BLS WORKING PAPERS 

 U.S. Department of Labor 

U.S. Bureau of Labor Statistics

Office of Compensation and Working Conditions 

Matching Matters in 401(k) Plan Participation

Keenan Dworak-Fisher, U.S. Bureau of Labor Statistics

Working Paper 434

February 2010

All views expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the

U.S. Bureau of Labor Statistics.
Matching Matters in 401(k) Plan Participation 

February 2010 

Keenan Dworak-Fisher 

Research Economist 

Compensation Research and Program Development Group 

Office of Compensation and Working Conditions 

U.S. Bureau of Labor Statistics 

Dworak-fisher.keenan@bls.gov 

Abstract 

This study offers new evidence on the effects of the matching contributions made by 

employers to 401(k) plan accounts on plan participation rates, exploiting microdata from 

the National Compensation Survey, a large, nationally representative, establishment 

dataset. It addresses the potential endogeneity of the matching contributions by 

employing coworker and labor market characteristics as instruments. The results indicate 

that employer matches have substantial effects. They also indicate that higher match 

rates tend to be correlated with workers having lower propensities to save; correcting for 

this endogeneity produces estimates that are bigger than those seen through direct crosssectional comparisons. 

Acknowledgments: I would like to thank John Bishow, Brandy Dickerson, Mike Lettau, 

and Erin McNulty for help in understanding and assembling the data; and Al Blostin, 

Julia Coronado, Maury Gittleman, Mark Loewenstein, Brooks Pierce, and Bill 

Wiatrowski, and seminar participants at the University of North Carolina – Greensboro 

and the 2005 AEA-ASSA meetings for helpful comments on earlier versions of this 

paper. 
2

Introduction 

How do the provisions of a 401(k) plan affect the participation rates of 

employees? As traditional pensions continue their long decline and various changes to 

Social Security are contemplated, this question is increasingly crucial to those concerned 

about the sufficiency of retirement savings among US workers. In 2003, 39.9 percent1of 

U.S. private industry workers had access2

to a 401(k) plan in which employees must 

contribute to participate and employers matched some of those contributions. Yet, only 

67.9 percent of those with access to these plans participated; among lower-paid workers, 

the take-up rate was even lower (59.6 percent). These facts feed the concern that many 

workers may be saving too little for retirement and strengthen the imperative for plan 

provisions that promote participation effectively. 

The literature on the effects of 401(k) plan design has produced conflicting 

accounts of how 401(k) plan provisions affect participation. One picture of these effects 

has been portrayed in a number of papers by Choi, Laibson, and Madrian (2004). 

Primarily exploiting an extensive administrative database collected by Hewitt Associates, 

a large human resources consulting company, these authors have found that a significant 

fraction of workers act passively with regard to their 401(k)-related saving decisions. 

 

1 Author‟s calculations using the National Compensation Survey (NCS) microdata 

collected from newly-initiated NCS sample members in 2003. 

2 Access to a benefit plan is defined in the National Compensation Survey according to 

the presence of a plan in the job/establishment pair; some workers are defined as having 

access even if they do not meet the applicable eligibility requirements. 
3

Consistent with this behavior, Choi, et al find that the rate at which employers match 

employee contributions has a small, if any, effect on participation; the impact of 

automatic enrollment is much greater. Beshears, Choi, Laibson, and Madrian (2007) 

have additionally argued that the presence of an automatic enrollment provision 

diminishes the need for employers to provide generous matches. Yet, a different set of 

results has emerged when researchers have exploited an extensive, administrative data set 

from The Vanguard Group, a large investment management company. Huberman, 

Iyengar and Jiang (2007) and Mitchell, Utkus, and Yang (2005) both find that employer 

match rates significantly increase 401(k) participation. 

The variety of results emerging from these non-representative, administrative 

datasets underscores the need for evidence from representative samples. But such 

evidence has been limited by deficiencies in the available datasets. In particular, the 

challenge of obtaining accurate and complete information about the relevant plan 

parameters is a high obstacle for representative surveys to clear. Household surveys like 

the Current Population Survey generally rely on workers to report the details of their 

retirement plans, resulting in a large error rate.3

 Establishment-based sources such as 

the Form 5500 tax data filed by employers with the IRS do not generally seek 

information about plan provisions in a very detailed manner. And special interest surveys 

such as the Health and Retirement Survey that obtain both establishment and household 

data generally limit their scope to a subset of the relevant population, making 

generalization to all relevant workers an uneasy proposition. 

 

3

See, e.g., Herz, Meisenheimer and Weinstein (2000) and Chan and Stevens (2008). 
4

In this study, a large, nationally representative dataset from the National 

Compensation Survey is exploited to provide measures of the effects of 401(k) plan 

provisions on the participation rates of employees. The dataset contains accurate 

measures of plan details, including those governing employer matches, and its coverage 

is very broad, having been sampled to represent virtually all US private industry workers 

in 2002-2003. The completeness of its description of plans‟ match provisions allows the 

study to explore functional forms that offer separate measures of causal and sorting 

effects. The dataset also contains information about coworkers working at the same 

establishment, as well as the generosity of retirement benefits among other employers in 

the same labor market. These additional pieces of information are used to construct 

instrumental variables estimates of the causal effect of employer matches on plan 

participation. Together, the results of these various inquiries provide evidence in support 

of studies using data from The Vanguard Group: the rate at which employers match 

employee contributions has a significant, positive effect on plan participation. Further, 

the results support the findings of Even and MacPherson (2005) and others in the 

literature who have concluded that direct cross-sectional comparisons may underestimate these causal effects due to negative selection arising from employers‟ efforts to 

remediate the behavior of low-saving workers. 

