Who Benefts from Retirement Saving Incentives in the U.S.?

Evidence on Racial Gaps in Retirement Wealth Accumulation∗

Taha Choukhmane Jorge Colmenares Cormac O’Dea Jonathan Rothbaum

Lawrence D.W. Schmidt

November 2023

Abstract

U.S. employers and the federal government devote more than 1.5% of GDP annually towards

promoting Defned Contribution retirement saving. We study the distributional and lifetime

impact of these savings incentives across racial groups using a new employer-employee linked

data set covering millions of Americans. The average contribution rate of Black and Hispanic

workers is roughly 40% lower than that of White workers. The rich and the children of the

rich save more; racial diferences in own and parental incomes account for a large share of the

racial contribution gaps. Tax and employer matching subsidies further amplify these saving

diferences by channeling more resources to those who save more. We estimate that breaking

the link between contribution choices and saving subsidies, through revenue-neutral reforms,

would signifcantly reduce racial gaps and intergenerational persistence in wealth.

∗Choukhmane: MIT Sloan School of Management, tahac@mit.edu; Colmenares: Harvard University, jcolmenares@fas.harvard.edu; O’Dea: Yale University, cormac.odea@yale.edu; Rothbaum: US Census Bureau,

jonathan.l.rothbaum@census.gov; Schmidt: MIT Sloan School of Management, ldws@mit.edu. We are very grateful to

Jackson Howell and Cashua Wang who provided outstanding research assistance. We thank Franca Glenzer, Luigi Guiso,

Paschal Noel, and Natasha Sarin for illuminating discussions of this paper. We also thank Amir Kermani, Debbie Lucas,

Olivia Mitchell, Jim Poterba, John Sabelhaus, Angelino Viceisza, and Stephen Zeldes for extremely helpful conversations

and comments. We thank Cristina Tello Trillo for her assistance in building the bridge from the Form 5500 data to the

individual-level data. We are grateful to numerous seminar and conference participants for their helpful comments and

suggestions. This report is released to inform interested parties of ongoing research and to encourage discussion. Any views

expressed on statistical, methodological, technical, or operational issues are those of the authors and not necessarily those

of the U.S. Census Bureau. The data in this paper has been cleared by the Census Bureau’s Disclosure Review Board

release authorization numbers CBDRB-FY22-SEHSD003-001, CBDRB-FY22-SEHSD003-017, CBDRB-FY22-SEHSD003-033,

CBDRB-FY23-SEHSD003-043, and CBDRB-FY23-0494. The research reported herein was performed pursuant to a grant from

the U.S. Social Security Administration (SSA) funded as part of the Retirement and Disability Research Consortium through

the Michigan Retirement and Disability Research Center Award RDR18000002. The opinions and conclusions expressed are

solely those of the author(s) and do not represent the opinions or policy of SSA or any agency of the Federal Government.

Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or

implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of the contents of this

report. Reference herein to any specifc commercial product, process or service by trade name, trademark, manufacturer, or

otherwise does not necessarily constitute or imply endorsement, recommendation or favoring by the United States Government

or any agency thereof. We are very grateful to the MIT Institute Community & Equity Ofce, the MIT Sloan School of

Management, the Yale University Tobin Center for Economic Policy, and the Yale University Arthur M. Okun Research and

Policy Fund for cofunding this work.

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1 Introduction

Every year, the equivalent of 1.5% of U.S. GDP is devoted to encouraging contributions to retirement savings plans such as 401(k) and 403(b) accounts.1 Around 100 million Americans have

access to such plans through their employers, and these accounts ofer an attractive vehicle for

long-term saving. Contributions are taxed favorably, and over 80% of employers further subsidize

savers by matching their employees’ contributions (Arnoud et al. (2021)). At an average match of

approximately 50 cents per dollar contributed, saving in a tax-favored employer-sponsored account

is one of the best, if not the best, fnancial investment opportunities available to build wealth. This

institutional design, therefore, rewards those who can, and do, save more for retirement. Employees

who do not contribute receive neither tax benefts nor employer-matching contributions.

In this paper, we use newly collected data on employer-sponsored retirement plan characteristics combined with administrative data on the contribution and withdrawal behavior of millions

of American employees to study the distributional impacts of the design of retirement saving institutions, with a particular focus on impacts by race. The data show large gaps in retirement

saving across the three largest racial and ethnic groups in the U.S.: non-Hispanic White, nonHispanic Black, and Hispanic employees.2 Black and Hispanic workers with access to a 401(k) or a

403(b) plan and a modest degree of labor market attachment (at least $8,000 in annual earnings)

contribute approximately 40% less (or, respectively, 1.8 pp and 1.6 pp of salary less) than White

workers (Figure 1A). Employer matching amplifes these contribution gaps by an additional 0.7 and

0.6 pp, respectively, of salary. We fnd that employer matching and tax benefts are more unequally

distributed than wages, as illustrated in Figure 1B. While the median Black and Hispanic earners

receive 75 cents and 79 cents, respectively, for every dollar of earnings received by the median White

earner, median Black and Hispanic earners receive only about 50 cents for every dollar of matching

that median White earners receive. For the tax expenditure, comparing workers near the median

lifetime earnings for each group, Black and Hispanic workers receive 31 cents and 62 cents for every

dollar of the tax expenditure received by White workers, with larger gaps for Black workers being

driven by a substantially higher propensity of Black workers to take early withdrawals.

Our focus on racial gaps in retirement wealth accumulation is motivated by two key facts. First,

1In 2021, the federal government tax expenditure on defned contribution (DC) retirement accounts amounted to

$119 billion (US Department of the Treasury (2023)). In 2020, private sector employers contributed more than $190

billion into these accounts (Department of Labor (2022))–mainly in the form of matching contributions. 2We focus on three racial and ethnic groups: non-Hispanic Whites, non-Hispanic Blacks, and Hispanics, who

together make up 93% of the individuals in our sample. We will often use “race” to refer to both race and ethnicity,

“White” to refer to non-Hispanic White, and “Black” to refer to non-Hispanic Black.

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racial wealth inequality in the U.S. is large and persistent; for example, White Americans have,

on average, six times the level of wealth of Black Americans, a racial wealth gap that has not

changed much since the 1960s (Oliver and Shapiro (1989), Derenoncourt et al. (2022)). There is

also a large wealth gap between Hispanic and non-Hispanic White individuals, with the latter being

approximately four times wealthier (Sabelhaus and Thompson (2021)). Second, within American

households’ balance sheets, tax-advantaged retirement accounts are the largest source of fnancial

wealth and the second-largest asset class after housing (Board of Governors of the Federal Reserve

System (2021)). Brown (2021) argues that the design of retirement institutions favors activities that

are more likely to be carried out by White Americans (retirement saving) and penalizes activities

that are more likely to be carried out by Black Americans (early withdrawals). Quantitative

evidence on how much employer and tax incentives contribute to racial wealth disparities has been

limited due to a lack of systematic data on retirement plan characteristics across racial groups.

This paper aims to fll that gap.

We divide our analysis into four parts. First, we document racial gaps in retirement saving

contributions and how they vary with worker- and retirement plan-level characteristics. Second, we

analyze the contribution of immediate and extended family characteristics to the observed racial

diferences in contributions among workers with similar individual characteristics. Third, we extend

our distributional analysis to dimensions other than race, and study the distributional efects of

savings subsidies by family structure, parental background, education, and tenure level. Finally,

we develop a microsimulation model to examine the cumulative efect of employer matching and

tax subsidies on the distributions of wealth at retirement.

In the frst part of the paper, we report large diferences in retirement saving contributions across

the three groups we study. We fnd that racial diferences in age and income account for only onehalf of each of the raw Black–White and Hispanic–White gaps that we document in Figure 1A.

This leaves a sizable residual contribution gap: Black and Hispanic workers, respectively, contribute

(including employer-matching contributions) 1.1 pp and 0.96 pp less than White workers with the

same age and income. We explore the role of other individual-level characteristics that mediate

racial savings gaps – such as education, occupation, tenure, and employer. Even after accounting

for these mediating efects, gaps remain large at 0.89 pp and 0.44 pp for Black and Hispanic workers,

respectively.

What accounts for diferences in contributions among workers with similar incomes and individuallevel characteristics? In the second part of the paper, we show that racial diferences in household

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composition and parental background account for, respectively, nearly 40% and 50% of the residual estimated gap between Black or Hispanic workers and their White counterparts. Single tax

flers, particularly those with dependent children, have lower average contribution rates, and these

fling statuses are more common for Black and Hispanic workers. We also fnd that higher levels of parental income correlate with higher retirement saving (even conditional on our battery

of individual-level characteristics, including own income). Black and Hispanic workers tend to

have lower-income parents than White workers with similar earnings; therefore, racial diferences

in parental backgrounds account for part of the residual contribution gap. This fnding suggests

that the design of retirement saving institutions tends to reward those who have richer parents and

contribute more, propagating wealth inequality across generations.

Why does the design of retirement accounts induce lower contributions among Black and Hispanic workers compared with their White counterparts? We fnd evidence that Hispanic and, to a

greater extent, Black workers have stronger liquidity needs and may be more liquidity constrained.

In the raw data, White, Black, and Hispanic workers with at least $1,000 in recent contributions

have 12.3, 23.3, and 14.5 pp probabilities, respectively, of withdrawing some resources early from

their retirement accounts each year. Gaps shrink very modestly when we add controls; Black and

Hispanic workers are, respectively, 9.3 pp and 1.3 pp more likely to make an early withdrawal

of at least $1,000 relative to White workers with similar worker-level characteristics. The higher

likelihood of tapping into these accounts early—despite facing potential tax penalties—indicates a

lack of access to alternative sources of liquidity (Coyne et al. (2022)). Consistent with this, Ganong

et al. (2020) fnd that Black and Hispanic households cut their consumption by substantially more

than White households in response to a similarly sized income shock. Racial diferences in liquidity

valuation could also explain why family structure and parental background correlate with retirement contributions. For instance, single-parent households may have stronger liquidity needs than

married couples, while workers with richer parents may beneft from access to familial support,

while workers with poorer parents may need to retain liquidity to insure themselves or their family

(Chiteji and Hamilton (2002), Francis and Weller (2022)). Unlike for other asset classes, such as

housing, the illiquid nature of retirement accounts is a policy choice. By subsidizing contributions

and penalizing withdrawals, the current institutional design amplifes disparities between more and

less liquidity-constrained groups.

In the third part of the paper, we examine diferences in contributions across dimensions other

than race. We fnd that, holding income constant, there are marked diferences in saving, and so in

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the receipt of savings subsidies, by dimensions such as family structure, parental income, education,

and job tenure. This implies that breaking the link between saving and each of compensation

(through matching), and the federal retirement saving tax expenditure could improve retirement

outcomes for single parents, children of lower-income parents, those with less education, and those

who experience more frequent job separations.

In the last part of the paper, we develop a microsimulation model that uses our data on fows of

earnings, employee contributions, employer matches, and early withdrawals to compute wealth and

consumption in retirement (taking social security benefts into account). The impact of employer

matching and tax subsidies is quantitatively large, accounting for more than 40% of lifetime DC

wealth accumulation across all lifetime earnings groups. We then consider revenue-neutral reforms

that would redistribute employer-match dollars within each frm and federal tax expenditures across

the population so that they are distributed 1) proportionally to earnings and 2) independently of

workers’ own contribution choices. Within each of the bottom three quintiles of the population

earnings distribution, these reforms would increase consumption in retirement by 5 to 10% and

also reduce racial DC wealth gaps between Black or Hispanic and White workers by more than

30%.

The frst branch of the literature to which we contribute is that concerned with race and wealth

in the U.S. The gap between Black and White wealth has been shown to be large (Oliver and

Shapiro (1989), Darity and Nicholson (2005)) and, over the last approximately half-century, stable

(Derenoncourt et al. (2022)). A rich empirical literature shows that these wealth gaps are larger

than can be statistically accounted for by earnings diferences (Blau and Graham (1990), Barsky

et al. (2002), Altonji and Doraszelski (2005), Wolf (2017), and Kuhn et al. (2020)). The diferences

in broad measures of wealth that these papers document are also refected in retirement wealth

accumulation (see Ariel/AON Hewitt (2009), Hou and Sanzenbacher (2021), Francis and Weller

(2021), Viceisza et al. (2022), and Wolf (2023)), though measures of wealth that include Social

Security, due to its progressive nature, display narrower gaps than measures without (Catherine and

Sarin (2023), Sabelhaus (2023)). Our contribution to this literature is to study one channel that

contributes to wealth inequality by race: the interplay between race and the take-up of explicit

subsidies for wealth accumulation that are central to retirement saving institutions in the U.S.

Derenoncourt et al. (2022) emphasize that racial diferences in rates of return are the dominant

factor shaping the lack of convergence of racial wealth gaps over the past 30 years – precisely the

period in which DC accounts have emerged as the main vehicle for private retirement savings. Our

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results shed light on one previously overlooked mechanism generating such diferences in efective

rates of returns across racial groups, even holding portfolio risk constant.

The second branch of the literature to which we contribute is that concerned with race and

earnings in the U.S. Earnings gaps by race have been well documented: Altonji and Blank (1999)

ofer a comprehensive review of studies to that date, and Bayer and Charles (2018), Chetty et al.

(2020), and Derenoncourt and Montialoux (2021) provide more recent evidence. Our contribution

is to measure an often-unmeasured component of earnings—the employer match—which gives a

wage premium to those who save more.

