Daniel M. Holland

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: Private Pension Funds: Projected Growth
Volume Author/Editor: Daniel M. Holland
Volume Publisher: UMI
Volume ISBN: 0-87014-411-1
Volume URL: http://www.nber.org/books/holl66-1
Publication Date: 1966
Chapter Title: Projections of Benefit Payments, Contributions, and Fund
Accumulations
Chapter Author: Daniel M. Holland
Chapter URL: http://www.nber.org/chapters/c1582
Chapter pages in book: (p. 53 - 61)3. Projections of Benefit Payments,
Contributions, and Fund Accumulations
The preceding chapter discussed the projections of the number of
covered workers and beneficiaries; this chapter will derive the money
amounts that are of primary concern—contributions, earnings, benefit
payments, and,their net resultant, pension fund accumulations.
Projection of total contributions and benefit payments was done as
follows. Given some number of covered workers (W) and an estimate
of contributions per worker (C/W), then total contributions (C) is
derived as their product. Similarly, total benefit payments are esti-
mated as the product of B and P/B, were B is the number of bene-
ficiaries and P/B is payments per beneficiary.
The earlier discussion indicated that, for covered workers, and
beneficiaries, developing' a number of alternative estimates was the
best method; no single estimate could be suggested as unequivocally
the best. Similarly, several estimates of C/W and P/B were used.
Each of them incorporates either a realistic possibility or illustrates
the implications of a particular policy imposed on the composite
pension structure through specified accomplishments in OASDI or
private industrial plans. In any event, each C/W and P/B is ex-
plained, and the reader has a basis for choosing from among them as
he wishes.
While no particular C/W and P/B could be defended strongly
enough to exclude all others, one group, analyzed in the chapter that
follows, seemed the natural and likely one because it is based on the
structure of industrial pension plans. Alternatives are examined in
Chapter 6.
The physical magnitudes—number of covered workers and bene-
ficiaries—described by two symbols (i.e., our have already been
determined and are relevant within very broad limits no matter what
assumptions a particular or may be based on.54 PrivatePension Funds: Projected Growth
Assume that the existing set of industrial pension plans constitutes
a structure or a system that has a dynamics (or momentum) that will
persist over the next twenty years and whose essence can be captured
from the experience of the last decade. In other words, assume that
the forces that determine (C/W) and (P/B) will operate in the same
way over the next generation as they have over the last decade. Thus
each year's C/W and P/B can be derived by projecting its values
from a linear regressibn on time. It is more convenient to start with
the estimate of P in which deriving P/B is the first stage.
Specifically, the linear trend for P/B computed for the period
1950—61 was:
P/B =$845.38+ $16.94X,
($2.43)
where X =time=1,2, ..,n,and the number in parentheses is
the standard error of the slope coefficient. This isa satisfactory
regression; with an R (correlation coefficient) of .92, about 85 per
cent of the variation in P/B is explained, and the coefficient of the
time variable is significant at the .01 (or .001) level. Thus the projected
value for 1962 was equal to $845.38 + 12 ($16.94) =$1,048.66,and
for 1981it was $845.38 + 31($16.94) =$1,370.43,with each year
differing from the previous one by $16.94.
Basic tables incorporating all the projections and their components
have been compiled.' Those in the set based on (P/B) and (C/W)
derivedfrom trends are designated• by a triple of numbers and letters
—e.g., (As, C,, rh), where r is either an interest rate or C + E (con-
tributions plus earnings)—and comprise the first eighty pages of the
supplement. (The most "likely" projections in this set constitute the
basis for the discussion in Chapter 4.) In Chart 3 projected benefit
payments (along with contributions and the excess of contributions
over benefit payments) are plotted for the years 1962—8 1 for one of
the two preferred projections—A.25C3. Under this set of assumptions,
total benefit payments, which come to $1.9 billion in 1961, are
projected at $3.0 billion for 1966, $4.9 billion for 1971, $7.4 billion
for 1976, and $10.4 billion for 1981. This, of course, is a sharp increase,
but it is not unreasonable. Indeed, a really pronounced rise in benefit
i.Thecomplete set of tables referred to as the tabular supplement are on file
at the library of the National Bureau.Benefits,Contributions,and Fund Accumulations55
CHART 3
Projected
the Difierences
Benefit. Payments, Contributions,
Between Them Under Projection
Pension Plans, 1961—81
and
A 25C3,
SourceTables 24 and 25.
