds.
d. Labor and capital.
SOURCE: Authors’ calculations.

only $25,700, and for females, only $100. Thus,
education spending cancels much of the net
taxes that the rest of the reference policy imposes on the youngest generations.
At the same time, the recalculation also lowers projected purchases (by classifying education outlays as transfers) and thereby reduces
the residual burden on future generations.
Thus, at 19.2 percentage points, the arithmetic
difference in the recalculated lifetime net tax
rates of future generations and current newborns is nearly as large as when education outlays are counted as purchases.

U.S. fiscal policy has improved markedly from
that reported in the accounts using 1993 as the
base year (GA1993).18,19 Given the economic
outlook and policy schedule of two years ago,
GA1993 estimated that future generations would
pay a lifetime net tax rate of 84.4 percent. That
rate falls to 49.2 percent under the reference
scenario for base year 1995 (GA1995).
What explains this improvement? Most of it
stems from lower projected federal spending for
medical care, which is now about 10 percent
less than what was anticipated two or three
years ago. As a result, projected transfer spending for health care is growing from a lower base
and remains a smaller share of output (see figure 1). The output shares of other projected
taxes, transfers, and government purchases are
also below levels seen two years ago. The reason for the lower purchases growth is that projections for state and local government purchases are below GA1993 levels.
We examine the effects of moving from
GA1993 to GA1995 by cumulatively updating
their underlying assumptions. The change from
base year 1993 to 1995 means that the accounts
treat people born in 1994 and 1995 as current
rather than as future generations. In GA1995,
these two generations no longer assume a
share of the accumulating residual burden that
falls on future generations. Thus, time and
compound interest alone raise the lifetime net
tax rate on future generations to 87.4 percent
(see table 6). The updated projections for population, however, reduce that rate to 85.3 percent. As noted, the newer projections for transfers (especially for health care) decrease the
rate much farther—more than 40 percentage
points. The lower transfers projected for
GA1995 entail higher net taxes on living generations and thus a smaller residual burden on
future ones. The more recent estimates of current government net wealth and projected purchases by state and local governments lighten
that burden still more. By contrast, the lower
■ 18 See Auerbach, Gokhale, and Kotlikoff (1995). The base calculation in 1993 used the OMB’s economic and budget projections
through 2030. Those projections were extended by assuming that per
capita taxes, transfers, and purchases by age and sex grew at the same
rate as labor productivity.
■ 19 These calculations, and those that follow, treat government
outlays for education as purchases.

T A B L E

Lifetime Net Tax Rates
under Alternative Health
Care and Federal
Purchase Assumptions a
Slower
Purchases
Growthb

Slower
Health
Care
Growthc

Slower
Health Care
and Purchases
Growth

23.9
27.5
29.6
31.3
32.5
33.4
33.3
32.4
30.8
29.3
28.6

23.9
27.5
29.7
31.4
32.9
34.0
34.1
33.6
32.4
31.4
30.9

49.2

44.6

38.1

33.5

Generation’s
Year of
Birth
Reference

1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
1995
Future
generations d

a. Percent.
b. Federal purchases are held constant in real terms after the year 2000.
c. Per capita spending by age for health care grows 2 percentage points
slower than under the reference policy through 2003, and expands at the
same rate as labor productivity thereafter.
d. Generations born in 1996 and thereafter.
SOURCE: Authors’ calculations.

revenue projections of GA1995 reduce the lifetime net tax rate on current newborns and raise
that on future generations.

III. Sensitivity
to Alternative
Assumptions
Alternative Projections
for Government Purchases
and Health Care
The reported calculations depend on many
uncertain or arguable economic and budgetary
assumptions. For instance, the reference scenario assumes that real federal discretionary
spending falls through 2007 at an average rate
of 1.3 percent per year; after that, it grows at the
same rate as output. By contrast, the Balanced
Budget Act of 1997 limits discretionary spending
only through 2002, although subsequent legislation may extend such limits even more.20
In the near term, both the Budget Act and
the reference policy would intensify the
post–Korean War period’s secular decline in

discretionary spending as a share of output. In
the long run, however, it may be difficult to
keep such a tight rein on discretionary spending (mostly purchases). For instance, federal
nondefense purchases since the 1950s have
not changed much as a fraction of output.
Moreover, the current replacement schedule
for aging defense systems may strain prospective budgets.
Similar uncertainty besets projections of federal mandatory spending (mostly transfers),
especially for health care. Through 2007, the
reference scenario assumes that real per capita
Medicare outlays by age outpace labor productivity by an average of 3.4 percentage points
per year. That difference tapers to zero by 2020,
after which time Medicare spending is assumed
to grow at the same rate as labor productivity.
On average through 2020, per capita Medicare
spending by age grows 2.4 percentage points
per year faster than labor productivity.21
Projections for health care outlays are notoriously uncertain. For many years, analysts
underpredicted the per capita spending for
these rapidly expanding programs. In the past
several years, however, such outlays have
increased much more slowly than expected. No
one is entirely sure of the reasons behind this
slowdown, and it is possible that rapid growth
may resume. On the other hand, growth may
continue at its slower pace or slacken even
more, and budgetary pressures may require
limits on the expansion of medical programs.
How much do the accounts change if we
look at alternative budgetary assumptions in
order to allow for uncertainty or ambiguity? To
find out, we examine the effects of two optimistic policies that specify lower spending for
purchases and health care.22 The first holds
real federal purchases constant after 2000; the
second slows the growth rate of per capita
Medicare outlays by age. Under the latter policy, per capita medical spending through 2003
grows at an average rate that is 2 percentage
points per year slower than under the reference
policy. After 2003, per capita outlays expand at
the same rate as labor productivity.

■ 20 The Act itself extended the limits on discretionary spending set
by the Omnibus Budget and Reconciliation Act of 1993.
■ 21 The Health Care Financing Administration (1997) makes similar assumptions.
■ 22 Projected federal purchases under this assumption serve as
a proxy for federal discretionary outlays. Purchases now make up about
90 percent of federal discretionary spending, which in turn accounts for
around 37 percent of non-interest federal outlays.

These policies depart significantly from current conditions and from the reference policy.
For example, federal purchases now represent
6.0 percent of output. In 2070, that share is 4.2
percent under the reference policy, but only
1.5 percent if real federal purchases stay constant after 2000. Total spending for Medicare is
now equal to 2.7 percent of output. In 2070, it
reaches 7.1 percent under the reference policy,
but only 4.3 percent if that spending grows
more slowly.
Given the other reference assumptions, these
alternative policies reduce the generational
imbalance, but do not eliminate it. If real federal
purchases remain constant after 2000, the lifetime net taxes of living generations remain unchanged. However, the policy lowers projected
spending for purchases. That decrease leaves a
smaller residual burden on future generations,
reducing their lifetime net tax rate from 49.2 to
44.6 percent (see table 7). Unlike constant purchases, slow Medicare growth boosts the per
capita net taxes of every living generation (because it lowers their projected transfers). Like
constant purchases, however, slow Medicare
growth lessens the burden that current generations leave for future generations, and their lifetime net tax rate falls to 38.1 percent. A policy
of both constant real federal purchases and
slow Medicare growth yields lifetime net tax
rates of 33.5 percent for future generations and
30.9 percent for current newborns. Therefore, a
small generational imbalance remains despite
optimistic assumptions for federal purchases
and Medicare outlays.
The response of lifetime net tax rates to
slower Medicare growth may seem paradoxical.
Slow growth raises the lifetime net tax rate for
the oldest generation the least, although that
generation receives the lower transfers now. By
contrast, slow growth increases that rate for the
youngest generation the most, although these
individuals collect the lower benefits later. This
pattern occurs in part because people over age
65 will receive the smaller benefits for fewer
years until death, a fact that reduces its cumulative lifetime impact.
More fundamentally, the pattern occurs
because slower growth makes a greater difference over a long time horizon. For instance, if
per capita benefits rise 1 percentage point per
year less, benefits at age 65 will be 1 percent
lower for this year’s 64-year-old, 2 percent lower for this year’s 63-year-old, and so forth.
Moreover, the decline in benefits at age 65 is
discounted not to the base year, but to the generation’s year of birth. Thus, slow Medicare
growth cuts the present value of the newborn’s

benefit at age 65 by proportionately more than
that of the one-year-old. Slower growth thus
raises the lifetime net taxes (reduces the lifetime net transfers) of the current newborn by
more than those of the one-year-old, boosts the
net taxes of a one-year-old by more than those
of a two-year-old, and so on.

