Defined Contribution Pension Plans: Determinants of Participation and Contributions Rates Gur Huberman &
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Assets in Personal Accounts % of Total House holds IXI (population) Vanguard Figure 6 Fractions of households at each wealth level J Finan Serv Res
individual characteristics X ij , plan policies Z j , and X
j represents the plan-level averages of individual characteristics: U ij ¼ g 0 þ g 1 X ij þ g 2 Z j þ g
3 X j þ e ij ; e ij ¼ h
j þ e
0 ij : ð1Þ The plan-level averages of individual attributes serve as control variables; A later paragraph explains how these variables dampen the influence of endogeneity and peer effect on the coefficient estimation. The disturbance term can be decomposed into a plan-specific unobserved effect, η j , which is assumed uncorrelated across different plans, and an individual disturbance, e 0 ij
η j and e 0 ij could be heteroskedastic across plans or individuals, but are assumed to be independent of the regressors. The individual will participate if U ij >0, or PART ij ¼ 1 ; if U
ij > 0;
0 ; otherwise: & ð2Þ
Determinants of participation can be analyzed using the linear probability model or maximum likelihood methods such as Probit. Conditional on participation, the employee ’s desired contribution is described by: y Ã
¼ b 0 þ b 1 X ij þ b 2 Z j þ b
3 X j þ d ij ; d ij ¼ ϕ
j þ d
0 ij : ð3Þ The disturbance δ ij
ij . Due to the max-out restriction, the observed contribution for a participant is: y ij ¼ y à ij ; if y à ij < v ij ; v ij ; otherwise: : & ð4Þ
where v ij is the maximum allowed contribution. The IRS limit constrains v ij to be the lower of $10,500 and 25% of compensation. If contribution level is expressed as percentage of compensation, v ij
model in Eq. 4 allows for individual truncation levels (as $10,500/compensation varies with compensation levels). Further, some plans may be subject to plan-specific restrictions on the maximum contribution levels. We discuss the potential effect of such restrictions in Section 3.3
. For non-participants, the observed contribution is zero, and their desired contribution is left unspecified. Note the distinction between corner solution and data censoring: zero observed contribution is due to corner solution and maxed-out contribution is a result of data censoring. Since contributions are between zero and the maximum limit, it is tempting to analyze them with a two-sided Tobit regression analysis. However, the standard Tobit estimation is not robust to heteroskedasticity, and unfortunately, diagnostic tests (e.g., J Finan Serv Res
Fig. 5 ) show that the error terms are highly heteroskedastic which could cause bias in estimation. The estimation tool used here is the censored median regression which is a special case of the censored least absolute deviations (CLAD) proposed by Powell ( 1984 ).
i is observed uncensored, then its median would be the regression function x 0 i b under the condition that the errors have a zero median. When y i
0 i b is in the uncensored region. However, if x 0 i b is on one of the two corners, then more than 50% of the distribution will “pile up” at the corner in which case the median of y i does not
depend on x 0 i b . Thus, the computation of the estimator alternates (till convergence) between deleting observations with x 0 i bb that are outside the uncensored region, and estimating the regression coefficients by applying the median regression to the remaining observations. For this reason, coefficients are not identified for observations with conditional median contribution (given the individual and plan characteristics) outside the non-censored region [0, 10,500]. For the present sample, roughly speaking, the method does not offer sharp predictions on behavior for people who earn below $20,000 or above $150,000 (about 10% of the sample). Analysis of this sub-sample is deferred to Section 4 . In Eq. 3 , individual characteristics (X ij ) include: (1) Annual compensation in $10,000 or in logarithm (COMP); (2) The wealth rank (IXI rank from 1 to 24) of the nine-digit zip neighborhood where the individual lives or the log of average household wealth in that IXI bracket (WEALTH). Strictly speaking, the WEALTH variable measures the average financial wealth of the neighborhood the employee lives in, which could be a noisy indicator of total personal wealth. On the positive side, this measure is also less susceptible to the endogeneity of personal wealth to savings propensity. This WEALTH variable has great explanatory power for participation/contribution, especially participation, but leaving it out of the regressions does not affect other coefficients (except compensation) significantly; (3) A gender dummy (FEMALE); (4) Age in years in excess of 18 (AGE); (5) The length (in years) of the individual ’s tenure with the current employer (TENURE). Plan policy variables include the presence of company stocks as an investment option (COMPSTK), the presence of DB plans (DB), and number of funds offered to employees (NFUNDS). Variables for the intensity of employer match very slightly differently in specifications depending on the context. A binary variable, MATCH, is equal to one if the employer offers any match. The match rate which appears in the analysis of participation probability is the average match rate for the first 2% of salary, denoted MATCH_INI. The match rate used in the contribution analysis is the average match rate for the first 5% of salary, denoted MATCH_AVG. About 39% of the employees in the sample face tiered match schedules. The separate measures of match intend to capture the different nature of the strength of the incentive for participation and contribution decisions. In the decision on whether to make any positive contribution (participation), the relevant incentive is the match rate for the first dollar