Private Industrial
Contributions
BLilion dollars
II
10
9
8
7
6
5
4
3
2
1
0
Benefit payments
——— — — ——
,
Contributions less
benefit payments
I I I I I I I I I I I....I I I I I I
1961'63 '65 '67 '69 '71 '73 '75 '77
I I
'79 '8156 Private Pension Funds: Projected Growth
payments is to be expected as the lagged counterpart of the spurt
of contributions witnessed over the last two decades. However, benefit
payments are not "running away," which can be seen from the
declining rate of growth as summarized by the year-to-year percentage
changes in Table 24 and the faint suggestion of a maximum absolute
annual change in 1978. The trend-projected growth in (P/B) is modest,
TABLE 24
Pro jected Number of Beneficiaries, Total Benefits,
and Year-to-Year Percentage Change in Benefits, Private
Industrial Pension Plans, Projection A,25C3, 1962-81
Average Benefits First Ye ar-to-Year
Number of Per Difference Percentage
Benefi- Benefi- Total in Total Change in
ciariesa ciary Benefits Benefits Total Benefits
Year(thousands)(dollars) (billiondollars)
1962 1,993. 1,049 2.09 — —
1963 2,179 1,066 2.32 0.23 11.0
1964 •2,360 1,082 2.55 0.23 9.9
1965 2,535 1,099 2.79 0.24 9.4
1966 2,703 1,116 3.02 0.23 8.2
1967 2,936 . 1,133 3.33 0.31 10.3
1968 3,235 1,150 3.72 0.39 11.7
1969 3,524 1,167 4.11 0.39 10.5
1970 3,800 1,184 4.50 0.39 9.5
1971 4,060 1,201 4.88 0.38 8.4
1972 4,378 1,218 5.33 0.45 9.2
1973 4,753 1,235 5.87 0.54 10.1
1974 5,110 1,252 6.40 0.53 9.0
1975 5,449 1,269 6.91 0.51 8.0
1976 5,765 1,286 7.41 0.50 7.2
1977 6,122 1,303 7.97 7.6
1978 6,520 1,320 8.60 0.63 7.9
1979 6,898 1,337 9.22 0.62 7.2
1980 7,251 1,354 9.81 0.59 6.4
1981 7,576 1,370 10.38 0.57 5.8
Source: NBER projections.
aAverage number of beneficiaries in.yeartisequal to the average number
attheendofyearst—landt.•Benefits, Contributions, and Fund Accumulations57
justunder $17peryear, the great increase in benefit payments being
due to the sharp increase in beneficiaries.
Initially the attempt was made to derive C/W in the same way as
(P/B) i.e., by extending the trend as measured from the data for the
period 1950—6 1. The regression of C/W on time was:
C/W =$262.06—$1.02X,
($0.79)
where, as before, X =time=1,2,...,n.This regression is not
very useful, however. The size of the standard error of the slope
coefficient indicates that it is not significant by any reasonable stand-
ard. Moreover, the coefficient of .X is so small that it makes little
difference if the constant term alone is used. Further, the minus sign
on the coefficient is not appropriate for projecting into the future,
since the likelihood for a continually decreasing C/W, no matter
how slightly decreasing, is not great. Finally, R is .39, which means
that only 15 per cent of the variation in C/W can be "explained".by
time. The explanatory value of this equation is close enough to zero
to be considered negligible. It seemed preferable, all things considered,
simply to average C/W for the last four years for which data were
available and to use this constant value ($252.10) 2asthe projected
C/W.