Data 

The data come from the National Compensation Survey (NCS), a large, nationally 

representative survey conducted by the U.S. Bureau of Labor Statistics. Data from the 

NCS is used to calculate the Employment Cost Index, which estimates the growth in 
5

compensation costs, including those arising from employer-provided benefits, for a fixed 

bundle of workers. The NCS is collected with a rotating panel design, with a new panel 

initiated approximately once per year. When a panel is initiated, brochures for 

employers‟ benefit plans are collected along with the employer cost and benefit 

participation information. The details of these plan brochures are coded into the NCS 

database, and the incidence of various detailed plan provisions are reported in official 

bulletins. This study uses NCS microdata from the respondents initiated in 2002 and 

2003, focusing on the detailed provisions data collected from 401(k) plan brochures and 

the contemporaneous participation data collected from the corresponding establishments. 

The NCS microdata are collected at the job level: within each sampled 

establishment, a small number of narrowly defined jobs are selected.4 The resulting 

wage, benefit costs, and participation data consist of averages among the employees at 

the establishment having that job description. Jobs are defined at as detailed a level as 

possible, identifying a specific set of job duties, required skills, and responsibilities. 

Each job corresponds roughly to a 6-digit occupational unit within the sampled 

establishment, further narrowed down so that all workers in the job have the same union 

and full-time/part-time statuses, the same pay basis (time vs. incentive), and the same 

benefit offerings. This taxonomy does not guarantee that workers in a given job work 

together, but it means that all workers in a job perform very similar functions. For 

example, an establishment might employ various classes of Accountants in a number of 

different divisions (accounts receivable, accounts payable, etc.), where each class 

indicates a different level of responsibility. The NCS would classify each class of 

 

4 Depending on the size of the establishment, between 4 and 8 jobs are sampled. 
6

accountant as a separate job, but would not necessarily specify different jobs for different 

divisions.

Most job-level observations in the NCS correspond to a small number of 

individuals, but there are some exceptions, mostly accruing to necessary compromises 

made in collection. For example, some employers may make their compensation 

available only at more aggregate levels, necessitating job quotes that have large numbers 

of workers. An investigation of 2007 data showed that the median number of workers in 

a job was 5, and the third quartile worker count was 22. But a few large quotes drove the 

mean up to 90.2. Within jobs, quotes are relatively homogenous in compensation 

offerings; in 2007, 97.3 percent of the wage variance among individual workers in the 

NCS sample occurred between job quotes. 

The focus of this study is on one variant of 401(k) plans: the savings and thrift. 

Such plans entail voluntary (tax deductible) contributions by the employee that are 

matched to some extent by the employer. This is easily the most prevalent form of 

401(k) plan, making up more than 80 percent of 401(k) plans in which the employer 

made some contributions in 2002-2003.5 Not included in the study are plans to which 

employers make no contributions, which are also fairly prevalent.6 

 

5 Author‟s calculations using the National Compensation Survey (NCS) microdata 

collected from newly-initiated NCS sample members in 2002 and 2003. 

6

 In 2005, an estimated 16 percent of private industry workers had access to cash deferred 

arrangements with no employer contributions. These are not considered to be retirement 

benefit plans by the BLS, (BLS Summary 05-01) so their participation rates are not 
7

Table 1 provides some summary statistics about the plans in the sample. The 

average participation rate in the sample, defined as the fraction of workers in the job that 

participate in the plan is .72. This variable can generally be considered a take-up rate: 

almost all employees in a job with access to the plan are eligible, although some plans 

have eligibility requirements based on months of service. 82 percent of the sample is 

made up of plans with flat match rate profiles – one percentage is applied to each 

employee‟s contributions, up to a specified percentage of the employee‟s salary. Another 

13 percent apply a variable match rate, where employees receive one match rate to a first 

amount of their contributions and another (usually lower) rate on additional contributions, 

up to some limit. The remainder of the sample has different match profiles for different 

employees within a job, depending on the employees‟ tenure.7 The average match rate on 

the first dollar contributed by employees is 75.37 percent; the log of this first-dollar 

match averages 4.21 with a standard deviation of 0.49.8 Plans in the sample provided 

matches on employee contributions up to 5.16 of the corresponding salary, on average. 

 

collected. For more details about these “zero-match” plans, see section 9.5 of Holmer, 

Janney and Cohen (2008). 

7 A small number of plans have matches that vary from year to year, depending on 

employer profits or the employer‟s discretion; these were dropped from the sample. 

8

 To calculate measures among the plans whose match profiles vary by tenure, the tenure 

distribution of each corresponding record was imputed based on the available direct 

information and detailed occupational averages. The match provisions were then 

averaged across these imputed distributions. 
8

To capture the overall generosity of the plans, we calculated the “total potential 

match” – the amount that employers contribute, as a percentage of wages, when 

employees contribute enough to exhaust the employer‟s match offer. For example, if a 

plan offers a 50% match on the 6 percent of wages the employee contributes, then the 

total potential match is 3 percent. The average total potential match in the sample is 3.57 

percent of salary, while the log of the total potential match has a mean of 1.12 and a 

standard deviation of 0.58. 

The data give a fairly complete picture of the benefit offerings of the employers in 

the sample, including other salient features of the 401(k) plans themselves. A majority of 

the sample allows employees to choose how the funds in the 401(k) account are invested, 

with control over funds contributed by the employee slightly more prevalent than control 

over funds contributed by the employer. A small percentage of the observations (6 

percent) in the sample are governed by the automatic enrollment provisions advocated by 

Choi, et al. Meanwhile, 40 percent of the jobs indicate that they also provide a defined 

benefit plan, while 21 percent provide an additional defined contribution plan.9

 The 

average observation has a wage of $22.66 per hour, a health benefit costing the employer 

$2.21 per hour worked, and a defined benefit cost of $0.52 per hour worked. The data 

also contain detailed (6-digit) occupation and industry identifiers, as well as the location 

and employment of the establishments and whether workers in the job are unionized. 