Third, our paper contributes to the literature that investigates whether features of the policy

landscape and economic environment interact with race in contributing to disparities in economic

outcomes. This includes research examining whether, and to what extent, racial disparities exist

in the implications of policies including welfare (Darity and Myers, 1983, 1987), unemployment

insurance (Kuka and Stuart (2021); Skandalis et al. (2022)), mortgage access (Myers Jr (1995),

Ross and Yinger (2002), Bhutta and Hizmo (2021)), housing returns (Kermani and Wong (2021)),

property tax assessments (Avenancio-Le ́on and Howard (2022)), and fnancial aid for college (Levine

and Ritter (2022)). Hamilton and Darity (2017) argue that “if the existing federal asset-promotion

budget were allocated in a more progressive manner, federal policies would go a long way toward

eliminating racial disparities and building an inclusive economy for all Americans.” We quantify

how much changing a major component of the US asset-promotion budget, namely the design of

retirement savings subsidies, would afect racial and intergenerational wealth inequality.

The fourth line of literature that we contribute to is that on intergenerational persistence in

wealth. The correlation in wealth across generations has been well documented (Charles and Hurst

(2003)). Recent work emphasizes the importance of heterogeneity in rates of return for crosssectional wealth inequality (Fagereng et al. (2020)). Our paper draws a link between these two

phenomena. While it has long been known that the rich save more (Dynan et al. (2004)), we

show that, additionally, the children of the rich save more, even conditional on their own earnings.

The saving in question here is, by virtue of matching, one with an extraordinary rate of return.

This correlation between the resources of one generation and the rates of return availed of by the

next will, in general, directly contribute to intergenerational persistence in wealth. This channel

also relates to a theme that has been emphasized in the literature on wealth gaps by race in the

U.S. Chiteji and Hamilton (2002) and Charles and Hurst (2002) highlight the role of the family in

savings decisions, and the direction of intergenerational transfers: Black individuals are both more

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likely to provide support to their parents and less likely to receive support from their parents than

White individuals.

The paper proceeds as follows. Section 2 discusses the institutional background. Section 3

introduces our new employer–employee linked data set. Section 4 gives our results on racial gaps

in retirement saving rates and how they relate to individual characteristics. Section 5 studies the

role of household structure, parental background, and liquidity constraints in accounting for these

gaps. Section 6 looks at gaps in saving along dimensions other than race. Section 7 uses our data

and a microsimulation model to study the distributional impact of the savings patterns that we

observe and the retirement saving subsidies that we study on wealth at, and consumption during,

retirement. Section 8 concludes.

2 Institutional Background

Defned contribution (DC) plans have become the dominant vehicle through which Americans save

for retirement. Sixty percent of U.S. civilian workers now have access to an employer-sponsored

DC plan (Myers and Topoleski, 2020). Participants in these plans can make pretax contributions

to their accounts (up to a limit on employee contributions of $20,500 in 2022), thereby deferring

income taxes to when they retire and when they will (likely) face lower tax rates. In addition to

the advantages that this deferral brings, dividends and capital gains are untaxed provided that

they remain in the account. Wealth held in DC plans is, due to policy choices associated with the

current system, illiquid. Participants generally face tax penalties on withdrawals made before the

age of 59.5, though some plans permit borrowing against existing DC balances.

DC plans provide substantial fexibility and discretion to participants in deciding how much

to save and in which assets to invest. This structure contrasts substantially with defned beneft

(DB) plans, in which the choice facing an employee is typically limited to whether to participate,

and employer contributions do not depend on any choice that the employee makes. The secular

shift away from DB toward DC plans in recent years shifts considerable risk related to fnancing

retirement income from employers to employees.3 Whereas traditional pension plans insure against

mortality risk and the lion’s share of risks associated with fuctuations in investment returns, DC

plans force households to self-insure against these risks.

3Only a quarter of civilian workers now have access to a DB pension (Myers and Topoleski, 2020), a share that

continues to fall. DC plans are becoming, alongside Social Security, one of the largest sources of income in retirement.

Devlin-Foltz et al. (2016) show that, over the past 30 years, the dynamics of retirement wealth have had a moderating

impact on overall wealth inequality. They also fnd, however, that DC wealth is more concentrated than DB wealth.

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In the vast majority of plans, the amount that the employer contributes depends on how much

the employee chooses to save. Typically, employers match employee contributions at some rate up

to a cap. Appendix Figure C.1 shows the full set of matching schedules in our data, the construction

of which is described in the next section.

In contrast, the rules governing both employee and employer Social Security contributions are

more rigid. Specifcally, Social Security payments are fnanced via non-discretionary FICA payroll

tax contributions from both employers and employees on each dollar of labor earnings up to a

taxable maximum, and Social Security benefts are computed based on a formula that depends

on a worker’s earnings history. These beneft amounts are somewhat progressive, implying that

low-income workers generally receive larger beneft payments per dollar of payroll tax contributions

than higher-income workers in the same cohorts.

As DC plans become more dominant and DB coverage recedes, there is greater scope for individuals’ decisions to afect retirement wealth, and employer plan design can amplify the implications

of these decisions for wealth inequality. Endogenous DC participation also implies that the benefts paid to employees in the form of matching contributions will not be equally distributed across

workers, even among workers with identical earnings. To study the interplay between individual

saving decisions and frm matches, we need data that contain both the saving decisions made by

individuals and the full match schedules ofered by their employers.

3 Data

We form our data set by linking administrative data on the retirement saving and demographics of a

large sample of U.S. employees with a newly constructed data set on employer-sponsored retirement

plan characteristics. Sections 3.1 and 3.2 describe respectively our employee and employer data.

3.1 Employee data

Our baseline sample is all individuals ever observed in the 2008–2017 American Community Surveys

(ACS).4 We link ACS respondents to other administrative data using protected identifcation keys

4From 2005 to 2019, the average number was over 3.2 million, including a sample expansion from 2010 to 2012.

Refer to https://www.census.gov/acs/www/methodology/sample-size-and-data-quality/sample-size/ for more

information on the ACS sample and response rates over time; accessed 11/17/2021.

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(PIKs).5 Some 90%–94% of ACS respondents are successfully assigned a PIK in any given year

(Ferrie et al., 2021).6 Next, we link ACS respondents with their 1040, W-2, and 1099-R flings. The

ACS provides individuals’ race, year, age, education, gender, occupation, and location at the time

of the survey. The 1040 and W-2 flings provide other socioeconomic and demographic indicators,

including family structure, employer identifcation number (EIN), tenure, spousal income, and

intergenerational linkages (parental income and parental DC access). We restrict our sample to

those between ages 24 and 59 and a half, and our regressions also impose that workers have a

modest degree of labor market attachment in the ACS year. Specifcally, we impose that the sum

of nominal Box 1 wages and deferred compensation exceeds $8,000, which translates to roughly

20 hours per week at the current Federal minimum wage. We also require that individuals make

strictly more than $0 in Box 1 wages. Appendices A.2.1 and A.1.3 provide, respectively, detailed

overviews of our data build and variable construction.

3.2 Employer retirement plan data

All employers must submit an annual regulatory form (Form 5500) on their U.S. retirement plans

to the federal government. Plans with over 100 participants provide narrative descriptions of plan

characteristics, including match schedules, vesting schedules, and auto-features. We create a data

set by extracting these descriptions from the original free-form text.7 We do this for the largest 4,800

plans in the US and a random sample of 1,000 smaller plans. These employers cover a substantial

portion of the U.S. population; in 2017, 37 million employees were eligible for these large plans,

constituting 55% of employees with access to private and nonproft sector DC retirement plans.

Appendix A.2.2 provides further details. These plan-level data, further detailed in Arnoud et al.

(2021) and Choukhmane et al. (2023), include information on vesting schedules, auto-enrollment,

and crucially for our question, match schedules. These match schedules are typically concave

functions of employee contribution rates, often linear up to a threshold. Figure C.1 illustrates the

observed variation in match schedules in our 2017 employer-sponsored plan-level data.

To match the retirement plan data with our employee data, we use a multistage fuzzy matching

5PIKs are assigned by a probabilistic matching algorithm that compares the characteristics of records in Census,

survey, and administrative data to those in a reference fle constructed from the Social Security Administration

Numerical Identifcation System and other federal administrative data. PIKs correspond one-to-one with SSNs and

so allow us to link individuals over time and across data sources. For more information, see Wagner and Layne (2014). 6As noted in Bond et al. (2014), there is some selection into linkage, for example by age, race, and citizenship

status. However, we do not believe that the magnitudes of these diferences will bias our estimates substantially. For

example, in 2010, the linkage rate for Black ACS respondents was 91.4%, compared to 93.5% for White respondents. 7https://www.dol.gov/agencies/ebsa/about-ebsa/our-activities/public-disclosure/foia/

form-5500-datasets.

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procedure with numeric identifers such as the EIN, telephone number, name, and address felds.

We impose two key restrictions: i) the employer must use the same matching formula for all employees and ii) the frm-level employer share of contributions (the ratio of frm-level aggregate employer

match divided by the sum of frm-level aggregate employer match plus employee deferred compensation) for each employer must be within 15 pp of our W-2 imputation. Note that while employers

include frms, hospitals, non-profts, and other non-frm employers, “frm” and “employer” are used

interchangeably throughout this paper.

3.3 Samples

We defne three main samples: i) our “full ACS sample”, ii) our “matching sample” of individuals

for whom we have employer-level retirement plan data, and iii) the “parent-matching sample”,

which is the sample for whom we can link individuals to their parents. We start with the full ACS

cross-section of approximately 12,480,000 unique individuals. The “full ACS sample” contains the

observations in the ACS cross-sections for whom we have data on all individual-level characteristics.

Next, the “matching sample” corresponds to the subset of ACS respondents for whom we have

collected employer-sponsored retirement plan information from Form 5500 flings. This serves as

the primary sample in most of our analysis. Finally, the “parent-matching sample” corresponds to

the subset of the “matching sample” for which we can link respondents to their parents, and who

are in the 1978–1992 birth cohort. Appendix A.3 provides more details on the diferent samples.

We distinguish the samples by our sampling procedure. All three samples include ACS individuallevel survey data, and thus follow ACS survey procedures. However, our matching and parent

matching samples efectively sample from two populations, frst from the U.S. population via the

ACS and then sampling employees at certain employers from the employer population. We thus

combine ACS and employer-level weights. In contrast, our full ACS sample, which is not matched

with employer retirement plans, simply uses the ACS weights. See Appendix A.2.3 for a detailed

explanation of the sampling and weighting procedures.

3.4 Retirement savings outcomes

Our four primary measures of saving and withdrawals are: i) Employee contributions: real

deferred compensation reported in Box 12 of the W-2 tax form. This amount generally corresponds

to contributions to an employer-sponsored contribution plan (such as a 401(k)). We defne the

employee contribution rate as a percentage of salary using the ratio of the employee contribution

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reported in Box 12 to the sum of the taxable wage reported in Box 1 of the W-2 form and the

Box 12 employee contribution. ii) Participation: is a dummy equal to one if the individual makes

a positive contribution to a retirement savings plan. iii) Employee plus employer matching

contributions: the sum of the employee contribution and the employer match contribution we can

calculate using match formulas gleaned from Form 5500 fling. iv) Early withdrawals: we create

a dummy equal to 1 if an individual between the ages of 25 and 548 has a positive distribution

from a retirement account reported in tax Form 1099-R. Appendix A.1.2 gives further details on

variable construction.

4 Racial Gaps in Retirement Wealth Accumulation

In this section, we document the following facts about the racial gaps in retirement savings rates:

they are large, get amplifed by employer matches, persist even after we condition on a rich set of

individual characteristics, and are larger in subgroups in which White workers save more.

4.1 Gaps in retirement savings by race are large, and employer matching contributions amplify the savings and total compensation diferences

We begin by characterizing some basic facts about the distribution of employer and employee

contributions in the raw data. Figure 1A reports the ratio of average contributions to average

labor income. In our “matching sample” (which is our primary sample), White workers save on

average 4.2 pp of their labor income per year in employee contributions to DC retirement accounts,

while Black (Hispanic) workers save 2.4 pp (2.6 pp). This raw gap is large, implying that the savings

rate of Black (Hispanic) employees is 43% (38%) lower than that of White employees. Figure 1A

also illustrates the additional impact of matching. White employees gain an additional 2.1 pp of

salary, worth $1,974 a year on average, from employer matching contributions. Meanwhile, Black

(Hispanic) employees receive an increase of only 1.4 pp (1.5 pp) of salary, i.e., $857 ($993) a year

from employers. Altogether, White workers’ DC infows average 6.3 pp of their labor income,

while Black (Hispanic) workers’ average 3.8 pp (4.2 pp). For the rest of the main text, unless

otherwise specifed, we refer to contribution rates as the sum of employee and employer-matching

contributions.

These diferences in saving rates imply substantial gaps in the component of compensation com8After this age, withdrawals on separations from an employer mean that there is no tax penalty.

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ing from matching benefts. In Figure 1B, we compare the racial disparities in employer matching

with disparities in other employee compensation (i.e., wages plus deferred compensation). We

characterize these gaps for workers who are around the median of the labor income distribution

by race in each year. Figure 1B plots the average earnings for workers between the 45th and 55th

percentiles—a quasi-median—of earnings for their specifc race and normalize it to $1 for the level

of earnings earned by White workers near the median. In our data, a Black (Hispanic) worker near

the median earns 75¢ (79¢) for every dollar earned by a White worker near the median. While our

sample difers somewhat from that in other studies (in that we drop some workers with low earnings

and focuses on frms with DC plans) our results are largely consistent with fndings in the most

recent literature on the gaps in labor income across races (Bayer and Charles, 2018; Derenoncourt

and Montialoux, 2021). Figure 1B documents the average employee matching benefts received for

this same group of workers, again expressing values relative to the level accruing to White workers.