Is it not peculiar to project a constant C/W over the next twenty
years for the industrial pension plan structure? In other words, is
not the projection of a constant C/W inconsistent with the projected
increase in P/B; i.e., do not rising benefit payments per beneficiary
require increasing contributions per covered worker? The answer is,
not necessarily. Indeed, there are good grounds for expecting a sub-
stantially unchanged C/W over the future. First, as more and more
workers are covered for a longer and longer period, less in the way of
contributions .will be required on the score of past service credits, so a
seemingly monetarily constant C/W will be de facto a rising one. More-
over, earning rate assumptions incorporated in private industrial pen-
sion plans have proved more conservative than actual results; and if
this differential continues, contributions will not have to increase as
much as they otherwise would have. Finally, the increments to coverage
over time will generally involve less generous pension arrangements
2Computedfrom Social Security Bulletin, April 1963, p. 12, Table 5.58 Private Pension Funds: Projected Growth
than those incorporated in
those for currently covered
lower than average rewards);
tions lower than average will
to tone it down.
Annual values of the C3 projection's total (employer and employee)
contributions appear in Table 25. Contributions too are expected to
grow substantially over the twenty years between 1961 and 1981.
TABLE 25
Projected Annual Total Contributions and Year-to-Year
Percentage Changes, Private Industrial Pension Plans,
Projection C3, 1962-81
(billion dollars)
.
Year Contributions
.
FirstDifference
of Contributions
Year-to-Year
Percentage
Change in
Contributions
162 5.85 — —
1963 6.15 0.30 5.1
1964 6.44 .0.29 4.7
1965 6.73 0.29 4.5
1966 7.02 0.29 4.3
1967 7.30 0.28 4.0
1968 7.57 0.27 3.7
1969 7.84 0.27 3.6
1970 8.10
8.35
0.26 3.3
1971 0.25 3.1
1972 8.60 0.25 3.0
1973 8.83 0.23 2.7
1974 9.06. 0.23 2.6
1975 9.28 0.22 2.4
1976 9.49 0.21 2.3
1977 9.70 0.21 2.2
1978 9.90 0.20 2.1
1979 10.11 0.21 2.1
1980 10.32 0.21 2.1
1981 10.54 0.22 2.1
Source: NBER projections.
the already established plans or than
workers (because of younger ages and
therefore, a component with contribu-
be added to the total each year, tendingBenefits, Contributions, and Fund Accumulations59
From$5.3 billion in 1961, they are projected to be $7.0 billion by
1966, billion by 1971, $9.5 billion by 1976, and $10.5 by 1981.
Thus they will almost double over the twenty years. (This, of course,
is at the same rate as the growth of coverage over this period, since
(C/W)isprojected as unchanged over the whole of the twenty years.)
That growth is considerably less vigorous than the projected spurt
in benefits, and indicates a credible relation between benefits and
contributions that helps to keep fund accumulations from becoming
explosive.3 That the first differences of total contributions tend to
tail off over time is a comforting feature of the projections.
Looking back to Chart 3, we note that contributions and benefits
appear as smooth curves. Smoothness, of course, is a function of how
the variables were projected; it is not a guarantee that there is any
inherent economic sense in the projections. Yet, because many eco-
nomic processes have this characteristic, it does the projections no
discredit. And the shape of the difference between total contributions
and total benefits rises smoothly to a maximum and then declines.4
This maximum difference between them is a credible feature of a
pension plan and of a set of plans, i.e., a pension structure, but should
not be confused with the net annual additions to pension funds.5
In projecting pension fund earnings, it seemed once again most
reasonable to use alternative assumptions. The rates assumed by
actuaries in developing plans could not be used, for clearly they are
tentative, subject to revision, and generally too low.6 Nor was it clear
what past experience indicated for the future course of interest rates.
3Sucha relation helps, but it does not by itselF necessarily determine this result,
for fund earnings also have to be considered. Earnings are discussed below.
4InChartthe specific data of A•25C3 are plotted. The difference between
contributions and benefits peak in different years for the different projections.
