ACTUARIAL NOTE 

Number 137 
SOCIAL SECURITY ADMINISTRATION 
November 1996 
Office of the Chief Actuary 
OASDI SHORTRANGE SENSITIVITY ANALYSIS
by Nettie J. Barrick, A.S.A.
The financial and actuarial status of the OASDI program is
traditionally evaluated for both shortrange (the next 10 years) and
longrange (the next 75 years) periods. For this note, the shortrange period
covers calendar years 1996 through 2005 as it
did for the 1996 Trustees Report.^{1}
A number of different measures are calculated for evaluating
the financial status of the program. For the longrange period,
these measures are generally based on relative scales because of the difficulty
in comparing dollar values for different periods.
These relative measures include (1) the annual amounts of future income and
outgo as a percentage of the amount of earnings
subject to the OASDI payroll tax (income rates and cost rates), (2) the annual
differences between these income and outgo
figures, and (3) summarized values representing these figures over various
periods. For the shortrange period, the level of
trust fund assets relative to annual expenditures is often used as a measure
for evaluating the financial status of the program.
The assets in the fund at the beginning of the year as a percentage of
disbursements from the fund during the year is referred to
as a "trust fund ratio" or "contingency fund ratio".
The Trustees Report includes estimates based on three
alternative sets of assumptions regarding future economic and
demographic trends. This is useful because of the inherent uncertainty in
estimates for as long as 75 years into the future.
Designated as alternatives I, II, and III, these sets of assumptions range
from low cost (alternative I) to high cost (alternative
III), with alternative II representing the set of intermediate cost
assumptions. The low cost set is more optimistic from the
standpoint of OASDI financing and the high cost set is more pessimistic. The
intermediate set of assumptions is considered to
be the "best estimate". The estimates based on the three alternative
sets of assumptions illustrate the effects of varying all of the
principal assumptions simultaneously in order to portray a generally more
optimistic or pessimistic future, in terms of the
financial status of the OASDI program.
This note presents estimates which illustrate the sensitivity
of the shortrange trust fund ratios of the OASI, DI, and combined
OASI and DI programs to changes in selected individual assumptions. The 1996
Trustees Report included a sensitivity analysis for the longrange period using
summarized income rates and cost rates.^{2}
This note supplements that analysis.
In this note, the trust fund ratio of the combined OASI and DI
Trust Funds will be referred to as the OASDI trust fund ratio.
The following table shows the OASI, DI, and OASDI trust fund ratios after 5 years
and after 10 years for each of the three
alternative sets of assumptions used in the 1996 Trustees Report.
In the sensitivity analysis presented in this note, the
intermediate (alternative II) analysis is used as the reference point, and one
assumption at a time is varied within that alternative.
Table 12 is provided
at the end of this note, which summarizes the
alternative values for each of the eight individual assumptions. Similar
variations in the selected assumptions within the other
alternatives would result in similar relative variations in the shortrange
estimates. Each table that follows shows the effects of
changing a particular assumption on the OASI, DI, and OASDI trust fund ratios
after 5 years and after 10 years. All other
assumptions remain the same as they were assumed to be for the intermediate
estimates.
Table 2 shows the estimated OASI, DI, and OASDI trust fund
ratios, on the basis of alternative II with various assumptions
about the ultimate total fertility rate. These assumptions are that the
ultimate total fertility rate will be 2.2 children per woman
(as assumed for alternative I), 1.9 (as assumed for alternative II), and 1.6
(as assumed for alternative III). The rate is assumed
to change gradually from its current level and to reach the various ultimate
values in 2020. By the end of the shortrange
period, the projected fertility rates reach 2.1 children per woman
(alternative I), 2.0 (alternative II), and 1.9 (alternative III).
During the shortrange period, changes in fertility have
little, if any, effect on the working population. Higher fertility rates result
in an increase in benefit payments as a result of an increase in the number of