contributed. In our sample, this corresponds to match rate for the first 2% of compensation. For the contribution decision, the relevant incentive is the match for the total range, and most plans in our sample match up to 5% of employees. Finally, plan-level control variables include: (1) average compensation (COMP_ MEAN); (2) average age (AGE_MEAN); (3) average tenure (TENURE_MEAN); (4) average wealth (WEALTH_MEAN); (5) log number of employees (NEMPLOYEE), (6) the rate of web registration among participants within the plan in percentage points (WEB). In the absence of information about employee education, WEB proxies for the average education level, the sophistication level of the plan participants, or some other firm attribute that is correlated with Internet penetration. COMP_MEAN and WEALTH_MEAN are in the same units as COMP and WEALTH in the same regression. To a large extent, J Finan Serv Res these variables can be viewed as exogenous, i.e., out of the control of plan policy makers. Adding these variables in the regressions serves two purposes in addition to the role of conventional control variables. First, they serve as instruments for possible endogeneity of plan policies in response to characteristics and behavior of people within the plan. For example, Mitchell et al. ( 2005
) show that there is a strong tax motivation in employers matching programs subject to the federal non-discrimination rules. As a result, plan- offered match schedules are affected by the average compensation of employees (or those separately of the highly compensated and non-highly compensated employees). If the common component in behavior of employees belonging to the same plan is due to aggregate individual characteristics such as average income, the part of plan-level policies that is orthogonal to plan-level aggregate individual characteristics can be considered as exogenous (see, e.g., Chamberlain, 1985 ). Second, they serve as instruments to control for potential peer effect, that is, the influence of colleagues participation and contribution choices on an individuals own choices. (Manski 1993 , offers detailed analysis of peer effects; Duflo and Saez ( 2003
) examine peer effects in retirement savings decisions.) 3 Participation and Contribution: Full-sample Analyses 3.1 Individual Participation Table
1 reports participation regressions (Eq. 2 using both the linear probability (Columns 1 and 2) and the probit models (Columns 3 and 4). In linear probability models, COMP and WEALTH are expressed in log dollars because they are both highly right-skewed variables, and Fig. 3 suggests a concave relationship between participation and compensation. MATCH_INI is the average match rate (in percentage points) for up to 2% of salary. (This is the match rate relevant to the participation, as opposed to the contribution decision.) Reported standard errors adjust for heteroskedasticity (both within and across groups, and group-specific disturbances) as well as within group correlation (due to the group-specific disturbance δ j ). A comparison of the two columns indicates that the marginal effect of individual attributes is not much affected by the plan policies. Bear in mind that when standard errors are adjusted for plan random effect ( η j ) in Eq. 1 , the “effective” sample size for coefficients estimates of individual variables is of the order of the total sample size (about 700,000) while that for coefficients estimates of plan variables is of the order of the number of plans, or just 647. (Wooldridge 2003 , offers a general analysis on the asymptotics of cluster samples, especially where number of observations within clusters is large relative to the number of clusters.) In Probit estimation, COMP and WEALTH are both in dollar terms and in logarithms (the plan-level average COMP and WEALTH carry the same units in the same regression.) The marginal probabilities reported (setting all non-dummy variables at their mean values, and all dummy variables at zero) are comparable to the coefficients from linear probability models. Measures of goodness-of-fit are pseudo R-squared and incremental probability of correct prediction. The former is defined as the likelihood ratio 1 À Ln L ð Þ=Ln L
0 ð Þ, where L 0
b Pr by i > 1 2 y i > 0 j À Á þ b
Pr by i < 1 2 y i
j À
À 1, where b Pr is the empirical frequency, and by i
the predicted probability from the estimation. The null value of this probability is zero, and a value of one indicates perfect prediction. The analysis has close to 800,000 observations, and just a handful explanatory variables. Viewed in this context, the explanatory power of J Finan Serv Res T able
1 D eterminants of individua l participation. Depe ndent
variable is P A R T . The
all-sample par
ticipation rate
is 70.8%.
All coef
ficients are
multiplie d b y 100.
COMP and
WEAL TH are expres sed
in log
dolla rs in Column s (1) –(3) . In colu mn (4), COM P is exp ressed
in $10,000,
and WEAL
TH is exp ressed in IXI ranks from
1 to 24. Column s (1) and (2)
are res
ults from
the linea
r prob
ability mode
l. The
t- statistics adjust for
both heteroskedasticity (both within
and across
grou ps,
and group-s
pecific disturbances) and within
grou p correlation (due to the group-s pecific
distur bance).
Co lumn
s (3)
and (4)
report results
from prob
it estim
ation . The stan dard
err ors
are adju
sted for
cor relation
within the
sam e plan. Pseudo R-squa
red is reporte d for
good ness-of
-fit. Th e mar ginal
probab ilities
are ca lculated b y settin g all
non- dummy
variables at their mea n valu es, and
all dummy
vari ables
at zero.
The sample
contains 793,
794 eligible
emp loyees
in 647
plan s. Th e ef fective sam ple
size on indiv idua l (pla n) variables is the
numb er o f empl
oyees (pla
ns) Linear
probab ility
Pr obit
(1) (2)
(3) (4)
COEF SE COEF SE COEF
SE Mar
gl. Pr . COEF SE Mar gl. Pr . I CNST
− 214.