Alternative
Discount and
Productivity
Growth Rates
The accounts also depend on uncertain assumptions about the rates of discount and productivity growth. As noted, the reference case
uses a real discount rate of 6 percent (r = 0.06)
and assumes that labor productivity eventually
increases 1.2 percent per year (g = 0.012).
A 6 percent discount rate is roughly equal to
the historical real rate of return on equity, but
there are arguments for using a lower or higher
rate. For example, it may be reasonable to use
a discount rate closer to the real rate of return
on long-term government debt (2 or 3 percent),
or to the real pretax rate of return on private
capital (10 or 12 percent). That range reflects
ambiguity about how to deal with such issues
as risk, opportunity cost, and the equitypremium puzzle (see CBO [1995], pp. 41–43).
In the same vein, the trend of labor productivity has varied significantly in the past, growing at an average annual rate of 1.3 percent
from 1902 to 1929, 1.2 percent from 1929 to
1948, 2.8 percent from 1948 to 1966, and 0.9
percent from 1966 to 1996.23 Moreover, productivity growth swung wildly during the
1929–48 period in response to the Depression,
World War II, and demobilization. To examine
the results’ sensitivity to these assumptions, we
next calculate generational accounts using
alternative discount and productivity growth
rates. The alternative assumptions are 3 percent and 9 percent for the discount rate and
0.7 percent and 1.7 percent for the productivity
growth rate.
Given the reference policy, generational
accounts remain imbalanced under all combinations of these growth rates, with the degree
of imbalance ranging from 28 to 146 percent
■ 23 For consistent comparison, labor productivity is defined in this
example as GDP per worker. The periods seem to define growth epochs,
with the first three spanning nonsuccessive peaks in the annual business
cycle. There was no peak in 1966, but economists generally agree that the
trend in labor productivity growth changed about then. Neither was there
a peak in 1996, but it is the most recent full year for which we have data,
and comes after a long (six-year) expansion.

T A B L E

Percent Difference in Lifetime
Net Tax Rates of Current Newborns
and Future Generations under
Alternative Discount and Growth
Rate Assumptionsa
Growth Rate ( g)

0.007

0.012

0.017

79
88
146

53
72
130

28
55
115

Discount Rate (r)

0.03
0.06
0.09

a. Current newborns are the generation born in 1995. Future generations
are those born in 1996 and thereafter.
SOURCE: Authors’ calculations.

T A B L E

Percent Difference in Lifetime
Net Tax Rates of Current Newborns
and Future Generations under
Alternative Discount and Growth
Rate Assumptions, with Slower
Health Care Growth and Constant
Real Federal Purchasesa

Alternative
Demographic
Projections
Uncertainty about population growth also
Growth Rate ( g)

0.007

0.012

0.017

1
6
40

–4
8
45

–10
11
51

Discount Rate (r)

0.03
0.06
0.09

a. Current newborns are the generation born in 1995. Future generations
are those born in 1996 and thereafter.
SOURCE: Authors’ calculations.

F I G U R E

(see table 8). Given the alternative spending
policies, some combinations of discount and
productivity growth rates tip the generational
scales in favor of the future. Most do not, however, and the degree of imbalance ranges from
–10 to 51 percent (see table 9). Lifetime net tax
rates on future generations fall below those on
current newborns only at a low discount rate
and a moderate or high growth rate.
The degree of imbalance responds more to
the differences considered for the discount rate
than the productivity growth rate. A higher
discount rate typically makes the residual burden accumulate faster and thereby raises the
degree of imbalance.24 On the other hand,
higher productivity growth tends to boost
income and output, and they in turn feed into
higher values for purchases and the net taxes
of living generations (see CBO [1997b]). That
phased-in response dilutes the impact of
higher productivity growth on the lifetime net
tax rates of all generations.25

U.S. Population and Projectionsa

a. Actual data through 1995.
SOURCES: Social Security Administration; and authors’ calculations.

afflicts generational accounts (or any other longrun projection). As noted, the accounts use the
SSA’s intermediate projection for a base case

■ 24 This statement is true as long as the sum of the current value of
government net debt, NWGt , plus the present value of prospective government purchases, PVGt , exceeds the present value of prospective net taxes
of living generations, PVLt . The condition is easily satisfied for any reasonable values.
■ 25 Seemingly paradoxical reversals sometimes occur. For example, suppose that the discount and productivity growth rates shown in
table 8 move from 3 to 6 percent and from 0.7 to 1.2 percent, respectively.
The degree of imbalance then falls from 79 to 72 percent. However, it subsequently rises to 115 percent as the discount and productivity growth
rates move higher to 9 percent and 1.7 percent. Such reversals occur both
because the degree of imbalance is a ratio and because the discounting
process can lead to the same kind of “reswitching” issues that arise in
capital theory. A higher discount rate reduces the absolute present value
in any year a tax is paid or a wage transfer is received. A higher productivity growth rate raises those absolute present values. Therefore, a lifetime
net tax rate may go up or down if both the discount and productivity
growth rates are higher. Moreover, people generally pay taxes in youth and
middle age and receive transfers in old age. Other things equal, a higher
discount rate reduces the present value of both taxes and transfers, so that
the present value of net taxes (taxes less transfers) may rise or fall. A
higher discount rate is more likely to raise the present value of net taxes in
the following cases: the initial discount or productivity growth rate is
higher, the recipient receives a given transfer at a later age, or the recipient
gets a larger transfer at a given age (as in the earlier case of slow Medicare
growth, when the newborn’s benefit at age 65 is cut by proportionately
more than that of the one-year-old).

F I G U R E

Old-Age Dependency Ratio
under Alternative Population
Projectionsa

a. Population aged 65 or older as a share of population aged 20 to 64.
SOURCES: Social Security Administration; and authors’ calculations.

T A B L E

Generational Accounts
under Alternative
Demographic Assumptionsa
Net Tax Payments under Alternatives
Generation’s
I
II
III
Age in
1995
Male
Female
Male
Female
Male Female

0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
FGb
Percent
difference

75.4
94.1
118.8
149.3
183.3
195.8
195.7
187.7
170.0
138.3
93.3
37.6
–24.8
–76.3
–87.5
–86.1
–75.6
–66.9
–52.8
116.6

50.3
62.1
77.1
95.1
114.8
121.7
119.4
112.5
98.1
72.2
37.3
–4.8
–51.0
–89.4
–98.8
–98.6
–88.1
–72.0
–54.8
77.8

52.1

77.4
51.9
95.7
63.4
119.5
78.1
149.1
95.7
182.2 115.0
196.2 122.6
196.8 120.7
189.0 113.8
171.2
99.0
139.2
72.8
93.7
37.4
37.5
–5.2
–25.5 –52.0
–77.7 –91.2
–89.2 –101.0
–87.9 –101.0
–77.2 –90.2
–68.3 –73.5
–53.8 –55.8
134.6
90.2
71.9

79.8
97.7
121.0
149.8
181.9
196.5
197.2
189.2
171.7
139.8
94.0
37.3
–26.3
–79.0
–90.9
–89.7
–78.9
–69.6
–54.8
153.7

53.6
65.0
79.4
96.7
115.6
123.6
121.8
114.8
99.7
73.2
37.4
–5.7
–53.0
–92.8
–103.1
–103.2
–92.2
–75.1
–56.8
103.3

89.5

71.9

Lifetime Net Tax Rates (percent) c
Current
newborns
FGb

26.8
40.9

28.6
49.2

30.3
57.6

a. Present value in thousands of 1995 dollars.
b. Future generations.
c. Lifetime net tax rates are population-weighted averages across males
and females.
SOURCE: Authors’ calculations.