 

9

 A very small fraction of sample members have more than one savings and thrift plan. 

In such cases, we focus only on the plan that had the highest participation rate. 
9

The sample consists of 2,708 jobs in 587 establishments10, with 67 percent of jobs 

observed in 2003 and the rest observed in 2002. 

Empirical Analysis 

We begin by laying out a simple model to describe some key aspects of the 

relationship between plan participation and the employer match on 401(k) contributions. 

We then use the model to describe the identifying assumptions inherent in the various 

empirical strategies we employ. 

Consider the participation decisions of workers in a given establishment offering 

a plan with given provisions. Let the matching provisions at employer k be defined by 

one generosity parameter, Mk. Let other observed characteristics of the employer, such 

as other provisions of its 401(k) plan, be denoted as Ek, and let relevant, unobserved 

characteristics of the employer, such as its culture as regards retirement saving, be 

denoted as ck. Workers in job j at employer k determine whether or not to participate in 

the plan according to Mk, Ek, ck, and their own attributes – both observed attributes such 

as their income levels, denoted as Xjk, and unobserved attributes such as their innate 

attitudes toward retirement saving, denoted as ajk. Letting Pjk be the participation rate of 

workers in job j of establishment k, allow expected participation to have the form: 

 

10 This sample reflects all NCS sample members initiated in 2002 or 2003 for which 

valid data on match rates and participation were collected, with 1 establishment dropped 

due to outlying benefit cost values. Among establishments appearing in the sample in 

both years, only 2003 data were used. 
10

jk PE ( )

10 jk 2 jk 3 k 4 k 5 MEcXa k

(1) 

where Φ denotes the cumulative Normal distribution function. 

Now consider the determination of Mk, which we divide into two steps: first the 

overall generosity of the plan‟s match provision is set; then the structure of the provision 

is determined. As discussed above, a good measure of a plan‟s generosity is the total 

potential match that a worker can receive by contributing up to the match threshold. We 

denote the total potential match offered by employer k as Tk. 

Several factors affect the relationship between Tk and the worker and 

establishment characteristics ajk, Xjk, Ek, and ck. Most saliently, workers with high 

propensities to save may disproportionately choose to work at establishments with high 

levels of plan generosity. Accordingly, some employers may purposely set their plan 

generosity levels to attract and maintain these workers (Ippolito, 2002). This sorting 

dynamic is worked out within the context of the alternatives available to workers; the 

same sorting outcome for establishment k would be expected to require a higher plan 

generosity, the higher the generosity of other employers in the same labor market. 

Letting 

k

a

and 

X k

represent averages across the establishment of ajk and Xjk, we 

represent this relationship as: 

Tk 10 k 2 k 3 k 4 k 5 OEcXa ek

, (2) 

where Ok represents the generosity of other employers in the same labor market as 

employer k. 

Next, the profile of the plan‟s employer match is derived. Will a given level of 

plan generosity be achieved by a relatively high match rate applied to a relatively small 
11

range of employee contributions, or by a relatively low match rate applied to a relatively 

large range of employee contributions? The factors driving this determination are 

somewhat less clear than the sorting dynamic governing Tk. We explore two different 

possibilities. The first is that the first dollar match rate Mk is random with respect to the 

other variables in the model: 

M k 10 T ek

(3a)

Here, we assume that, once the employer chooses an overall generosity level, the 

marginal match rate(s) and corresponding range of employee contributions to which it 

(they) apply is chosen according to the idiosyncratic tastes of decision-makers, historical 

accident, or some other extraneous considerations. 

The second possibility we consider is that Mk|Tk is set to elicit a particular savings 

response from workers at the establishment; e.g., to raise savings among some or all 

workers. Perhaps the employer has a target participation rate, reflecting either its longterm budgeting goals or its need to meet the non-discrimination requirements governing 

401(k) plans under ERISA. In this case, Mk may be better captured by: 

M k 10 k 2 k 3 k 4 k 5 TEcXa ek

. (3b) 

Unlike in equation (2), we expect that the coefficients on 

k

a

and 

X k

may be negative: if 

the first-dollar match rate has a significant effect on participation rates, the employer 

might choose a steeper profile the lower the savings propensity its employees to have. 

Such a dynamic is consistent with other components of retirement plan management 

documented elsewhere. For example, Bernheim and Garrett (2003) and Bayer, Bernheim 

and Scholz (1996) provide evidence that a remedial impetus is prevalent for employer-
12

provided financial education programs. Madrian and Shea (2001) note that the employer 

they study adopted its automatic enrollment provision because it was having trouble 

meeting non-discrimination standards. 

The model may be consulted in a number of ways to measure the causal effect of 

the first-dollar match Mk on plan participation Pjk. One approach is to estimate equation 

(1) directly, including as many controls for the important worker and establishment 

characteristics as possible. We pursue this strategy by implementing the Bernoulli QuasiMaximum Likelihood Estimator (BQMLE) developed by Papke and Wooldridge (1996), 

using the log of the first dollar match rate as the key explanatory variable. The BQMLE 

assumes that the expected value of Pjk is captured by the standard normal cumulative 

density function conditional on the specified explanatory variables (Zjk):

)()|(

jkjk ZxPE jk

(4) 

and is computed by maximizing 

(log[)( )] PbZPb (1log[)1( bZ )] jk jk jk jk jk  . (5) 

Estimating plan participation using the BQMLE has the advantage of dealing 

appropriately with fractional dependent variables having masses in the distribution at 0 

and 1. It results in coefficient estimates similar to those resulting from probit analysis; 

we transform these coefficients into average partial effects estimates (APEs). As 

discussed by Wooldridge (2005), APEs are the logical item of interest for standard 

analytical frameworks, corresponding intuitively to OLS estimates. In addition, focusing 

on APEs allows us to avoid concerns over attenuation biases accruing from unobserved 

heterogeneity. 
13

Table 2 gives the APEs when the BQMLE is applied directly to the cross-section. 