14 36.8
8 − 196. 39 40.05
− 926.76
81.03 – − 173. 06 86.2 1 – COM P 15.27
0.21 15.2
1 0.23
57.3 4 4.72 18.1 2 1 1.54 0.94
3.71 WEAL
TH 5.96
0.06 5.93
0.07 23.1
6 1.30
7.32 2.14
0.34 0.69
FEM ALE
5.64 0.50
4.66 0.84
18.8 8 1.29 5.97 20.1
1 0.93
6.47 AG E 0.21 0.05
0.22 0.08
0.32 0.44
0.10 0.88
0.51 0.28
AG E^2
0.00 0.00
0.00 0.00
− 0.01
0.01 0.00
− 0.01
0.01 0.00
TENUR E 1.30 0.08 1.17
0.14 4.79
0.47 1.51
5.07 0.55
1.63 TENUR
E^2 − 0.03 0.00 − 0.03 0.00 − 0.12 0.01 − 0.04 − 0.12
0.02 − 0.04 II MA TCH_I NI 0.12
0.02 –– 0.44 0.04 0.14
0.41 0.04
0.13 COM
PSTK 3.50
1.60 –– 9.47 4.40 3.01
7.53 3.58
2.41 DB − 0.28 1.45
–– 1.01
2.1 1 0.32 0.26 2.60
0.09 NFUND
S − 0.23 0.1 1 –– − 0.92
0.31 − 0.25 − 0.78
0.34 − 0.25 III COM
P_MEA N 3.30 4.50 3.46
5.39 7.36
6.12 2.32
2.77 0.94
0.89 WEAL
TH_ MEAN
− 1.70
2.62 − 1.12 3.13 − 5.38 4.58 − 1.70 − 5.31
2.56 − 1.71 AG E_MEAN
1.49 0.32
0.99 0.59
4.53 1.50
1.43 5.27
2.02 1.70
TENUR E_MEAN
− 1.09
0.29 − 0.77 0.38 − 3.78 0.70 − 1.19 − 4.17
0.92 − 1.34 WEB 0.07
0.08 0.18
0.09 0.31
0.14 0.10
0.65 0.14
0.21 NEMP
LOY EE − 2.89 0.52
− 3.37
0.77 − 9.55 2.10 − 3.02 − 9.80
2.02 − 3.15 Pseudo R-square
d 0.19
0.18 0.18
0.13 J Finan Serv Res the reduced form linear model is remarkable: R 2 is about 19% and incremental probability of correct prediction is about 30%. Income and wealth are the most important determinants for participation in DC plans. Other things equal and on average, a $10,000 increase in annual compensation is associated with about 3.7% higher probability of participation (unless otherwise stated, reported numbers are the marginal probability estimates from the Probit model in column (4) of Table
1 ). Females are 6.5% more likely to participate than their male counterparts. The stock phrase “other things equal” is particularly pertinent here. Women’s overall participation rate is 70.0%, less than the 71.3% participation rate of men. However, women typically earn less than men —their median wage is $39,500, whereas men’s’ median wage is $54,000 in this sample —and they have shorter tenure—a median tenure of 9.5 years compared with men ’s 10.5 years in this sample. The 6.5% gender difference in participation rates applies after controlling for these and the other variables. Older and longer tenured employees are more likely to participate. For an average 18- year old who just starts on her job, each year of advance in age (tenure) is associated with an increased 0.2% (1.6%) participation probability, and both marginal effects are decreasing in years. The tax-deferred nature of 401(k) contributions suggests that controlling for income (and the marginal tax rate that goes with it) it is more beneficial to contribute early in one
’s career. However, earlier in one’s career is when liquidity constraints are likely to reduce the propensity to save for retirement. Moreover, the salience of retirement (and the need to save for it) may increase with age. Finally, the pattern documented here may arise because employees who join 401(k) plans are very unlikely to leave them. Analysis of a long panel of records can determine the validity of this hypothesis. With the exception of DB, the plan-level policy variables seem to affect individual participation. Table 1 suggests that participation rate could be about 13% higher in a plan that offers 100% match than in an otherwise equal plan that offers no match. Using MATCH_AVG, the sensitivity estimate is about 1 percentage point lower. Further (results not tabulated), the mere existence of a match (regardless of the magnitude) increases participation by 6.3%, and each 1% rise in match rate further increases participation by 0.08%. When company stock is an investable option, the participation probability increases by 2.4%. One caveat regarding company stock: By and large, firms where company stock is an investable fund are publicly held. It may well be that “company stock” proxies here for “publicly held firm.” Unfortunately, the records available for this study (plan identities are removed) do not allow a further investigation of the issue. The big surprise is the coefficient on DB, which is small in magnitude and statistically indistinguishable from zero. Controlling for individual and other plan level attributes, it seems that participation rates of those covered and not covered by a DB plan are similar. Moreover, the same result (not tabulated) emerges when the analysis is repeated for the subsample of employees who are at least 40 years old with at least 10 years of tenure. It is those over 40 who are more likely to be conscientious about the status of their retirement savings, and, among them, those with at least 10 years of tenure to have accumulated considerable rights to retirement benefits if their employer offers a DB plan. Their participation rates are similar to comparable employees not covered by a DB plan. Even and Macpherson ( 2003
) report similar findings based on Current Population Survey of 1993. The similarity in behavior suggests that, counter-intuitively, the presence of a DB plan does not affect the participation decision in a 401(k) plan, or that employees who have stronger taste for savings are more likely to work for companies that offer multiple retirement savings vehicles. J Finan Serv Res Controlling for other variables is crucial to this result and its interpretation because a comparison of the raw data leads to the opposite conclusion. Participation rates for the full sample are 68 and 76%, for employees working for firms that offer or do not offer DB plans, respectively. When attention is confined to the subsample of those over 40 and with at least 10 years of tenure, the corresponding participation rates are 71 and 86%, respectively. However, employers with DB plans tend to be larger employers and the average compensation and wealth levels of those employed by firms that offer DB plans are lower (the correlations