Gaps in employer matching are much larger than the gaps in earnings that have been the focus of

the literature: Black (Hispanic) workers near the median of their race-specifc income distribution

earn 47¢ (52¢) for every dollar of matching that their White counterparts receive.9

These diferences of 1.6–1.8 and 0.7-0.8 pp in own and employer contributions, respectively, are

quite large in relation to the average rate DC contribution rates in our sample and the typical fow

of savings in aggregate data. For instance, the Bureau of Economic Analysis reports an average

personal saving rate of approximately 6% of disposable income between 2005 and 2019. The tax

treatment, as we will quantify in Section 7 further amplifes these discrepancies in terms of the

value of these contributions at retirement. As a result, these diferences in behavior can add up to

very large diferences in racial wealth accumulation, as we quantify in greater detail below.

4.2 Diferences in worker-level characteristics account for a signifcant share of

racial contribution diferences

Given that racial groups difer along a number of observable and unobservable dimensions, we use

regressions to explore the extent to which diferences in economic characteristics across groups help

to account, in a statistical sense, for the gaps documented above. We interpret these results not as

explaining away part of the racial contribution gap but rather as providing indicators of diferent

9It is not possible to evaluate the corresponding gaps in retirement incentive–related tax expenditure without the

use of a model of saving and withdrawals over the lifecycle. Section 7 provides such a model. We fnd there that, for

each dollar of this tax expenditure received by the median White earner approximately 31 (62) cents is received by

the median Black (Hispanic) earners. Details are deferred to that section.

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channels that mediate racial disparities in saving rates. We leverage the rich set of data on the

demographic and economic characteristics of employees with access to a DC account to estimate

linear models for worker i of the form:

′ yi = α + βracei + Xiδ + εi, (1)

in which we progressively add observable characteristics such as dummies for age (in fve-year bins

for ages 25–29 to 55–59.5), year, deciles of labor income (i.e., defated W-2 income plus deferred

compensation), education group (i.e., did not receive a high school diploma or equivalent, high

school graduate or equivalent, college degree, and graduate degree), gender, occupation, county,

employer identifcation number (EIN), and tenure bin. To ensure that our estimates are representative of the population of frms fling the long form of Form 5500, we use a composite weight that

accounts for diferences in sampling frequencies in the ACS and our likelihood of including a frm

in our sample of DC retirement plans. We cluster the standard errors at the employer’s EIN level.

For reference, Table 3 shows coefcients from a specifcation that includes the full set of individual

characteristics as well as family structure and spousal income.

Equation (1) is fairly standard in the literature on wage gaps (see, e.g., Cahuc et al., 2014,

Ch. 8). The vector racei includes indicators for Black, Hispanic, Asian, Native American, Pacifc

Islander, and Two or More racial groups, and the omitted category is White workers. Our analysis

restricts attention to the three largest racial groups in the U.S.; therefore, the coefcients we report

are the elements of β on the dummies for Black and Hispanic group membership. In Figure 2, we

plot the estimated βˆs using the data from our primary sample, where we start from the univariate

version of Equation (1) and, at each successive point, add an additional group of variables until the

model becomes fully saturated.10 In each step of this “regression cascade,” β captures diferences

′ in the mean of yi that cannot be accounted for by Xiδ; hence, the addition of a new variable

shrinks the gap only if it incrementally predicts yi and there is a correlation between the variable

and group membership.11 Before discussing fndings from this analysis, we recognize it is often

unclear the extent to which one should partial out many of the characteristics that we consider

here when assessing the magnitudes of racial gaps, especially given that some of the diferences in

10Fully saturated in the context of this section means that the regression includes indicators for year, age, income,

education, gender, occupation, county, EIN, and tenure. While Figure 2 also reports estimates from regressions which

include household and family characteristics, we defer our discussion of these controls until in Section 5.1. 11In Figure C.5 in Appendix C, we visualize these relationships more directly. Specifcally, we summarize the

distribution across age, income, education, and spousal income bins (which we discuss in Section 5.1) alongside the

coefcients associated with bin membership coming from the saturated regressions reported in Table 3.

13
the distribution of Xi across racial groups may refect racial barriers faced by Black and Hispanic

workers.12 We emphasize that changes in β estimates from inclusion of a new variable provide

incremental information about the joint distribution of Xi, race, and savings rates.

In Figure 2A, the main outcome variable is the employee contribution to the DC retirement

plan plus the employer matching rate as a percentage of income, though we also display the component coming from the employee’s own contribution rate in the darker color. Collectively, the

main economic characteristics that we consider (columns through “Tenure” in Figure 2A) reduce

the estimated Black-White and Hispanic-White gaps from 39% (34%) (as a share of the average

contribution rate for a White worker) to 14% (7%). Nonetheless, Black (Hispanic) employees still

contribute nearly 1 pp (0.5 pp) less than their White colleagues with similar observables—i.e., workers with the same age, income, education and gender, working in the same occupation and frm, with

similar job tenure, and living in the same county. Figures 2B and C consider the breakdown into

the intensive (savings rate conditional on participation) and extensive (participation rate) margins,

respectively. While gaps persist on both the intensive and extensive margins, racial diferences in

worker-level characteristics can account for a large part of the extensive margin participation gap

while most of the intensive margin contribution gap remains unaccounted for.

Next, for each of the individual-level characteristics that we include in this analysis, we discuss

the following: potential economic rationales for why the characteristics may impact DC savings

rates, the relationship between these variables and average savings rates, and the extent to which

they impact the racial gaps in contribution rates. For part of this discussion, we examine the

estimated coefcients from our most detailed multivariate specifcations, which include all variables

and are reported in Table 3.

Year : Recent years have seen a substantial evolution in the DC landscape (e.g. the growth

of auto-enrollment). To account for these, as well as savings diferences over the business cycle,

we include year fxed efects. Their inclusion has little impact on the estimated gaps since the

composition of these racial groups was fairly stable over this time period. Appendix Figure C.7

further shows that gaps are fairly similar across calendar years.

Age: Age is an important driver of retirement saving: fnancing consumption in retirement is

likely to be a central fnancial objective for older workers, whereas younger workers face a number

of other competing savings objectives. Black and Hispanic workers are younger on average than

12See, for example, Neal and Johnson (1996); Lang and Manove (2011); Carneiro et al. (2005) for a discussion

about test score and education controls in racial wage gap regressions.

14
White workers, and so understanding the extent to which age diferences account for the gaps we

observe is important. We fnd the expected relationship that savings rates are increasing in age

(see, e.g., Gourinchas and Parker, 2002): relative to those aged 25-29, those aged 30-34 have saving

rates that are 0.6 pp higher and those of the 55-59.5 group are 2.6 pp higher. Accounting for age

diferences and including year controls reduces the estimated Black–White (Hispanic–White) gap

from 39% (34%) (as a share of the average contribution rate for a White worker) to 36% (29%).

Income: Income is the characteristic which has been a traditional focus of the literature (and

legislation) on distributional analysis of the retirement system. It is well established that the rich

save more (Dynan et al., 2004) and there are many reasons why this would be the case. Social

Security replacement rates benefts decline in income, the tax benefts are highest for those with the

highest income (Congressional Budget Ofce, 2021), income risk tends to decline with income over

most of the distribution outside of the top decile (Guvenen et al., 2014), and fnancial literacy is

typically increasing in income (Lusardi and Mitchell, 2014). Furthermore, there are well-established

diferences in the distribution of income across races (see Figure 1 and Appendix Figure C.5B).

We construct income groups by sorting workers into deciles of labor income within each calendar

year and age bin. Table 3 shows that average contribution rates increase across the bottom nine

deciles, with employees in the bottom decile contributing 1.6 pp less than workers in the ffth decile.

Workers in the top income decile contribute slightly less than those in the ninth decile – this refects

the impact of tax limits on maximum contributions which are most likely to bind for those with the

highest incomes. Income gradients are especially strong with respect to the decision on whether

to participate or not13 but also have an association with saving rates, conditional on participation.

The measured racial contribution gap (relative to the average contribution rate of a White worker)

between Black (Hispanic) workers and their White counterparts decreases from 36% (29%) to 17%

(15%) when comparing workers in the same income bin. Figures 2B and 2C show that the impact

of income on estimated contribution gaps is particularly large on the extensive margin.

Education: Education attainments could afect saving beyond their correlation with income

levels, through several channels: lifecycle trajectories in expected income levels and income risk

vary with education, and fnancial literacy is increasing in education. We consider the role of the

highest degree attained, which we capture via four dummies for less than high school, a high school

degree, a college degree, and a graduate degree. We fnd a strong relationship between educational

13Column 3 of Table 3 shows that, relative to workers in the ffth income decile, workers in the bottom and top

deciles are 24 pp less and 15 pp more likely to participate, respectively, conditional on all other controls.

15
attainment and savings. Conditional on other worker-level characteristics, those without a high

school diploma or equivalent contribute 0.19 pp less to a DC account than those with a high school

diploma, 0.83 pp less than those with a college degree and 1.2 pp less than those with a graduate

degree. Accounting for racial diferences in education attainments has a modest efect on the

estimated Black–White contribution gap (the gap as a share of average White contribution falls to

16% from 17%), but these education attainments account for a larger share of the Hispanic–White

gap, which decreases to 11% from 15% after accounting for diferences in education attainment.

This fnding refects the fact that a larger share of Hispanic workers have lower levels of educational

attainment relative to Black and White workers (see Figure C.5C).

Gender : Men and women may save diferent amounts for a variety of reasons such as diferences in lifecycle earnings profles (Goldin, 2021), risk preferences, life expectancy, and/or expected

retirement benefts (Barber and Odean, 2001; Watson and McNaughton, 2007). We fnd that,

conditional on the full set of characteristics we include, female workers are 4.3 pp more likely to

participate and contribute 0.55 pp of salary more to DC accounts than men. Given, though, that

gender ratios are similar for workers across the racial groups we consider, gender has little impact

on the estimated contribution gaps.

Occupation and County: Occupation may be relevant for savings, as it can correlate with expected future earnings, income risk, fnancial literacy (indeed, we consider an occupation-based

proxy for fnancial literacy below), and potential diferences in risk or time preferences. Perhaps

surprisingly, the inclusion of occupation fxed efects has little impact on estimated racial contribution gaps. Racial composition difers across space, which may correlate with various factors such

as the cost of living in retirement, so we additionally absorb county fxed efects. We fnd that

absorbing county fxed efects shrinks the Black–White (Hispanic–White) estimated gap from 16%

(10%) to 14% (8%) relative to the average White contribution rate.

Employer (EIN): Our data allow us to absorb EIN fxed efects, which allows us to identify

racial contribution gaps among coworkers within the same employer. In addition to a number of

economic characteristics that may difer across frms (for example, expected income trajectories, and

employment stability), a natural possibility is that workers sort into frms that difer in terms of the

quality of the retirement benefts that they ofer.14 For example, there is substantial heterogeneity

14We test a simple aspect of this sorting hypothesis in column 8 of Table 3. We run a version of our main specifcation

with everything except the EIN fxed efects where the main dependent variable is the aggregate matching rate at

the frm level (average employer match/average labor income) and examine whether Black and Hispanic workers are

more likely to work at employers with lower average matching rates. The diferences in these average matching rates

are fairly small at +2 bp and -4 bp for Black and Hispanic workers relative to White workers, respectively.

16
across frms in the generosity of matching incentives, the nature of vesting schedules, and autoenrollment and other default policies. Absorbing EIN fxed efects allows us to hold many of these

features constant. We measure virtually no additional impact on the Black–White gap, while the

Hispanic–White decreases slightly from 8% to 7% as a share of the average contribution rate of

White worker (driven by a decline in the extensive-margin gap).

Tenure: The fnal economic characteristic that we consider is job tenure, which we split into bins

for 1, 2, 3, and 4+ years. Tenure may relate to saving through its correlation with employment risk

(e.g., Farber, 1994, shows that the probability of job separation decreases for workers with higher

tenure), the probability that a worker’s contributions will vest, and workers’ awareness of plan

benefts, among other channels. Compared to employees with less than a year of tenure, employees

with one year of tenure contribute 0.47 pp of salary more to a DC account, while employees with

at least three years of tenure save 1.8 pp more. Taking racial diferences in tenure into account has,

however, little efect on the residual contribution gaps.

Taking Stock. We fnd that workers who are older, higher income, female, more educated,

and have longer tenures contribute substantially more toward retirement and, thus, receive much

more in employer matching benefts. Accounting for diferences across workers in these observable

characteristics can account, in a statistical sense, for part but not all of the racial gaps that we

document. We interpret the role of these diferent characteristics as channels mediating racial

disparities in retirement contribution rates. Figures 2B and 2C illustrate the intensive margin and

extensive margin efects: our estimates refect a mix of both efects.

Before proceeding, it is useful to address two additional potential concerns. First, in the analysis

above, individual characteristics are accounted for using an additive specifcation. To evaluate

whether this additivity is concealing consequential interactions between characteristics, we rerun

the analysis in the frst 5 layers of the cascade by reweighting the cells based on observables. Figure

C.3 in Appendix C shows a cascade similar to that in Figure 2A for all the individual characteristics

up to gender, and the qualitative lessons are unchanged. For the remaining analysis, we discuss

the results based on the linear model. A second potential concern relates to the representativeness

of our sample. In Figure C.4 in Appendix C, we conduct the same regressions for the full ACS

sample, and the baseline results are not meaningfully afected.