In the first two columns, the estimates reflect a direct application of equation (1), with 

observable job characteristics, meant to stand in for worker attributes

X jk

, and 

observable employer characteristics Ek included as controls. Since this type of 

specification is prevalent in previous work, we refer to it as the “base model.” The 

controls include a dummy for whether the job is unionized, dummies for 9 occupational 

groups, the average compensation paid workers in the job, and the average compensation 

squared, as well as establishment size, and other provisions of the 401(k) plan. Also 

included are imputed values for four demographic variables: the average age of workers 

in the job, the percentage of workers who are male, the percentage having graduated from 

college, and the percentage who are white.11 In addition, controls accounting for the 

composition of workers‟ compensations have been included: the wage component of 

compensation, the health care component, the component associated with any Defined 

Benefit plan present for the job, and a dummy indicating whether workers in the job have 

access to another Defined Contribution plan. These controls are entered as proxies for 

workers‟ unobserved savings propensity 

j

a

. The logic of these proxies is that high 

savers are more oriented towards minimizing future risk, so for a given compensation 

level they are likely to prefer other benefits such as health insurance instead of wage. 

Finally, broad controls for 4 geographic regions and 4 industrial groupings are 

 

11 These imputations were generated by matching the detailed (3-digit) industry and 

occupation information, along with the observed wage rate in the job, to 2002 Current 

Population Statistics data and using regression analysis to predict values for each job. 
14

contemplated as controls for unobserved employer characteristics cj. We include two 

specifications: one with and one without region and industry dummies.12

The results of the base model indicate a small but significant effect of employer 

match rates on plan participation, with an APE of .0567 or .0580. This means that, on 

average, a one standard deviation change in the log match rate corresponds to a 2.8 or 2.9 

percentage point increase in participation. These results might be questioned, however, 

to the extent that we have not been able to control for all the relevant correlates that 

appear in both equations (1) and (2) – i.e., if significant variation in the unobserved 

factors aj and ck remain. Most saliently, if workers with high (unobserved) savings 

propensities sort into employers with higher match rates as envisioned by a positive value 

of 

1

in equation (2), then this “sorting effect” will positively bias the base model‟s 

estimates of the causal effect of Mk on Pjk. 

Before exploring alternative strategies for estimating match effects, we note the 

measured effects of several other variables in the base model. Automatic enrollment 

provisions are associated with an increase in participation by 7.75 percentage points. 

This is likely a downwardly biased estimate of the causal effect of automatic enrollment, 

because in some sample members the provision may only apply to a fraction of the 

workers, such as those who have recently been hired.13

 Still, it is within the margin of 

 

12 Dummies for year of observation and eligibility requirements of at least 1 year of 

service are also included in both specifications. 

13 Note, however, that the sample also likely includes many plans in which the automatic 

enrollment provision has only recently been added. In such cases, the APEs measured do 

not reflect the long run effects of automatic enrollment, tending instead to be higher. 
15

error of the 11 point increase that Madrian and Shea (2001) find studying one large 

employer. Providing workers with a choice of how to invest their own contributions has 

a small but significant, negative association with participation. This is consistent with the 

results of Iyengar, Jiang and Huberman (2003), who argue that too much choice can 

impart complexity costs that reduce plan enrollment. But having choice over the 

employer‟s contributions does not appear to have any appreciable effect on participation. 

Both of these APEs contradict Papke (2003), who finds dramatic positive effects. The 

ability to draw loans from one‟s account appears to have an insignificant effect on 

participation. 

The included controls for compensation level and imputed demographic traits 

show results that are broadly consistent with the previous literature. The two 

characteristics that have most consistently been found to have positive, significant effects 

on participation are income and age; we replicate that here. Some evidence (Even and 

MacPherson, 2005; Englehardt and Kumar, 2007) also suggests that white workers are 

more likely to participate than are blacks; the base model results agree, albeit with large 

standard errors. Education and gender are sometimes found to be significant coorelates 

of 401(k) participation, but they have often been estimated to have insignificant effects in 

multivariate analyses (Munnell, Sunden and Taylor, 2001/2; Bernheim and Garrett, 2003; 

Mitchell, Utkus and Yang, 2005). The base model finds no significant effects of percent 

of workers having a college graduation or percent male. 

Finally, consider the measured effects of the composition of workers‟

compensation, which have not been included in previous studies. The results show that 

having a higher health plan component of compensation is significantly associated with 
16

higher participation in one‟s 401(k). The presence of other Defined Contribution plans is 

also associated with higher participation. These results suggest some savings propensityrelated job sorting on these two benefit categories. But even with these controls, the 

estimated effect of the employer match remains positive and significant. 

A second approach to estimating the effects of the employer match rate is to add a 

control for the overall generosity of the plan. To see the basis for this approach, 

substitute equation (3a) directly into equation (1). The effect of Mk on Pjk is then 

estimated based on the residual variation in Mk denoted as φe in equation (3a). The 

results of pursuing this approach are shown in the third and fourth columns of Table 2. 

The main thing to notice about these results is that, controlling for overall plan 

generosity, the effect of the match on participation remains significant, although it is 

diminished by about a quarter: a one standard deviation change in the log match rate 

causes the participation rate to rise by 2.0 to 2.3 percentage points. The APEs of the 

other correlates are qualitatively similar to those seen in the base model. These results 

suggest that the positive association between participation and match rates seen in the 

base model embody, to a large extent, a causal relationship. But such a conclusion rests 

on the validity of the restriction embodied in equation (3a): that the determination of 

Mk|Tk is random with respect to the unobserved variables aj and ck. 