between DB and plan size, plan average compensation, plan average wealth are 0.44, −0.12, −0.20, respectively). Excluding those plan-average variables would produce a negative and significant coefficient on DB equal −3.0%; further excluding WEALTH from the explanatory variables would yield a coefficient of −3.6%. Therefore, the present result does not contradict Cunningham and Engelhardt ( 2002 ). However, DB has no effect on participation only after controlling for these and the other variables in the analysis. Unfortunately, hazard model-type analysis (used, e.g., in Choi et al. 2002 ) accommo- dating changing behavior over time is not feasible here because the data underlying this study consist of a single cross-section. If plan policies change over time and the participation of employees is sensitive to these policies as they evolve, the estimates reported here could be subject to measurement errors. This observation is especially pertinent to MATCH which could vary from year to year. The behavior of the 63,043 employees hired in 2001 serves as sensitivity check because their decision to participate was based only the plan policies prevailing in 2001. Using the same specification as the first column in Table 1 on the new hires subsample, the participation probability is 11% higher for employees who were offered 100% match compared to those without match (significant at less than the 1% level). Still, about 19% of the employees who are offered employer match of at least 50% choose not to participate, and among those who participate, 45% do not contribute up to the match threshold. Such evidence is echoed in Choi et al. ( 2005
) (these authors further estimate that the foregoing matching contributions average 1.3% of the annual pay of the under-contributing employees). Further, the participation probability is 2.2% higher when the company stock is an investable option, and is 2.8% lower when a DB plan is also present, but neither of the effects is statistically significant at less than 10% level after adjusting for the plan random effects. Interpreting results from this subsample, however, requires some caution. First, some non-participants, especially those who were hired for less than a couple of months, may be simply taking time in making their decisions rather than choosing not to participate. (The subsample participation rate is 45%, as opposed to the all sample participation rate of 71%). Second, the new hires sample is skewed toward the young, inexperienced, and low-income subpopulation of the 401(k) eligible employees, the inference from which may not extend to the general population. Finally, restricting the sample to people who were hired during one particular year may reflect a shock that is particular to that year. 3.2 Individual Contributions This subsection employs censored median regressions to estimate the relations between individual contribution and individual characteristics as well as plan policies. Table
2 reports the estimates of three censored median regressions with different dependent variables: contribution in dollar amount; and saving rate in percentage (i.e., the ratio of contribution to compensation). The censoring in the median regressions is designed to account for zero being the lower bound on savings and the lower of $10,500 and 25% of J Finan Serv Res employee compensation being the upper bound. Robustness checks further assess the impact of additional plan-imposed constraints on contributions made by highly compen- sated employees. The dollar amount specification suggests that other things equal, contributions increase by $909 for an increase of $10,000 in compensation, and that women contribute $482 more than men. The sensitivities to individual attributes were also estimated separately for each of the 483 plans that had more than 100 employee records. The average estimates from all plans (which assign equal weights on plans regardless of their size) on compensation and gender are $916 and $478, almost identical to the two coefficients from pooled regressions. Age seems to be negatively associated with contributions for younger employees (below 40) but positively associated with contributions for older employees. A match increases contributions: an increase in the match from zero to 100% will increase contributions by $457. Further, among companies that offer company stock as an investment option, the effect of 100% match is stronger by $159 when the match is restricted to company stock. (Results not tabulated.) The presence of company stock among the investable funds does not seem to have a consistent impact on contribution. It is slightly negative (but not distinguishable from zero) in the first specification (Column (1) where both contribution and compensation are expressed in dollars), but is positive and significant in the savings rate specification (Columns (2)). The estimation from the latter specification assigns more weight to the low-income employees. The next section shows that they are more responsive to the presence of company stock, which explains the difference in outcome between the first specification and second and third specification. The presence of a DB plan increases employee contributions by $180. Again, it is important to interpret this observation in the context of controlling for other variables. In the raw data, the median contribution of employees working for firms that have DB plans is $504 lower than their no-DB counterparts; and among employees who are 40 years or older and have at least ten years of tenure, the difference of medians is $1,580. (Unlike average contribution, plan median contribution is not affected by non-participants and maxed-out contributions.) This property in the raw data is consistent with findings of negative relation between the presence of DB plans and contribution rates summarized in Clark and Schieber ( 1998 ).
