Co ntributio n--P articipants
Co ntributio n--Full Sample
P articipatio n
Figure 7 Marginal effect of $10,000 increase in compensation on participation and contribution
J Finan Serv Res
attempt to affect the most people whereas the findings regarding higher income employees
should inspire policies that attempt to affect the most savings.
depicts, for each compensation level, the sensitivity of participation probability
and contribution to a $10,000 change in compensation, holding other variables constant.
Marginal participation probability peaks at around 15% for those earning $30,000 and
declines thereafter. (To appreciate the magnitude, note that the 15% marginal probability is on
top of the average participation probability of those earning $30,000 which is 55%.) It is not
negative for any compensation level, and for those earning more than $100,000 it is near zero.
The marginal effect of compensation on contribution of the eligible employees peaks around
a compensation of $60,000 at $1,208. (The $1,208 marginal contribution is on top of the
$3,868 average contribution of those earning $60,000.) Even for those earning between
$100,000 and $150,000 the marginal contribution ranges between $800 and $500. The
15 20 25
30 35 40 45 50 55
60 65 70 75 80 85
90 95 100 110 120 130 140 150
Com pensation ($1,000)
Figure 8 Excess participation rates and contribution levels of women
Figure 9 Excess participation rates and contribution levels of those covered by DB
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marginal contribution of eligible employees is greater than that of the participants since the
marginal participation probability is non-negative.
depicts, for each compensation level, the difference in participation probability
and contribution between women and men, holding other variables constant. The average
participation probability of men earning $30,000 is 49% whereas that of women with the
same compensation and similar other attributes is 12% higher. The difference declines for
higher wages, but even at the highest compensation levels, women
probabilities are at least 2% higher than men
’s. The contributions of women are higher
’s at all compensation levels, and the difference increases (for the whole
population) from around $300 (for those earning around $20,000) all the way to $1,500 (for
those earning above $100,000).
15 20 25
30 35 40 45 50 55
60 65 70 75 80 85
90 95 100 110 120 130 140 150
Com pensation ($1,000)
Figure 10 Excess participation rates and contribution levels of company-stock employees
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150
Com pensation ($1,000)
Figure 11 Marginal effect of 100% match on participation and contribution
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One explanation for the gender difference is that women are residual income earners in
their families: many more low-compensation women than men are married to working
spouses and among the majority of working couples, women earn less than men. Consistent
with this hypothesis, the data show that women tend to live in wealthier neighborhoods
than men of comparable compensation, age and tenure. (Not tabulated.)
If the participation and contribution decision reflects the family
’s, as opposed to just the
’s needs, then low-income women will participate and contribute as if they had
higher incomes than their recorded compensation. This observation may explain the gender
gap at the low end of the pay scale, although even here the inclusion of the WEALTH
variable should control for the
“family” effect. Moreover, if this were the only explanation,
women at the higher income levels should behave similarly to men of similar income. But
they do not: women earning six digit figures have 2% higher participation probabilities and
contribute more than a thousand dollars more than their male counterparts.
depicts the difference in behavior between employees in companies with and
without DB plans. The counterintuitive results on higher participation rates and contributions
that transpire from Tables
surface here as well, with the additional insight that they
are concentrated among those in the middle of the earnings distribution, peaking at incomes
Remarkably, contributions of participants with and without DB plans are statistically
indistinguishable at all income levels. The graph suggests that once an employee decides to
participate, the contribution level is unaffected by the presence or absence of the DB plan.
The reason that contributions of eligible employees with DB plans are higher than of those
without DB plans is that participation probabilities are higher.
depicts the impact of including company stock among the investable funds.
For those earning less than $42,000
—41% of the sample—participation probability is
higher in the presence of company stock; for those earning $30,000 or below
—30% of the
sample, presence of company stock enhances participation probability by about 7%.
(Overall participation probability of employees at this income level is 48%.) For those
earning below $35,000 contributions are also higher if company stock is an investable fund,
but they are lower for employees earning more than $35,000. Note that conditional on
participation, employees contribute less in the presence of company stock. Presumably,
employees attracted to the program by the presence of company stock tend to contribute
considerably less than those who would participate regardless of the presence of company
stock in the investable funds.
For those earning above $40,000, the effect of company stock on participation
probability is slightly negative (between 0 and
−2%), but mostly indistinguishable from
zero. More puzzling, and harder to explain is the behavior of contributions: they are lower
in the presence of company stock in the investable funds. They can be lower by as much as
–750 for those earning between $65,000 and $130,000. Why the presence of
company stock should adversely affect contributions is unclear, since its presence in the
investable funds can be safely ignored by eligible employees and participants, in which
case it would leave participation probabilities and contributions unaffected. But this seems
not to be the case.