child beneficiaries. Hence, the program cost
slightly increases, in the short range, with higher fertility. This slightly
larger level of benefit payments results in a small, but
growing, decrease in interest income to the trust funds. During the shortrange
period, however, changes in fertility have such a
small impact on trust fund income and outgo that there is no change, within
rounding, in the trust fund ratios.
Table 3 shows the
estimated OASI, DI, and OASDI trust fund ratios, on the basis of alternative
II with various assumptions
about future reductions in death rates. The analysis was developed by varying
the percentage decrease assumed to occur in
future death rates. The decreases assumed for the shortrange period,
summarized as changes in the agesexadjusted death
rate, are about 4.0 percent (as assumed for alternative I), 9.7 percent (as
assumed for alternative II), and 13.9 percent (as
assumed for alternative III). It should be noted that these reductions do not
apply uniformly to all ages. Some variation by age
was assumed consistent with the objective of selecting assumptions for
alternatives I and III that are relatively more optimistic
and more pessimistic, respectively, in terms of the longrange financing of
the OASDI program. For example, under
alternative III, death rates are lower than they are under alternative II for
people who have attained the retirement eligibility
age of 62 but are higher than under alternative II at many of the ages at
which people are usually in the labor force.
Under the death rates assumed for alternative I, the number
of retiredworker and survivor beneficiaries are lower than under
alternative II death rate assumptions and, therefore, the amount of retirement
and survivors benefits paid from the OASI Trust
Fund is lower. At the same time, the variation of death rates by age causes the
number of covered workers and, therefore,
contributions to both the OASI and DI Trust Funds to be higher than they would
otherwise be. Due to this lower outgo and
higher income, the OASI trust fund ratios increase when a smaller reduction in
death rates is assumed. The variation of death
rates by age leads to an increase, from alternative II levels, in the number
of DI beneficiaries and, hence, DI benefit payments.
These higher benefit payments and the increased contributions mentioned above
are virtually offsetting.
If the death rates from alternative III are substituted in
place of the alternative II rates, the effects on the trust fund ratios are of
about the same magnitude, but in the opposite direction, as compared to the
effects of the alternative I rates. The OASI trust
fund ratio varies by 89 percent in 2005 due to alternative assumptions in
death rates, while the DI trust fund ratio does not
change.
Table 4 shows the
estimated OASI, DI, and OASDI trust fund ratios, under alternative II with
various assumptions about the
magnitude of net immigration. These assumptions are that the annual net
immigration, in the year 2000 and later, will be
1,150,000 persons (as assumed for alternative I), 900,000 persons (as assumed
for alternative II), and 750,000 persons (as
assumed for alternative III). The net immigration estimates are projected to
phase into these levels from assumed 1995 levels
of 1,100,000 persons, 865,000 persons, and 700,000 persons for alternatives
I, II, and III, respectively.
Immigration occurs at relatively young ages, thereby
increasing the numbers of covered workers earlier than the numbers of
beneficiaries. Therefore, the shortrange trust fund ratios increase with
increasing rates of net immigration. Although higher net
immigration assumptions eventually lead to higher projected benefit payments,
the additional outgo in the short range is much
more than offset by additional contributions due to more people in the labor
force.
The realwage differential is the difference between the
assumed annual percentage increase in average wages in covered
employment and the assumed annual percentage increase in the Consumer Price
Index (CPI). Table 5 shows the estimated
OASI, DI, and OASDI trust fund ratios, on the basis of alternative II with
various assumptions about the realwage
differential. These assumptions are that the ultimate realwage differential
will be 1.5 percentage points (as assumed for
alternative I), 1.0 percentage point (as assumed for alternative II), and 0.5
percentage point (as assumed for alternative III). In
each case, the ultimate annual increase in the CPI is assumed to be 4.0
percent (as assumed for alternative II), yielding
