**New Estimates of the Future Path of 401(k) Assets**

By

James Poterba

MIT and NBER

Steven Venti

Dartmouth College and NBER

David A. Wise

Harvard University and NBER

April 2007

**Abstract:** Over the past two and a half decades there has been a
fundamental change in saving for retirement in the United States, with a
rapid shift from employer-managed defined benefit pensions to defined
contribution saving plans that are largely controlled by employees. To
understand how this change will affect the well-being of future
retirees, we project the future growth of assets in self-directed
personal retirement plans. We project the 401(k) assets at age 65 for
cohorts attaining age 65 between 2000 and 2040. We also project the
total value of assets in 401(k) accounts in each year through 2040 and
we project the value of 401(k) assets as a percent of GDP over this
period. We conclude that cohorts that attain age 65 in future decades
will have accumulated much greater retirement saving (in real dollars)
than the retirement saving of current retirees.

The research reported herein was pursuant to a grant from the U.S.
Social Security Administration (SSA) funded as part of the Retirement
Research Consortium . We also received funding from the National
Institute of Aging through grant P01 AG005842 to the National Bureau of
Economic Research.  The findings and conclusions expressed are solely
those of the authors and do not represent the views of SSA, any agency
of the Federal Government or the NBER.

Over the past two and a half decades there has been a fundamental change
in saving for retirement in the United States, with a rapid shift from
saving through employer-managed defined benefit pensions to defined
contribution retirement saving plans that are largely controlled by
employees. In 1980, 92 percent of private retirement saving
contributions were to employer plans; 64 percent of these contributions
were to defined benefit plans. By 2000, about 87 percent of private
contributions were to plans in which individuals decide how much to
contribute to the plan, how to invest plan assets, and how and when to
withdraw money from the plan. Following the 2000 stock market decline,
this proportion declined somewhat as employers made \"catch-up\"
contributions to under-funded DB plans.

In this paper we consider how the change in the way people save for
retirement will affect the well-being of future retires. We project the
future growth of assets in self-directed personal retirement plans. The
most important of the large number of personal retirement plans is the
401(k). We consider not only 401(k) plans *per se* but 403(b), section
457, and related tax-deferred retirement saving plans, as well as
traditional defined contribution plans. We refer to all of these plans
collectively as \"401(k)\" or as "401(k)-type" plans. In a companion
paper, Poterba, Venti and Wise (2007a), we consider the future decline
of assets in defined benefit plans.

Our analysis is based on cohort data on individual 401(k) participation
rates. We use these data as a foundation from which to project 401(k)
participation rates and asset accumulation in the future. These
projections are combined with the Social Security Administration\'s
demographic forecasts to project the stock of 401(k) retirement plan
assets in each year between 2006 and 2040. And we project the
accumulated 401(k) assets at age 65 for all cohorts attaining age 65
between 2006 and 2040

Other studies have also based projections on individual data. Holden and
VanDerhei (2002a, 2002b) project the evolution of the proportion of
pre-retirement income that will be replaced by 401(k) asset
accumulations. The studies simulate 401(k) assets by projecting the
future accumulation of assets held in 2000. Because their sample
consists only of plan participants, their projections do not consider
the future increase in 401(k) participation rates and do not consider
future demographic trends. Two studies by the Congressional Budget
Office (2004a, 2004b) develop a framework to project asset flows into
and out of defined benefit (DB), defined contribution (DC), and IRA
plans. These analyses are based primarily on the 1997 Information
Returns Master file from the IRS, supplemented with data from the Survey
of Consumer Finances, Form 5500 data, and other sources. The studies
project DC balances by assuming that future participation and
contribution rates will equal the age-specific rates observed in 1997.
These studies also do not consider the future spread of 401(k) plans or
the effects of demographic trends on the accumulation in personal
retirement plans.

The paper is organized into five sections. In the first section, we
describe the spread of 401(k) saving programs since these saving plans
first became widely available in the early 1980s. In the second section,
we explain how we project the level of future assets in 401(k) plans. We
detail key assumptions about employment trends, participation rates,
contribution rates, as well as withdrawal patterns once 401(k)
participants reach retirement. In section 3 we present projections of
401(k) assets at retirement (age 65) for each cohort that retires
between now and 2040. In addition we project the total value of assets
in 401(k) plans by year, through 2040. We also compare projected assets
in 401(k) plans with the declining benefits from DB plans. In section
four, we summarize our results and discuss the implications of the
findings.

**1. The Spread of 401(k) Plans Between 1984 and 2003**

We use data from the Survey of Income and Program Participation (SIPP)
to track the spread of 401(k) plans over the past two decades and to
develop projections of future 401(k) assets. Various SIPP surveys
provide data on eligibility for and participation in 401(k) plans in
1984, 1987, 1991, 1993, 1995, 1998, and 2003. Each SIPP survey is a
random cross-section sample of the population. The cross-section data
from the SIPP surveys can be used to create "synthetic" cohorts. For
example, to construct cohort data for the cohort that was age 25 in 1984
we use the 1984 panel to obtain data for persons 25 in that year, the
1987 panel to obtain data for persons who were 28 in that year, the 1991
panel to obtain data for persons who were 32 in that year, and so forth.
The cohort that was age 25 in 1984 was age 44 in 2003. We sometimes
label a cohort by the age of the cohort in 1984 and sometimes by the
year in which the cohort attains age 65. For example, the cohort that is
age 25 in 1984 attains age 65 in 2024 and is referred to as the C25 or
the R2024 cohort.