(and extend it as described earlier). However,
the SSA also projects high- and low-growth
paths to try to describe a reasonable range of
uncertainty about its estimates for the probable
actuarial balance of the Social Security trust
fund. The three population projections represent low-cost (Alternative I), mid-cost (Alternative II), and high-cost (Alternative III) outcomes.
The differences in populations depend on
differences in their fertility, mortality, and net
immigration rates. Alternative I assumes the
highest rates for all of those demographic factors, and Alternative III assumes the lowest.
Higher rates imply more workers paying taxes
and fewer retirees receiving transfers; lower
rates imply the opposite. Compared to Alternative II, the population of Alternative I about
doubles, while the population of Alternative III
falls to about half the size (see figure 2).26
All of the alternatives show a rise in the oldage dependency ratio—the population aged
65 or older as a share of the population aged
20 to 64. As the baby boom generations retire,
that ratio increases during the years from about
2010 to 2035 (see figure 3). The ratio for Alternative II then levels off, with fertility and immigration rates largely offsetting its mortality rates
to roughly stabilize the size and age composition of the population. The ratio for Alternative
I falls, since higher mortality rates reduce the
relative number of old people, and higher fertility and immigration rates expand the relative
number of working-age people. The opposite
occurs under Alternative III.
For living generations, higher mortality and
immigration rates usually imply higher generational accounts for the old and lower ones for
the young (see table 10). For instance, the accounts of old generations are higher (less negative) under Alternative I than under Alternative
II, while the accounts of very young generations
are lower. The higher mortality rates associated
with Alternative I imply that fewer people of any
age live to any given year in the future. People
now old will receive less in transfers, and people
now young will pay less in taxes (whose present
value is greater than that of the later transfers
they would otherwise receive).
The pattern is not strictly consistent, because
net immigration boosts the later size of some
young generations. For instance, the generational account for 20-year-old males is highest

■ 26 Another way to compare these alternatives is to look at their populations in 2200 as ratios of the population in 1995. Under Alternative I, the
population increases by the year 2200 to more than 300 percent of its 1995
level; under Alternative II, it rises to about 150 percent of its 1995 level; and
under Alternative III, it declines to about 70 percent of its 1995 level.

under Alternative I. That apparent anomaly
reflects the prospective U.S. net taxes of the
current foreign 20-year-old males who will
immigrate later. That is, the population count in
the base year excludes their present numbers,
but the generational account includes their
prospective taxes and transfers. In effect, the
accounts assign those prospective net taxes to
the current population of 20-year-old U.S.
males. That assignment raises the (per capita)
generational account; a higher immigration rate
increases it still more.
The accounts of living generations typically
vary by less than 2 percent in response to population differences. The percentage differences
tend to be greatest at the ages with the highest
mortality rates—newborns and seniors. The
alternative populations assume greater differences in their mortality rates and thus imply
greater proportional differences in their generational accounts. Fertility rates affect only the
population of future generations, not the accounts of current generations.
For future generations, fertility, mortality,
and net immigration rates all play a role. The
higher fertility rates of Alternative I imply
larger future generations to share the residual
burden, thereby reducing their lifetime net tax
rates. Higher mortality rates play a smaller and
partly offsetting role. Fewer young people live
to pay taxes in middle age, fewer middle-aged
people live to collect benefits in old age, and
fewer old people live to collect them for as
long a period. Given the age pattern of net
immigration, a higher immigration rate implies
relatively more workers.
The lifetime net tax rates of future generations respond more to alternative populations
than do those of current newborns. Even if differences in mortality produce a relatively small
change in the account of any one current generation, their combined effect produces a relatively large change in the residual burden on
future generations. Under the various population assumptions, the lifetime net tax rate for
future generations ranges from about 41 percent
under Alternative I to about 58 percent under
Alternative III. The degree of generational
imbalance ranges from 52 percent under Alternative I to 90 percent under Alternative III.
Thus, even under optimistic assumptions about
the population, the reference policy remains
unsustainable.

IV. Policies for
Eliminating
Generational
Imbalance
Alternative Ways
to Indicate the Extent
of Generational
Imbalance
So far, we have assumed that living generations
pay net taxes as scheduled for the rest of their
lives. The spending side of the fiscal schedules
examined here have followed the reference
policy or an alternative policy (either constant
real federal purchases or slow growth in
Medicare outlays, or both). We have further
assumed that all future generations share the
resulting residual burden proportionately by
paying the same lifetime net tax rate. Given the
other reference assumptions, each policy we
have considered has been generationally imbalanced (that is, future generations must pay a
higher lifetime net tax rate than current newborns) and is thus unsustainable.
Some observers have criticized this way of
analyzing the generational stance of fiscal policy, arguing that if a fiscal schedule is unsustainable, lawmakers will change it so that some
or all living generations will pay higher net
taxes, and future generations will pay less than
they otherwise would have (see, for example,
Eisner [1994] and Haveman [1994]).27 To address this concern, we now calculate policy
changes that would equalize the lifetime net tax
rates of current newborns and future generations. The policies we examine involve permanently raising particular taxes or cutting particular outlays by a policy-specific percentage
starting in 1998, 2003, or 2016. The different
policies result in different equalized lifetime net
tax rates on current newborn and future generations, and require different dollar amounts of
tax increases or outlay cuts in the first year of
their implementation.

■ 27 Another criticism stems from the Ricardian equivalence proposition, which states that current generations, perceiving that higher current
deficits entail higher net taxes on future generations, will respond by
increasing their saving and bequests. However, formal tests fail to detect
the altruistic behavior required for Ricardian equivalence to hold. See
Altonji, Hayashi, and Kotlikoff (1992, 1997).

T A B L E

Policies for Equalizing the
Lifetime Net Tax Rates of Current
Newborns and Future Generationsa
Required Percentage Change

No change in lifetime net tax rates
Current newborns
Future generations

Ref.
(1)

Slower
Purchases
Growthb
(2)

—
—

Slower
Slower Health Care
Health
and
Care
Purchases
c
Growth
Growth
(3)
(4)

—
—

Equalized Lifetime Net Tax Rate
Slower
Slower
Health
Slower
Health
Care and
Purchases
Care
Purchases
Ref.
Growthb Growthc
Growth
(5)
(6)
(7)
(8)

28.6
49.2

28.6
44.6

30.9
38.1

30.9
33.5

Panel A: Policy Change in 1998

Tax increases
Income tax d
Income tax (federal only)
Payroll tax
Other taxes e
All taxes
Transfer cuts
Social Security f
Health care
All transfers
Purchases cuts
Entire government
Federal

20.4
24.9
31.0
39.7
8.9

15.8
19.4
24.1
30.8
6.9

7.1
8.7
10.8
13.8
3.1

2.6
3.1
3.9
5.0
1.1

31.9
31.9
32.4
33.3
32.3

31.1
31.1
31.6
32.2
31.5

32.1
32.1
32.3
32.6
32.2

31.3
31.3
31.4
31.5
31.4

47.5
36.8
18.5

36.9
28.6
14.3

16.5
16.8
7.3

5.9
6.0
2.6

30.1
31.3
31.0

29.8
30.7
30.5

31.4
31.8
31.7

31.1
31.2
31.2

15.4
38.7

12.3
31.1

5.3
13.5

2.0
5.0

28.6
28.6

30.9
30.9

Panel B: Policy Change in 2003

Tax increases
Income tax d
Income tax (federal only)
Payroll tax
Other taxes e
All taxes
Transfer cuts
Social Security f
Health care
All transfers
Purchases cuts
Entire government
Federal

25.3
31.0
38.7
50.8
11.2

19.7
24.1
30.1
39.5
8.7

8.8
10.8
13.5
17.7
3.9

3.2
3.9
4.8
6.4
1.4

32.6
32.6
33.4
34.0
33.1

31.7
31.7
32.3
32.8
32.1

32.3
32.3
32.6
32.8
32.5

31.4
31.4
31.5
31.6
31.5

57.4
42.2
21.8

44.6
32.8
16.9

20.0
20.2
8.8

7.2
7.3
3.2

30.3
31.6
31.3

29.9
31.0
30.7

31.5
31.9
31.8

31.1
31.3
31.3

19.5
50.1

15.8
40.6

6.8
17.4

2.5
6.5

28.6
28.6

30.9
30.9

Panel C: Policy Change in 2016

Tax increases
Income tax d
Income tax (federal only)
Payroll tax
Other taxes e
All taxes
Transfer cuts
Social Security f
Health care
All transfers
Purchases cuts
Entire government
Federal

45.4
55.3
70.3
102.0
20.6

35.2
43.0
54.6
79.2
16.0

15.8
19.2
24.5
35.5
7.2

5.7
6.9
8.8
12.8
2.6

35.5
35.6
36.9
35.9
35.9

34.0
34.0
35.0
34.3
34.3

33.3
33.3
33.8
33.5
33.5

31.8
31.8
32.0
31.9
31.8

94.9
63.7
34.6

73.8
49.5
26.9

33.0
32.7
14.6

11.9
11.7
5.2

30.8
32.7
32.4

30.3
31.8
31.5

31.7
32.3
32.2

31.2
31.4
31.4

35.4
92.5

30.0
78.4

12.3
32.2

4.8
12.6

28.6
28.6

30.9
30.9

a. Current newborns are the generation born in 1995. Future generations are those born in 1996 and thereafter. Figures are percentages.
b. Federal purchases are held constant in real terms after the year 2000.
c. Per capita spending by age on health care grows 2 percentage points slower than under the reference policy through 2003, then
increases at the same rate as labor productivity.
d. Federal, state, and local.
e. Includes excise taxes, other indirect taxes, and property taxes.
f. Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds.
NOTE: Calculations incorporate CBO projections.
SOURCE: Authors’ calculations.