ultimate percentage increases in average annual wages in covered employment
of 5.5, 5.0, and 4.5 percent under alternatives
I, II, and III, respectively. These ultimate levels are assumed to be reached
at the end of, or just after, the shortrange period.
For each year of the shortrange period, the realwage differential is assumed
to be at the level projected, for that year, for
that alternative, in the Trustees Report, while the percentage increase in the
CPI is assumed to be at the level projected, for
that year, for alternative II.
Higher realwage levels increase the taxable payroll and,
therefore, the contributions. Since benefit increases are not affected,
the trust fund ratios increase with increasing realwage differentials.
Although the initial benefit levels are higher because of the
higher wages, these increases are more than offset by the increases in the
contributions of future workers. Because of the
surplus of additional contributions over additional outgo, there is also
increased interest income.
For each increase of 0.5 percentage point in the ultimate
realwage differential, the OASDI trust fund ratio increases by
approximately 6 to 8 percentage points by 2000 and by approximately 27 to 32
percentage points by 2005.
Table 6 shows the
estimated OASI, DI, and OASDI trust fund ratios, on the basis of alternative
II with various assumptions
about the rate of increase of the Consumer Price Index. These assumptions are
that the ultimate annual increase in the CPI will
be 3.0 percent (as assumed for alternative I), 4.0 percent (as assumed for
alternative II), and 5.0 percent (as assumed for
alternative III). These ultimate levels are reached before the end of the
shortrange period. In each case, the ultimate
realwage differential is assumed to be 1.0 percentage point (as assumed
for alternative II), yielding ultimate percentage
increases in average annual wages in covered employment of 4.0, 5.0, and 6.0
percent under alternatives I, II, and III,
respectively. For each year of the shortrange period, the percentage
increase in the Consumer Price Index is assumed to be
at the level projected, for that year, for that alternative, in the Trustees
Report, while the realwage differential is assumed to
be at the level projected, for that year, for alternative II.
When assuming a change in the rate of increase in the CPI
(in conjunction with a constant realwage differential), both taxable
payroll and benefit payments increase with a higher rate of CPI increase.
During the shortrange period, the increase in benefit
payments is largely attributable to the increase in the annual costofliving
adjustments (COLAs). In the longrange period, the
effect of the higher COLAs "fades out". That is, a few years after
a benefit increase is effective, the percentage of people on
the rolls who received that benefit increase has diminished. The effect of
the COLAs "fades out" faster for DI than for OASI.
During the longrange period, the increase in benefit payments is largely
attributable to the increase in average annual wages in
covered employment (which affects initial benefit levels).
Since both taxable payroll and benefit payments increase
when a higher CPI increase is assumed, both the level of assets in
the fund at the beginning of the year and the disbursements from the fund
during the year increase. Therefore, the effect on the
"trust fund ratio" is not immediately clear.
In this sensitivity analysis, the following effects were
observed. Under alternative I CPI increase assumptions (with CPI
increases that are lower than those under alternative II), disbursements
during the year decrease faster than assets at the
beginning of the year for both OASI and OASDI. This results in higher OASI
and OASDI trust fund ratios throughout the
shortrange period. For DI, assets at beginning of year decrease faster than
disbursements. This results in a decrease in DI
trust fund ratios during the shortrange period. Under alternative III CPI
increase assumptions, disbursements increase faster
than assets at beginning of year for OASI, DI, and OASDI during the first
half of the shortrange period. This results in lower
trust fund ratios in 2000. During the latter half of the shortrange period,
the increase in assets at beginning of year is faster
than the increase in disbursements, particularly for DI. By 2005, the trust
fund ratios are as high or higher than those projected
for alternative II.
The figures shown in table
6 are especially asymmetrical about
alternative II due to the specific annual CPI increases assumed
for the economic scenarios in alternatives I and III (see