The unit of observation in the SIPP is the individual and most of our
calculations are performed at the level of the individual. In addition,
we sometimes present results for families by grouping individual
responses, treating unmarried persons as single-person families and
matching spouses to create two-person family units. A family is eligible
for (or participates in) a 401(k) plan if at least one member of the
family is eligible for (or participates) in a plan. The \"age\" of a
two-person family is assumed to be the age of the male spouse.

![](media/image1.wmf){width="5.990277777777778in"
height="4.097222222222222in"}

We first consider data on family eligibility, organized by cohort. The
SIPP provides some data for 54 cohorts. Figure 1-1a shows these data for
9 cohorts, five years apart, denoted by the age of the cohort in 1984.
Consider cohort C25 that was 25 years old in 1984. In 1984, about 7
percent of the C25 cohort families were eligible for a 401(k) plan. By
1987, the percent of this cohort that was eligible for a 401(k) plan had
risen to about 20 percent. By 2003 this cohort is over 40 years old and
eligibility was slightly more than 70 percent. The most important
feature of the figure is the increase in eligibility over time for
families of a given age. For example, the dashed vertical line
highlights the increase in the eligibility of families in cohorts that
attained age 40 in successively later years. Cohort C40 was 40 years old
in 1984 and about 16 percent of the C40 cohort was eligible for a 401(k)
at age 40. Cohort C35 attained age 40 in 1989 and about 34 percent of
the C35 cohort was eligible for a 401(k) plan at age 40. The C25 cohort
was age 40 in 1999 and almost 70 percent of the C25 cohort was eligible
for a 401(k) plan at age 40. Similar increases in eligibility are
evident at other ages.

![](media/image2.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

![](media/image3.wmf){width="5.990277777777778in"
height="4.097222222222222in"}

Figure 1-1b shows eligibility data for every other cohort for which data
can be obtained from the SIPP. Figure 1-1c shows data for every cohort,
from C11 to C64. The youngest cohorts are shown in the upper left of the
figure and the oldest are shown in the upper right.[^1] Again, the
dashed vertical lines highlight increases in eligibility for cohorts
that reached given ages in successively later years. In Figure 1-1b, it
is clear that with few exceptions cohorts that reached a given age in
successively later years had successively higher 401(k) eligibility
rates. The same pattern is shown in Figure 1-1c, with surprisingly few
"cross-overs" in the individual cohort trends even though in this figure
each successively younger cohort, from bottom-right to top-left in the
figure, is only one year younger than the prior cohort.

The increase in eligibility rates reflects the spread of 401(k) plans to
more firms and especially to smaller employers. As described in Poterba,
Venti, and Wise (2004), for example, a large fraction of employers who
first adopted 401(k) plans in the early and mid-1980s also offered DB
plans; few of these employers discontinued the DB plan when the 401(k)
plan was adopted. Employers who instituted 401(k) plans later were less
likely to have existing DB plans and were typically smaller firms.

The participation rates in 401(k) plans show patterns similar to those
for eligibility rates. Family participation rates in 401(k) plans are
shown by cohort in Figures 1-2a, 1-2b, and 1-2c. As in the eligibility
Figures 1-1a, 1-1b, and 1-1c, the dashed vertical lines highlight the
increase in the participation rate of families who attained a given age
in successively later years. For example, Figure 1-2a shows that only
about 10 percent of the C40 cohort, those who were age 40 in 1984,
participated in a 401(k) plan. But over 50 percent of the C25 cohort,
which attained age 40 in 1999, participated in a 401(k) plan. More
detail is shown in Figures 1-2b and 2c. Figure 1-2b shows participation
rates for every other cohort and Figure 1-2c shows participation rates
for each of the cohorts for which data are available in the SIPP.

![](media/image4.wmf){width="5.990277777777778in"
height="4.097222222222222in"}

![](media/image5.wmf){width="5.990277777777778in"
height="4.097222222222222in"}

![](media/image6.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

The cohort figures show a very large increase in 401(k) eligibility and
participation rates between 1984 and 2003. In particular, cohorts that
reached a given age in successively later years had successively higher
eligibility and participation rates. The increase in eligibility and
participation rates at selected ages between 1984 and 2003 is summarized
in Table 1-1. The table shows the eligibility rate and the participation
rate for cohorts in the age intervals 30-34, 45-49 and 60-64 in 1984 and
2003. While only 14.8 percent of the cohort age 30-34 in 1984 was
eligible for a 401(k) plan, 66.8 percent of the cohort that attained age
30-34 in 2003 was eligible. Only 8.2 percent of the cohort that attained
age 30-34 in 1984 participated in a 401(k) plan, but 53.9 percent of the
cohort that attained this age by 2003 participated.

The table also shows the percent of those eligible who participated in
1984 and 2003. For each age, the participation rate given eligibility
increased very substantially over this period. For example, in 1984,
55.5 percent of eligible families with heads aged 30-34 participated in
a 401(k) plan. By 2003, 80.7 percent of those who were eligible also
participated. Of families with heads aged 45-49, participation given
eligibility increased from 68.6 percent to 85.9 percent between 1984 and
2003.

> ![](media/image7.wmf){width="4.176388888888889in" height="2.90625in"}

More detail on participation given eligibility is shown in Figure 1-3.
The figure shows that, given eligibility, the participation rate
increased between 1984 and 2003 for all age groups, especially for
younger age groups~~.~~ The figure also shows that in 2003 the
participation rate given eligibility was about the same (80 percent) for
each of the age intervals from 40-44 to 60-64. The data also suggest
that participation rates given eligibility are higher for younger
cohorts.