17
4.3 Other potential factors contributing to diferences in retirement wealth

accumulation

While we discussed the contribution of several worker-level characteristics to the estimated racial

contribution gaps, other factors could matter for the observed diferences in retirement contributions

across racial groups. In this subsection, we discuss briefy some of these potential factors.

Retirement plan-level characteristics. Black and Hispanic workers may contribute less

than their White counterparts if they are more likely to work at employers who do not sponsor a

DC plan or have access to plans with diferent or less desirable features (i.e., matching formula,

vesting schedule, or auto-enrollment). In Appendix Figure C.2 we show that diferences in access

to an employer-sponsored retirement plan are small, especially after controlling for worker-level

characteristics. In Appendix Figure C.2B, we fnd that on average Black and Hispanic employees

have access to plans with less generous employer contributions, however, this diference is no longer

signifcant for Black employees and is signifcant but very small in magnitude for Hispanic workers

once we adjust for individual-level characteristics. In Appendix Figure C.4, we show that contributions gaps are just as large when restricting the sample to workers who are fully vested in the plan

(that is workers who, if they separate, would retain all previously-received employer contributions),

suggesting that these diferences are not driven by racial diferences in the risk created by the vesting schedule. Finally, comparing employees hired before and after the adoption of auto-enrollment,

we fnd that auto-enrollment raises the average level of participation but has little to no efect on

the racial contribution gaps conditional on characteristics (Figure 2A). Taken together, these results suggest that, conditional on worker-level characteristics, retirement plan characteristics have

little efect on racial contribution gaps.

Financial literacy and life expectancy. There is a large empirical literature establishing

the importance of fnancial literacy and life expectancy for retirement saving decisions (see Lusardi

et al. (2017) and De Nardi et al. (2009) for examples respectively). Our data does not permit us

to directly measure the contribution of these factors to racial contribution gaps. We do not have

any measures of fnancial literacy at an individual level but can defne a proxy of fnancial literacy

based on the knowledge content of diferent occupations. Using this measure, and with the caveat

that our proxy is only at the occupation level, we fnd that, if anything, racial contribution gaps

are largest for workers predicted to have higher levels of fnancial literacy (see Appendix Figure

C.18). On life expectancy, our conditioning on age and income capture much of the variation in life

18
expectancy. While life expectancies for Black Americans are lower than those for White Americans,

who in turn have lower expectancies than Hispanics, Chetty et al. (2016) show that diferences by

race are small when comparing individuals with similar income levels.

4.4 The racial gaps are larger in groups with higher average levels of retirement

saving contributions among White workers

Thus far, our analysis has focused on understanding diferences in average contributions by race.

Here, we examine the heterogeneity in the size of the racial savings gaps across workers with diferent

characteristics. More precisely, we augment our baseline estimating Equation (1) as follows:

′ yi = α + βracei × Zi + Xiδ + Zi

′

γ + εi, (2)

where Zi is a vector of dummies for an additional category of interest. We summarize the main

takeaways from this analysis here and present more detailed heterogeneity results in Appendix

Figures C.7-C.18 (including raw diferences along the diferent observable characteristics).

Heterogeneity by Age and Income. Figure 3 illustrates pattern of contributions by age and

income across racial groups after controlling for other characteristics such as occupation, education,

and EIN (see Appendix Figures C.8 and C.9 for similar patterns without controls). Across all

groups, contributions increase with age and income, but Black (Hispanic) workers aged 40–44 (35–

39) contributes only as much on average as White workers aged 25–29. Furthermore, racial savings

gaps increase with income. We observe no diferences in contributions for individuals in the bottom

decile of incomes (i.e., contributions are uniformly low). In contrast, we fnd Black (Hispanic)

workers in the 9th decile of income save 1.7 pp (0.98 pp) less than their White counterparts.

Broader patterns of heterogeneity. We estimate the heterogeneity in racial savings gaps

along six additional dimensions: education, gender, tenure, fnancial literacy, generosity of employer

matching contributions, and health insurance status. Figure 4 summarizes the results from this

heterogeneity analysis results in the fully saturated model.15 The broad pattern is one in which the

higher are the White saving rates for the group in question (on the horizontal axis), the larger are

the gaps (on the vertical axis). Conversely, the racial disparities in retirement savings tend to be

narrower among groups who save less for retirement. These disparities widen as individuals gain

the resources and capability to contribute more towards their retirement savings. The fgure shows

15Note that, for specifcations that are homogeneous within occupation (e.g., fnancial literacy) or EIN (e.g.,

employer matching generosity), the fully saturated model does not include the corresponding fxed efects.

19
that workers who are more educated, are female, have longer tenure, are more fnancially literate,

face more generous matching subsidies, and have private health insurance tend to contribute more

to retirement plans, and these are also the groups for whom racial disparities in contribution are

more pronounced. We give more detail on patterns of heterogeneity in Appendix A.5.

5 Potential Drivers of Racial Diferences in Contributions among

Workers with Similar Individual-Level Characteristics

The previous section documented that a signifcant share of the diference in contributions across

racial groups is mediated by diferences in age, income, and other individual characteristics. Still,

signifcant contribution gaps persist even after accounting for a large set of individual-level characteristics. Black (Hispanic) workers contribute 14% (7%) less than White workers with similar

individual-level characteristics. In this section, we examine how household structure and parental

background impact saving levels across races, and we discuss the role of liquidity constraints.

5.1 Household and extended family characteristics explain a signifcant share

of the residual contribution gap

In this section, we explore the role of family structure and parental resources in retirement saving

decisions. We fnd that racial diferences in these characteristics can account for nearly half of the

residual gap in contributions gaps remaining after partialing out individual-level characteristics.

5.1.1 Family structure and spousal resources

The incentives to save can vary with the size and composition of a worker’s household. For instance,

the marginal utility of a given level of consumption may be higher for workers who have larger

families with more dependents. Further, dual earner households may be better diversifed and,

therefore, more willing to invest in an illiquid retirement account. Oliver and Shapiro (1989) found

marked gradients in wealth by family structure and argued that these patterns are relevant for

understanding racial wealth inequality. Here, we evaluate the extent to which savings rates vary by

the structure of the household (i.e., number of adults and/or the presence of dependent children),

as well as the level of spousal income, if any.

We measure household composition by dividing households into fve groups based on an individual’s tax fling status. Four of these groups represent single or married flers with or without

20
dependent children. A ffth group is formed of those who do not fle taxes and for whom information

on marital status and children is missing. Nonflers and single tax flers, particularly single flers

with children, tend to have lower contribution rates across all three racial groups, even after we

account for worker-level and retirement plan characteristics (as is illustrated in Figure 5A).

We measure spousal resources with 12 indicator variables, one for each age-adjusted decile of

spousal income, one for spousal income of zero, and one for observations with missing spousal

income, for instance, because the worker is a single fler (see Appendix Figure C.5D for details).

Table 3 reports regression coefcients for each of these indicator variables and shows that the spouses

of high earners save more: workers with spouses in the top decile of spousal income contribute 0.78

pp more than otherwise similar workers with spouses in the bottom decile.

These results show that family composition and the presence and level of spousal income are

important determinants of saving. In each case, Black and Hispanic workers are more likely to

have characteristics associated with lower saving: they are, respectively, 3.5 and 2.4 times more

likely to be single flers with children than are White workers and, when married, they have lowerincome spouses than otherwise similar White workers. Consequently, accounting for diferences in

household composition and spousal income reduces the measured racial contribution gaps. Figure

2 shows that doing so reduces the estimated Black–White (Hispanic–White) gap from 14% (7%)

to 11% (6%) as a share of the average contribution rate of a White worker. These increments are

substantial since they follow after the mediating efects of individual-level characteristics (such as

income, education, and occupation) have been accounted for.

5.1.2 Parental resources

In this sub-section, we investigate the role of parental income in retirement saving. An advantage

of our data is that we can link individuals to their parents for a subsample of younger individuals

(born between 1978 and 1992) who were claimed as dependent by their parents at age 16 (see

Section 3.3 for more details). While the broad patterns we have documented remain true in this

sub-sample of younger workers, there are some diferences in magnitudes. Across all racial groups,

contribution rates are lower in this younger sample; thus, the gaps we estimate are slightly smaller:

Black (Hispanic) workers’ employee contributions are, on average, 1.3 pp (0.9 pp) of earnings lower

compared to their White counterparts. Employer matching increases these contribution gaps to 2.0

pp (1.4 pp). As with the full sample, accounting for individual and household characteristics shrinks

these estimated gaps in contributions (i.e., employee plus employer-matching contributions): the

21
residual gap in contributions between Black (Hispanic) workers and their White counterparts after

accounting for individual characteristics is 0.70 pp (0.37 pp) and after additionally accounting for

family structure and spousal income is 0.57 pp (0.32 pp). These patterns are shown in Panel A in

Figure 6.

We fnd that higher parental income levels are associated with higher retirement contribution

rates, even after accounting for diferences in own earnings and other individual and household

characteristics. Panel B of Figure 6 shows coefcients on parental income deciles from our fully

saturated regression. It shows that the children of the rich save more: workers with parents in

the top parental income decile contribute approximately 0.7 pp more than those with parents in

the bottom half of the parental income distribution. One potential channel consistent with these

patterns is intergenerational insurance. Richer parents can support their children fnancially and

insure them against shocks (Fagereng et al., 2023), while poorer parents may require the fnancial

assistance of their adult children (Chiteji and Hamilton (2002), Francis and Weller (2022)). The

extent to which one’s relative can provide fnancial insurance (or require fnancial support) may

afect workers’ decision to save in an illiquid account.

This association between parent income and own saving is relevant for the racial saving gap—

Panel C of Figure 6 shows the average income of parents for workers of each race in a given income

decile. A White worker in the middle-income decile has parental income (averaged over both

parents if present in the household) of approximately $90,000, on average. For Black and Hispanic

workers in the same income decile, the average parental income is approximately $50,000. Panel D

of Figure 6 further illustrates the diference in the distribution of parental income by plotting the

relative shares of workers falling into diferent deciles of the parental income distribution by race.

Taken together, these two facts–that the children of the rich save more, and that the parents

of White workers are richer than those of Black and Hispanic workers–imply that parental income

can play a mediating role in the racial savings gap. We quantify this efect in Panel A of Figure

6. Including indicators for each decile of parental income at age 16 reduces the estimated Black–

White (Hispanic–White) gap from 0.57 pp (0.32 pp) to 0.44 pp (0.19 pp). Put diferently, it

reduces the residual contribution gap (i.e., the estimated gap that remains after accouting for the

part mediated by individual- and family-level characteristics) by 23% and 40% for, respectively,

Black and Hispanic workers relative to their White counterparts.16

16We also evaluate the importance of including a dummy for parents having contributed to a DC account, a proxy

for familiarity with and exposure to these accounts. This does not afect the size of the residual contribution gap.

22
5.2 Racial disparities in early withdrawals highlight the role of liquidity constraints

Black and Hispanic workers may choose to forgo the generous subsidies associated with retirement

contributions because they face stricter liquidity constraints. Coyne et al. (2022) highlight that the

propensity to tap into retirement accounts early—despite the potential tax penalties—can serve as a

measure of diferences in liquidity valuation. Those who are more likely to take an early withdrawal

reveal a high preference for liquidity and a lack of access to alternative sources of liquidity. We

fnd that Hispanic, and to a greater extent Black, Americans are more likely to withdraw resources

early than are White workers with similar worker-level characteristics.

While employer-sponsored retirement savings plans are designed to be a vehicle for saving to

fnance consumption in retirement, individuals are allowed to access these resources early. These

early distribution options are, however, discouraged by the tax code. Unless the distribution

qualifes for an exception, withdrawals before the age of 59.5 are subject to a 10% tax penalty and,

prior to 2020, additionally trigger a minimum six-month suspension from contributing to the plan.

Despite these restrictions, early withdrawals are common: Goodman et al. (2021) fnd that fows

out of DC plans and IRAs over a 12-year period accounted for over 20% of the value of fows in.

We measure early withdrawal rates using data from the 1099-R tax forms of individuals older

than 25 and strictly younger than 55.17 We defne individuals as taking an early withdrawal if we

observe a withdrawal of at least $1,000 (in 2017 dollars) in the calendar year following the ACS

year.18 Due to data limitations, we cannot distinguish between penalized early withdrawals—those

subject to the 10% tax penalty—from nonpenalized hardship distributions. Because those who

have never contributed cannot take early distributions we restrict the sample to individuals who

have made at least $1,000 of retirement contributions over the preceding 4 years. We discuss this

and other sample restrictions and variable defnitions in Appendix A.

Before the of age 55, on average, 12.3% of the White retirement savers in our sample take an

early distribution each year, compared to, respectively, 14.5% and 23.3% of Hispanic and Black

savers, respectively (Table 1). The Black–White gap is striking: Black retirement savers are nearly

twice as likely as their White counterparts (i.e., have a 90% higher probability) to withdraw at

17Early withdrawals are not penalized for individuals who separated from their employer at or after age 55 or for

any individuals older than 59.5. 18Employers are allowed to implement an automatic cash-out for terminated employees with a balance smaller than

$1,000. Therefore, early withdrawals smaller than $1,000 may not refect an active decision of the individual. Our

rationale for looking at the year after the year a worker is included in our main regression sample is to allow for the

possibility that earnings go to zero (i.e., we do not want to condition on workers being employed).