Percentage
Changes Needed
in Various Programs
to Reach Balance
The first two rows of table 11 repeat the lifetime
net tax rates on current newborns and future
generations under the alternative assumptions.
The remaining rows list alternative tax, transfer,
or purchase policies that may be used to restore
generational balance, while the columns indicate the assumptions (reference, constant real
purchases, slow health care growth, and so on)
underlying the calculations. The first four columns show the required percentage change,
and the last four columns indicate the equalized
value of the lifetime net tax rate under each
row-specific policy and column-specific
assumption.28
Given the other reference assumptions, balance can be achieved in 1998 by permanently
raising the schedules for all income taxes on
current generations by 20.4 percent (panel A,
row 1, column 1). That equalizes lifetime tax
rates at 31.9 percent, raising the rate on current
newborns from 28.6 percent and lowering the
rate on future newborns from 49.2 percent
(panel A, row 1, column 5). If real federal purchases remain constant after 2000, the required
hike in income taxes is 15.8 percent, implying
an equalized lifetime net tax rate of 31.1 percent (panel A, row 1, columns 2 and 6). If
Medicare spending grows slowly, the income
tax hike is even smaller (7.1 percent), but the
equalized lifetime net tax rate rises (32.1 percent). With constant real federal purchases and
a deceleration in Medicare outlays, the required
tax increase is smaller yet (2.6 percent), and the
equalized lifetime net tax rate is 31.3 percent.
Similarly, if we fix the other reference assumptions and change the various fiscal programs, balance can be reached via several alternative policies, including a hike in taxes of
8.9 percent, a cut in Social Security transfers of
47.5 percent, a cut in health care outlays of 36.8
percent, or a reduction in all purchases of
15.4 percent (column 1). These policies equalize the lifetime net tax rates of current newborns and future generations at values that
differ by policy, namely, 32.3 percent for raising all taxes, 30.1 percent for cutting Social
Security benefits, 31.3 percent for cutting all
health care benefits, and 28.6 percent for cutting all purchases. (The reasons for these differences are explained below.)

Variation in
Percentage Changes
and Equalized
Lifetime Net
Tax Rates
Why do the percentage changes and the equalized lifetime net tax rates differ across each
row and down each column of table 11? Moving across each row, the respective percentage
changes are lower because the underlying
assumptions involve progressively smaller
degrees of initial imbalance. Hence, restoring
balance requires progressively smaller percentage changes in a row-specific policy.
Across each row, there is no general pattern
for the level of the equalized lifetime net tax
rate, but there is a pattern for the change in the
lifetime net tax rate of current newborns. For a
change in a given tax or transfer, the change in
that lifetime rate is smaller as we move across
each row. For example, an increase in the
income tax that restores balance raises the lifetime net tax rate of current newborns by 3.3
percentage points under the reference policy
(31.9 percent versus 28.6 percent). But that lifetime rate rises by 2.5 percentage points when
real purchases remain constant, by 1.2 percentage points when Medicare spending grows
slowly, and by 0.4 percentage point when real
purchases remain constant and Medicare
spending grows slowly.
For a cut in purchases, the net taxes of all
living generations remain unchanged, so the
lifetime net tax rate of current newborns stays
at its initial value as we move across each row.
However, cutting purchases lowers the residual
burden on future generations, and achieving
balance requires that the cut be large enough
to reduce the rate on future generations until it
equals that on current newborns.
For a column-specific initial policy, variation
in the outcome depends largely on which generations are most affected by the row-specific
change in policy. On average, older individuals
pay more in taxes on capital income and
receive more in transfers from Social Security,
Medicare, and Medicaid. Thus, a change in the
schedule for such a tax or transfer will make
every living generation contribute more—the
old now, the young later. By contrast, a change

■ 28 A table indicating the initial dollar amounts of revenue
increases and transfer or purchase reductions for each of the policies
considered in table 11 is available from the authors upon request.

in the schedule for a program that primarily
affects young individuals effectively reduces the
number of generations that make additional
contributions. Therefore, between two programs of the same initial size, an equalizing
policy that affects the old more than the young
will require both a smaller percentage change
and a smaller increase in the lifetime net tax
rate on current newborns. The aging of the
population and the rapid rise in medical costs
greatly magnify these effects.

government purchases must fall or scheduled
net tax rates must rise—if not for living generations, then for future ones. We have described
the sizes of hypothetical policy changes that
would restore generational balance. They appear large, but failure to act soon will require
even bigger changes in the future.

Appendix 29

Costs of Waiting

The Method of
Generational
Accounting

Waiting for five years, until 2003, before under-

The method of generational accounting takes as

taking such policies requires larger changes
than acting sooner (compare the first four
columns in panel B with those in panel A).
Under the reference scenario, the delay in trimming purchases again leaves the equalized lifetime net tax rate at the same level as that for
current newborns. However, the required percentage cut is larger than when action is taken
sooner (19.5 versus 15.4 percent). Acting later
to raise taxes or to cut transfers results in a
higher equalized lifetime net tax rate than does
acting sooner. The delay implies that some living generations escape the higher taxes or
lower transfers, meaning that living and future
generations must each bear higher lifetime net
tax rates.
Waiting until the year 2016—about the time
the largest baby boom generations will retire—
requires even greater changes (see panel C).
Again, except for purchase cuts, the lifetime net
tax rates in panel C are higher than their counterparts in panel B. Such a long delay in restoring balance will involve unrealistically high tax
increases, benefit cuts, or purchase reductions.
For example, it would mean defaulting on
95 percent of Social Security’s implicit obligations to living generations.

its starting point the government’s present-value
(intertemporal) budget constraint. This constraint is the same as equation (1) in the text
and is reproduced here only for convenience.

Conclusion
Reasonable economic and demographic
assumptions imply that the generational stance
of U.S. fiscal policy remains seriously imbalanced. Although the degree of this imbalance
has declined from two years ago, the reference
scenario implies lifetime net tax rates of 49.2
percent for future generations and 28.6 percent
for current newborns. The schedule of such a
policy cannot persist. At some point, projected

(A1)

PVGt = NWGt + PVLt + PVFt .

Equation (A1) says that at time t (the base
year), the present value of prospective government purchases of goods and services, PVGt ,
must be paid for by the sum of three items: the
net wealth of the government, NWGt ; the present value of prospective aggregate net tax payments by generations living at time t, PVLt ; and
the present value of aggregate net tax payments
by future generations born after time t, PVFt .
The term “net tax payments” refers to taxes
paid to the government net of transfers received from it. The “generational account” is a
dollar amount, defined as the actuarially discounted present value of per capita net tax payments of a generation over the rest of its life.
Note that equation (A1) can be viewed as a
financing constraint. Under a given policy for
prospective government purchases, future generations must pay for the purchases that are not
covered by the government’s current net wealth
plus living generations’ prospective net taxes.
Generational accounting examines how alternative fiscal policies would affect the size of the
aggregate required net payment, its division
between PVLt and PVFt , and, under certain
assumptions, its distribution across living and
future generations. The following discussion
describes the method for estimating the components of equation (A1).

■ 29 This Appendix draws heavily on Gokhale (1998).