![](media/image8.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

The rapid spread of 401(k) eligibility and participation rates has
resulted in very rapid growth in aggregate contributions to 401(k)
plans. Figure 1-4 shows contributions to 401(k) plans and, for
comparison, to all other private pension plans from 1975 to 2002.[^2]
Contributions to 401(k) plans are shown by the lined bars. Contributions
to 401(k) plans were first made in 1982. By 2000, total contributions to
401(k) plans had reached \$182 billion and accounted for 73 percent of
contributions to all private pension plans. Counting IRA, Keogh, and
traditional employer provided non-401(k) DC plans, 87 percent of
contributions were to personal accounts. This percentage fell to 61
percent by 2002 because of unusually large DB catch-up contributions
triggered by the decline in the stock market.

![](media/image9.wmf){width="5.996527777777778in"
height="4.086805555555555in"}

The increase in total pension plan contributions between 1982 and 2000
was accounted for almost entirely by the increase in contributions to
401(k) plans. Contributions to defined benefit (DB) plans fluctuated
substantially over this period, but were about \$15 billion, or 31
percent, lower in 2000 than in 1981 before increasing in 2001 and 2002
in response to the stock market decline. Contributions to non-401(k)
defined contribution (DC) plans changed little between 1981 and 2002.
There was a substantial spike in IRA contributions in 1982 through 1986.
Thereafter IRA contributions fell by about 75 percent, when the tax
advantage of IRA contributions was reduced for a small proportion of
contributors. Since 1987, the sum of IRA and Keogh plan contributions
has changed very little. Most of the inflows to IRAs today are
roll-overs of previous accumulations in defined contribution accounts,
rather than traditional contributions.

**2. Projecting Future 401(k) Contributions**

We first set out the calculations that are the basis for our projections
of 401(k) wealth. We denote persons by the
subscript![](media/image10.wmf). Cohorts are denoted by subscript
![](media/image11.wmf). Associated with each person in each cohort is a
lifetime earnings profile. The earnings of person
![](media/image10.wmf)in cohort ![](media/image11.wmf) at age
![](media/image12.wmf) are denoted by![](media/image13.wmf). The
zero-one indicator that person ![](media/image10.wmf)in cohort
![](media/image11.wmf)participates in a 401(k) plan at age
![](media/image12.wmf)is denoted by![](media/image14.wmf), the rate of
return earned on 401(k) assets that were held at the beginning of the
year when the person attained age a is denoted by![](media/image15.wmf),
and the contribution rate is denoted be ![](media/image16.wmf)
(expressed as a proportion of earnings). The value of the 401(k) assets
held by person ![](media/image10.wmf) in cohort c at age a is given by

\(1\) ![](media/image17.wmf)

where ![](media/image18.wmf)and where ![](media/image19.wmf)is the
contribution rate. This calculation is made for every person (i.e.
earnings history) for every age in every cohort. In practice, separate
calculations are made for wealth in stocks and bonds and the assumed
rates of return do not vary by individual. In particular, the 401(k)
wealth of person ![](media/image10.wmf)in cohort
![](media/image11.wmf)at 65 is given by

\(2\) ![](media/image20.wmf)

This accumulation is calculated for each person (earnings history) in
our sample.

We then obtain the average wealth held by the population of all persons
age 65 for a cohort![](media/image11.wmf). To do this we need to know
how many persons of type ![](media/image10.wmf)are in the population.
Denote the number of persons with lifetime earnings profile i in cohort
c at age 65 by ![](media/image21.wmf)(to be determined by population
projections). Then the average of 401(k) assets held by all persons in
cohort c at age 65 is given by

\(3\) ![](media/image22.wmf).

where J is the number of persons (earnings histories) in the sample. In
practice, we don't have population forecasts associated with each
earnings history in the sample. Instead, we project total assets using
population projections for groups of persons with the same demographic
characteristics. The Office of the Actuary of the Social Security
Administration has developed population projections by calendar year and
age and by gender and marital status. Each earnings history in our
sample can also be identified by the gender and marital status of the
person. We first calculate the average
of![](media/image23.wmf)separately for each of the four gender-marital
status pairs and denote this average by![](media/image24.wmf). Then the
average wealth at 65 for each cohort is determined by

\(4\) ![](media/image25.wmf)

where the sum is over the four gm (gender-marital-status groups) and the
number of persons in each of these groups is taken from the Social
Security Administration demographic projections.

We also present projections of total 401(k) assets in each year through
2040. To do this, we use the identity that the wealth of person
![](media/image10.wmf)in cohort ![](media/image26.wmf)in calendar
year![](media/image27.wmf) is given by

\(5\) ![](media/image28.wmf)

Then, the total value of assets held in 401(k) accounts in year y is
given by

\(6\) ![](media/image29.wmf)

To implement these calculations we need to develop projections of future
401(k) participation rates and earnings and we need to make assumptions
about future 401(k) contribution rates, rates of return, cash-out
probabilities, and 401(k) withdrawals. We begin by describing
projections of average 401(k) participation rates for each cohort. We
then describe the other assumptions that are needed to obtain estimates
of 401(k) asset accumulation.

**Participation rates:** We use SIPP data for 1984, 1987, 1991, 1993,
1995, 1998, and 2003 to track the spread of 401(k) plans over the past
two decades and to develop projections of future 401(k) participation
rates. We sometimes label a cohort by the age of the cohort in 1984 and
sometimes by the year in which the cohort attains age 65. For example,
the cohort that is age 25 in 1984 attains age 65 in 2024 and is referred
to as the C25 or the R2024 cohort. These calculations are based on the
person data as reported in the SIPP. For the figures discussed above we
combined these person data to form families.