23
least $1,000 early in a given year. The disparity is also large, albeit much smaller, for Hispanic

savers, who are 21% more likely to take an early withdrawal than their White counterparts. In

Panel A of Figure 7, we plot a cascade similar to that in Figure 2A, but the outcome variable here

is an indicator for an early withdrawal. Accounting for diferences in income decreases these racial

withdrawal gaps to 84% and 16%, respectively, for Black and Hispanic individuals. Including EIN

fxed efects, which capture potential diferences in hardship distribution rules across employers,

can explain some of the residual racial diferences in withdrawals, but the gaps remain large even

after we include the whole set of individual characteristics.

The propensity to take an early distribution is higher when liquidity needs are higher. To

illustrate this, we sort workers into 20 ventile bins based on the growth rate of income between

year t (the year in which the respondent flls out the ACS and in which we measure savings gaps)

and year t + 1. Figure 7B reports the average propensity to take an early withdrawal of more than

$1,000 by race across the twenty income growth bins. Those who experience large income declines

are more likely to tap into their retirement assets early: 52% (41%) of Black (Hispanic) workers in

the bottom ventile of income growth take an early withdrawal of at least $1,000, compared to 35% of

White workers.19 Other proxies of stricter liquidity constraints, such as having a larger expenditure

share dedicated to housing costs, are also correlated with higher levels of early withdrawals (see

Appendix Figure C.15 for details).

We interpret these large diferences in the propensity to take an early distribution as evidence

that Hispanic and, to a greater extent, Black savers have stronger liquidity needs and are more

liquidity-constrained than White savers with similar incomes. Consistent with this interpretation,

Ganong et al. (2020) fnd that Black and Hispanic households cut their consumption substantially

more than White households following a similarly sized income shock. Racial diferences in liquidity valuation could also explain why family structure and parental background correlate with

retirement contributions. For instance, single-parent households may have stronger liquidity needs

than married couples, and as shown in Panel B of Appendix Figure 5, across all three racial groups,

single flers with dependent children are more than 5 pp more likely to take an early withdrawal in

a given year than dual flers without children. Similarly, those with richer parents may beneft from

easier access to liquidity through familial support, and as shown in Panel B of Appendix Figure

19Very high and very low values of income growth tend to correlate with job separations. Appendix Figure C.6

shows that the probability of remaining at the same main employer between t and t + 1 is an inverse U-shaped

function of the earnings growth rate. Around 55% of workers in the bottom ventile of earnings growth switch jobs

(which includes transition into non-employment and zero earnings realizations).

24
6

C.14, the racial gaps in early distributions shrink for those with parents in the top decile of the

parental income distribution.

Binding liquidity constraints could also explain the lower levels of participation and contributions among Black and Hispanic workers. A partially illiquid retirement account is a less desirable

savings vehicle for those facing more acute liquidity needs. This is consistent with evidence from

Mitchell et al. (2007) that access to a loan option increases participation in 401(k) plans and evidence from Briere et al. (2022) that workers avoid less liquid investment options in French retirement

plans. Unlike other asset classes, such as housing, the illiquid nature of retirement accounts is a

policy choice. Early withdrawals are penalized by the tax system and in most plans, 401(k) loans—

which provide liquidity to currently employed participants—must be fully repaid at job separation

in most plans, a time when liquidity needs are heightened. By subsidizing contributions and penalizing withdrawals, the current institutional design ties a worker’s total compensation and tax

liabilities to her ability to forgo immediate access to funds, furthering disparities between more and

less liquidity-constrained groups.

Gaps in Retirement Wealth Accumulation on Dimensions Other

than Race

Our primary focus in this paper is to document and better understand savings gaps by race. These

diferences in saving rates generate diferences in remuneration across workers and the incidence of

tax subsidies provided by the government.

In Section 4.2, we discussed the contribution of a number of individual characteristics to our

estimates of residual racial contribution gaps. In this short section, we emphasize the extent

of their independent association with saving, and therefore the extent of their association with

saving incentives. Just as the matching and tax subsidies associated with the current system will

disproportionately accrue to White workers relative to their Black and Hispanic coworkers, these

subsidies will also disproportionately accrue to other groups with higher saving rates.

Figure 8 shows coefcients which we obtain from the following model

′ yi = [Di ⊗ Zi]′

ω + Xiδ + εi, (3)

where Di is a set of indicators for income deciles and Zi is a vector of dummies for an additional

25
characteristic. As before, Xi captures controls for year, age, gender, occupation, education, county,

EIN, and tenure (where we omit Zi from inclusion in Xi where applicable). As illustrative examples, we will consider four characteristics: education, job tenure, family structure, and parental

income. In each clustered column chart, diferent shading represent group categories, and each set

of clustered columns corresponds to a diferent income decile. The main coefcients of interest are

in ω, which reveal diferences in contributions in a given income×group bin relative to the omitted

category (which is indicated with a dashed vertical line) and a coworker with similar Xs.

Taking education frst, even for workers with similar income levels, we fnd that the workers

with higher levels of educational attainment save more—the gaps are quite large, especially in the

top half of the income distribution.20 Gaps are also large by tenure, which is correlated with both

job stability and likely awareness of the matching benefts that a frm ofers. The bottom row of

Figure 8 considers two measures of family background, family structure (bottom left) and parental

income (bottom right). Since non-flers and single parents tend to save less, they will tend to

participate less and therefore enjoy fewer matching and tax subsidies relative to their coworkers.

Finally, conditional on own income, those with richer parents save more. These results suggest

that, among workers with the same earnings, the current system will tend to redistribute towards

those with more education, those with higher job tenure, dual flers, and those with richer parents.

Our fnal section will focus on diferences in lifeycle aggregates by earnings, race and parental

income. The analyses in this section serve to emphasize that, more generally, the system of retirement incentives redistributes from workers who, all else equal, save less to those who save more and

that saving correlates in systematic ways with many economic and demographic characteristics.

7 Aggregate Efect of Retirement Savings Subsidies on the Distributions of Wealth and Consumption

We have documented substantial heterogeneity in annual contributions to and withdrawals from

DC accounts. In this section, we combine our data on these fows with a microsimulation model to

examine the distributional impact of retirement saving subsidies on key outcomes that we do not

directly observe: specifcally measures of wealth at retirement. The model, which is described in

full in Appendix B, simulates data on wealth and consumption in retirement by bringing together

20Gaps are slightly more muted in the top income bin, refecting the fact that contribution limits bind more

frequently for those in this bin.

26
i) our data on fows in and out of DC funds, ii) a specifcation of the federal tax code (from NBER

TAXSIM), iii) Social Security rules and iv) assumptions about portfolio composition, asset returns,

and the draw-down of wealth in retirement.

We use this model to conduct three types of exercises. First, we measure the distributional

impact of the federal tax expenditure across race groups. Second, we decompose DC wealth into

the shares coming from employee contributions, employer matching contributions, and federal tax

expenditures. Third, we evaluate the distributional impact of changing the design of tax and

employer saving subsidies.

7.1 Microsimulation model

The full model is outlined in Appendix B. Here, we summarize key inputs and outputs. The model

inputs are simulated data on earnings over the lifecycle, employee and employer matching contributions to employer-sponsored DC accounts, and withdrawals from those accounts over working life.

We do not observe full lifecycle paths (we have at most 13 years of data for any one individual),

so we construct simulated data using the data that we do have and a hotdeck-based imputation

procedure (described in Appendix B.2).

The key model outputs are:

• DC wealth: ADC

i . This is the discounted value of after-tax withdrawals from the simulated

DC account balance. We assume that savers employ a draw-down rule that keeps withdrawals

constant in retirement. We further divide DC wealth into three components:

– AT is the part of DC wealth arising from its favorable tax treatment. We defne this as i

the diference between ADC

i and the discounted value of withdrawals that i would have

received if she had instead saved in a taxable account.21

AEE – i and AER are, respectively, the parts of DC wealth, exclusive of tax benefts (i.e.,

ADC − AT ), accruing from employee and employer contributions and withdrawals. i i

– We will often present wealth measures as a multiple of simple average annual earnings

computed over the worker’s life cycle.

21As a plausibility check of our model, we compare our estimates of aggregate tax expenditure to DC savings

with ofcial Treasury Department fgures. In 2023, the Treasury estimated the net value of tax liability foregone

because of DC treatment to be $119 billion in 2021 (see US Department of the Treasury (2023)). When we estimate

a comparable fgure for the US population using our simulations, we obtain $117b. See Appendix B.8.1 for more

details.

27
• Consumption in retirement: We defne a broad measure of wealth—denoted as Consumption

(Ci)—as the sum of DC wealth (ADC) and the discounted value of Social Security payments. i

• We will group individuals by the discounted value of the sum of their earnings and deferred

compensation—we refer to this as lifetime earnings (LEi). When showing results by lifetime

earnings, we divide the population into 6 groups: the bottom four quintiles and the top

two deciles. We split the top quintile as IRS contribution limits generate diferences in saving

between the top two deciles. We will also use this quantity in our counterfactual experiments,

this will be our basis for redistributing the federal tax expenditure.

Figure 9 illustrates the key model outputs. Panel 9A shows average earnings by race over the

lifecycle. Panel 9B shows patterns of DC wealth at retirement by race and lifetime earnings. DC

wealth is expressed as a proportion of average annual lifetime earnings. For all lifetime earnings

groups except the top decile, DC wealth is highest for White workers and lowest for Black workers,

and intermediate to these for Hispanic workers. Due to the diferences in both contributions and

in early withdrawals that we have documented,22 the Black–White gap amounts to approximately

100%–150% of average annual earnings, while the Hispanic–White gap is approximately half that.

Panel 9C shows selected percentiles of wealth for each race and income group, and highlights that

there is substantial heterogeneity within income and race groups. Panel 9D shows a similar fgure

for Social Security wealth (measured as the discounted value of the stream of entitlements). Given

that Social Security benefts are largely determined by earnings history,23 there are no diferences

by race conditional on income.

7.2 Quantifying the distributional impact of the DC federal tax expenditure

Figure 1B illustrated racial gaps in the receipt of each of earnings, employer matches, and the tax

expenditure. Those last estimates were calculated using the model described here, and Figure 10

provides a more granular analysis. It shows, for every dollar of the tax subsidy received by White

workers on average, the average that is received by Black and Hispanic workers. The fgure shows

results by lifetime earnings group, and the two panels difer by how they defne the groups. In

Figure 10A earnings groups are defned based on the race-specifc distributions (and so the bottom

group for Black workers, for example, corresponds to the poorest 20% of Black workers). In Figure

22Appendix Figure C.22 shows the future value of early withdrawals at retirement by race and lifetime earnings. 23In our model, they are completely determined—rather than largely determined, as in reality—by earnings history,

as we abstract from heterogeneity in claiming age and family benefts.

28
10B, on the other hand, groups are defned based on the distribution of lifetime earnings in the

whole population (and so the bottom group for Black workers corresponds to Black workers in the

poorest 20% of the population).24 For every dollar of the tax expenditure received the poorest 20%

of White workers, approximately 30 (60) cents is received by the poorest 20% of Black (Hispanic)

workers. Holding earnings constant by defning groups at the population level, gaps are smaller but

remain large—for example, for every dollar received by White workers in the bottom population

quintile, 61 cents is received by Black workers and 77 cents is received by Hispanic workers.

7.3 Quantifying the contribution of employer matches and tax expenditures to

wealth at retirement

Figure 11 shows the contribution of employer matches and the tax expenditure to retirement wealth

along the race-specifc earnings distribution (panel A) and the overall population earnings distributions (panel B). High-earners save more (Dynan et al., 2004), and so saving subsidies favor them.

In the bottom quintile of lifetime earnings, cummulative tax and employer subsidies are worth less

than 70% of (annual) lifetime earnings. By comparison, these saving subsidies are worth more than

250% of (annual) lifetime earnings for individuals in the top decile of earnings.

Diferences are also large across racial groups, even within the same earnings bin. White workers

in the middle quintile of population earnings accrue a combined subsidy from employers and the

government worth 161% of their average annual earnings, compared to 119% for Black workers and

148% for Hispanic workers. Diferences by position in the race-specifc lifetime earnings distribution

are even starker: for the middle quintile of White workers, the total subsidy is worth 171% of lifetime

earnings; for Black workers, it is 85%, and for Hispanic workers, it is 134%.25

Figure 12 shows a similar decomposition of DC subsidies, in this case splitting by parental

income rather than race.26 In both panels, each successive set of fve bars represents a group based

on an individual’s lifetime earnings. Within each group, the individual bars correspond to quintiles

of parental income. In Figure 12A, income groups are formed within parental income groups; in

12B, they are population groups. Within each own-income group, those with richer parents receive

more in savings subsidies. That is, because the children of the rich save more, even conditional on

24The population in this case is composed only of White, Black and Hispanic workers. 25Appendix Figure C.24 complements this fgure by (in panel A) adding DC wealth arising from employee saving,

and (in panel B), showing the shares of DC wealth arising from employee, employer and government contributions.

Shares difer somewhat by income: at the bottom of the income distribution shares coming from employee contributions, employer contributions and tax expenditures are respectively approximately 60%, 25% and 15%, while at the

top they are 50%, 25% and 25%. Shares from each component by race conditional on income, are very similar. 26Figure C.23 in Appendix C.3 shows a comparable analysis, splitting by own earnings and education.