The sum of generational accounts over all
members of living generations, PVLt , can be
written as
D

(A2)

PVLt = ^ (n mjt ,t p mjt ,t + n fjt ,t p fjt ,t ),
jt = 0

where D is the maximum age of life, p mjt ,t and
p jtf ,t represent the populations of males and
females, and n mjt ,t and n jft ,t represent the generational accounts in year t of males and females
aged j in year t (indexed by jt )—that is, the
respective present values as of year t of the per
capita net taxes they will pay over the rest of
their lives.
The generational account, n xjt ,t , where the
superscript x stands for male or female, is
defined by
(A3)

n xj ,t =
t

1
p xjt , t

t + D – jt

^ p xjt ,s ^ q xi,jt ,s R s – t ,

s=t

i =1

where R = 1/(1 + r), and r is the discount rate.
Equation (A3) expresses the actuarially discounted value of prospective per capita net
payments of a generation aged j at time t. The
account for each generation is calculated by
1) finding the algebraic sum of the per capita
taxes and transfers paid in each year s by the
members surviving in that year (including people of that age and sex who have immigrated
since year t), 2) multiplying that sum by the
population in year s, 3) discounting the result
back to time t, 4) aggregating such discounted
values over the generation’s lifetime, and 5)
dividing the result by the generation’s population in year t. In equation (A3), q xi,jt ,s stands for
the per capita payment (or receipt, when q is
negative) of type i in year s (>t) by a generation of sex x aged j in year t. The per capita
net payment—after accounting for all (m) types
of taxes and transfers in year s —is given by the
sum in parentheses. This term, multiplied by the
population of such persons in year s, p xj , s ,
t
yields the aggregate net payment that individuals of sex x aged j in year t make in year s. 30
Summing such discounted values for each year
s over the remaining life of individuals aged
j in year t (from t to t + D – jt ) yields the discounted value of their aggregate net payments.
Division by p xj ,t , the population of such persons
t
in year t, converts this actuarially discounted
sum to a per capita amount and represents the
generational account of the generation aged j
in year t.

The prospective per capita payments of each
type of tax (or transfer) are estimated by distributing projected aggregate payments of that type
by age and sex. In making the distribution, generational accounting begins with projections of
population and of aggregate taxes and transfers. To each type of aggregate tax or transfer
projection, it applies a relative profile by age
and sex normalized to a 40-year-old male. For
example, the relative profile value for a 38year-old woman is the ratio of her payment to
that of a 40-year-old man. Relative profiles for
various taxes and transfers are estimated from
survey data, and the latest available profiles are
used to distribute projected aggregate payments by age and sex in future years.31 Projections of aggregate payments may be unavailable for years far into the future. In this case,
the relative profiles are used to distribute, by
age and sex, the aggregate payments in the last
available year (actual or projected). This yields
per capita payments by age and sex for that
year. Per capita values for later years are
obtained by making the per capita values for
the last available year grow at the same rate as
labor productivity (g). Hence, if the last available year is s,
(A4)

q xi,j , s + k = q xi,j ,s (1 + g )k, i = 1, 2, ...m.
t

The relative profiles and associated aggregate payments and receipts specify the pattern
of prospective per capita payments and receipts imposed on various generations living at
time t, and therefore collectively embody the
generational stance of fiscal policy at time t.
Because all relative profiles are normalized to
average payments by 40-year-old males, the
per capita payment by 40-year-old males can
be expressed as
(A5)

q xi,40 , t =
t

Qi,t
D

jt = 0

r mi, j ,t p mj ,t
t
t

.
+

r i,f j ,t
t

p jf ,t
t

■ 30 For the United States, estimates of p xj , s are those of the SSA.
t

■ 31 For the United States, these estimates are taken from the University of Michigan’s Survey of Income and Program Participation, the
Census Bureau’s Current Population Survey, the SSA’s Annual Statistical
Supplement to the Social Security Bulletin, the Health Care Financing
Administration, and the Survey of Current Business. For a discussion of
the treatment of individual taxes and transfers, see Auerbach, Gokhale, and
Kotlikoff (1991, 1994) and Kotlikoff (1992).

Here, r xi, j , t represents the per capita payt
ment (or receipt, if negative) of type i that a
person aged j in year t makes relative to the
payment of a 40-year-old male in year t, and
Qi, t represents the aggregate payment of type
i made in year t. Of course,

males to that of future females born in the
same year is kept equal to the corresponding
ratio under the assumed policy for current newborn males and females (who are members of
living generations). Hence,
(A7)

(A6)

PVGt is estimated by discounting prospective aggregate government purchases back to
year t. If projections of aggregate purchases are
unavailable or need to be extended, they are
estimated by distributing, according to age, the
per capita purchases in the last year (actual or
projected) for which an aggregate figure is
available, by making the per capita purchases
by age grow at the same rate as labor productivity, and finally, by using a population projection to aggregate the per capita figures.32 As
with the per capita distribution of taxes and
transfers, the estimates for purchases assume a
constant relative profile by age—a set of empirically determined ratios that represent an
element of the current generational stance of
fiscal policy.
Government net wealth, NWGt , can be estimated by cumulating the sum of past government surpluses (or deficits, if negative). The
government’s existing tangible assets, such as
parks and infrastructure, are excluded from
NWGt , and their prospective service flows,
which represent the consumption of public
goods, are excluded from PVGt . If these assets
were included in NWGt, their service flows
would have to be included in PVGt . Because
the value of the assets must, by definition,
equal the present value of their consumption
flows, they would cancel each other if they
were included in equation (A1). Thus, the
exclusions do not affect the trade-off between
PVLt and PVFt .
Because equation (A1) must hold at time t,
and because three of the four elements in that
equation have been estimated, the fourth term,
PVFt , can be calculated as a residual. The distribution of this residual aggregate net payment
among unborn generations is indeterminate. As
an illustrative device, therefore, generational
accounting distributes the residual burden,
PVFt , among all future generations on an equal
(growth-adjusted) basis. That is, if labor productivity grows at rate g, the generational
account of each future generation is (1 + g)
times that of its immediate predecessor. The
ratio of the generational account of future

x =m, f; jt = 0... D.

PVGt – NWGt – PVLt =
∞

q xi, j , t = q xi,40 ,t r xi, j ,t

m
0s ,s

s = t +1

p m0 ,s + n 0f

s ,s

p 0f

s ,s

s – t,

where n x0 ,s is the generational account of the
s
generation of sex x aged 0 in year s, and p x0 ,s
s
is the population of such individuals in year s.
To normalize the generational accounts of each
future generation to that of the males of that
generation, let fm be 1, so that f f = n 0f ,s /
s
nm0 ,s , s = t + 1,... ∞, is the ratio of the generas
tional account of future females born in year s
to that of future males born in year s. Further,
let the generational accounts of future males
grow generation by generation at rate g, so that
nm0 ,s + 1 /nm0 ,s = (1+g), s = t,...∞. Dividing
s +1

and multiplying the right side of equation (A7)
by nm0 , t + 1 and manipulating the expression
t+1
within parentheses yields
(A8)

nm0

,t +1

t +1

∞

^
s = t +1

= PVGt – NWGt – PVLt /

m
0s , s

+ f fp 0f

s ,s

s–t (1+g) s – (t +1).

The term on the left side of equation (A8)
is the generational account as of year t +1 for
males born in that year, and n 0f , t + 1 =
t +1
f fn m0 , t + 1 is the generational account for
t +1
females born in that year.33 Because at any
time t, both newborns and future generations
have their entire lives ahead of them, it is legitimate to compare the generational accounts of
the generation born in year t to that of the generation born in year t +1. Note, again, that the
latter represents an equal (growth-adjusted) distribution among future generations of the aggregate residual burden, PVFt . The difference

■ 32 Many yearly government purchases, such as for defense and
general administration, cannot be assigned to specific age groups and are
prorated to all individuals alive in that year. Note that generational accounting uses estimates of government purchases by age only to mechanically
extend the projections of those purchases. Ordinarily, it does not try to
assign the benefits of purchases by age and sex.
■ 33 Note that the summation in the denominator goes to infinity,
while our population projections extend only through 2200. The calculations assume that beyond that year, the size and the age composition of the
population remain fixed at their 2200 levels.

between the measures for current newborns and
future generations computed as a percentage,
(A9)

nm0

,t+1
t+1

m (1+g)
0t ,t

2 3 100,

provides a gauge of the degree of “imbalance”
implied by the assumed fiscal policy.
An alternative measure of the fiscal burden
on a generation is the lifetime net tax rate that
it faces under the assumed policy. This rate is
computed as the ratio of the generational
account at birth to the present value at birth of
per capita labor income over the generation’s
entire life. Thus, we can express the lifetime
net tax rate, t, as
n xj ,t – j
t
t
,
(A10) t xj , t – j =
t

t + D – jt

^ lxj , s R s – (t – jt )

s = t – jt

where t xj , t – j is the lifetime net tax rate of the
t
t
generation of sex x aged j in year t, and lxj , s
t
is this generation’s per capita labor earnings
in year s.34 Note that net taxes are summed
over the entire life of the generation, and the
present values for both the numerator and the
denominator are computed as of the generation’s year of birth, t – jt . The lifetime net tax
rate represents the fraction of the present value
at birth of lifetime labor earnings that will be
paid to the government. Hence, in computing
lifetime net tax rates for living generations, it is
necessary to include past as well as prospective
net taxes in the numerator, and past as well as
prospective labor earnings in the denominator.