We begin with historical participation rates for individuals by cohort,
as shown in Figure 2-1. The earliest SIPP data are for 1984 and the most
recent data are for 2003. We will use these data to project 401(k)
participation at ages 25 through 65 for a large number of cohorts,
ranging from the cohort that attains age 65 in 1982 through the cohort
that attains age 65 in 2040. Only a few of the cohorts (shown in the
bottom right of Figure 2-1) had attained age 65 by 2003. Thus for all
but a few of the cohorts we must project participation rates from the
last observed age in 2003 to age 65.

The participation rate is the eligibility rate times the participation
rate given eligibility. The future eligibility rate will depend in
particular on the spread of 401(k) plans to small employers. We know
that eligibility rates have increased very rapidly over the past two
decades, and that participation, given eligibility, increased
substantially over the 1984 to 2003 period, as shown in PVW (2004). We
have not found a compelling way to formally project future rates of
eligibility or participation conditional on eligibility. Thus we have
simply made "plausible" assumptions about future participation rates and
use them to project future cohort participation rates for persons in
cohorts not covered in the SIPP data.

![](media/image30.wmf){width="5.996527777777778in"
height="4.090277777777778in"}

Simple extrapolations of the cohort data are likely to yield implausibly
large participation rates. Consider, for example, the participation
rates at age 44 highlighted by the vertical dashed line in Figure 2-1.
The C44 cohort attained age 44 in 1984 and had a participation rate of
5.8 percent at that time. The C25 cohort attained age 44 in 2003, 19
years later, and had a participation rate of 44.3 percent. On average,
the participation rate at age 44 increased about 2 percentage points
with each successively younger cohort. Were this rate to continue, the
participation rate of the C12 cohort at age 44 (that the C12 cohort will
attain in 2016) would be 70.3 percent (44.3+13x2). We suspect that this
estimate of the future participation rate is too high, because 401(k)
plans have already diffused through the segments of the corporate
population that have workforces that find these plans most attractive,
and that have the lowest per-employee administrative costs of
implementing a plan.

Estimation of cohort effects by fitting the above profiles shows some
compression with successively younger cohorts. In addition, Figure 2-1
suggests that within cohorts, the increase in participation rates was
lower between the last two data points for each cohort, 1998 and 2003,
than for earlier intervals of comparable length. These features of the
data suggest that the rate of growth of 401(k) participation may be
slowing.

To recognize the apparent compression in the cohort effects and the
apparent decline in the rate of within-cohort increase in participation
rates, we make future projections for each cohort based on its observed
2003 participation rate. We assume that the annual increase in future
participation rate will be smaller than that between 1998 and 2003. In
particular, we assume that the future annual rate of increase declines
by 0.12 percent per year. With this assumption, the projected future
participation rates for the C25 and the C12 cohorts would be as shown in
Figure 2-2, which also shows the actual participation rates for these
cohorts in 2003 and earlier years. Based on these projections, the
participation rate of the C12 cohort when it attains age 44 in 2016
would be 61.7 percent, compared to 44.3 percent for the C25 cohort,
which attained age 44 in 2003. At age 64, the participation rate would
be 56.6 percent for the C25 cohort and 69.4 percent for the C12 cohort.

![](media/image31.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

Figure 2-3 shows the projected average participation rates after 2003
for selected cohorts from one of the youngest cohorts, C11 (R2038), to
one of the oldest cohorts, C64 (R1985). The figure also shows the
interpolated participation rates between the years for which data are
available prior to 2003. The decline in the rate of growth of 401(k)
participation between 1998 and 2003 (the last two years for which SIPP
data are available) is noticeable for many of the cohorts shown in the
figure. The figure shows projections for selected cohorts. The
projection algorithm we use includes projections for all cohorts from
C65 (R1984) through C9 (2040).

Participation rates also vary by the level of earnings, given age and
cohort. We have incorporated this variation in our projections but we do
not report projections of 401(k) assets by earnings decile in this
paper. Variation in 401(k) asset accumulation by earnings is the focus
of Poterba, Venti and Wise (2007b). A detailed explanation of the
procedure used to project participation rates by earning decile is
presented in that paper.

![](media/image32.wmf){width="5.993055555555555in"
height="4.072916666666667in"}

**Allocation and** **Rate of Return:** We assume that 60 percent of
401(k) contributions are allocated to large-capitalization equities and
40 percent to corporate bonds. The projections use actual annual pre-tax
returns through 2005. Beginning in 2006 we make projections based on two
rate of return assumptions. First, we assume that the average annual
nominal return on equities is 12 percent and that the average nominal
return on corporate bonds is 6 percent. Ibbotson Associates (2006)
reports that the historical arithmetic mean of pretax returns on
long-term corporate bonds has been 6.2 percent per year, while
large-capitalization stocks have returned an average of 12.3 percent
over the period 1926-2005. Second, we assume that the rate of return on
equities is 300 basis points less than the historical rate. These
returns are the pretax returns available on a portfolio with no
management fees. We have not as yet accounted for asset management fees.
The average dollar weighted management fee on stock funds is currently
about 70 basis points.

**Job Separation, Lump Sum Distributions, and Cashouts:** At age 25 each
person is assigned to a 401(k) job based on the participation
probability for that person\'s age, cohort and earnings. In subsequent
years each person either remains in the 401(k) job or leaves the 401(k)
job. Job separation rates are estimated from the 1998 SIPP for five-year
age intervals. These rates are shown in the first column of Table 2-3.
Separation rates are allowed to vary by age, but not by time in job.
Estimated annual rates range from a high of 23 percent for the youngest
workers to 12.1 percent for workers age 50 to 54. After leaving a 401(k)
job persons enter a pool of "non-participants." In each year members of
this pool are selected for a new 401(k) job at a rate that makes the
overall participation rate for persons of a particular age and cohort
equal to the projected probability for that age and cohort. A similar
projection algorithm, with an identical treatment of transitions in and
out of 401(k) participation, is described in Poterba, Venti, and Wise
\[2001\].