table
12).
Table 7 shows the
estimated OASI, DI, and OASDI trust fund ratios, on the basis of alternative
II with various assumptions
about the annual nominal real interest rate for special publicdebt
obligations issuable to the trust funds. These assumptions are
that the ultimate annual real interest rate will be 3.0 percent (as assumed
for alternative I), 2.3 percent (as assumed for
alternative II), and 1.5 percent (as assumed for alternative III). These
levels are reached at the end of the shortrange period.
In each case, the ultimate annual increase in the CPI is assumed to be 4.0
percent (as assumed for alternative II), resulting in
ultimate annual yields of 7.1, 6.4, and 5.6 percent under alternatives I,
II, and III, respectively.
In general, higher interest rates lead to higher trust fund
ratios. However, during the shortrange period, varying the real
interest rate has little effect on the trust fund ratios because the changed
rates only affect new bond purchases, not the existing
stock of bonds. Each year, assets allowing, bonds are purchased which have
maturity dates from 1 year to 15 years in the
future. The amounts of the bonds are calculated such that bonds totaling
approximately onefifteenth of the total bond amount
mature each year. Therefore, after 5 years only about one third of the total
bond amount would be subject to the changed real
interest rates.
Since the real interest rates are graded into the ultimate
assumed rate, projected real interest rates for the first few years vary
little from one alternative to another. Therefore, in the fifth year, the
trust fund ratios remain the same, within rounding, as they
were using the alternative II ultimate annual real interest rate. By the
tenth year, the OASDI trust fund ratio varies slightly (by 2
percentage points) when the ultimate real interest rate is changed to the
level assumed for alternative I or III.
Table 8 shows the
estimated OASI, DI, and OASDI trust fund ratios, on the basis of alternative
II with various assumptions
concerning future disability incidence (award) rates.
Alternative II shortrange incidence rates are developed,
by sex and single year of age, through a series of preliminary
projections reflecting judgment on the expected number of awards from nonHIV
related impairments. This forms the
"baseline" projection for award rates. HIVrelated impairments are
then considered and the two categories are aggregated to
produce one series of award rates for each age and sex. As a final step,
award rates may be modified to reflect recent
legislative changes to the DI program. Disability incidence rates for
alternatives I and III are developed by varying the
alternative II baseline projection of nonHIV related impairments and
combining the results with separate alternative I and III
projections of HIVrelated impairments.
Under the relatively low incidence rates assumed for
alternative I, the DI trust fund ratio increases by 17 percentage points
from the level reached under alternative II disability incidence rates, by
the fifth year. The DI trust fund ratio decreases by 19
percentage points under the relatively high incidence rates assumed for
alternative III. For the tenth year, the DI trust fund
ratio increases from the alternative II level by 59 percentage points under
the incidence rates assumed for alternative I and
decreases by 63 percentage points under the incidence rates assumed for
alternative III. Varying the disability incidence rates
has only a minimal effect on the OASI trust fund ratios. An increase in the
disability incidence rates results in more disabled workers, and hence,
fewer workers who might retire prior to normal retirement age.
The OASDI trust fund ratios move in the same direction as
the DI trust fund ratios, but to a smaller extent, because of the
relative sizes of the OASI and DI programs. The OASDI trust fund ratio
changes by approximately 3 percentage points for
the fifth year and by approximately 10 to 12 percentage points for the tenth
year under alternative DI incidence rate
assumptions.
Table 9 shows the estimated OASI, DI, and
OASDI trust fund ratios, on the basis of alternative II with various assumptions
about future disability termination rates.
Termination of disability benefits are categorized by reason
which includes death, recovery, conversion at normal retirement
age, and "other". Alternative II shortrange disability termination
rates are developed by reason, sex, and single year of age.
Termination rates based on death and "other" are expected to vary