29
their own earnings (as shown in Figure 6), subsidies for savers advantage them. The diferences

across groups are substantial: among those in the middle population lifetime earnings quintile, the

subsidies range from 140% of average annual earnings for those with parents in poorest income

decile to 168% for those with parents in the richest group.

7.4 The lifetime efect of alternative retirement saving policies

In this section, we use the microsimulation model to evaluate a budget-neutral counterfactual

exercise that would break the link between private saving and the amount of employer matching

benefts and tax subsidies that individuals receive. In Appendix C.3, we present results from two

additional counterfactuals to assess the separate efect of changing the tax treatment of retirement

contributions and the design of employer contributions.

7.4.1 Description of the counterfactual policy exercise.

The counterfactual exercise changes the design of both employer and tax subsidies for retirement.

A full description of the exercise is given in Appendixes B.9, B.10, and B.11, here we provide a

summary.

Employer contributions. We frst redistribute the employer matching contributions within

each frm. That is, we calculate the aggregate employer matching contribution made by each

employer, and we divide these contributions such that every employee in that frm receives the

same employer contribution as a percentage of salary regardless of how much the employee chooses

to contribute to the plan.27

Tax expenditures. Next, we calculate the aggregate tax expenditure on DC retirement savings

under the existing regime (which includes the tax advantage from deferring the taxation of contributions, tax-free growth of assets, and tax penalties on early withdrawals). Then, we redistribute

this tax expenditure such that that every individual receives a direct government contribution to

their retirement account calculated as a proportion of lifetime earnings. This proportion is uniform

across individuals and keeps the aggregate tax expenditure constant.

Behavioral responses. In our baseline exercise, we assume that individual saving rates (and

therefore the individual component of DC wealth and retirement consumption) are unchanged

27While employer-matching contribution formulas are chosen by employers, the government can encourage employers to adopt specifc contribution formulas. Arnoud et al. (2021) estimates that a majority of employees are covered

by plans with a safe-harbor matching formula. Our counterfactual can be thought of as a change in safe harbor rules

that shifts all employers away from ofering matching contributions and toward ofering non-elective contributions.

30
across the diferent counterfactual exercises. Before showing results, we discuss this assumption.

Our counterfactual exercise removes employer matching and tax incentives. As a result, individuals may choose to consume more during their working life and save less for retirement. Whether

such behavioral responses change the conclusion of our distributional analysis depends on the

policy’s goal. On the one hand, if there is no concern about undersaving for retirement, abstracting from these behavioral responses may not change the conclusion of the distributional analysis:

groups that receive more employer and tax resources in the counterfactual exercises are better of

whether they decide to allocate these new resources toward consumption in working life or toward

consumption in retirement. On the other hand, in the presence of a concern about undersaving

for retirement, increasing consumption during working life and reducing employee retirement contributions could change the distributional impact of the counterfactual policies. The magnitude of

this efect depends on the size of the behavioral response.

There is no consensus in the literature on how much private saving responds to employer matching and tax incentives. Engen et al. (1996) and Poterba et al. (1996) review and debate the implications of the early literature on saving incentives. In a more recent contribution, Choi (2015)

reviews the literature on matching and fnds that it is associated with a small positive efect on

participation and an ambiguous efect on average contribution rates.28 Regarding tax incentives, a

recent review by Friedman (2015) notes that “tax subsidies appear to primarily afect the allocation

of savings across accounts, rather than the total amount of savings.”29

Given the lack of consensus and overall small efects found in the empirical literature, we assume

no behavioral response in private saving in the baseline specifcation of our counterfactual exercises.

In an extension, we recalculate the results assuming that each dollar of employer matching or tax

subsidies generates 10 cents of additional employee savings (which corresponds to the upper bound

of the 95% confdence interval in Chetty et al. (2014)). We show those results in Figure C.28. For

robustness, we also present results assuming a larger response of 20, 30 or 40 cents of additional

employee savings per dollar of employer match or tax incentive.

28Engelhardt and Kumar (2007), using cross-sectional data, estimate that an increase in the match rate of 25 cents

per dollar increases 401(k) participation rates by 5 pp, while Dufo et al. (2006), in a randomized controlled trial

with a one-time saving subsidy, fnd that increasing the match rate from 0% to 50% increases take-up by 11 pp.

However, the positive efect of matching on take-up and employee contributions may not translate into higher wealth

accumulation if employees reduce their nonretirement saving or increase borrowing in response. Choukhmane and

Palmer (2023) estimate that approximately two-thirds of increased employee pension contributions in the UK are

fnanced through reduced nonretirement saving and increased credit card borrowing. 29Ramnath (2013) fnds no statistically signifcant efect of the U.S. saver’s tax credit on the level of retirement

contributions. Similarly, Chetty et al. (2014), using administrative data from Denmark, estimate an elasticity of net

saving of less than 1 cent per Danish kroner (DKr) of tax expenditure on subsidies for retirement saving.

31
7.4.2 The reform would reduce inequality in retirement wealth accumulation by own

earnings, race, and parental income.

In this section, we discuss the results from our baseline counterfactual exercise; selected companion

results for two additional counterfactuals changing, separately, the tax treatment of retirement

savings and the design of matching contributions are shown in Appendix C.3.

Results by own income. We fnd a revenue-neutral reform that redistributes tax expenditures

and employer contributions in proportion to lifetime earnings (rather than in proportion to saving)

would increase consumption in retirement by 5 to 10% for individuals in the bottom half of the

earnings distribution (Figure 13D). These gains would come at the expense of an approximately

5% drop in retirement consumption in the top decile of the lifetime earnings. Because the losses are

concentrated among those with higher lifetime income and the gains are concentrated among those

with lower lifetime income, the relative gains (in percentage of lifetime income or consumption)

from this counterfactual policy are signifcantly larger than the relative losses.30

Results by race. Such a policy would also lead to a sizeable reduction in racial gaps in DC

wealth. As shown in Table 5A, the reform would reduce the gap between the DC wealth of Black

(Hispanic) workers and White workers by 21% (20%) for those with earnings around the median of

each race-specifc labor earnings distribution. Proportional changes in racial gaps are even larger

when we form bins based on the population earnings distribution, refecting the fact that our

counterfactual scenarios does not address diferences in average income across racial groups. As

shown in Table 5B, the Black-White (Hispanic-White) retirement wealth gap drops by 34.9% (27%)

for individuals with earnings around the median. Gains are also large in absolute terms, Black and

Hispanic individuals in the bottom half of their race-specifc earning distribution experience an

increase in retirement wealth equivalent to more than one year of earnings (Figure 13A).

Results by parents’ income. Figure 14 shows a similar analysis, but with groups defned

based on individuals’ own earnings and their parents’ income.31 The patterns of winners and

losers from this reform refect the patterns of winners and losers under the status quo that were

illustrated in Figure 12. Those in the bottom population lifetime earnings bin with parents in the

bottom income quintile would gain wealth at retirement worth approximately 125% of their average

(annual) lifetime earnings, thereby increasing their retirement consumption by approximately 7.5%.

30While these reforms are designed to be revenue neutral for the government and aggregate compensation neutral

for the frms, they lead to a net increase in wealth on retirement, as matching resources are transferred from older

workers to younger workers, who have more time to retirement to beneft from asset returns. 31Appendix Figure C.25 shows a similar picture by education.

32
8

The gains (as a proportion of lifetime earnings) then fall with own earnings and, conditional on

those earnings, fall with parental income. Those in the top population earnings bin with parents in

the top income quintile would lose wealth at retirement worth approximately 50% of their average

(annual) lifetime earnings—and their retirement consumption would fall by approximately 5%.

Conclusion

Since the introduction of the permanent income tax system in 1913, the U.S. has promoted retirement saving with tax subsidies and employer contributions. A long-standing concern is that these

subsidies are regressive and largely favor higher-income individuals. This concern has sparked a

long tradition of economics research studying the distributional efects and optimal design of the

retirement system (Diamond, 1977; Kotlikof et al., 1982; Geanakoplos et al., 2000; Moser and

Olea de Souza e Silva, 2019). This concern is also refected in the regulatory framework: since

1942, U.S. pension plans have been required to pass an annual nondiscrimination test to ensure

that the benefts of the plan do not disproportionately accrue to highly compensated employees.32

The income-regressive nature of retirement saving subsidies is therefore balanced by other aspects

of the U.S. retirement system, which tend to be more progressive. In addition to income-based

nondiscrimination tests, the Social Security formula is progressive and ofers higher replacement

rates for individuals with lower lifetime income.

In this paper, we examine the distributional properties of retirement saving subsidies among

individuals who have similar incomes but difer along other demographic dimensions (with a focus

on racial and ethnic identity). We fnd that the current system channels more tax and employer

resources toward workers who are White, possess a college degree, and have richer parents or

spouses than it channels toward their similar-income coworkers who are Black or Hispanic, are

single parents, and have lower-income relatives. The consequent efects on wealth are large and are

not directly addressed by other aspects of the retirement system. The Social Security formula does

not vary by race, education, or parental background, and employer nondiscrimination tests consider

only current compensation. Our results thus suggest that future research on the optimal design

and distributional impact of retirement systems should look beyond diferences along the income

distribution to better understand the interplay between retirement saving policies and inequality.

32To pass the nondiscrimination test, the employer must show that diferences between the average employee and

employer contribution rates for highly compensated and non–highly compensated employees are sufciently small.

Employers can avoid these annual tests by adopting a set of plan features that qualify a plan as a safe harbor plan.

33
Figures

Figure 1: Racial gaps in employer matching benefts are much larger than gaps in income

Employee 

4.2%

Employer

2.1%

Employee

2.4%

Employer

1.4%

Employee

2.6%

Employer

1.5%

0

1

2

3

4

5

6

Average contribution rate (p.p.)

Panel A: Average DC contribution rates

among workers with access to a DC plan

79¢

47¢

52¢

31¢

62¢

0

.2

.4

.6

.8

1

Normalized to $1 for the median White level

Labor

income

Employer 

matching benefits

Simulated tax 

benefits

Panel B: Gaps in labor income, DC matching and

DC tax benefits around the median earnings

White (W) Black (B) Hispanic (H)

White Black Hispanic W B H W B H W B H 

75¢

Notes: Panel A shows the average employee DC contribution rate (bottom bars) and average employer matching

rate (top bars) as a proportion of salary among workers with access to an employer-sponsored DC plan and at

least $8,000 in annual earnings. Panel B shows average gaps in labor income, matching contributions, and DC

tax benefts for individuals around the median labor income of each group (with the White level normalized to 1).

The frst (second) set of three bars shows mean labor income (employer matching contributions) for those between

the 45th and 55th percentiles of the race-specifc labor income distribution. The third set of three bars in Panel

B reports calculations from our lifecycle microsimulation model in Section 7. It shows mean model-implied tax

benefts for individuals in each group between the 40th and 60th percentiles of the race-specifc lifetime earnings

distribution. This quantifes the present discounted value of the deferral of taxation and exemption of returns

from taxation, net of tax penalties on early withdrawals.

34
Figure 2: Racial gap estimates for key retirement savings measures

39%

36%

17% 16% 17% 16% 14% 14% 14%

11% 11% 11%

34%

29%

15%

11% 11% 10% 8% 7% 7% 6% 6% 6%

0

-.5

-1

-1.5

-2

-2.5

(i)

Raw (ii)+Year+Age

(iii) +Income (iv) +Education (v) +Gender (vi)

+Occupation

(vii)

+County

(viii)

+EIN (ix)+Tenure (x) +Fam. Struc. (xi) +Spouse Inc.

(xii)

+AE

Panel A: Employee Contribution Rate + Employer Match Rate

20%

18%

12% 12% 12% 12% 12% 11% 11%

9% 9% 9%

14%

11%

7%

5% 5% 5% 5% 5% 5% 4% 4% 4%

-2

-1.5

-1

-.5

0

(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii)

Panel B: Employee Contribution Rate (conditional on participation)

18% 17%

5% 4% 5% 4%

3% 3% 2%

1% 1% 1%

20%

19%

10%

7% 7% 6%

4%

2% 2% 2% 2% 2%

0

-5

-10

-15

(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii)

Panel C: Participation rate

Share (p.p.) diff. relative to White

Model specifications

Black Hispanic 95% CI

Notes: These fgures give estimates on the gap between non-Hispanic White and Black or Hispanic workers,

respectively, for key retirement savings measures across various model specifcations. Model (i), or “Raw” as

referenced in the fgure, represents the univariate regression of the outcome variable on the categorical race

variable: yit = α + β0racei + εit. α and εit are the constant and error terms, and race identifes, among others,

the non-Hispanic White, Black, and Hispanic groups. The racial group indicators come from the ACS. In all the

models, White is absorbed as the omitted category, so the coefcient on the race term, β0, which we plot in the

fgures, measures the average gap between White and Black or Hispanic. Each subsequent clustered bar graph

plots these Black and Hispanic coefcients from a regression model with additional mediating channels. For

example, Model (ii), which is for “+ Year + Age”, is yit = α + β0racei + β1yeart + β2agebini + εit, where yeart

and agebini are vectors for year and fve-year age bins, respectively. Next, we add potential mediating channels

at the individual- and household- level. The potential mediating channels at the individual-level are as follows:

(iii) income deciles (calculated based on the distribution of taxable wages for the given year within age bins);

(iv) educational attainment bins; (v) a female dummy; (vi) occupation; (vii) county, (viii) employer fxed efects

(we use the employer identifcation number (EIN) for each worker’s main source of income), (ix) and tenure bins.