The probability that a 401(k) accumulation is cashed out is determine by
the job separation rate, the probability that the employees takes a lump
sum distribution (LSD), and the probability that a lump sum distribution
is cashed out rather than rolled over into an IRA. That is, the
probability of a cashout is given by:

![](media/image33.wmf) ![](media/image34.wmf)

The probabilities associated with each of the components of the cashout
decision are shown in Table 2-1.

> ![](media/image35.wmf){width="5.575694444444444in"
> height="4.4631944444444445in"}

When employees separate from a job they may choose to keep their
accumulation with their old employer or they may decide to take a LSD.
The SIPP only provides information on the disposition of a LSD. Thus we
are unable to obtain the probability of a LSD given job separation by
age from the SIPP. We use the average rate of 57 percent obtained by
Hurd, Lilliard, and Panis based on data from the Health and Retirement
Survey (HRS). On average, the probability of a cashout in a given year
is (.151) x (.570) x (.272) = 0.0234.

This cashout probability differs from the probability in Poterba, Venti,
and Wise (2001). In that paper, we used an estimated average of about
0.0108. The principle reason for the difference is the job separation
rates. In the earlier paper we used estimates based on retrospective
information in the HRS. The average separation rate based on that source
was 0.048, compared to the average rate of 0.151 based on the SIPP
estimates.[^3] In the earlier paper our average estimate of the
(probability of a LSD) x (probability of cashout \| LSD) was 0.226. The
average of these two components used here is somewhat smaller: (.570) x
(.272) = 0.155.

**Withdrawals:** The projections reported here assume a crude withdrawal
scheme. Annual withdrawals are assumed to be 2 percent of balances
between ages 65 and 70 ½. At older ages, the amount withdrawn from the
401(k) is (1/Remaining Life Expectancy) times the 401(k) balance. These
withdrawal assumptions likely overstate amounts withdrawn from 401(k)
plans. Berkshadker and Smith \[2005\] show that over 50 percent of
current IRA holders do not make their first withdrawal before age 70.

**Earnings:** To estimate the 401(k) contributions of a cohort, we need
to determine the earnings and the contribution rates of cohort members.
The key to developing an earnings history is access to a long time
series of earnings by a single individual or a family. We use the HRS
that provides linked Social Security earnings histories for respondents
who agreed to the link. These data represent earnings histories for a
sample of individuals who were between the ages of 52 and 61 in 1992.
The implicit assumption in our analysis is that the distribution of
earnings histories that will be realized by younger cohorts will be
similar to the earnings histories of the HRS respondents.

To develop earnings histories for younger cohorts we begin with the
Social Security earnings histories of the HRS respondents, available for
the years 1951 through 1991.[^4] Earnings for 1992 through 2000 are
obtained directly from HRS respondents. We begin with the earnings of
the cohorts that attained age 65 in 1998, 1999, and 2000. We obtain
lifetime earnings for all single persons that attained age 65 in these
years and for all persons in two-person families in which the male
partner attained age 65 in these years. The earnings of the 1998 cohort
are "aged" two years and the earnings of the 1999 cohort are \"aged\"
one year, based on the Social Security average wage index. We then treat
these earnings histories as a random sample of the earnings of the
cohort that attained age 65 in 2000 (the "R2000" cohort). The sample
reports actual earnings histories, including years with zero earnings,
so it recognizes that individuals may not be employed in some years. We
implicitly assume that the employment rate and the distribution of
employment by age are similar for future cohorts as for past ones. (The
"R2000" cohort contains some female spouses who were not 65 in 2000.)

To make projections for the earnings of younger cohorts, we inflate the
"R2000" sample using the intermediate earnings growth assumptions
reported in the 2005 Annual report of the Board of Trustees of the
Social Security Administration. Similarly, to project a sample of
earnings for older cohorts we deflate the earning of the "R2000" cohort
based on the Social Security average wage index. This method does not
account for any potential change in the relative earnings of high and
low-wage persons.

**Contribution Rate:** We assume a contribution rate of 10 percent of
earnings, including both the employee and the employer contributions.
There are several sources of information on contribution rates. Data
from the 2003 SIPP are shown by age interval in Table 2-4. The overall
median of the total of employee and employer contributions is 9.8
percent. The employee and employer medians are 5.7 percent and 3.0
percent respectively. The overall mean is 12.6 percent. The mean rates
may be substantially affected by reporting errors.

> ![](media/image36.wmf){width="5.7625in" height="2.8340277777777776in"}

Poterba, Venti, and Wise (1998) reported contribution rates based on the
1993 Current Population Survey (CPS). The average employee contribution
rate was 7.1 percent and the average employer rate was 3.1 percent.
Holden and VanDerHei (2001) analyzed the responses to an Employee
Benefit Research Institute (EBRI)-Investment Company Institute (ICI)
survey and report that in 1999 the average total contribution rate was
9.7 percent. The 1998 Form 5500 data show that about 32 percent of
dollars are contributed by employers, which is roughly consistent with
the 2003 SIPP median percent and with the 1993 CPS values. Engelhardt
and Cunningham (2002) report that based on HRS data the average employee
contribution rate was 6.6 percent in 1991, which is again generally
consistent with the estimates based on SIPP and on CPS data.