We can relax this assumption by turning to equation (3b), which models Mk|Tk as 

a function of observed and unobserved employer and employee characteristics. Consider 

the equation obtained by substituting equation (2) into equation (3b): 

Mk 10 k 2 jk jk 4~3 k 5 k 6 OEcXXa ek

. (6) 
17

This equation contains two elements that do not appear in the participation equation (1). 

First, Pjk depends on only the characteristics of job j workers Xjk and not on the 

characteristics of other workers in the establishment, while Tk and Mk|Tk are both 

determined in relation to all of establish k workers. This distinction is made explicit in 

equation (6) by splitting 

X k

into own-job and coworker components, 

X jk

 and 

X~ jk

. 

Second, the labor market variables Ok also do not affect the worker‟s participation 

decision despite playing a key role in the sorting equilibrium described by equation (2). 

These two elements can be used to implement an instrumental variables strategy of 

estimating the effects of Mk on participation, although some fairly strong assumptions are 

required: the instruments cannot directly affect the plan participation of worker j, and 

they cannot be correlated with the unobserved variables aj and ck. 

Several measures of 

X ~ jk

were calculated from the data, reflecting the average 

compensation, age, proportion with a college degree, proportion male, and proportion 

white. To capture

Ok

, two variables were generated from NCS data measuring the 

average proportion of compensation paid to defined contribution plans among other 

employers in the corresponding labor market.14

 The first of these measures used 

geography to define the relevant labor market, taking advantage of the cluster sample 

design of the NCS, in which a small set of (predominantly metropolitan) areas is selected 

as primary sampling units. Within each of these areas, the average fraction of 

 

14 Measures of Ok were calculated using the larger NCS dataset measuring employer 

costs for all units in the NCS panel, pooling NCS observations over the 2001-2005 

period. The resulting sample for creating the instruments contained 6768 employers. 
18

compensation spent by employers on Defined Contribution plans was calculated. The 

second measure of 

Ok

was calculated similarly, but using 2-digit industry definitions as 

the relevant labor market concept. 

These instruments were applied to the data using the instrumental variables 

methodology described Wooldridge (2005). First, equation (6) was estimated using OLS, 

and the residuals, 

e

ˆ

, were added to the base BQMLE model. Then, the corrected 

standard errors were estimated using the methodology described in Papke and 

Wooldridge (2008). This methodology also readily allows testing of the validity of the 

instrumental approach: standard t-tests (using the corrected standard errors) can be 

applied to the estimated coefficient on 

e

ˆ

. The resulting APEs are listed in the top panel 

of Table 3. The top row contains the APEs of the first-dollar match rate, and the second 

row contains the APEs of the first-stage residuals, which measure the effects of 

endogenous variation in Mk. The results for different sets of instruments are shown: the 

co-worker instruments 

X ~ jk

, the labor market instruments 

Ok

, and the combination of 

all instruments. As in Table 2, we consider specifications with and without broad 

controls for area and industry.15

All of the APEs of the first-dollar match rate in the table are greater than the base 

model estimates, and all are statistically significant. Using the co-worker instruments 

alone, the estimated APE is .091 when broad area and industry controls are not included 

and .199 when they are included, indicating that a one standard deviation increase in the 

 

15 These estimates were generated using a slightly reduced sample of 2,372 observations 

in 464 establishments; establishments with data for only one collected job are excluded. 
19

match rate increases participation by 4.5 to 9.8 percentage points. Using only the labor 

market instruments, the estimated APEs are substantially greater: the APE of .426 when 

broad area and industry controls are included implies a 21.1 percentage point effect from 

a one standard deviation increase in Mk. Using all co-worker and labor market 

instruments, the estimated APEs are similar to those using only the coworker instruments, 

albeit with a slightly larger range. 

A salient feature of the results in Table 3 is that the estimated APEs are markedly 

greater when broad controls for area and industry are included in the specification. This 

indicates some negative covariation between match rates and participation at these broad 

levels. Even and MacPherson (2005) provide a potential explanation: they note that a 

negative bias in the cross-section can occur if workforce sectors having low average 

savings propensities prompt employers in those sectors to employ higher matches to 

attract workers at the top of the savings propensity distribution. If this interpretation is 

accurate, then it is appropriate to include the controls in our estimation. Note, however, 

that we did not see this pattern in the base model results of Table 2; the sensitivity of the 

results to the controls may also reflect the reduced explanatory power of our instrumental 

variables approach. So while we prefer the specifications that include the broad controls, 

we continue to show the results in the remaining tables both with and without the broad 

controls. 

The bottom panel of Table 3 provides information from the first stage of the 

estimation. The coefficients on the coworker instruments depict a mix of influences on 

the match rate. Workers with relatively well-compensated co-workers tend to have 

higher match rates, all else equal; this suggests that positive sorting as we might expect 
20

from equation (2) plays a key role. On the other hand, match rates also tend to be higher 

when co-workers are younger, and when they are non-white; this suggests an important 

role for the remedial impetus discussed earlier in regards to equation (3b). The 

coefficients on the labor market instruments suggest that employers consider the 

offerings of other employers in the same industry when determining the generosity of 

their retirement plans, but they indicate no significant role for geographic competitors. 

At the bottom of the table, the partial R-Squared and F-Test on the excluded instruments 

as discussed by Bound, Jaeger and Baker (1995) and Shea (1997) are listed. These 

indicate that the instruments are relatively weak, together explaining less than 2 percent 

of the residual variation in the match rate, but that they are strong enough to assuage 

concerns about finite-sample bias. 

The increased magnitudes of the estimated match effects in Table 3 are notable. 