According to Fig.
which depicts the relevant sensitivities of participation and
contribution to a 100% match, the presence of such a match increases participation at all
compensation levels, and such inducement is stronger the lower the compensation. In fact, a
100% match (up to 5% of salary) would lift the average participation rates of those earning
$20,000 by 19%. (Recall that the overall participation rate of employees in this income
range is 43%.) Contributions of eligible employees at all income levels are higher when a
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match is available. In fact, for those earning less than $35,000, a 100% match would
increase contributions by about $550
(For reference, see Fig.
contribution levels at various income levels).
The positive impact of a match on all employees
’ contributions is in contrast with its
effect on participants only. It seems that only participants earning above $130,000 increase
their contributions in response to the match. Participants earning between $35,000 and
$120,000 seem to reduce their contributions in response to a match. To understand this
counterintuitive finding requires analysis of the relation between the policy variables
existence of the match, the match rate, and the upper limit on the match
choices to participate and, if they participate, how much to contribute. Choi et al. (
and Engelhardt and Kumar (
) summarize how a match affects participants
through income and substitution effects.
It is possible that behavioral factors are also necessary to explain the match
’s influence on
’ choices. A substantial fraction of the contributions are at or near the point where
they exhaust the employer
’s match: the contributions of about 18 (22%) of the participants
whose employers offer a match are no more than $100 ($200) away from the upper
limit of their employers
’ match. A similar phenomenon is noted by Choi et al.
) on the contribution behavior of participants in one plan that changed the upper
limit of match.
A substitution effect could lead participants to cluster their contributions at the point
where the employer caps the match. But a substitution effect alone does not cause
participants to contribute less when the match rate increases.
A simple explanation for the propensity to contribute an amount which exhausts the
’s match is that the maximal match point is a focal point and interpreted by
participants as an implicit suggestion that it is the optimal amount to contribute
(Madrian and Shea
). This explanation is consistent with the behavior gleaned from
Figure 12 Contribution levels and savings rates for men and women
Using an experiment setting, Duflo et al. (
) find that a 50% match increase the take-up rate of low- and
middle-income subjects into IRA contribution by 11 percentage points compared to no match; and increase
the contribution by $345. These numbers seem to be in the same order of magnitude as our findings.
J Finan Serv Res
, that participants who receive a match contribute less than those who do not receive
a match when their incomes are at least $40,000. The following calculations are consistent
with this observation.
A typical upper limit on the match is 5% of salary. It inspires very different contribution
levels for low- and high-income participants. The average (median) contribution of
participants earning $40,000 is about $2,740 ($2,315), but 5% of $40,000 is $2,000. Thus,
participants earning around than $40,000 who contribute just the matched amount will
contribute less than their counter-parts who are offered no match. This effect is
strengthened when looking at higher earnings, say $90,000. The average (median)
contribution by participants in this income range is $7,121 ($7,239), but 5% of $90,000 is
only $4,500. Thus, participants who use the upper limit on the match as their focal
point to choose their contribution level will contribute less than those who do not
receive a match at all.
5 Discussion and Concluding Remarks
This is the first study on 401(k) participation and contribution to use non-survey individual-
level data that covers a large number of plans (companies) and includes information about
non-participants. It offers a few novel and counterintuitive observations on participation in
and contributions to 401(k) plans, and provides sharp estimates of sensitivities of these
choices to various individual and plan-level variables. The surprising findings are: women
are more aggressive users of 401(k) plans; coverage by a DB plan does not adversely affect
usage of a 401(k) plan; matching programs positively affect participation rates and
contribution of all employees, especially low-income ones, but negatively affect
contributions of mid-to-higher income participants.
Other studies have considered some of the issues covered here. However, the results
reported here are particularly compelling because of the size and nature of the data used
actual employee records, including non-participants
’ records, from hundreds of plans.
Individual-level data are important because in general, it is inappropriate to estimate a
relation on an aggregate level and then infer that an analogous relation holds at the
—a problem known as the “aggregation bias” (see, e.g., Freedman
). For example, at plan level, a $10,000 increase in average compensation
would increase average contribution by $480, while at individual level the same coefficient
is $907. Further, since individuals choose whether to participate in 401(k) plans and how
much to contribute to them, records of non-participants are essential to analyze the
participation and contribution decision.
summarizes some of the main findings, plotting contribution and savings rate
levels for each gender using predicted contribution imputed from two-sided Tobit
coefficients. By the nature of corner solution at zero, the predicted unconditional
contribution amount (i.e., accounting for non-participation) could go negative in which
case the predicted observed contribution would be zero. The Figure shows that
contributions rise with compensation, which is not surprising. It also shows that savings
rates rise with compensation, a more remarkable finding. Whether those who earn more
also save a larger fraction of their incomes has been a well known question, going back
decades prior to Friedman
) classic work on the consumption function. Recently,
Dynan et al. (
) re-visit the issue and conclude that those with higher expected lifetime
earnings also have higher savings rates.