For several reasons, however, the contribution rate in future years is
uncertain. One reason for uncertainty about future contribution rates is
the effect of increases in contribution limits. Legislation over the
past several years has increased contribution limits very substantially
and now future increases are indexed to inflation. The legislated
increases in 401(k) and related plans are summarized in an appendix. Our
projections assume that contributions as a percent of salary will be
unaffected by the rising limits. In part, the effect of the limit
increases depends on how many participants are constrained by the
contribution limits now and whether fewer participants or more
participants will be constrained by future limits. Holden and VanDerhei
(2001) report that in 1999 eleven percent of participants with incomes
over \$40,000 contributed at the legislated maximum, thirteen percent of
those with incomes between \$70,000 and \$80,000, and eighteen percent
of those with incomes between \$80,000 and \$90,000 contributed at the
legislated maximum. Thus one question is how wage growth will interact
with rising contribution limits to affect the proportion of persons at
the limit. Even though the limits have increased and are now indexed to
the CPI, wages are likely to increase faster than the CPI. The Social
Security Administration assumes future wage growth of 3.9 percent and
future inflation of 2.8 percent. The legislated maximum, however, may
not be the effective limit for many employees. Holden and VanDerhei
report that 52 percent of participants in 1999 faced employer imposed
limits below the legislated maximum. The number of participants that is
constrained by these limits is unknown. And how the limits set by
employers might change in the future is also unknown.

In addition, we have not accounted for the recent Pension Protection Act
of 2006 that gives employers latitude to set more \"saving friendly\"
defaults in 401(k) plans. Beshears, Choi, Laibson, and Madrian (2006)
survey some of the recent evidence on how changing defaults for
enrollment, contribution rates, and asset allocation can significantly
increase retirement saving through 401(k) plans. Thus our 401(k)
projections may underestimate the actual accumulation of assets in these
plans. Finally, the legislated increases in contribution limits may
affect participant decisions of how much "should" be saved for
retirement. The government-set limits may serve to "frame" employee
decisions. .

**3.** **Assets in 401(k) Plans at Retirement and Total Assets by Year**

We first show 401(k) assets at retirement by cohort and then consider
the total value of assets in 401(k) plans by year.

**401(k) Assets at Retirement:** The average [per]{.underline}
[person]{.underline} of 401(k) assets at age 65 (in 2000 dollars) is
shown in Figure 3-1, for cohorts R1982 to R2040. Two profiles are shown,
one assuming the average historical rate of return for equities and the
other assuming the historical rate less 300 basis points. The projected
average increases very substantially over the next 35 years. If the
historical rate of return on equities is assumed, the average increases
from about \$29,700 in 2000, to \$137,000 in 2020, to \$452,000 by 2040.
Assuming the historical rate of return on equities less 300 basis
points, the average increases from \$29,700 in 2000 to \$269,000 by
2040. The projected increase is due to the increase in the participation
rates of younger cohorts and to the increase in the number of years that
401(k) contributions were possible for successively younger cohorts. The
401(k) program effectively began in 1982 so cohorts retiring before 2020
could only make contributions over part of their working lives. Persons
who attained age 65 in 2000 could have contributed to a 401(k) plan for
at most 18 years. For the cohort that will attain age 65 in 2040, 401(k)
plans will have been available over the entire working life.

![](media/image37.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

![](media/image38.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

Figure 3-2 shows the average of 401(k) assets at retirement for persons
who have 401(k) plans. For persons with plans, the average increases
from about \$87,000 in 2000 to \$580,000 by 2040 (in 2000 dollars)
assuming historical rates of equity returns to and \$335,000 assuming
historical returns less 300 basis points.

![](media/image39.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

For comparison, the maximum average (over all persons) of the present
value of DB benefits at age 65 was about \$73,000, attained in 2003.
Thereafter benefits in DB plans decline, based on the projections in
Poterba, Venti, and Wise (2007a). The comparison is shown in detail in
Figure 3-3 that is the same as Figure 3-1 but with the addition of the
DB projections.

To check our projection algorithm, we compared our estimate of the mean
401(k) assets of persons who attained age 65 in 2000 with the mean
401(k) assets of HRS respondents between the ages of 63 and 67 in 2000.
The HRS mean is \$25,892, compared to our projected mean of \$29,708.
However, the mean 401(k) balance in the HRS excludes amounts that were
originally accumulated in 401(k) plans but later rolled into IRAs; our
projected 401(k) balance includes amounts that were rolled over into an
IRA. A large fraction of assets in IRA plans are "rollovers" from 401(k)
plans. Many new retirees "rollover" 401(k) assets into an IRA plan when
they retire. For example, 89 percent of flows into IRA accounts were
rollovers in 1996, 89 percent in 1997, 93 percent in 1998, 95 percent in
1999, and 96 percent were rollovers in 2000.[^5] Thus it appears that
our projection is quite plausible compared to the HRS mean.

**Total 401(k) Assets by Year:** Figure 3-4 shows the total value of
assets in 401(k) plans by year. Assuming the historical rate of equity
return, the total reaches \$36.2 trillion by 2040 and grows to \$22.8
trillion assuming historical returns less 300 basis points (both in year
2000 dollars). Thus these projections suggest a very substantial
increase in retirement saving over the coming decades. To place these
values in a broader economic context, Figure 3-5 shows the total value
of 401(k) assets as a proportion of the Social Security Administration
intermediate projections of future GDP, also in year 2000 dollars. Total
401(k) assets grow from essentially zero percent of GDP in 1982 to about
38 percent of GDP in 2005. Our projections indicate that 401(k) assets
continue to increase after 2005, reaching 155 percent of GDP in 2040
assuming historical equity returns and 98 percent of GDP assuming the
historical equity return less 300 basis points. Both projections show a
slowdown in the rate of 401(k) asset growth relative to GDP following
the retirement of the last of the baby boom cohorts around 2030.