Following the individual-level channels, we add household characteristics. The frst household characteristic is (x)

family structure (a categorical variable that records whether the individual is a single or dual fler and whether

she has children). The second is (xi) spousal income, categorized into decile bins, similar to individual income,

but with additional bins for those with zero income and missing spousal income (includes both single flers and

those with spouses who do not submit a W-2). Finally, the fully saturated model (Model (xii) or “+ AE”) comes

at the end of each panel: yit = α + β0racei + β1yeart + β2agebini + β3incomebini + β4educbini + β5femalei +

γoccupation + δcounty + λEIN + β6tenurei + β7f amilystructurei + β8spousalincomebini + β9AEi + εit. Since our

data set is a repeated cross-section, we calculate clustered standard errors by EIN.

35
Figure 3: Racial savings gaps by age and income

-1

0

1

2

3

4 Share (p.p.) diff. relative to Age 25-30, White

25-29 30-34 35-39 40-44 45-49 50-54 55-59.5

Age Bins

Panel A: Age

-4

-2

0

2

4 Share (p.p.) diff. relative to decile 5, White

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Income Deciles

Panel B: Income

White Black Hispanic 95% CI

Notes: This fgure illustrates racial gaps in savings for diferent age groups (Panel A) and income deciles (Panel B).

Panel A shows coefcients on race interacted with age from a regression where the dependent variable is employee

plus employer match contribution rate. The regression contains dummies for year, age, income, education, gender,

occupation, county, EIN, and tenure. For age, the regression is yit = α + β1yeart + β2agebini + β3incomebini +

β4educbini + β5femalei + γoccupation + δcounty + λEIN + β6tenurei + ζ(agebini · racei) + εit, where we graph the

coefcients in ζ. The omitted dummy is for White workers Age 25-30. The coefcients in Panel B are for an

analagous regression where ζ is a coefcient on income dummies interacted with race, rather than age, where the

omitted category is for White workers in the ffth income decile.

36
Figure 4: Heterogeneity in racial savings gaps across groups relative to average savings rates of

White workers in each group

-2

-1.5

-1

-.5

0 Black-White gap (p.p.)

2 4 6 8

Panel A: Black

-1

-.5

0

.5 Hispanic-White gap (p.p.)

2 4 6 8

White average rate (%)

Panel B: Hispanic

Age Income Education Parental Income Gender Family Structure

Tenure Fin. Lit. Housing Empl. Gen. Health Insur.

Notes: This fgure shows heterogeneity in gaps in employee plus employer matching contribution rates by diferent

mediating channels and race, relative to the corresponding White average rate. The aim is to show the broad

pattern between levels of saving and gaps. Our mediating channels are age, income, education, gender, tenure,

family structure, parental income, fnancial structure, housing costs as a share of income, fnancial literacy,

employer generosity, and health insurance. We include dummies for year, age, education, gender, occupation,

county, EIN, and tenure. The basic model for variable, vari, is yit = α + β1yeart + β2agebini + β3incomebini +

β4educbini+β5femalei+γoccupation+δcounty+λEIN +β6tenurei+β7vari+ζ(vari ·racei)+εit. We omit variables

as necessary to avoid multicollinearity. For example, our fnancial literacy model is collinear with γoccupation, so

our specifcation is yit = α + β1yeart + β2agebini + β3incomebini + β4educbini + β5femalei + δcounty + λEIN +

β6tenurei + ζ(f inancial literacy · race)i + εit. For specifc defnitions and construction procedures for the listed

mediating channels and other variables included in the models, please see Appendix A.1.4 and A.1.3, respectively.

37
Figure 5: Racial savings gaps and early withdrawals by family structure

-1.5

-1

-.5

0

.5

1

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

Panel A: Employee Contribution + Matching Rate

0

5

10

15

20

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

Panel B: Early Withdrawal Rate (withdr. > $1000) Share (p.p.) diff. relative to Single, No Kids, White

White Black Hispanic 95% CI

Notes: This fgure illustrates racial gaps in savings (Panel A) and early withdrawals (Panel B) by family

structure. The graphs show coefcients from regressions, where the dependent variables are employee plus

employer matched contribution rate (Panel A), and an indicator for early withdrawal (Panel B). Regressions

include dummies for year, age, education, gender, occupation, county, EIN, and tenure. The specifcation is

yit = α + β1yeart + β2agebini + β3incomebini + β4educbini + β5femalei + γoccupation + δcounty + λEIN +

β6tenurei + β7f amilystructurei + ζ(f amilystructurei · racei) + εit. We graph the coefcients in ζ. The omitted

category is White single flers with no children.

38
Figure 6: Racial savings gaps by parental demographics 14%

12%

9% 9%

8% 7%

4% 4%

0

-.2

-.4

-.6

-.8

-1 rate (p.p.)

Individual controls +Household controls +Parent Income +Parent Awareness

Panel A: Employee Contribution+Employer Match Rate

-.2

0

.2

.4

.6

.8 Share (p.p.) diff. relative to Parent Income Decile 5

1 2 3 4 5 6 7 8 9 10 Parent Income Deciles

Panel B: Parent income coefficients

0

50000

100000

150000

200000 Average Parental AGI (in 2017 USD) 1 2 3 4 5 6 7 8 9 10 Own Income Decile

Panel C: Average parental income by own income

0

.5

1

1.5

2 Group share rel. to pop. shares 1 2 3 4 5 6 7 8 9 10 Parent Income Deciles

Panel D: Parent decile shares by race White Black Hispanic

Notes: This fgure illustrates the relationship between parental income and DC saving. The sample for these

fgures is our ‘Parent Matching’ sample– the sample of younger workers for whom we can link to their parents.

Panel A shows estimates of the Black-White and Hispanic-White gaps in employee contribution rates and employer

matches gaps in the manner of Figure 2. The frst set of two bars are regression coefcients from a specifcation

that includes the individual covariates up to specifcation (ix) in Figure 2. The second set of bars adds household

structure and spousal income. The third set of bars adds dummies for parental income decile. The fnal set of

bars adds an indicator for our observing parental DC contributions. Panel B gives the coefcients for each parent

income decile dummy in our fully saturated model (that which is the basis for the fnal set of columns in Figure

6). The outcome variable is the employee contribution plus employer match rate in Panel A. Panel C shows the

average parental income by population-level income bins for our observed White, Black, and Hispanic workers.

Panel D illustrates the racial composition for parents within each parent income decile. For example, the height

of the green bar in parental decile 1 gives the ratio of the share White workers who have parents in population

income decile 1, to the the share of all workers who who have parents in population income decile 1.

39
Figure 7: Early withdrawals from retirement savings by race and income growth 89% 90%

84% 83% 83% 83%

80%

76% 76%

66% 66% 66%

18% 21%

16% 15% 15% 15%

11% 10% 10%

7% 7% 7%

0

3

6

9

12 Rate (p.p)

Raw + Year + Age + Income + Education + Gender + Occupation + County+ EIN+ Tenure + Family Structure + Spousal Income + Auto-Enrollment

Black Hispanic 95% CI

Panel A: Early withdrawal rate (>$1000 withdrawal)

0

10

20

30

40

50

60 Probability (p.p.) of early withdrawal (over $1000)

0 10 20 30 40 50 60 70 80 90 100

Income Growth Bins (Ventiles) White Black Hispanic

Panel B: Early withdrawal rates by income growth ventile

Notes: These fgures show the probability of taking an early withdrawal of at least $1,000. The sample is our

matching sample. Panel A follows the same structure as Figure 2A and shows the progression of the gaps for Black

and Hispanic workers relative to White workers as we add potential mediating channels. We include dummies

for year, age, income, education, gender, occupation, county, EIN, tenure, spousal income, and auto-enrollment.

Panel B shows the breakdown, by race, in the probability of early withdrawals over $1,000 in year t+ 1 by income

growth ventile from year t − 1 to year t (where t is the year we observe individuals in the ACS). We generate

early withdrawal dummies only for people who i) contributed over $1,000 in deferred compensation in the prior 4

years, ii) withdrew more than $1,000 in the year following our survey year, and iii) were younger than 55 at the

time of the withdrawal. All workers in our sample were employed in the survey year. Appendix A.1.2 provides a

detailed explanation of our early withdrawal dummies; Appendix A.2 provides a list of restrictions.

40
Figure 8: Employee plus Employer Contribution, by income interacted with demographics

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

No HS Graduated HS

Graduated college Graduate degree

Education

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

<1 year 1 year

2 years 3+ years

Tenure

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Non-filer Single, Kids Single, No Kids

Dual, Kids Dual, No Kids

Family Structure

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Parent Income Gap

Notes: This fgure shows gaps in employee plus employer matched contribution rates by selected mediation

channels and income decile, relative to individuals in the 5th income decile who are in our selected base category.

The dashed line indicates the base category (for example, age bin 25–29 for our age covariate). Beginning from

the top left, we have education, tenure, family structure, and parent income. Each group of bars corresponds to

an income decile. Each individual bar represents the group of people in that income decile. The legend defnes

each category. Our model resembles our main specifcation with individual level controls and but additionally

includes an interaction between income and our mediating channel under study. We include dummies for year,

age, education, gender, occupation, county, EIN, and tenure. For example, our model for family structure is as

follows: yit = α + β1yeart + β2agebini + β4educbini + β5femalei + γoccupation + δcounty + λEIN + β6tenurei +

ζ(f amilystructure ·incomebin)i +εit. We omit variables as necessary to avoid multicollinearity For example, for

our tenure model, which is collinear with the tenure variable, we set: yit = α+β1yeart +β2agebin+β4educbini +

β5femalei + γoccupation + δcounty + λEIN + ζ(tenure · incomebin)i + εit.

41
Figure 9: Microsimulation model: Key outputs 20 40 60 80 100 Thousands of Dollars

25 35 45 55 65

Age Bin

White Black Hispanic 100 200 300 400 500 600 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) Earnings (b) Mean DC wealth

0 500 1000 1500 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

0 500 1000 1500 2000 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(c) DC wealth distributions (d) Social Security distributions

Notes: This fgure illustrates the features of main outputs from our microsimulation model. Panel A shows mean

values by race and age bins 25–29, 30–34, . . . , 60–65. Note that the last age bin contains six ages. In Panel A,

earnings are the sum of wage income and deferred compensation. Panel B shows, for each race and population

earnings bin group, DC wealth at retirement divided by the simple average of earnings during working years.

Lifetime earnings groups are divided into six bins–the bottom four quintiles and the top two deciles. Panel C

illustrates the heterogeneity in DC wealth at retirement within each race and lifetime earnings group. Percentiles

shown are p10, p25, p50, p75, and p90. The measure of wealth shown is the same one which was illusrated in

Panel B. DC wealth at retirement divided by average lifetime earnings. Panel D shows the same percentiles for

the present value of all Social Security distributions over average lifetime earnings.

42
Figure 10: Total tax subsidy relative to White value by race and earnings

100

30

60

100

28

58

100

31

62

100

35

65

100

35

57

100

41

64

0 20 40 60 80 100 Percent of White Value

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic

100

61

77

100

65

79

100

74

89

100

83

93

100

87

91

100

79

89

0 20 40 60 80 100 Percent of White Value

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) By own-race quintiles (b) By population quintiles

Notes: This fgure quantifes the lifetime tax subsidy by race and earnings, expressed as a percentage of the

average tax subsidy given to White savers of the same earnings group. There are six lifetime earnings group–the

bottom four quintiles and the top two deciles. The fgures in the two panels difer by how lifetime earnings groups

are defned. In Panel A they are calculated within each race group, while in Panel B they represent population

earnings groups.

Figure 11: Contributions of employer and tax subsidies to retirement wealth, by race

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

(a) By own-race quintiles (b) By population quintiles

Notes: This fgure quantifes the efect of employer matching and tax subsidies on wealth at retirement by race and

earnings. The darker bars are the value at retirement of all employer matches, accounting for any preretirement

withdrawals. The lighter bars are the value at retirement of the various tax advantages given to DC accounts

throughout the lifecycle. Wealth levels are divided by average annual lifetime earnings to standardize comparisons

across earnings levels. Lifetime earnings groups are divided into six bins–the bottom four quintiles and the top

two deciles. The fgures in the two panels difer by how lifetime earnings groups are defned. In Panel A they are

calculated within each race group, while in Panel B they represent population earnings groups. Appendix Figure

C.24 shows versions of the graphs by population lifetime earnings group which adds employee contributions.

Panel A in the Appendix Figure shows the level of wealth and supplements Panel B in this fgure, Panel B in the

complementary appendix fgure expresses wealth in shares and gives the proportion for each groups coming from

employee contributions, employer matches, and the tax expenditure.

43
Figure 12: Contributions of employer and tax subsidies to retirement wealth, by parental income

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Group Earnings Bin (Outside Axis), Parental Income Quintile (Inside Axis)

Employer Subsidy Tax Subsidy

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Population Earnings Bin (Outside Axis), Parental Income Quintile (Inside Axis)

Employer Subsidy Tax Subsidy

(a) By own-group quintiles (b) By population quintiles

Notes: This fgure quantifes the efect of employer matching and tax subsidies on wealth at retirement by parental

income and own earnings. The darker bars are the value at retirement of all employer matches, accounting for

any preretirement withdrawals. The lighter bars are the value at retirement of the various tax advantages

given to DC accounts throughout the lifecycle. We divide these amounts by average annual lifetime earnings to

standardize comparisons across earnings levels. Quintiles of parental income (i.e., 1, 2, 3, 4, and 5) are graphed

by own-income quintile, with the top own-earnings quintile split into two deciles. Panel A has quintiles calculated

within each parental-income group, while the quintiles in Panel B are calculated across parental income groups.