little from their current levels, whereas recovery rates are
highly sensitive to the number of continuing disability reviews (CDRs)
performed and, therefore, fluctuate with budget
estimates on the future volume of such reviews. Disability termination rates
for alternatives I and III are determined based on a
flat percentagepoint increase (alternative I) or decrease (alternative III)
in the annual change in termination rates for
alternative II.
For the fifth year, the DI trust fund ratio increases by
four percentage points, from the alternative II level, under the relatively
high termination rates assumed for alternative I. The ratio decreases, from
the alternative II level, by four percentage points
under the relatively low termination rates assumed for alternative III. For
the tenth year, the DI trust fund ratio changes by 13
percentage points under the termination rates assumed for alternatives I and
III. Within rounding, the OASI trust fund ratios
do not change.
The OASDI trust fund ratios move in the same direction as
the DI trust fund ratios, but to a smaller extent, because of the
relative sizes of the OASI and DI programs. For the tenth year, the OASDI
trust fund ratio changes by 2 percentage points
under alternative DI termination rates.
By varying only one assumption at a time, we are able to see
the relative size of the effect of changing each assumption.
Table 10
below shows the ranking, for the shortrange period, of the effect
on the trust fund ratios of changing each of the
assumptions. The assumptions are ranked from 1 to 8 for OASI and DI with 1
representing the greatest effect and 8 representing the smallest effect.
Table 11
which follows shows the ranking, for both the shortrange period and the
longrange period, of the effect on the OASI and DI Trust Funds, combined,
of changing each of the assumptions.
From tables 10 and
11, we can see that, of the eight categories
considered, varying the realwage differential has the greatest
effect on the OASI and OASDI trust fund ratios and the second greatest effect
on the DI trust fund ratio during the
shortrange period. Under alternative I realwage assumptions, the OASDI trust
fund ratio for 2005 increases by 27
percentage points. Under alternative III realwage assumptions, the OASDI
trust fund ratio for 2005 decreases by 32
percentage points. For the longrange period, varying the realwage
differential has the second greatest effect on the
combined OASI and DI Trust Funds.
During the shortrange period, varying the disability
incidence rates has the greatest effect on the DI trust fund ratio and the
second greatest effect on the OASDI trust fund ratio. Under alternative I or
III disability incidence rate assumptions, the DI
trust fund ratio for 2005 changes by 5963 percentage points. The OASDI
trust fund ratio for 2005 increases by 10
percentage points (alternative I) and decreases by 12 percentage points
(alternative III).
In the shortrange period, the second largest effect on
the OASI trust fund ratio and the third largest effect on the OASDI
trust fund ratio is seen when death rate assumptions are varied. Under
alternative I death rate assumptions, the OASDI trust
fund ratio for 2005 increases by 8 percentage points. Under alternative III
death rate assumptions, the OASDI trust fund ratio
for 2005 decreases by 7 percentage points. For the longrange period, varying
the death rate assumptions has the greatest
effect on the combined OASI and DI Trust Funds.
Varying each of the other five assumption categories has
little effect on the OASDI trust fund ratio during the shortrange
period. Using alternative disability termination assumptions has the third
largest effect on the DI trust fund ratio, but, because
of the relative sizes of the OASI and DI Trust Funds, this has little
effect on the OASDI trust fund ratio.
The reader should note that the effects of varying the
eight assumption categories individually does not add up to the effect
noted when all assumptions are changed simultaneously. This analysis does
not take into account the interaction among
assumptions which occurs when two or more assumptions are varied at the
same time. This analysis also does not include the
effect of varying unemployment assumptions.
Table 12.  Alternative assumptions used for the shortrange sensitivity analysis
Year
 Fertility rate^{1}
 Death rate^{2} (per 100,000)
 Net immigration (in thousands)
 Realwage differential^{3}
(percent)
 Increase in Consumer Price Index^{4
}(percent)
 Real interest rate^{5}
(percent)
 Disability incidence rate^{6}
(per 1,000)
 Disability termination rate^{7}