![](media/image40.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

![](media/image41.wmf){width="5.995138888888889in"
height="4.090972222222222in"}

The rise in 401(k) saving and the decline in DB pension savings also
means that 401(k) pensions will dominate the pension landscape in the
future. Figures 3-6 and 3-7 show the value of 401(k) assets together
with projected assets held by DB plans. The DB projections are taken
from Poterba, Venti, and Wise (2007a). Again, both are shown as a
proportion of the Social Security Administration intermediate
projections of future GDP, also in year 2000 dollars. Figure 3-6 is
based on the average historical equity return and Figure 3-7 is based on
the historical return less 300 basis points. It is clear from both of
these figures that the share of total pension assets accounted for by
401(k) plans grows steadily over time, from well under one-half today to
87 percent in 2040 assuming historical equity returns and 81 percent in
2040 assuming historical returns less 300 basis points.

![](media/image42.wmf){width="5.996527777777778in"
height="4.090277777777778in"}

![](media/image43.wmf){width="5.996527777777778in"
height="4.090277777777778in"}

**4. Summary and Discussion**

Over the past two and a half decades there has been a fundamental change
in saving for retirement in the United States, with a rapid shift from
saving through employer-managed defined benefit pensions to defined
contribution retirement saving plans that are largely controlled by
employees. To understand how this change will affect the well-being of
future retirees, we project the future growth of assets in self-directed
personal retirement plans.

Our projections indicate the 401(k) assets of persons who attain age 65
in 2040 will be much greater than the 401(k) assets of persons who
attained age 65 in 2000. If the historical rate of return on equities
continues in the future, the average (over all persons) increases from
about \$29,700 in 2000 to \$452,000 by 2040 (both in year 2000 dollars).
Assuming the historical rate of return on equities less 300 basis
points, the average increases from \$29,700 in 2000 to \$269,000 by
2040. There are three principal reasons for the growth of 401(k) assets
between 2000 and 2040. First, the 401(k) system was not fully mature in
2000. Retirees in 2000 could have contributed to a 401(k) plan for at
most 18 years and on average participants had contributed just over 7.
Beginning in about 2020 retirees working for employers offering a 401(k)
will have been able to contribute for their entire working lives.
Second, future retirees will benefit from real wage growth, assumed to
be 1.1 percent per year in our projections. Third, we project continued
growth of 401(k) coverage, albeit at a slower rate than in the recent
past, as 401(k) plans continue to spread to smaller firms in the private
sector, as well as to employers in the public sector.

To place the growth of 401(k) assets in a broader economic context, we
also calculated the total value of 401(k) assets as a proportion of the
Social Security Administration intermediate projections of future GDP
(in year 2000 dollars). Total 401(k) assets grow from essentially zero
percent of GDP in 1982 to about 38 percent of GDP in 2005. Our
projections indicate that 401(k) assets continue to increase after 2005,
reaching 155 percent of GDP in 2040 assuming historical equity returns
and 98 percent of GDP assuming the historical equity return less 300
basis points.

In addition, we find that the decline in DB pension assets is far
outweighed by the increase in 401(k) assets. Total pension assets,
including both DB and 401(k) plans, grow from about 52 percent of GDP in
1982 to 179 percent of GDP assuming historical rates of equity return,
and to 121 percent of GDP assuming historical rates less 300 basis
points. Thus we conclude that the increase in the pension assets of
future retirees will be much greater than the assets of current
retirees.

**References**

Bershadker, Andrew and Paul Smith. 2005. \"Cracking open the Nest Egg:
IRA Withdrawals and Retirement Finance.\" Mimeo. Federal Reserve Board
of Governors.

Congressional Budget Office. 2004b. \"Tax-Deferred Retirement Savings in
Long-Term Revenue Projections.\" CBO Paper, May.

Congressional Budget Office. 2004b. \"A Model to Project Flows into and
Out of Tax-Deferred Retirement Saving Accounts.\" CBO Technical Paper
2004-15.

Engelhardt, Gary and Christopher Cunningham, \"Federal Tax Policy,
Employer Matching, and 401(k) Saving: Evidence from HRS W-2 Records,\"
National Tax Journal. Vol. LV No. 3. pp 617-645. September 2002.

Holden, Sarah, Kathy Ireland, Vicky Leonard-Chambers, and Michael
Bogdan, \"The Individual Retirement Account at Age 30: A
Retrospective,\" *Perspective*. Investment Company Institute. vol. 11,
no. 1, February

Holden, Sarah and Jack VanDerhei. 2001. "Contribution Behavior of 401(k)
Plan Participants," EBRI Issue Brief Number 238, October.

Holden, Sarah and Jack VanDerhei. 2002a. \"Can 401(k) Accumulations
Generate Significant Income for Future Retirees?\" *Perspective*.
Investment Company Institute. vol. 8, no. 3, November

Holden, Sarah and Jack VanDerhei. 2002b. \"Appendix: EBRI/ICI 401(k)
Accumulation Projection Model\" *Perspective*. Investment Company
Institute. vol. 8, no. 3a, November

Poterba, James, Steven Venti, and David A. Wise, 1998, "Implications of
Rising Personal Retirement Saving," In D.A. Wise, (ed.), Frontiers in
the Economics of Aging, University of Chicago Press.

Poterba, James, Steven Venti, and David A. Wise, 2001, "Preretirement
Cashouts and Foregone Retirement Saving: Implications for 401(k) Asset
Accumuluation," In D.A. Wise, (ed.), Themes in the Economics of Aging,
University of Chicago Press.