DB plans tend to have more employees who have longer tenure, but less financial wealth. It is possible that these controls also capture some employees ’ propensity to save. Such individuals may tend to work for larger companies (that presumably offer safer employment) in which employees stay longer with their employers. The results are even more surprising to the extent that the control variables capture a taste for savings. Papke ( 2004a
) uses survey data and OLS regressions in which she controls for income, wealth, gender and marital status. She reports that DB coverage is associated with higher contributions to DC plans, but the effect is statistically insignificant. The results reported here are far more reliable because the underlying data are of higher quality and the analysis itself exploits the higher data quality by controlling for plan-level characteristics and allowing for censoring in the contributions. Nonetheless, it is worth remembering that the DB measure reported here (as well as in other studies) is a crude indicator of coverage rather than the more desired measure of the employee ’s cumulative rights within the plan. Still, to the extent that this measure is correlated with the employees ’ non-DC benefits upon retirement, the results are valid and the positive correlation between the presence of DB future benefits and current DC contributions is surprising indeed. J Finan Serv Res T able
2 Determinants of indiv
idua l con tribution: censored
med ian
regression analysis. The depend
ent variables are: contribu
tion in dolla rs (Columns
(1) , (3) and (5)),
and savi
ngs rate
(equals con
tribu tion/comp ensation , Column s (2)
and (4)).
Ce nsored
med ian
reg ression
(P owell
( 1984
)) is applied to all
spec ifications. Co lumns
(1) to (4) use the
full sam
ple. Co lumn (5) exc
ludes all
highl y-comp
ensated emp
loyees (HC
Es, who
ea rned
$85, 000
or more).
Column s (1) and (2)
incorpo rate
con tribution cens oring
due to the IRS limit
(the lower
of $10,500
or 25%
of compen
sation). Column
s (3)
and (4)
fur ther
inco rporate
potential plan
-specific limits
w here
an observati on is
upper -censo
red if (1) the employe
e contribu
tes to the IR S limit; or (2)
the employe
e is in a “pote
ntially limited
plan ” and has clos
e to the max imum
cont ribution
deferral rate
in the
plan (within
0.25 %).
A “pote
ntially limited
plan ” is def ined
as a plan that (1)
nobo dy in the plan
has total
contribu tion
up to 25% of com
pensatio n; (2) at least
five emp
loyees in the plan (who
con tribute
less than
$10,500) hav
e con
tribut ion
deferral rates
clus ter
at the
plan maximum
(within 0.5%).
Pseudo R-squa
red is the prop ortion
of the
sum of abso lute dev
iations in the dependent variable
explained by the regression IRS
limit only
Plan-specific limit
adj. HCE-
exclude d (1) Linear (2)
Sa ving
rate (3)
Linear (4)
Saving rate
(5) COEF
SE COEF
*100 SE*1
00 COEF
SE CEOF*10
0 Se*100
COEF SE I CNS T − 3,95 8.64
590. 84 − 591.06 161.
61 − 3,88 9.52 580.
97 − 573.25 168. 40 − 3,737.80 648.99
COM P 909. 99 1 1.57 88.6 6 5.47 91 1.78
1 1.36
175.38 14.6
0 912.86
32.3 2 WEAL TH 81.2
2 4.81
16.3 8 1.27 81.6 8 4.82 9.72 0.87
73.5 7 6.69 FEM ALE
481. 05 24.8 4 100.16
7.18 485.
70 24.6
5 100.34
7.35 435.51
38.9 9 AG E − 33.3 7 8.09
− 4.88
2.74 − 33.6 3 7.95
− 2.48
2.91 − 26.2 9 10.1
2 AG E^2 1.1 1 0.16 0.21 0.05
1.12 0.16
0.14 0.05
0.96 0.21
TENUR E 78.8 3 7.15
18.4 0 1.49 79.4 0 7.00 13.3 9 1.43 71.5 6 7.20 TENUR E^2
− 2.07
0.24 − 0.46 0.05 − 2.08 0.24 − 0.34 0.04 − 1.90 0.24 II MA TCH_A VG 4.60 0.76 1.32
0.20 4.64
0.76 0.95
0.16 4.66
0.83 COM
PSTK − 12.9 7 54.9
5 20.7
4 16.4
4 − 16.6 1 54.6
1 18.4
2 15.9
1 − 0.43 60.5 5 DB 177. 89 55.9 1 25.1
3 12.7
7 182.
06 56.1
2 7.65
1 1.24
170.01 63.8
7 NFUN
DS − 5.45 3.74 − 2.15 0.93 − 5.74 3.74 − 0.96 0.77 − 2.45 4.34 III
COM P_ME
AN 14.0
0 15.3
8 8.67
3.57 13.9
6 15.2
5 2.92
2.07 5.31
16.6 0 WEAL TH_ MEAN
− 103.
58 30.6
8 − 29.5 2 9.18
− 105.