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In general, the estimation of expected lifetime earnings and of savings is thorny, perhaps
intractable. This study uses 2001 compensation records of wage earners, whose incomes
fluctuate less than those of the self-employed. The unit of observation is the wage earner,
not the household. And savings are narrowly defined as contribution to a 401(k) plan.
Keeping these simplifications in mind, Fig.
shows quite clearly that savings rate in DC
accounts increase with compensation.
The gender difference also transpires from Fig.
: Relatively more women save, and
they save more than men, a result consistent with the findings of Warner and Pleeter (
who study US military personnel offered a choice between a lump sum and an annuity upon
release from the US armed forces. At the contemporary US government borrowing rate of
7% the present values of the annuities were double those of the corresponding lump sums.
Nonetheless, most people took the lump sums. Warner and Pleeter estimate that women
probability of choosing the annuity was 2% higher than men
’s. Generalizing this finding,
one would expect that women are more likely to participate in and contribute to DC plans
that defer current consumption into future on favorable terms.
One explanation for the gender difference is that women have a stronger taste for saving,
perhaps because they live longer on average. A second explanation starts with the
assumption that participation and contribution decisions are made at the household, not the
employee level. Women are more likely than men to have working spouses, and women
working spouses earn more than men
’s working spouses. Thus, comparing a man and a
woman with the same income, the woman is likely to live in a household with a higher
income, and therefore more likely to participate in a DC plan, and contribute more to it.
Without information about marital status, it is difficult to identify such effects. However,
the analysis control for the wealth level of the neighborhood in which the household lives
(and women do overall live in wealthier neighborhood compared to men of equal earning
power), which should to some extent offset the first effect. The second explanation suggests
that the gender difference should be strongest for low-income employees and disappear for
high-income employees. The differences between women
’s and men’s participation
probabilities are indeed highest for those earning less than $40,000, where they exceed
10%. But these differences are still around 2
–3% for those earning over $100,000. Also, the
gender gap in contribution rates increases rather than decreases with compensation. Thus,
the data are consistent with one prediction of the second explanation, but suggest that it is
not the only valid explanation.
’s findings on DB plans and matching programs are also relevant to those
interested in promoting savings. New tax-preferred savings programs can attract new
savings (i.e., money that would have been used for consumption) or money from competing
savings channels. In the latter case, there would be no increase in aggregate savings. This
study shows that surprisingly, other things equal, employees covered by DB plans tend to
participate more in, and contribute about the same amount to DC plans once they
participate. It is possible that employees have separate mental accounts (Shefrin and Thaler
) for different accounts of retirement money, and when choosing whether
to participate in, and how much to contribute to DC plans, they do not take into account
whatever rights they have in their employers
’ DB plans. Of course, there could be a
selection effect at work here: retirement savings-conscientious employees are more likely
attracted to firms that provide both DB and DC plans. Moreover, the stronger usage of DC
plans by those already covered by DB plans suggests that the presence of a DB plan
increases awareness of the need to save for retirement.
The overall impression is that employees save as much in 401(k) plans with or without a
DB plan. Thus, the evidence presented here is consistent with the view of Poterba et al.
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“believing that IRA and 401(k) contributions represent new saving”) and not that of
Engen et al. (
“we conclude that little, if any, of the overall contributions to existing
saving incentives have raised saving.
”) The implication, then, is that the introduction of
new tax-preferred savings programs will likely increase overall savings. This conclusion,
however, is not airtight. It is possible that those eligible for DB benefits who are aggressive
contributors to 401(k) plans make their contributions with money that would be saved
through other channels not covered in the records used in this study.
Match programs increase participation rates, and contributions, primarily of low-income
employees. This finding clearly suggests that voluntary participation and contributions in
individual retirement accounts are likely to increase if the government were to match the
contributions. Moreover, the match will have the strongest impact on the low-income
members of society. And, if policy makers find it desirable to limit the subsidy to high-
income people, match rates could be set to decline with income.
It does not seem surprising that an employer
’s match program should increase
overall contributions since it increases the compensation, albeit in a deferred form.
However, individuals in the medium income range, conditional on participation, seem to
contribute less when the match is generous. Two explanations come to mind. First, if plan
participants have desired levels of total savings, they will contribute less in the presence of
employer match than what they would in the absence of such matching. Another influence
comes from upper limits on the contribution that is matched, which all plans have. (Usually
it is 5
–6% of compensation.) The upper limit can serve as a focal point suggesting a desired
contribution. Choi et al. (
) indeed report that many participants contribute exactly to
the point where matching ends. To the extent that retirement savings rate increases with
compensation, such a focal point will increase contributions of low-income participants and
reduce that of mid-to-high-income participants, relative to their counterparts who receive no
or little match.