References
Altonji, J., F. Hayashi, and L.J. Kotlikoff. “Is
the Extended Family Altruistically Linked?
Direct Tests Using Micro Data,” American
Economic Review, vol. 82, no. 5 (December
1992), pp. 1177–98.
_______ , ______ , and _______ . “Parental
Altruism and Inter Vivos Transfers: Theory
and Evidence,” Journal of Political Economy, vol. 105, no. 6 (December 1997),
pp. 1121–66.
Auerbach, A.J., J. Gokhale, and L.J. Kotlikoff. “Generational Accounts: A Meaningful
Alternative to Deficit Accounting,” in D.
Bradford, ed., Tax Policy and the Economy,
vol. 5. Cambridge, Mass.: MIT Press and the
National Bureau of Economic Research,
1991, pp. 55–110.
______ , _______ , and _______ . “Generational
Accounting: A Meaningful Way to Evaluate
Fiscal Policy,” Journal of Economic Perspectives, vol. 8, no. 1 (Winter 1994), pp. 73–94.
_______ , _______ , and _______ . “Restoring
Generational Balance in U.S. Fiscal Policy:
What Will It Take?” Federal Reserve Bank of
Cleveland, Economic Review, vol. 31, no. 1
(Quarter 1 1995), pp. 2–12.
Congressional Budget Office. Who Pays and
When: An Assessment of Generational
Accounting, November 1995.
_______ . Long-term Budgetary Pressures and
Policy Options, March 1997a.
________ . An Economic Model for Long-run
Budget Simulations, July 1997b.

■ 34 Ideally, the method would use lifetime total income, including
income from labor and capital and (private) net transfers from other generations. To the extent that capital income represents the normal return on
saving, the present value of this income equals the amount of that saving.
If this were the only source of income other than labor, the present value at
birth of a generation’s total income would equal that of its labor income.
However, if a generation receives higher-than-normal returns on saving
(including capital gains) and/or private net transfers from other generations, this result will not be true. The difference due to these items is typically less than 10 percent, but unlikely to be as large as 20 percent.
Because of a lack of reliable data on these income sources, generational
accounting ignores private intergenerational transfers and extranormal
returns in computing lifetime net tax rates.

________ . The Economic and Budget Outlook:
An Update. Washington, D.C.: U.S. Government Printing Office, September 1997c.
Eisner, R. “The Grandkids Can Relax,” The
Wall Street Journal, November 9, 1994.
Gokhale, J. J. “Demographic Change, Generational Accounts, and National Saving in the
United States,” in A. Mason and G. Tapinos,
eds., Sharing the Wealth: Demographic
Transfers and Economic Transfers between
Generations. International Union for the
Scientific Study of Population, 1998
(forthcoming).

Haveman, R. “Should Generational Accounts
Replace Public Budgets and Deficits?”
Journal of Economic Perspectives, vol. 8,
no. 1 (Winter 1994), pp. 95–111.
Health Care Financing Administration.
Annual Report of the Board of Trustees of the
Federal Hospital Insurance Trust Fund, 1997.
Kotlikoff, L.J. Generational Accounting:
Knowing Who Pays, and When, for What
We Spend. New York: The Free Press, 1992.
Social Security Administration. Annual
Report of the Board of Trustees of the Federal
Old-Age and Survivors Insurance and Disability Insurance Trust Funds, 1997.
U.S. Department of Education. Digest of Education Statistics, 1995. Office of Educational
Research and Improvement, National Center
for Education Statistics, Washington, D.C.:
U.S. Government Printing Office, 1997.

Does Intervention
Explain the Forward
Discount Puzzle?
by William P. Osterberg

Introduction
Although neither the Federal Reserve System
nor the U.S. Treasury has intervened in foreign
exchange markets since August 1995, the policy has not been officially abdicated by the
United States, Germany, or Japan.1 Several
Southeast Asian central banks have conducted
interventions recently in an attempt to maintain exchange-rate pegs and counter the volatility associated with capital flows. This implies
a belief that intervention can alter either the
level or the volatility of exchange rates.2
A large body of research, however, questions
intervention’s usefulness, generally finding that
the policy has consequences that seem to vary
with the period being studied, effects that are
inconsistent with the theoretical mechanisms
through which intervention might operate, and
ultimately, little impact. Such findings must be
evaluated in light of the general failure of economic theories of exchange-rate movements
when it comes to explaining actual rates. Unfortunately, most central banks provide little
day-to-day information about intervention actions, making it difficult to test hypotheses
about intervention’s effectiveness. This lack of
data supports speculation that intervention

William P. Osterberg is an economist at the Federal Reserve Bank
of Cleveland. He thanks Joseph
Haubrich, Owen Humpage, Peter
Rupert, and James Thomson for
helpful comments and suggestions, and Jennifer DeRudder for
research assistance.

might explain some of the anomalies in international finance.
Recent research has provided insight into
one such anomaly—the forward discount puzzle. This refers to the finding that the currencies
of countries with high interest rates appreciate
in value, instead of declining, as uncovered interest parity (UIP) might imply. The relevance
of the relationship between interest-rate differentials and movements in currency values is
obvious from even a casual perusal of the financial press’ analyses of currency market developments. These stories usually explain currency appreciations in terms of unexpected
economic strength, which would imply higher
short-term interest rates. One might be tempted
to conclude that the financial press accepts the
■ 1 By law, the Treasury could intervene alone. Typically, however, the
Treasury and the Federal Reserve act together and with equal authority. All
official exchange-market transactions are conducted by the Federal Reserve
Bank of New York, which maintains one account for the Treasury and one for
the Federal Reserve (see Humpage [1994] for further discussion).
■ 2 It is not clear at this time whether the 1997 intervention operations conducted by Southeast Asian central banks were sterilized so as to
have no direct impact on monetary aggregates. Unsterilized intervention is
not distinct from monetary policy.

anomaly as fact.3 The forward discount puzzle
can also be described as the finding that the
forward rate on foreign exchange predicts the
wrong direction of movement for the spot
exchange rate. The myriad studies that have
focused on this puzzle have been dominated
by issues of statistical inference, although a few
papers have demonstrated a role for exchangerate policies.
In this article, I utilize official data on U.S.
and German central bank interventions to examine the connection between these actions
and the forward discount puzzle for the German mark/U.S. dollar (DM/$) and Japanese
yen/U.S. dollar (Yen/$) exchange rates from
1985 to 1991. This work is motivated partly by
the findings of Flood and Rose (1996; henceforth FR) that countries with higher interest
rates are more likely to have their currencies
appreciate (the forward discount puzzle) if their
exchange rate is floating rather than fixed.
Another motivation comes from evidence, presented in Baillie and Osterberg (1997), that is
consistent with intervention affecting a risk premium in the forward market. Because interventions are often motivated by a desire to influence the level (or volatility) of the exchange
rate, by some measures they could be related
to the distinction between fixed and floating
exchange-rate regimes.4 I thus estimate regressions of exchange-rate changes on interest-rate
differentials for the full sample period and for
subperiods when intervention was relatively
heavy or when policymakers expressed willingness to intervene. At least for the DM/$, the
forward discount puzzle is stronger during the
interventionist subperiods. This appears to
strengthen FR’s finding that policy is an important determinant of exchange rates’ response to
interest-rate differentials.
This article is organized as follows: Section I
reviews the relevant portion of the literature
analyzing the impact of central bank intervention. Section II summarizes recent studies of
the forward discount puzzle, including some
papers that suggest a role for intervention. Section III discusses the data and the simple analytical framework used here to discover if intervention might explain a portion of the puzzle.
Section IV presents the results, and section V
states the conclusions.