Sorting effects have been the main concern in the literature when match rate estimates 

have been considered, and the usual intuition is that such effects bias cross-sectional 

estimates upward.16 But the results in Table 3 suggest that the cross-sectional estimates 

of our base model are negatively biased, if anything. In fact, in specifications including 

broad area and industry controls, the coefficients on the first-stage residuals indicate 

negative correlations between Mk and Pjk that are both substantively and statistically 

significant. 

 

16 Note, however, that some other studies (e.g., Even and MacPherson, 2005; Englehardt 

and Kumar, 2007) also find that addressing endogeneity in the relationship between Mk

and Pjk results in higher estimated match effects. 
21

One possible explanation is that the instruments are not valid – that they have a 

direct relationship with the dependent variable Pjk as well as affecting Mk. Such a direct 

relationship could occur through peer effects – high savings propensities may be 

contagious. Duflo and Saez (2002) show that such networking effects are prevalent 

among co-workers who have frequent contact with each other. But Duflo and Saez also 

find that, when co-worker measures match dissimilar workers, networking effects 

become insignificant. We follow that intuition in Table 4, where we instrument with 

adjusted co-worker measures that are calculated only using co-workers who do not share 

the same (1-digit) occupation as the reference worker. If workers primarily interact with 

coworkers who perform similar functions, then peer effects in the participation decision 

should not be a factor here. It‟s also less likely that job-searchers would choose 

employment at a given establishment based on the characteristics of prospective 

coworkers in distant occupational categories. The cost of using these adjusted co-worker 

measures is that it reduces the power of the instruments by reducing the amount of data 

being used, diminishing the first stage R-squareds and increasing the standard errors. 

The APEs estimated with the adjusted instruments are smaller than their counterparts in 

Table 3. This suggests that some of the effects observed in Table 3 may have been due to 

peer effects, although the relatively high levels of imprecision make comparisons of this 

sort difficult. In our preferred specifications (including broad area and industry controls),

the match rate APEs are positive, although due to large standard errors they are only 

statistically significant when both coworker and labor market instruments are employed. 

And these results are not robust to the exclusion of the area and industry controls. 
22

Another avenue for the instruments to be invalid is if they are themselves 

correlated with the unobserved characteristics ajk and ck. For example, in the case of the 

coworker instruments, positive assortativeness in the matching of workers to employers 

could generate a direct correlation between the characteristics of other workers at the 

establishment and the unobserved savings propensities ajk. In the case of the labor market 

instruments, sectoral differences in plan generosity may proxy for sectoral differences in 

the establishment savings cultures ck. Indeed, the significance of area and industry 

sectoral controls at a broad level suggests that such a dynamic may, in fact, be present. A 

fundamental problem is that equation (2) describes a relationship in which causality runs 

in both directions; this creates the possibility for feedbacks between the instruments and 

the dependent variable. 

An identification strategy that alleviates these concerns is to focus on the variation 

in Mk inherent in equation (3b). In this equation, it‟s easier to think of the right-hand side 

variables as being exogenous determinants of the match rate. To pursue this strategy, we 

control for Tk and instrument for Mk with X~jk. Note that Ok is not available as an 

instrument in this construct: it enters the model only through the determination of the 

control variable Tk. The results, shown in Table 5, reinforce those of Table 4. Without 

broad industry and area controls, the APEs of the employer match are statistically 

insignificant. But when the broad controls are included, the match rate APEs are 

positive, large, and significant. Using the adjusted coworker instruments, we estimate an 

APE of .261, indicating that a one standard deviation increase in the match rate yields an 

increase in plan participation of 12.9 percentage points. This specification also yields a 

significantly negative APE on the first stage residual, indicating a negative association 
23

between the match rate and the unobserved worker and establishment characteristics. 

These results indicate that the results in column (2) of Tables 3 and 4 were driven by 

variations in Mk|Tk. Accordingly, they support the notion that employers steepen the 

match profile to elicit additional plan participation when participation is otherwise low, 

causing cross-sectional estimates to be biased downward. These conclusions should be 

tempered, though, by their sensitivity to the inclusion/exclusion of area and industry 

controls. 

Conclusion 

This study makes two key contributions to the literature on the effects of 

retirement benefit plan design. First, it exploits an underutilized source of data: the 

National Compensation Survey, a nationally representative survey that combines 

accurate, detailed information about 401(k) plans with participation rates collected at the 

detailed job level. Using this data helps shed light on the divergent results produced by 

the various non-representative samples exploited elsewhere. Second, the study 

implements several strategies for identifying the causal effects of employer matches on 

plan participation. These strategies provide several plausible corrections for the 

endogeneity of the match provisions and are placed within the context of a coherent 

model or employer and employee behavior. 

The results of the study provide further evidence that employer matches provide a 

powerful incentive for employees to participate in their 401(k) plans, and that the level of 

the matches offered matters significantly. A one standard deviation increase in the match 

applied to the first dollar is found to raise participation by as much as 12.9 percentage 

points. This effect is similar in magnitude to the 11 point effect of the institution of an 
24

automatic enrollment provision as estimated found by Madrian and Shea (2001). A 

lesson that might be drawn from this result is that, while automatic enrollment provisions 

are a promising avenue for encouraging many workers to save for their retirements, the 

marginal incentives like employer matches that have been more traditionally offered may 

be even more important to some workers. In this sense, the study is in agreement with 

Duflo, et al (2006), who provide evidence that individuals respond to marginal saving 

incentives, but that important characteristics of the incentive program (e.g., level of 

complexity and accessibility) and the individual (e.g., income level and marital status) 

greatly affect the extent of the response. 

A second lesson of the study is that the endogeneity of the match rates observed 

in practice is not so straightforward to characterize. It is often assumed that sorting 

effects predominate, so that generous matches are positively associated with workers with 

high predispositions to participate. But such a viewpoint overlooks another impetus for 

employers to offer generous matches: they may do so to encourage saving among 

workers with low predispositions to participate. In fact, whether it is motivated by a 

paternalist impulse or a desire to meet certain legal requirements imposed by ERISA 

regulations, this remedial impetus appears to be prevalent enough so that cross-sectional 

estimates of match effects are biased downwards, not upwards. In this sense, the findings 

corroborate those of Even and MacPherson (2005). 