This is a study of choices of employees eligible to participate in 401(k) plans in 2001.
Most of the employees
’ choices were probably made prior to 2001, and a shortcoming of
the study is the records
’ silence on the timing of the employees’ choices. Some employee
attributes changed over time
—certainly age and tenure, and most likely compensation.
Moreover, some plan characteristics may have changed between the time an employee
made his most recent choice and 2001. A long panel of records can potentially fix some of
these issues, but not all. Ameriks and Zeldes (
) point out that the separation of age,
cohort and time effects requires assumptions outside the panel records.
The exploratory data analysis summarized here speaks to a variety of subfields. First, to
the growing community of students of retirement plans in general and defined contribution
plans in particular. Second, to those interested in savings behavior and especially how it
varies across income groups. And third, to those interested in gender differences in decision
making. Additionally, this descriptive paper is likely to inform discussions on designs of
retirement and savings plans.
Acknowledgement The authors are grateful to Steve Utkus and Gary Mottola from Vanguard® Center for
Retirement Research. They made the data available and provided us with constructive comments throughout
the process. We also thank Pierre Azoulay, Geert Bakeart, Charlie Calomiris, Sarah Holden, Brigitte
Madrian, Jim Powell, Thomas Steinberger, Ed Vytlacil, Elke Weber, Steve Zeldes, an anonymous referee,
and seminar participants at Columbia, Rice, Wharton Pension Research Council, New York Federal Reserve
Bank, CEPR workshop on Financing Retirement in Europe, and Wharton Workshop on Household Portfolio
Choice and Financial Decision Making for their helpful comments.
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The original data set provided by the Vanguard consists of 926,104 records of 401(k)
eligible employees. The following criteria cause elimination of observations: (1) The
employee is hired after January 1, 2001. (His recorded annual contribution might be
inaccurate.) (2) The employee is less than 18 years old (He might not be the decision
maker.) (3) The employee
’s annual compensation is less than $10,000 or greater than $1
million. 793,794 records survive.
The key variables deferral rate, contribution, and compensation appear in all the
records. All other individual variables have missing values that are more concentrated in
the non-participant sub-sample. 12.8% of the observations do not report gender, among
which 62.5% are non-participants; the same percentages for age, tenure and wealth are
12.3% (62.2), 12.2 (62.1%) and 25.6% (76.4). Elimination of all the observations with
missing values would cause the study to be based on a partially truncated sample,
which is likely to bias the results due to the influence of the selection. Hence the
choice to replace them with imputed values.
The imputed values are calculated as follows: (1) unidentified gender variables are
recorded as the percentage of females in the plan (a record identified as a female being
1 and as a male being 0); (2) missing age and tenure values are replaced with their
respective plan mean age or tenure. To fill in the missing values of wealth, the
following regression is estimated on non-missing values:
Þ ¼ b
Þ þ b
Þ þ e;
where DCASSETS is the total assets in the defined-contribution accounts. The specification
above was chosen among various models for both within-sample goodness-of-fit and out-
of-sample robustness. The next step is to predict out-of-sample values and map the
predicted values to the closest IXI brackets.
With the exception of the wealth level, IXI, missing values do not account for a
significant proportion (about 10%) of observations, and the symmetric trimming method
(Honore et al.
) is applied to conduct sensitivity check. That is, for each variable
create an artificial sample by first taking only records that report that variable (but may miss
other variables). The second step eliminates a given number of participants
’ records at
random, so that the participation rate in the subsample matches that of the original sample.
(This second step eliminates records of participants, since systematically it is the non-
participants whose records are likely to miss values.) Then estimate coefficients for the
resulting sub-sample. Repeating this process many times (e.g., 30 or 50), the coefficients
estimated on the full sample (with missing values imputed) are close to the average of
coefficients estimated on those symmetrically trimmed sub-samples.
For the wealth variable the same sensitivity check cannot be used because only a low
proportion of non-participant records have this information. Instead, the comparison is
between the inputted wealth variables and the general distribution of wealth in the
population. The following figure plots the histogram of wealth distribution for the
population (IXI), of the non-missing Vanguard data, and the amended Vanguard data. After
J Finan Serv Res
filling in the missing values, the sample studied here no long over-represents the wealthy
households. The sample still under-represents the very poor households (those with
negative or less than $1,000 in balance), and over-represent the lower-middle to middle
households (with balances ranging from $5,000 to $100,000), which is consistent with
evidences from the Survey of Consumer Finance and the Current Population Survey that
401(k) eligible employees are overall financially better-off than the general population in
the lower end.
Further, estimating the main regressions excluding the wealth variable, the coefficients
on all variables except compensation show little variation. (The loading on compensation is
increased, which is expected.)
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