25 30.1
1 − 15.3 1 8.07
− 99.2
4 35.8
6 AG E_MEAN 57.4 7 14.9 6 19.1
3 2.94
56.3 0 14.9 2 1 1.95 3.38 54.2
6 14.9
6 TENUR
E_MEA N − 67.4 5 17.9 3 − 17.2 0 3.37
− 67.0
9 17.8
5 − 1 1.49 3.39
− 64.5
4 19.3
0 WEB
19.0 2 3.25 3.74 0.67
19.3 2 3.27 2.13 0.63
17.1 0 3.75 NEM PLOYEE
− 1 15.1 5 20.4
1 − 37.7 2 6.35
− 1 18.6 6 20.2
9 − 27.9 7 5.75
− 1 16.1 8 28.3
0 No.
indiv iduals
& plan
s 793,
794 647
793, 794
647 793,794
647 793,
794 647
661, 104
643 Pseudo
R-squa red
0.25 0.10
0.25 0.1
1 0.19
J Finan Serv Res The savings rate specification (Column (2)) is quite consistent with the other specification, showing that an increase in compensation form $40,000 –$50,000 is associated with an almost 1% increase in the saving rate. Women ’s saving rates are 1.05% higher than those of men. Savings rate increase by 0.18% when company stock is an investable fund and by 0.25% when a DB plan covers the employee. 3.3 Plan-specific Limits on Contribution Some 401(k) plan sponsors might impose maximum contribution limits on their employees that are lower than the IRS limit ($10,500 or 25% of compensation). There are two types of such lower limits: uniform plan limits on contribution (usually the total contribution from both employee and employer) as a percentage of employee compensation; and contribution limits for highly compensated employees (HCEs, defined as those who earned $85,000 or higher in 2001) in compliance with the federal non-discrimination rules. This section analyzes both situations. First, the plan-specific limits for all employees in a plan. Some of the 401(k) plans in the sample have been historically organized as profit-sharing plans. As such, they were subject to the 15% limit on total employer and employee contributions as a percentage of employee compensation. Other sponsors might have raised the limit to 17 –18% or sometimes higher in order to encourage employee contribution. Unfortu- nately, no explicit information is available. Mitchell et al. ( 2005
) discuss the possible prevalence of these limits in this sample. We adopt the following algorithm to classify plans that are suspicious of having limits lower than that of the IRS: a plan is classified as a “potentially limited plan” with a limit of c%<25% if: (1) Nobody in the plan has total contribution deferral rate greater than c%; and (2) there are five people or more in the plan whose total contribution is more than (c% –0.5%), but lower than $10,500. 2 The second criterion ensures that there is some clustering at c% so that the observed upper bound is not a random incidence. Altogether there are 341 plans (out of 647) that satisfy both criteria above. About 54.5% of our sample eligible employees, and 84.3% of our sample participants are potentially subject to plan-specific limits, and 3.3% of participants are potentially constrained by such limits (that is, they contribute an amount that is lower than $10,500 but is at the putative plan- specific limits). Plan-specific limits require modification of Eq. 4 in estimation. An employee ’s contribution is upper-censored if any of the following holds: (1) He contributes $10,500 (we allow $25 for the rounding error); (2) he contributes 25% of his compensation (we allow 0.25% for the rounding error); and (3) he is in one of the “potentially limited plans” described above, and has the highest deferral rate in his plan (we allow 0.25% for the rounding error). If an employee ’s contribution is upper-censored for any of the three reasons, we record it as y ij ¼ v ij (for observed contribution) and y à ij
ij (for desired contribution) in the censored regression. Columns (3) and (4) of Table 2 report the results from the extended censored regression estimation. It should be noted that this specification might over-classify upper-censored 2 The 0.5% is to allow for rounding error. We err on over-classifying “potentially limited plans” to be on the conservative side. J Finan Serv Res
observations because the “potentially limited plans” may not actually have any mandatory limits. 3
savings rate specification the marginal effect of compensation is much strengthened (because highly-compensated employees are more likely to be constrained). The similarity arises because only a small portion of the employees are actually constrained although a great majority of them are subject to potential plan-specific limits: about 2.4% of the eligible employees and 3.3% of the participants invest up to the potential plan limits that are lower than the IRS limit. Second, plan-specific limits for HCEs. Encouraging savings of low- and middle- income American families has been an important mission for policy makers (see recent papers by Bernartzi and Thaler 2004
; Duflo et al. 2006