Several caveats to these results are worth noting. First, the identifying 

assumptions of the various strategies implemented in the study are in some cases fairly 

ambitious. While a fairly extensive set of controls is included for other correlates of plan 

participation, significant unobserved variation remains, and correlation between the 
25

instruments and these unobserved factors could affect the results. The study tries to 

address this concern by providing several alternative approaches and by elucidating the 

identification strategies within a model framework, but different readers may have 

lingering reservations about the results. Second, the results do not appear to be 

particularly robust to the exclusion of industry and area dummies. We believe that such 

variables do belong in the model as controls for sectoral variations in unobserved 

characteristics such as cultural attitudes toward saving, but the sensitivity of the empirical 

model to their inclusion might also be interpreted as a weakness. Finally, the results of 

this study leave several questions unaddressed. For example, increases in the 

participation of workers in their employer-provided 401(k) plan do not necessarily imply 

increases in retirement saving, either within the plans themselves or considering all 

savings vehicles together. But attempts to determine such impacts on the ultimate levels 

of retirement preparations should build into their consideration our main finding above: 

that matching does matter for at least some key components of employee saving. 
26

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28

Table 1: Summary Statistics for NCS Data Sample

(2,708 jobs in 587 establishments)

Variable Mean Standard Deviation

Participation Rate 0.72 0.30

Match Provisions

First Dollar Match Rate 76.68 39.19

Log First Dollar Match Rate 4.21 0.49

Percent of Salary Matched 5.08 1.95

Total potential match 3.55 1.94

Log Total potential match 1.12 0.58

Other Plan Provisions

Control over Investment of of Employee Contributions 0.84 0.37

Control over Investment of of Employee Contributions 0.74 0.44

Availability of Loans 0.69 0.46

Automatic Enrollment 0.06 0.24

Compensation

Total Compensation 33.10 23.68

Wage 22.56 16.45

Health Cost 2.21 1.19

DB Cost 0.54 1.40

DB Coverage 0.41 0.49

Other DC 0.21 0.41

Data Details

Year=2003 0.54 0.50
29

Table 2: Direct Cross-Sectional (BQMLE) Estimates of Average Partial Effects on 401(k) Participation

(standard errors in parentheses)

Total Potential Match and

Compensation

Base Model Components Included

(1) (2) (3) (4)

Log of First-Dollar Match 0.0567 0.0580 0.0396 0.0456

(0.0191) (0.0191) (0.0237) (0.0235)

Log of Potential Match 0.0225 0.0162

(0.0208) (0.0205)

Other Plan Provisions

Automatic Enrollment 0.0775 0.0712 0.0801 0.0728

(0.0439) (0.0440) (0.0439) (0.0443)

Investment Choice (Own Contribs) -0.0790 -0.0698 -0.0829 -0.0721

(0.0318) (0.0317) (0.0314) (0.0317)

Investment Choice (Employer Contribs) 0.0318 0.0250 0.0376 0.0263

(0.0303) (0.0300) (0.0302) (0.0302)

Loan Availability -0.0103 -0.0212 -0.0137 -0.0211

(0.0212) (0.0213) (0.0214) (0.0213)

Job-Level Attributes

Compensation 0.0078 0.0066 0.0072 0.0064

(0.0018) (0.0017) (0.0018) (0.0017)

Compensation Squared -0.000024 -0.000020 -0.000022 -0.000021

(0.000005) (0.000005) (0.000005) (0.000005)

Imputed Demographics

Average Age 0.0053 0.0055 0.0053 0.0056

(0.0025) (0.0024) (0.0025) (0.0024)

Percent College Grad -0.0578 0.0795 -0.0581 0.0785

(0.0666) (0.0730) (0.0669) (0.0732)

Percent White 0.3429 0.1950 0.3526 0.1949

(0.1406) (0.1443) (0.1406) (0.1443)

Percent Male 0.0196 -0.0141 0.0237 -0.0148

(0.0330) (0.0335) (0.0325) (0.0333)

Compensation Components

Wage -0.0026 -0.0020 -0.0024 -0.0027

(0.0019) (0.0017) (0.0019) (0.0018)

Defined Benefit Cost -0.0028 -0.0027 -0.0025 -0.0024

(0.0017) (0.0016) (0.0016) (0.0015)

Health Cost 0.0343 0.0329 0.0331 0.0330

(0.0091) (0.0090) (0.0090) (0.0092)

Other DC Plan Present 0.0850 0.0824 0.0862 0.0828

(0.0245) (0.0231) (0.0241) (0.0233)

Other Controls

Union, Occupation Controls Yes Yes Yes Yes

Estab Size Controls Yes Yes Yes Yes

Broad Region and Industry Controls No Yes No Yes
30

Table 3: Instrumental Variables (BQMLE) Estimates of Average Partial Effects on 401(k) Participation

Instruments Include All Co-Workers

(standard errors in parentheses)

Coworker Instruments Labor Market Instruments

Coworker and Labor Market 

Instruments

(1) (2) (3) (4) (5) (6)

Average Partial Effects of Match

Log of First-Dollar Match 0.0914 0.1994 0.1337 0.4264 0.0679 0.2226

(0.0463) (0.0621) (0.0569) (0.1399) (0.0366) (0.0537)

First-Stage Residual -0.0495 -0.1583 -0.0918 -0.3858 -0.0256 -0.1835

(0.0461) (0.0628) (0.0576) (0.1411) (0.0367) (0.0551)