I. Evidence on the
Impact of Central
Bank Intervention
Thorough summaries of evidence on the impact of central bank intervention are provided
by Edison (1993) and Almekinders (1995). Typically, U.S. intervention operations are sterilized
by an offsetting transaction with government
securities that leaves the monetary aggregates
unaffected. Because nonsterilized intervention
can be considered a form of monetary policy,
most research has focused on sterilized intervention, which is usually thought to operate
either through a portfolio balance channel or
by giving the marketplace signals of future government policies. In the former case, the magnitude of an intervention’s impact is predicted
to depend on the size of the intervention relative to the portfolios of investors choosing
between government debt denominated in different currencies.5 Given the immensity of currency holdings, it is perhaps not surprising that
researchers have usually found no significant
portfolio balance effect. The signaling channel
would be operative if the intervening authorities had information not already available to the
market. Such information might take the form
of economic data, which, if public, would suggest a higher market value for the currency. The
information could also take the form of policy
intentions to boost the value of the currency.
Generally, evidence regarding the portfolio
balance channel has been negative. Although
some impact is found, the coefficients’ signs are
often inconsistent with the theory, one implication of which is that purchases of domestic currency—and the offsetting sales of domestic
government securities—could induce investors
to hold relatively more domestic securities only
if the domestic currency increased in value.
However, the empirical performance of models
of the risk premium in foreign exchange rates
has generally been unsatisfactory.

■ 3 On the other hand, as can be inferred from equation (1), UIP
directly implies that interest differentials correspond only to expected
exchange-rate movements, not to actual movements. Thus, an apparently
anomalous increase in the currency value might itself be associated with
an expected depreciation that is greater than before.
■ 4 However, it is unclear what measure of intervention is relevant in
this context. Obvious candidates include the frequency of intervention and
its magnitude.
■ 5 The portfolio balance theory rests on two key assumptions: first,
that investors view bonds of different currency denominations as imperfect
substitutes, and second, that Ricardian equivalence does not hold.

Research on the signaling channel has had
little more success in explaining the comovements of intervention, monetary aggregates,
interest rates, and exchange rates. This likewise
might not seem surprising, considering the failure of monetary models of exchange-rate determination. After all, if monetary policy has little
predictive power for exchange rates, why
should we expect intervention’s impact on
exchange rates to be consistent with the future
monetary decisions that intervention implies?
The signaling mechanism does not make sense
unless the impact of intervention on exchange
rates (for example, U.S. authorities buying German marks with U.S. dollars, thus increasing
DM/$) is generally consistent with subsequent
monetary policy (such as decreased U.S. interest rates). Klein and Rosengren (1991) find no
predictable relationship between intervention
and monetary policy, and Kaminsky and Lewis
(1996) report that intervention’s impact on
exchange rates is sometimes inconsistent with
the monetary policy it appears to signal.6

II. Recent Research
on the Forward
Discount Puzzle
The forward discount puzzle can be understood
by considering two separate relations. Equation
(1) states UIP that equates the expected gross
return at time t from investing one U.S. dollar
for a period of length k at rate rt,k with the
expected gross return from converting the dollar
to a foreign currency (at rate st , which denotes
foreign currency units per dollar), investing the
proceeds at the foreign rate rt ,k *, and converting back to U.S. dollars at the future exchange
rate st + k .7
(1)

(3)

st + k – st = rt, k * – rt, k + vt, k ,

where s and r are in logarithms, and v reflects
the difference between the actual and expected
future spot rate. UIP is usually tested by estimating (4):
(4)

st + k – st = a + br (rt , k* – rt , k ) + vt, k .

The forward discount puzzle is that br , estimated from (4), is usually negative instead of
being equal to +1, as implied by (3). The findings regarding (4) are closely related to the
findings when the following version of equation (2) is estimated:8
(5)

st + k – st = a + bf ( ft , k – st ) + ut, k .

As Engel (1996) carefully documents, econometric estimates of bf are often negative and
almost always significantly different from +1.
Recent research, however, has advanced intriguing possibilities for explaining the puzzle.9
For example, Baillie and Bollersev (1997) demonstrate that the apparently anomalous estimates of bf might result from a combination of
persistent autocorrelation in the forward premium and the small size of the samples typically
studied. FR also provide evidence on the importance of the sample when they estimate (4)
with pooled data for exchange rates within the
exchange-rate mechanism (ERM) of the European Monetary System. The estimate of br declines when periods of realignment are excluded. This implies that the forward discount
puzzle might be explained partly by using samples in which realignments are anticipated more

Et (1 + rt ,k ) = Et [st (1 + rt,k *)/st + k ].

In this equation, only the future exchange
rate is unknown, and Et refers to the expectation based on knowledge available at time t.
A second relation defines the risk premium
as the difference between the expected future
spot exchange rate and the current forward rate
that would settle on the same date as the future
spot rate. Thus, the difference between the
actual future spot rate and the forward rate
equals the risk premium plus an error term
equaling the difference between the actual and
expected future spot rates (ut,k ):
(2)

In (2), s and f refer to the logarithms of the
spot and forward rates.
Equation (1) is often rewritten as

st, k – ft, k = rt, k + ut, k .

■ 6 A recent analysis of U.S. intervention in the 1990s (Humpage
[1997]) concludes that the authorities apparently had no information superior to that of the market. Such a finding is generally inconsistent with the
view that intervention signals new information about future monetary policy.
■ 7 Here, “uncovered” refers to the fact that the risk posed by uncertainty about the future exchange rate has not been eliminated (covered)
through use of a forward contract or other instrument. In covered interest
parity (CIP), the expected future exchange rate in (1) is replaced by the
forward rate.
■ 8 Adding ft, k – st to both sides of (2) yields (5) if the risk premium
equals 0, a = 0, and b = 1. Hence, rejecting a = 0 and b = 1 is often seen
as indicating the existence of a risk premium in the forward market.
■ 9 Another promising line of research utilizes term structure
models. See Bansal (1997).

F I G U R E

Exchange-Rate Changes and
Interest-Rate Differentials: DM/$

F I G U R E

Exchange-Rate Changes and
Interest-Rate Differentials: Yen/$

bolster a currency’s value because interest rates
are expected to increase, implying the relevance
of expected monetary policy. Obviously, any
correlation between interest-rate and exchangerate movements would also be affected by
interventions that successfully prevent currency
appreciation.
At least three studies suggest that exchangerate policy might provide a partial explanation
of the anomaly. FR estimate (4) using floatingrate data for several currencies’ quotes against
the dollar, and also using fixed-rate data for
currencies within the ERM, quoted against the
German mark. Their finding that estimates of
br became more positive for the fixed-rate
data suggests the importance of exchangerate regimes.
The analysis of (2) in Baillie and Osterberg
(1997) shows that central bank intervention
influenced risk in the forward market. This
points to the existence of a risk premium that
can be explained partly by central bank operations. Loopesko (1984) finds that central bank
intervention sometimes has explanatory power
for deviations from the UIP condition in equation (1).10 Taken together, these findings suggest that intervention might be related to the
forward discount anomaly. For example, if
intervention is interpreted as an attempt to “fix”
or control exchange rates, then periods of
heavy intervention might be associated with
more positive estimates of br .

III. The Data
and the Analytical
Framework
To see if the sign of the estimate of br varies

a. Calculated as log [s (t + k)] – log [s (t )].
b. Calculated as log [l + i *(t )] – log [l + i *(t )].
SOURCE: Author’s calculations.

frequently than they occur. This phenomenon is
often referred to as the “peso problem.”
That monetary policy—or exchange-rate
policy—could help explain the anomaly is suggested by the financial press’ interpretations of
short-term movements in exchange rates. News
of unanticipated economic strength is said to

among periods of light versus heavy intervention, I use the official daily intervention data
supplied by the Board of Governors of the Federal Reserve System and the Deutsche Bundesbank, in combination with 9:00 a.m. New York
quotes on DM/$ and Yen/$, as well as 3:00 p.m.
London 30-day Euromarket interest rates. Figures 1 and 2 depict movements in the logarithm
of exchange rates and in the difference in the
logarithms of interest rates. The intervention
series equal the net sales or purchases of U.S.
dollars vis-à-vis the foreign currency over the
24-hour period between consecutive business
day closings.

■ 10 Other analyses of the impact of central bank intervention on UIP
are summarized by Edison (1993).