 Alternative II

1995
 2.039
 764
 865
 1.3
 2.8
 3.9
 5.25
 .0944

1996
 2.034
 757
 875
 1.3
 2.8
 3.5
 5.23
 .0894

1997
 2.030
 750
 885
 1.1
 3.2
 3.2
 5.32
 .0924

1998
 2.025
 744
 885
 .8
 3.3
 3.1
 5.26
 .0885

1999
 2.020
 738
 885
 .9
 3.4
 3.1
 5.24
 .0876

2000
 2.015
 731
 900
 .8
 3.5
 2.9
 5.21
 .0864

2001
 2.010
 725
 900
 .7
 3.7
 2.7
 5.17
 .0863

2002
 2.005
 719
 900
 .7
 3.9
 2.5
 5.13
 .0863

2003
 2.000
 712
 900
 .9
 4.0
 2.4
 5.12
 .0805

2004
 1.994
 706
 900
 1.0
 4.0
 2.4
 5.10
 .0804

2005
 1.989
 701
 900
 1.1
 4.0
 2.3
 5.11
 .0804

 Alternative I

1995
 2.050
 758
 1,100
 1.3
 2.8
 3.9
 5.25
 .0944

1996
 2.057
 756
 1,110
 1.7
 2.4
 3.5
 4.92
 .0928

1997
 2.063
 755
 1,125
 1.8
 2.8
 3.3
 4.92
 .0970

1998
 2.070
 753
 1,125
 1.5
 3.0
 3.3
 4.78
 .0943

1999
 2.076
 751
 1,125
 1.7
 3.0
 3.3
 4.68
 .0935

2000
 2.082
 750
 1,150
 1.6
 3.0
 3.2
 4.59
 .0923

2001
 2.088
 749
 1,150
 1.5
 3.0
 3.1
 4.49
 .0921

2002
 2.094
 748
 1,150
 1.5
 3.0
 3.0
 4.40
 .0922

2003
 2.100
 747
 1,150
 1.6
 3.0
 3.0
 4.36
 .0863

2004
 2.106
 746
 1,150
 1.6
 3.0
 3.0
 4.30
 .0861

2005
 2.112
 745
 1,150
 1.6
 3.0
 3.0
 4.28
 .0861

 Alternative III

1995
 2.026
 765
 700
 1.2
 2.8
 3.9
 5.26
 .0944

1996
 2.009
 754
 700
 .5
 2.7
 3.5
 5.58
 .0859

1997
 1.993
 744
 725
 .4
 3.1
 3.1
 5.81
 .0876

1998
 1.976
 734
 725
 .2
 5.4
 3.0
 5.90
 .0826

1999
 1.959
 728
 725
 1.0
 5.4
 2.8
 6.01
 .0816

2000
 1.943
 720
 750
 .3
 4.5
 2.6
 6.12
 .0802

2001
 1.925
 712
 750
 .3
 5.0
 2.3
 6.16
 .0799

2002
 1.908
 702
 750
 .0
 5.0
 2.0
 6.17
 .0798

2003
 1.891
 691
 750
 .2
 5.0
 1.9
 6.14
 .0742

2004
 1.874
 680
 750
 .3
 5.0
 1.7
 6.09
 .0740

2005
 1.856
 668
 750
 .5
 5.0
 1.5
 6.05
 .0740

^{1} The total fertility rate for any year is
the average number of children who would be born to a woman in her lifetime
if she were to experience the birth rates by age assumed for the selected
year, and if she were to survive the entire childbearing period.
The ultimate total fertility rate is assumed to be reached in 2020.
^{2} These are the agesex adjusted death rates.
The agesex adjusted death rates are calculated as the crude rate that would
occur in the enumerated total population as of April 1, 1980, if that
population were to experience the death rates by age and
sex for the selected year.
^{3} The realwage differential is the difference
between the assumed annual percentage increase in average wages in covered
employment and the assumed annual percentage increase in the Consumer Price
Index. For each year of the shortrange
period, the realwage differential is assumed to be at the level projected,
for that year, for that alternative, in the Trustees
Report, while the percentage increase in the Consumer Price Index is assumed
to be at the level projected, for that year, for alternative II.
^{4} For each year of the shortrange period, the
percentage increase in the Consumer Price Index is assumed to be at the level
projected, for that year, for that alternative, in the Trustees Report, while
the realwage differential is assumed to be at the level
projected, for that year, for alternative II.
^{5} The alternative real interest rates shown here
are those used for the estimates illustrated in this note. These were phased in
from the current level to the ultimate level. These real interest rates differ
from those shown for alternatives I and III in the
original Trustees Report estimates because of fluctuations built into the CPI
increases (to simulate recessions) in those
estimates. These also differ from the alternative real interest rates which
were calculated when CPI sensitivity estimates were prepared.
^{6} These are the agesex adjusted disability
incidence rates. These rates were standardized to the 1995 disability incidence
rates, by sex, using 5year age groups.
^{7} These rates are derived by dividing the number
of terminations (including conversions) by the exposure of disabled workers in
force at the beginning of the year plus the exposure of disabled workers
awarded during the year.
^{1} The 1996 Annual Report of the Board of
Trustees of the Federal OldAge and Survivors Insurance and
Disability Insurance Trust Funds, June 5, 1996.
^{2} Section II.G,
LongRange Sensitivity Analysis.
Notes published in the 1990s