First-Stage Coefficients

Co-Workers' Compensation 0.0085 0.0074 0.0078 0.0072

(0.0022) (0.0023) (0.0022) (0.0023)

Co-Workers' Compensation Squared -0.000048 -0.000046 -0.000044 -0.000044

(0.000013) (0.000014) (0.000013) (0.000014)

Co-Workers' Age -0.0110 -0.0222 -0.0125 -0.0104

(0.0051) (0.0050) (0.0051) (0.0052)

Co-Workers' Percent Male -0.3181 -0.2803 -0.2726 -0.3024

(0.0611) (0.0686) (0.0616) (0.0685)

Co-Workers' Percent White -0.4718 -0.5542 -0.6168 -0.7267

(0.2784) (0.2857) (0.2790) (0.2869)

Co-Workers' Percent College Graduate 0.0863 0.1079 0.0562 0.1018

(0.0828) (0.0895) (0.0828) (0.0893)

DC Proportion of Compensation among Other 

Employers in Local Area 0.6889 -0.0189 0.1930 -0.6459

(1.9909) (2.0373) (1.9862) (2.0299)

DC Proportion of Compensation among Other 

Employers in Industry 8.1949 7.2916 7.0890 8.1102

(1.4581) (1.6888) (1.5313) (1.7474)

First-Stage Diagnostics

Partial R-Squared 0.0201 0.0146 0.0134 0.0079 0.0290 0.0236

Adjusted F-Test (p-value) 0.000 0.000 0.000 0.000 0.000 0.000

Other Controls

Union, Occupation Controls Yes Yes Yes Yes Yes Yes

Estab Size Controls Yes Yes Yes Yes Yes Yes

Broad Region and Industry Controls No Yes No Yes No Yes
31

Table 4: Modified Instrumental Variables Analysis (Coworker Instruments Exclude Workers in Same Broad Occupation)

(standard errors in parentheses)

Coworker Instruments

Coworker and Labor Market 

Instruments

(1) (2) (3) (4)

Average Partial Effects of Match

Log of First-Dollar Match 0.0013 0.1306 0.0307 0.2161

(0.0570) (0.0703) (0.0406) (0.0600)

First-Stage Residual 0.0424 -0.0880 0.0126 -0.1757

(0.0568) (0.0709) (0.0409) (0.0613)

First-Stage Coefficients

Co-Workers' Compensation 0.0063 0.0051 0.0056 0.0047

(0.0021) (0.0022) (0.0022) (0.0022)

Co-Workers' Compensation Squared -0.000041 -0.000037 -0.000037 -0.000035

(0.000014) (0.000014) (0.000014) (0.000014)

Co-Workers' Age -0.0081 -0.0050 -0.0091 -0.0067

(0.0044) (0.0045) (0.0044) (0.0045)

Co-Workers' Percent Male -0.2264 -0.1849 -0.1891 -0.2003

(0.0533) (0.0586) (0.0537) (0.0585)

Co-Workers' Percent White -0.3919 -0.4555 -0.4850 -0.5872

(0.2475) (0.2532) (0.2472) (0.2540)

Co-Workers' Percent College Graduate 0.1084 0.1266 0.0746 0.1202

(0.0734) (0.0784) (0.0736) (0.0782)

DC Proportion of Compensation among Other Employers in 

Local Area 0.4962 -0.3351

(1.9909) (2.0332)

DC Proportion of Compensation among Other Employers in 

Industry 7.2170 7.7851

(1.5297) (1.7404)

First-Stage Diagnostics

Partial R-Squared 0.0146 0.0101 0.0239 0.0185

Adjusted F-Test (p-value) 0.000 0.000 0.000 0.000

Other Controls

Union, Occupation Controls Yes Yes Yes Yes

Estab Size Controls Yes Yes Yes Yes

Broad Region and Industry Controls No Yes No Yes
32

Table 5: Instrumental Variables (BQMLE) Estimates of Average Partial Effects on 401(k) Participation

With Total Potential Match as a Control

(standard errors in parentheses)

Coworker Instruments

Instruments Include Instruments Exclude Workers

All Workers In Same Broad Occupation

(1) (2) (3) (4)

Average Partial Effects of Match

Log of First-Dollar Match -0.0700 0.1544 -0.0648 0.2606

(0.0777) (0.0811) (0.0979) (0.1132)

First-Stage Residual 0.0901 -0.1279 0.0844 -0.2345

(0.0775) (0.0814) (0.0980) (0.1139)

First-Stage Coefficients

Co-Workers' Compensation 0.0049 0.0063 0.0040 0.0052

(0.0016) (0.0017) (0.0016) (0.0017)

Co-Workers' Compensation Squared -0.000035 -0.000040 -0.000031 -0.000035

(0.000010) (0.000010) (0.000010) (0.000010)

Co-Workers' Age 0.0006 0.0015 0.0017 0.0033

(0.0038) (0.0039) (0.0033) (0.0034)

Co-Workers' Percent Male -0.1378 -0.1149 -0.0915 -0.0634

(0.0462) (0.0518) (0.0403) (0.0442)

Co-Workers' Percent White -0.8642 -0.7812 -0.6198 -0.5422

(0.2102) (0.2150) (0.1867) -(0.5422)

Co-Workers' Percent College Graduate -0.0398 -0.1081 -0.0221 -0.0906

(0.0625) (0.0676) (0.0554) (0.0592)

DC Proportion of Compensation among Other 

Employers in Local Area

DC Proportion of Compensation among Other 

Employers in Industry

First-Stage Diagnostics

Partial R-Squared 0.0146 0.0131 0.0096 0.0088

Adjusted F-Test (p-value) 0.000 0.000 0.000 0.000

Other Controls

Union, Occupation Controls Yes Yes Yes Yes

Estab Size Controls Yes Yes Yes Yes

Broad Region and Industry Controls No Yes No Yes
33