Details are not important for the purpose at hand, and differences among the
various projections can be most efficiently discussed by examining fund levels
and annual changes, i.e., the net resultant of the size of the flow of benefits, con-
tributions, and fund earnings.
5Fundearnings and benefit payments were about the same size in the middle
and later 1950's, and therefore contributions turned out to be equal to the net
annual additions to pension funds. That this will not generally be the case in
the future will be clear from the projections.
6Forexample, for 1954, of 117 self-administered single-employer plans in New
York State surveyed, all but six assumed earnings rates below 3 per cent, with
85 of the plans reporting the assumed interest rate at 2.50 or less. State of New
York, Insurance Department, Private Employee Benefit Plans—A Public Trust,
1956, p. 172. This is generally referred to as the "House" Report, after Martin
House who headed the research staff.60 Private Pension Funds: Projected Growth
In the early 1950's, 3.5 per cent on book value seemed reasonable;
by the end of the decade, closer to 4 per cent.7 Currently the rate is
probably somewhat higher.
Therefore, it seemed appropriate to establish likely ranges of values,
and to this end interest rates of 3.5, 4.0, and 4.5 per cent were
incorporated in the projections. The lowest of these was chosen out
of deference to history; 4.0 or 4.5 is really the more likely. There is
little ground for preference between these two; therefore, projections
using both are presented. And, of course, other things equal, greater
fund accumulations would be expected with the 4.5 per cent rate
than with 4.0. However, this could well be a false or misleading
finding for if earnings are consistently higher, but everything else is
unchanged, contributions will tend to fall because a higher proportion
of the fund can be built up from earnings. Thus fund accumulations
might not be too different whether the interest rate was 4.5 or 4.0
per cent. Indeed, it is probably sensible to concentrate on projections
based on one particular earning rate assumption, since the likelihood
is that, if, in fact, other rates did prevail, compensating adjustments
in contributions would keep funds from accumulating as rapidly (or
cause them to accumulate more rapidly) than would otherwise be the
case. Therefore, emphasis will be placed on the projections that
assumed a 4 per cent rate of earnings. The reader who prefers either
3.5 or 4.5 per cent will find the appropriate projections in the supple-
ment on file at the National Bureau of Economic Research.
The fact that, if earnings rates are high or low, contributions might
well be adjusted in compensation suggests that it might be useful to
isolate the behavior of earnings and contributions combined, call it
C + E, and project C + E for the years 1962—8 1 on the basis of this
relation.
Following the procedure used for projecting (P/B), contributions
plus earnings per covered worker ([C + E]/W) were regressed on time
for 1951 through 1961:
[C + E]/W =$270.16+$6.11 X,
($1.27)
7Thuscorporate pension funds earned 3.7 per cent on book value in 1956 and
4 per cent in1960. Computed from data in "Corporate Pension Funds," SEC,
Statistical Bulletin, May 1961, pp. 9—15 (investment income divided by average
of total book value of assets at beginning and end of year minus one.half invest-
ment income).Benefits, Contributions, and Fund Accumulations61
where Xtime =1,2,...,n,starting with 1951. The size of the
slope coefficient related to its standard error (in parentheses), plus
the fact that R =.85(i.e., about 73 per cent of the variation in
CC + E]/W is explained by variation in X) indicates that this is a
"good" relation. From this trend, annual values of [C + E]/W for
1962—81 were projected, and this provided the basis, given W, for
estimating C + E. From C + F we subtracted P, estimated as described
earlier, to arrive at each year's net additions to pension fund holdings.8
In summary, then, for every combination there were two ways
of proceeding. One involved estimating benefit payments, contribu-
tions, and fund earnings via an assumed interest rate; the other called
for estimates of benefit payments and contributions plus earnings as
a combined total. In principle, there is little to choose between them;
therefore the results of both procedures are presented and analyzed
in the next chapter.
8 Later, starting with Chapter 4, the symbol P is also used to designate a projec-
tion set. No confusion should stem from this duplication of symbols, however, for
whenever P stands for a projection set it is always followed by a number subscript.

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