T A B L E

Intervention and Uncovered
Interest Parity: DM/$
Generalized-Method-of-Moments
Estimates of Equation (4)
a (t-statistic) b (t: b = 0)

Sample criterion:
By intervention
9/23/85–
–0.13
11/12/85
(–3.6)
3/23/87–
–0.18
5/4/87
(–6.9)
8/4/87–
–0.27
9/9/87
(–8.8)
10/20/87–
–0.13
1/11/88
(–4.3)
6/9/88–
–0.32
9/27/88
(–5.5)
12/20/88–
–0.25
2/7/89
(–10.2)
4/25/89–
–0.41
6/30/89
(–10.2)
8/11/89–
–0.02
10/11/89
(–1.5)
8/6/85– end
–0.01
(–1.5)
Sample criterion:
EMS realignments a
8/6/85–
0.08
3/27/86
(0.85)
4/21/86–
–0.03
7/25/86
(–0.3)
8/18/86–
0.03
12/31/87
(0.5)
1/26/87–
–0.04
12/29/89
(–4.0)
1/22/90–
0.02
5/16/90
(5.8)
8/6/85–
–0.02
5/15/90
(–3.0)

–3.4
(–3.1)
–6.7
(–7.0)
–9.2
(–9.5)
–3.2
(–4.3)
–10.0
(–6.1)
–7.5
(–10.4)
–14.3
(–13.7)
0.6
(0.6)
0.06
(0.3)

3.25
(1.1)
–0.22
(–0.1)
3.95
(0.8)
–1.46
(–3.6)
7.7
(5.2)
–0.6
(–1.8)

Intervention Data (Number of observations)
Total

Description

Plaza Accord
Louvre Accord

*
After 10/87 crash
*
*
*
*
Full sample

Sample criterion:
By intervention
9/23/85–
11/12/85
3/23/87–
5/4/87
8/4/87–
9/9/87
10/20/87–
1/11/88
6/9/88–
9/27/88
12/20/88–
2/7/89
4/25/89–
6/30/89
8/11/89–
10/11/89
8/6/85– end

Unilateral Coordinated Buy/Sell

0/27

4/0

5/5

30/0

0/57

0/27

0/25

1,485

283

107/206

6/28

10/0

7/1

113

105

56/162

0/2

253

83/196

Sample criterion:
EMS realignmentsa
8/6/85–
3/27/86
157
4/21/86–
7/25/86
64
8/18/86–
12/31/87
90
1/26/87–
12/29/89
720
1/22/90–
5/16/90
79
8/6/85–
5/15/90
1,167

a. See Flood, Rose, and Mathieson (1991).
NOTE: Asterisks indicate periods of relatively heavy intervention. Numbers in parentheses are t-statistics.
SOURCE: Author’s calculations.

The sample period extends from August 6,
1985 through September 6, 1991, a period that
includes two well-publicized Group of Three
(G-3) attempts to influence dollar exchange
rates.11 The Plaza Accord in September 1985
stipulated that the G-3 countries’ central banks
would intervene to bring down the level of the
dollar, and the Louvre Accord of February 1987
included statements that central banks would
strive to reduce fluctuations in the dollar. Other
periods of intervention were defined by examining the actual intervention time series.

These periods were characterized by relatively
heavy or consistent intervention by one or two
of the central banks.
We utilize a generalized-method-of-moments
(GMM) technique to account for the fact that
the error term appearing on the right side of (3)
has a high-order moving average representation
because the data are daily observations on a

■ 11 G-3 refers to the three largest industrialized countries—
Germany, Japan, and the United States.

T A B L E

Intervention and Uncovered
Interest Parity: Yen/$
Generalized-Method-of-Moments
Estimates of Equation (4)
Sample criterion:
By intervention
9/23/85–
11/12/85
4/16/86–
8/7/86
3/24/87–
4/27/87
8/13/87–
9/9/87
10/27/87–
1/21/88
3/15/88–
4/20/88
10/27/88–
12/8/88
4/28/89–
7/21/89
8/7/89–
10/12/89
2/23/90–
4/19/90
8/6/85–
9/6/91

a (t-statistic)

b (t: b = 0)

–0.02
(–2.0)
0.09
(2.6)
–0.3
(–6.3)
0.13
(2.9)
0.08
(–1.1)
–0.02
(–2.9)
–0.08
(–1.8)
0.26
(4.1)
0.08
(4.5)
0.27
(5.4)
–0.01
(–2.4)

3.1
(4.9)
5.8
(2.6)
–11.3
(–6.6)
3.9
(2.7)
–2.3
(–1.1)
–0.9
(–3.4)
–2.3
(–2.4)
7.0
(3.9)
3.2
(4.2)
28.8
(5.7)
–0.2
(–1.1)

Description

Plaza Accord
*
Louvre Accord
*
After 10/87 crash
*
*
*
*
*
Full sample

Intervention Data (Number of observations)
Sample criterion:
By intervention
9/23/85–
11/12/85
4/16/86–
8/7/86
3/24/87–
4/27/87
8/13/87–
9/9/87
10/27/87–
1/21/88
3/15/88–
4/20/88
10/27/88–
12/8/88
4/28/89–
7/21/89
8/7/89–
10/12/89
2/23/90–
4/19/90
8/6/85–end

one-month interest-rate contract. I have matched
the future spot rate with the one-month Eurocurrency interest rate so that both settle on the
same day. As Baillie and Osterberg (1997) point
out, this implies an MA(21) representation. The
standard errors used to calculate the t-statistics
in the tables are also corrected for heteroscedasticity. The instrumental variables chosen are a
constant, the lagged interest-rate differential,
and the lagged change in the logarithm of the
exchange rate. Hamilton (1994, chapter 10) provides a useful review of the issues involved in
GMM estimation.

Total

U.S. Buy

U.S. Sell

38
1,464

0
66

13
116

NOTE: Asterisks indicate periods of relatively heavy intervention. Numbers in
parentheses are t-statistics.
SOURCE: Author’s calculations.

IV. Results
Table 1 presents the results of estimating equation (4) for the DM/$. For the entire sample
period, the estimate of b is slightly positive but
significantly less than one. The finding that the
coefficient is slightly positive is unusual, indicating that the results may be sensitive to the
sample. However, for seven of the eight intervention periods, the estimate of b is not only
significantly different from one but also significantly negative.12 For comparison with FR, I
estimated equation (3) for the periods between
EMS realignments. Unlike FR, I find that the sign
of the estimated b does not seem to depend on
whether these periods are excluded from estimation. However, the realignments and the
analysis in FR pertain to exchange rates of the
European currencies vis-à-vis the German mark.
Apparently, the ERM realignments were not reflected in the DM/$ or in the U.S. and German
interventions vis-à-vis the DM/$.
Table 2 presents similar results from estimating equation (4) for the Yen/$. The full-sampleperiod estimate of b is negative and significantly different from one. However, the results
for the subperiods provide less encouragement
that intervention could somehow explain the
forward discount puzzle: In only four of the 10
subperiods were the estimates of b significantly
negative. It is interesting that, in six of these
intervals, the estimate was significantly greater
than one.13 Overall, for the two currencies, 11
of the 18 subperiods showed estimates of br
that were significantly less than zero.

■ 12 These results appear to be robust to slight variations in the
length of the intervention periods.
■ 13 On the other hand, when I estimate the same equation for the
full sample period, including intercept and slope dummies equal to one
for the intervention periods, both dummies differ significantly from zero.

The second half of each table provides summary data on U.S. and/or German intervention.
In table 2, only official information about U.S.
intervention against the yen is available. Baillie
and Osterberg (1997) find evidence consistent
with the idea that U.S. buying—but not selling—of dollars affects risk in the forward market. Here, I find that in the case of the DM/$,
b is negative whether the intervention activity
was buying or selling. In the case of the Yen/$,
on the other hand, buying dollars is associated
with a negative estimate of b, while selling
implies a positive estimate.

V. Conclusion
My evidence on the importance of intervention
for the forward discount puzzle is strongest for
the DM/$. However, whereas FR find that b
became positive under fixed-rate regimes, I find
significantly negative estimates for intervention
periods. This suggests at least a need to clarify
the correspondence between my choice of intervention periods and shifts between floatingand fixed-rate regimes. However, the results
presented here are even more interesting when
one notes that estimated b was also negative
for both exchange rates following the Plaza and
Louvre agreements. Prior to each of these periods, public statements indicated the likelihood
of coordinated efforts to influence exchange
rates. Thus, we would have expected the results
in both instances to be similar to FR’s findings
for fixed-rate regimes.
The results also suggest that it would be
valuable to examine more closely the hypothesis that buying currencies and selling them
have different impacts. It is certainly possible
that market conditions have varied between
periods of buying and periods of selling. Noisetrading analyses, such as Hung (1997), discuss
the relevance of market thinness and the rules
followed by chartists.
Of course, recent research on the importance of sample size places rather stringent
qualifications on any conclusions I might draw.
Unfortunately, few central banks release highfrequency data on intervention, although the
recent collapse of fixed-rate regimes and increasing pressure for transparency on the part
of central banks might improve opportunities
to study the connection between exchange-rate
regimes, interest rates, and intervention.

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