Poterba, James, Steven Venti, and David A. Wise, 2004, "The Transition
to Personal Accounts and Increasing Retirement Wealth: Macro and Micro
Evidence," In D.A. Wise, (ed.), Perspectives on the Economics of Aging,
University of Chicago Press.

Poterba, James, Steven F. Venti, and David A. Wise, (2007a) \"The
Decline of Defined Benefit Retirement Plans and Asset Flows.\" *NBER
Working Paper #12834*.

Poterba, James, Steven F. Venti, and David A. Wise, (2007b), "The Rise
of 401(k) Plans, Lifetime Earnings, and Wealth at Retirement."

Stewart, Jay, 2002, \"Recent trends in Job Stability and Job Security:
Evidence from the March CPS,\" U.S. Department of Labor, Office of
Employment and Unemployment Statistics, Working Paper No. 356.

**Appendix on Tax Legislation and Retirement Saving Options: 401(k) and
Other Personal Retirement Accounts**

Personal retirement accounts were initiated in 1982. More recent
legislations has aimed to further increase personal retirement saving.
In particular, both the Taxpayer Relief Act of 1997 and the Economic
Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA) included
provisions that were designed to induce more retirement saving,
principally through tax-deferred personal retirement accounts. These
bills established Roth IRAs and increased contribution limits to
traditional IRAs, 401(k) plans, and other personal accounts. EGTRRA also
introduced tax credits for low-income taxpayers who make contributions
to IRAs, Roth IRAs, 401(k) plans, and other personal accounts. We
describe here some of the more important recent changes to the IRA and
401(k) programs.

**Contribution Limits for 401(k) Plans:** In 2001 there were three
restrictions on the amount that could be contributed to a 401(k) plan:
(1) a \$10,500 dollar limit on the employee\'s annual contribution, (2)
a \$35,000 limit on combined employee and employer contributions, and
(3) combined employee and employer contributions were limited to 25
percent of total compensation. By 2006, the annual limit on the
employee\'s contribution has increased to \$15,000, the combined dollar
limit had increased to \$40,000, and the percentage limit is now 100
percent of compensation. Both of the dollar limits will be indexed to
the CPI beginning in 2007.

**Catch-up Contributions to 401(k) Plans:** The 2001 legislation also
contains a catch-up provision for participants age 50 or older. The
allowable catch-up contribution was \$1,000 for 2002, and it increased
in steps until it reaches \$5,000 in 2007. After 2007, the catch-up
contribution for 401(k) is indexed to inflation.

**Contribution Limits for Traditional IRAs:** Contribution limits to a
traditional IRA were originally set in 1981 at \$2,000 per working
spouse and \$250 for a nonworking spouse. A provision in the Small
Business Job Protection Act of 1996 raised the deduction available to a
non-working spouse from \$250 to \$2,000 effective in 1997, thus
increasing the combined deduction for a family with a non-working spouse
from \$2,250 to \$4,000. The limits have since been raised to \$4,000
per person in 2006. The dollar limit will be indexed to the CPI
beginning in 2007. The tax-deductibility of the traditional IRA is
phased out for persons covered by an employer pension with incomes in
excess of \$50,000 for single persons and \$75,000 for married persons
in 2006.

**Roth IRA:** The Roth "back-loaded" IRA was introduced in 1997.
Contributions to the Roth IRA are not tax deductible, but no tax is paid
upon withdrawal if the funds are held for at least five years and if the
recipient is over age 59½. Like the "front-loaded" (traditional) IRA,
the investment return in a Roth IRA accrues tax-free. Contribution
limits and allowances for penalty-free withdrawals are the same as for
the traditional IRA. However, the Roth IRA contribution limit is
specified in after-tax dollars whereas the traditional IRA limit is in
pre-tax dollars. One consequence of this difference is that the
potential accumulation of retirement saving is higher under the Roth
IRA. In addition, the income at which eligibility begins to be
phased-out is much higher for the Roth IRA (\$95-110,000 for single
persons and \$150,000 to \$160,000 for married couples) than for the
traditional IRA.

**Catch-up Contributions for Traditional and Roth IRAs:** The catch-up
provision in the 2001 legislation allowed persons age 50 or older to
contribute an extra \$500 per year between 2002 and 2005 and an extra
\$1000 per year beginning in 2006. The catch-up contribution for IRAs is
not indexed to inflation after 2006.

**Saver's Tax Credit:** Beginning in 2002 and continuing until the end
of 2006, taxpayers who make contributions to personal retirement saving
plans---401(k), 403(b), 457(b), traditional or Roth IRAs, and other
plans---may receive a tax credit of up to 50 percent on the first
\$2,000 contributed. Eligibility for the deduction is determined by
income. For joint tax filers, the deduction is 50 percent for those with
incomes less than \$30,000 and is phased out at \$50,000. For single tax
filers the deduction is 50 percent for those with incomes less than
\$15,000 and is phased out at \$25,000.

[^1]: Data on 401(k) eligibility are not available for persons under the
    age of 25 in the SIPP. The C11 cohort in Figure 1c is observed
    twice, once at age 25 in 1998 and again at age 30 in 2003. Cohorts
    younger than the C11 cohort were younger than age 25 in 1998 and are
    thus observed only once (in 2003). These cohorts are not shown in
    the figure.

[^2]: More recent data from Form 5500 filings are not available.

[^3]: The estimate of 15.1 percent is approximately 5 percent lower than
    estimates reported by Stewart \[2002\], based on Current Population
    Survey data.

[^4]: We used a two-limit tobit specification (with a separate equation
    for each year) to impute SS earnings for persons censored at the
    upper Social Security earnings limit.

[^5]: See Figure 5 in Holden et. al. \[2005\]