). Some plans face additional limits on contributions made by HCEs under the federal non-discrimination rule with the stated goal that the DC plans do not overly disproportionately benefit the high-income people (see, e.g., Holden and VanDerhei 2001 ; Mitchell et al. 2005 ). The data set unfortunately does not provide information on such plan-specific restrictions on HCEs. As a sensitivity check, column (5) of Table 2 reports the regression estimates of the main specification (as in column (1)) on the subsample of employees who earned less than $85,000 (about 83% of the sample). Results seem to be consistent with those of the full sample. 3.4 Maximum Contribution As a by-product of individual contribution analysis, the decision to max out is also considered. Table 3 reports estimates of maxing out using the same model specifications as in the last two columns of Table 1 . The first two columns classify maximum contribution according to the IRS limit, while column (3) also includes potentially upper-censored observations due to plan-specific limits. The maxing-out rates among participants is 12.2% in the first two columns, and 15.5% in the third. All individual characteristics affect the probability of maxing out in the same direction as they do the probability of participation. Not surprisingly, the marginal probability of incremental compensation on maxing-out is higher when potential plan limits are taken into account (semi-elasticity of compensation, in logarithm, on maxing-out increases from 12.7 to 21.2 percentage points). Females are even more likely to max-out than males in the plan-limit adjusted specification: the gender difference increases from 1.4 to 3.2 percentage points (because the more savings-prone gender is more likely to be constrained by plan limits). The match rate seems to have a negative impact on maxing-out, but the effect goes away once plan specific limits are adjusted for. This difference is explainable by plan specific limits most of which are imposed on total contribution including employer match: for employees who intend to contribute close to the maximum allowable amount by the plans, employer match becomes substitutes for their own contribution. This effect is exacerbated by the positive correlation between the existence of potential plan limits and plan match 3 It could be that all employees in a plan voluntarily contribute less than certain percentage of their income, and a handful of them (five or more) contribute very close at the top (c%). This is more likely to be the case when c% is higher, such as those greater than 15%. For example, it is plausible that nobody contributes more than 20% of their compensation, even in the absence of any plan-specific limit. For people with compensation greater than $52,500, the $10,500 IRS limit binds first. For people from the lower compensation group, contributing 20% or more would imply low take-home pay. On the other hand, one can also argue that the classification method may miss-out limited plans, too. Under-classification is quite innocuous for the estimation purpose. Non-detectable plan limits imply that they are basically non-binding (except for maybe less than five people in a plan). A plan-specific limit only affects contribution when it is binding, that is, when the employees are constrained. J Finan Serv Res T able
3 Determinants of indiv
idua l maxing out. Depe
ndent variable
is MAXO
UT , and the estimation method is
it. The
max ing-out
rate amo
ng participants is 12.2
% ac cording to the
IR S limit (Columns (1)
and (2)
), and
15.5% takin
g into
account of maximum contribu tion
in “pote
ntially limited
plans ” (C olumn (3)).
The definition o f
limited plan
s” is the sam e as in T able 2 . A ll coef
ficients are
multiplied by 100. COM P and WEAL TH are expres sed
in log
dolla rs in colu mns
(1) and
(3); and
COM P is expres sed
in $10,000,
and WEAL
TH is exp ressed in IXI ranks from
1 to 2 4 in colu mn (2)
. Standard
errors are
adju sted
for within
plan cor
relation. Pse
ud o R-squa red is rep orted for
goodnes s-of-fit. Th e
ginal probab
ilities are
calcula ted
by settin
g all
non-dum my var iables at their mean valu
es, and
all dumm
y vari
ables at zero. Only par
ticipants are
included in estim ation. The
sam ple
contains 562,
013 par
ticipants in 647 plan s. The ef fective
sam ple
size on indiv idua l (pla n) vari
ables is the numb er of emp loyees
(pla ns)
IR S limit only Pla
n-spec ific
limit adj.
(1) Log-Com
p (2)
D ollar
-C OMP
(3) Log-Com
p COEF
SE Mar
gl. Pr . COEF SE Mar gl. Pr . COEF SE Mar gl. Pr . I CNST
− 2,879.19
55.03 – − 653. 18 53.3 2 – − 1,42 1.90
48.9 2 – COMP 207.
73 2.41
12.7 3 19.23 0.26 2.09
1 18.69
2.29 21.1
9 WEAL
TH 6.84
0.49 0.42
2.20 0.16
0.24 9.53
0.66 1.70
FEMA LE 22.7 9 1.24
1.40 13.17
1.41 1.43
18.16 2.23
3.24 AGE
− 0.87
0.36 − 0.05 0.62 0.41
0.07 − 0.71 0.54 − 0.13 AGE^2 0.04
0.01 0.00
0.01 0.01
0.00 0.04
0.01 0.01
TENURE 0.57
0.23 0.03
0.55 0.28
0.06 1.09
0.35 0.19
TENURE^ 2 − 0.02 0.01
0.00 − 0.01 0.01 0.00
− 0.03
0.01 − 0.01 II MA TCH_A VG − 0.27 0.04 − 0.02 − 0.19
0.04 − 0.02 − 0.10
0.07 − 0.02 COMPST K − 17.4 0 3.81 − 1.10
− 13.88
3.67 − 1.54 − 7.89
4.52 − 1.42 DB − 9.37 1.85 − 0.59 − 6.44
2.06 − 0.71 − 2.40
4.64 − 0.43 NFUNDS 0.55
0.15 0.03
0.70 0.20
0.08 − 0.31 0.33 − 0.05 III COMP_
MEAN − 1 1.10 4.95
− 0.68
− 1.16
0.58 − 0.13 − 0.80
0.82 − 0.14 WEAL TH_MEA
N 17.5
1 3.14
1.07 8.66
1.45 0.94
− 1.17
4.35 − 0.21 AGE_MEA N 4.79 0.84 0.29
4.35 0.88
0.47 − 2.33 1.08 − 0.42 TENURE_M EAN
− 2.29
0.32 − 0.14 − 2.35
0.37 − 0.25 0.57 0.83
0.10 WEB
0.99 0.10
0.06 1.28
0.10 0.14
0.69 0.21
0.12 NEMP
LOYEE 9.48
1.45 0.58
8.63 1.44
0.94 − 1.59 1.33 − 0.28 Pseudo R-squa
red 0.41
0.22 0.38
J Finan Serv Res rate (the coefficient of correlation is 0.18). Presence of company stock and DB plans do not seem to have consistent effects on participants ’ tendency to max out once plan limits are accounted for. 4 Participation and Contribution: The Impact of Variation in Compensation The evidence so far shows that compensation is a major determinant of participation and contribution. There are a few differences between low- and high-income employees that can lead to this result. One, the tax benefits of saving through a tax-deferred vehicle are more generous to the high-income employees. Two, low-income employees are more likely to face liquidity constraints that will prevent them from putting money away, even in a tax- deferred plan. Three, Social Security benefits offer high salary replacement rates to low- income employees, and render alternative retirement savings less urgent. Four, low-income employees may be less educated and sophisticated about the benefits and costs of participating in a 401(k) plan. Engen and Gale ( 2000 ) suggest that the savings behavior varies across earnings groups, and therefore 401(k) plans have different effects on household wealth. The differences between low- and high-income employees suggest a re-examination of the data separately for various levels of compensation, a luxury easily afforded by almost 800,000 records on hand. This section reports estimates of the probit analysis of the participation and estimates of two sets of Tobit regressions, done at different compensation levels. One is a two-sided Tobit, aimed at estimating a censored linear contribution model for all employees at a given compensation level. Another is a one-sided Tobit aimed at estimating a censored linear contribution model only for participants. The three estimated models produce three sets of slope coefficients. Juxtaposing these coefficients provides a more comprehensive understanding of the employees ’ decisions. Technically, estimating the models again for various compensation levels modifies specifications (1) –(2) and (3)–(4) above, by allowing the slope coefficients (i.e., sensitivity of participation and contribution to those factors) to depend on the compensation. Such a modification is reasonable in the absence of a rigid structural model, and enhances the exploration of the rich data set at hand. The following equation summarizes the relations among the three sets of coefficients (corresponding to probit, one-sided Tobit and two-sided Tobit estimates). Let y à ij
desired contribution (could be a latent variable) by individual i in plan j, and W ij be a personal or plan characteristic variable. Then: @E y
à ij W ij
h i @W ij ¼ Pr PART ij ¼ 1 Â Ã @E y
à ij W ij ; PART
ij ¼ 1
h i @W ij þ E y à ij W ij ; PART
ij ¼ 1
h i @ Pr PART ij ¼ 1
 à @W ij ð5Þ
In the equation, when the independent variable W is binary (e.g., gender or availability of a DB plan), a partial derivative represents a difference (i.e., the change in the dependent variable when the binary variable changes from zero to one.) The left hand side of the equation, @E y Ã
W ij j ½ @W ij , is the sensitivity of the desired contribution per employee to a change in a variable W (e.g., compensation, match intensity, gender, etc.) at a given level of compensation. On the right hand side, Pr[PART ij =1] is the probability of participation J Finan Serv Res given all attributes, and @E y
à ij W ij ;PART
ij ¼1 j ½ @W ij is the sensitivity of the desired contribution by an employee conditional on participation; E y
à ij W ij ; PART
ij ¼ 1
 à is the expected contribution amount conditioned on participation, and finally, @ Pr PART ij ¼1 ½ @W ij is the marginal change in participation probability to an incremental change in W. If the models are correctly specified, then the two-sided Tobit coefficients are consistent estimates of @E y
à ij W ij j ½ @W ij ; the one-sided Tobit coefficients are consistent estimates of @E y
à ij W ij ;PART
ij ¼1 j ½ @W ij , and the marginal probabilities from probit estimation are consistent proxies for @ Pr PART ij ¼1
@W ij . Equation 5 implies that the unconditional response to a unit change of an independent variable (two-sided Tobit) is larger (resp., smaller) than the same response conditional on participation (one-sided Tobit) if the variable is positively (resp., negatively) associated with participation probability (Probit regression). Figures
7 , 8 , 9 , 10 and
11 summarize the estimates of the three regressions for each compensation bin. They are similarly structured with three graphs each. Each graph corresponds to the estimates of one of the three sets of regressions. The horizontal axis, common to the three graphs, indicates the compensation bin. The right vertical axis is the scale of the marginal probability, and the left vertical axis is the scale of the marginal contribution, both for participants and for the whole population in the corresponding compensation bin. All figures depict smoothed coefficients, i.e., weighted averages of actual regression coefficients of the central bin regression (50% weight) and its two neighboring bin regressions (25% each). The dotted lines represent 95% confidence intervals. The regressions underlying Figs. 7 ,
, 9 , 10 and
11 are estimated independently. For each, the records used are of the employees (or participants, for the one-sided Tobit) whose compensation ranges from $5,000 ($10,000) below the central point of the subsample to $5,000 ($10,000) above it, if the central point of the subsample corresponds to compensation below (above) $100,000. Thus, for instance, the slope coefficients (sensitivities) of the regression labeled $50,000, are estimates using the records of those earning between $45,000 and $55,000. When considering the evidence sorted by compensation, it is helpful to remember that half the employees in the sample earn less than $47,000. On the other hand, those who earn more than $73,500 —23% of the sample—contribute half the money in the sample. Therefore, the findings regarding lower income employees should inspire policies that 0 200 400 600
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