Appendix Figure C.24 shows versions of the graphs by population lifetime earnings group which adds employee

contributions. Panel C in the Appendix Figure shows the level of wealth and supplements Panel B in this fgure,

Panel D in the complementary appendix fgure expresses wealth in shares and gives the proportion for each groups

coming from employee contributions, employer matches, and the tax expenditure.

44
Figure 13: Change in retirement wealth and consumption, by race -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) Change in ret. wealth by own-race quintile (b) Change in ret. wealth by pop. quintile -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(c) Change in ret. consumption by own-race quintile (d) Change in ret. consumption by pop. quintile

Notes: This fgure illustrates the impact of our baseline counterfactual exercise on wealth on retirement and

consumption in retirement. This counterfactual exercise distributes the aggregate employer matches in each frm

so that all workers in that frm receive the same proportion of their earnings, and distributes the aggregate federal

tax expenditure so that all workers receive a contribution that is in proportion to their lifetime earnings. We

show the efect on two outcomes: the top two panels (A and B) show the change in DC wealth on retirement,

with wealth expressed as a proportion of average annual working life earnings. The bottom two panels (C and D)

show proportionate change in consumption in retirement (where consumption is the sum of DC wealth and Social

Security). For both DC wealth and consumption, we show results by two diferent types of lifetime earnings bins.

The graphs on the left (Panels A and C) form lifetime earnings bins within race. In the graphs on the right

(Panels B and D) the bins represent population groups. In each case, lifetime earnings groups are divided into

six bins–the bottom four quintiles and the top two deciles.

45
Figure 14: Change in retirement wealth and consumption, by parental income -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

1 2 3 4 5 -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

1 2 3 4 5

(a) ∆ wealth, by parental inc., own-group quintile (b) ∆ wealth, by parental inc., pop. quintile -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

1 2 3 4 5 -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

1 2 3 4 5

(c) ∆ cons., by parental inc., own-group quintile (d) ∆ cons., by parental inc., pop. quintile

Notes: This fgure illustrates the impact of our baseline counterfactual exercise on wealth on retirement and

consumption in retirement. This counterfactual exercise distributes the aggregate employer matches in each frm

so that all workers in that frm receive the same proportion of their earnings, and distributes the aggregate federal

tax expenditure so that all workers receive a contribution that is in proportion to their lifetime earnings. We

show the efect on two outcomes: the top two panels (A and B) show the change in DC wealth on retirement,

with wealth expressed as a proportion of average annual working life earnings. The bottom two panels (C and D)

show proportionate change in consumption in retirement (where consumption is the sum of DC wealth and Social

Security). For both DC wealth and consumption, we show results by two diferent types of lifetime earnings bins.

The graphs on the left (Panels A and C) form lifetime earnings bins within parent income group. In the graphs

on the right (Panels B and D) the bins represent population groups. In each case, lifetime earnings groups are

divided into six bins–the bottom four quintiles and the top two deciles.

46
Tables

Table 1: Worker-level summary statistics, by respondent race

Panel A: White, not Hispanic Mean SD P10 P50 P90

Average age 42.06 9.99 28 43 55

Box 1 W-2 total compensation $81,310 $247,200 $19,300 $55,190 $145,700

Participation dummy 68.9% 46.29% 0% 100% 100%

Avg employer match ($) $1,974 $3058 $0 $846.80 $5,380

Employee contribution (%) of income 4.201% 4.76% 0% 3.223% 10.11%

Avg employer match (% of income) 2.092% 2.02% 0% 1.8% 5%

1099r withdrawal dummy 12.29% 32.83% 0% 0% 100%

Panel B: Black Mean SD P10 P50 P90

Average age 40.14 9.727 27 40 54

Box 1 W-2 total compensation $46,250 $79,220 $14,890 $35,730 $84,620

Participation dummy 56.25% 49.61% 0% 100% 100%

Avg employer match ($) $856.70 $1,603 $0 $125.40 $2,490

Employee contribution (%) of income 2.411% 3.273% 0% 1.009% 6.415%

Avg employer match (% of income) 1.43% 1.785% 0% .4522% 4%

1099r withdrawal dummy 23.27% 42.25% 0% 0% 100%

Panel C: Hispanic Mean SD P10 P50 P90

Average age 39.4 9.649 27 39 53

Box 1 W-2 total compensation $51,150 $121,400 $16,310 $37,960 $92,410

Participation dummy 54.83% 49.77% 0% 100% 100%

Avg employer match ($) $992.80 $1,885 $0 $106 $2,849

Employee contribution (%) of income 2.648% 3.635% 0% 1.009% 6.977%

Avg employer match (% of income) 1.512% 1.873% 0% .3652% 4.035%

1099r withdrawal dummy 14.52% 35.23% 0% 0% 100%

Notes: The table reports summary statistics for our wage earnings data from the matching sample (merged

employee and employer data), which covers the 2008–2017 period.

47
Table 2: Summary of retirement contribution amounts, by respondent race

Panel A: Percentage of salary Annual dollar amount

Employee Contributions All White Black Hispanic All White Black Hispanic

All workers 3.8% 4.2% 2.41% 2.65% $3,351 $3,882 $1,495 $1,793

By age

age 25 to 34 2.68% 3% 1.71% 2.03% $1,792 $2,067 $821 $1,111

age 35 to 44 3.71% 4% 2.4% 2.72% $3,408 $3,824 $1,542 $1,963

age 45 to 54 4.51% 4.86% 2.98% 3.16% $4,356 $4,915 $2,041 $2,343

age 55 to 59.5 5.31% 5.68% 3.45% 3.69% $4,895 $5,464 $2,288 $2,632

By income percentile

0 to 10 1.06% 1.22% .73% .79% $138 $159 $94 $103

10 to 20 1.56% 1.75% 1.15% 1.29% $325 $365 $237 $267

20 to 30 2.18% 2.42% 1.72% 1.74% $608 $675 $478 $483

30 to 40 2.68% 2.92% 2.18% 2.18% $932 $1,02 $753 $747

40 to 50 3.16% 3.45% 2.48% 2.55% $1,326 $1,455 $1,029 $1,049

50 to 60 3.66% 3.97% 2.81% 2.92% $1,841 $2,012 $1,395 $1,432

60 to 70 4.19% 4.47% 3.25% 3.31% $2,534 $2,723 $1,936 $1,938

70 to 80 4.88% 5.16% 3.68% 3.76% $3,632 $3,864 $2,697 $2,687

80 to 90 5.87% 6.07% 4.45% 4.56% $5,734 $5,956 $4,279 $4,273

90 to 100 5.9% 5.94% 4.92% 5.02% $10270 $10610 $7,735 $8,008

Panel B: Percentage of salary Annual dollar amount

Employer Contributions All White Black Hispanic All White Black Hispanic

All workers 1.93% 2.09% 1.43% 1.51% $1,707 $1,974 $856 $992

By age

age 25 to 34 1.57% 1.73% 1.14% 1.29% $1,008 $1,153 $530 $682

age 35 to 44 1.98% 2.12% 1.48% 1.58% $1,830 $2,075 $930 $1,123

age 45 to 54 2.15% 2.29% 1.65% 1.67% $2,157 $2,449 $1,102 $1,223

age 55 to 59.5 2.24% 2.36% 1.76% 1.76% $2,152 $2,406 $1,123 $1,234

By income percentile

0 to 10 0.56% 0.62% 0.45% 0.47% $73 $81 $59 $61

10 to 20 0.9% 0.98% 0.74% 0.8% $186 $202 $152 $165

20 to 30 1.27% 1.37% 1.09% 1.1% $350 $379 $300 $302

30 to 40 1.53% 1.63% 1.37% 1.35% $526 $562 $468 $459

40 to 50 1.75% 1.85% 1.55% 1.52% $724 $772 $637 $620

50 to 60 1.92% 2.02% 1.7% 1.68% $952 $1,01 $833 $814

60 to 70 2.11% 2.2% 1.91% 1.87% $1,256 $1,315 $1,12 $1,071

70 to 80 2.32% 2.41% 2.05% 2.05% $1,695 $1,77 $1,481 $1,434

80 to 90 2.67% 2.75% 2.36% 2.36% $2,556 $2,647 $2,224 $2,156

90 to 100 2.98% 3.02% 2.73% 2.69% $5,551 $5,809 $4,437 $4,482

Notes: The table reports summary statistics for our wage earnings data by race from the matching sample

(merged employee and employer data), which covers the 2008–2017 period. Values are rounded to the closest

integer.

48
49

Table 3: Racial gaps in contribution rates, regression estimates

Matched sample with plan information 

(1) (2) (3) (4) (5) (6) (7) 

Dependent Variable Own + Own Positive Own Match Max Positive A

match contrib. contrib. contrib. contrib. match - withdr. m

contrib. (% of inc.) dummy (% of inc., (% of inc.) own cont >$1000 

(% of inc.) (%) contrib.>0) (% of inc.) dummy 

Black -.67 -.52 -.66 -.82 -.16 .15 8.06 

(.04) (.03) (.23) (.03) (.01) (.01) (.28) 

Hispanic -.37 -.29 –1.47 -.35 -.08 .08 .85 

(.02) (.02) (.22) (.02) (.01) (.01) (.23) 

Female .55 .41 4.3 .3 .14 -.14 –1.33 

Age Dummiesage 25–29age 30–34 .62 .41 5.35 .38 .21 -.21 .77 

age 35–39 1 .69 7.54 .68 .31 -.3 1.59 age 40–44 1.3 .93 8.54 .97 .37 -.36 2.16 age 45–49 1.6 1.18 9.35 1.26 .43 -.42 2.91 

age 50–54 2.21 1.71 9.96 1.97 .5 -.49 4.24 age 55–59.5 2.64 2.11 9.95 2.53 .54 -.53 Education DummiesNo HSGraduated HS .19 .14 2.09 .13 .05 -.05 1.83 Graduated college .83 .64 4.75 .69 .19 -.19 -.14 Graduate degree 1.15 .94 4.84 1.01 .21 -.22 .2 Family StructureSingle, No KidsDual, No Kids -.04 -.01 -.96 .07 -.03 .03 -.35 Single, Kids -.47 -.34 –1.51 -.57 -.12 .12 4.52 Dual, Kids -.54 -.43 –1.97 -.47 -.11 .11 .54 Non-fler -.83 -.57 –5.68 -.59 -.26 .26 7.39 Tenure Dummies<1 year1 year .47 .32 -.72 .8 .15 -.16 .07 2 years 1.04 .7 2.49 1.26 .33 -.34 -.15 

3+ years 1.84 1.28 7.96 1.73 .56 -.56 –1.53 
50

Income percentile dummiesperc. 0–10 –1.64 -.98 –24.36 -.14 -.66 .66 .21 perc. 10–20 –1.19 -.73 –15.64 -.23 -.46 .46 .52 perc. 20–30 -.71 -.45 –8.63 -.14 -.26 .26 .56 perc. 30–40 -.36 -.24 –4.01 -.09 -.12 .12 .08 perc. 40–50perc. 50–60 .36 .26 2.97 .17 .1 -.1 -.34 perc. 60–70 .82 .59 5.86 .4 .23 -.22 -.94 perc. 70–80 1.4 1.04 8.63 .75 .36 -.36 –1.43 

perc. 80–90 2.17 1.63 12.08 1.17 .54 -.53 –2.74 perc. 90–100 2.01 1.34 15.3 .52 .67 -.65 –4.09 Spousal income percentile dummiesperc. 0 -.03 -.01 -.26 .01 -.02 .02 -.43 

perc. 0–10 -.11 -.07 -.62 -.03 -.04 .04 -.2 perc. 10–20 -.12 -.07 -.56 -.05 -.05 .05 -.43 perc. 20–30 -.1 -.09 -.22 -.09 -.01 .01 -.44 perc. 30–40 -.07 -.06 -.17 -.07 -.01 .02 -.36 perc. 40–50perc. 50–60 -.01 0 -.16 .01 -.01 .01 -.67 

perc. 60–70 .14 .09 .64 .08 .05 -.03 –1.68 

perc. 70–80 .1 .08 .09 .11 .02 -.01 –1.6 perc. 80–90 .36 .31 .56 .37 .05 -.04 -.89 perc. 90–100 .67 .61 .58 .76 .06 -.06 -.45 perc. Missing -.82 -.62 –3.86 -.55 -.2 .2 .22 Auto-enrollment .21 .03 8.28 -.19 .18 -.12 .9 Fixed EfectsYear x x x x x x x 

Occupation x x x x x x x 

County x x x x x x x 

EIN x x x x x x x

Notes: This table gives regression coefcients on race dummies (relative to White) forvarious measures. Regressions are of the fothe notes to Fig. 2. The dependent variable (yit) in column (1) is the sum of own and match contributions, as a proportion o

contribution rate. Column (3) studies extensive margin participation and yit is a dummy for plan participation. Column (4) studie

is own contribution rate in a sample only of those participating. In column (5) yit is the employer match contribution, as a pro

(6) investigates ‘money left on the table’–yit is the diference between the maximum match possible and match actually received, 

of salary. In column (7) yit is an indicator for taking a withdrawal of more than $1,000. The sample is those who have contribu

previous four years. Column (8) and (9) are frm level analyses. Column (8) studies plan generosity–yit is the maximum match that 

column (9), yit is an indicator for whether the frm ofers a DC plan. This is observed in the administrative data and so this analys

full ACS sample. We include indicators for fxed efects. Standard errors clustered by EIN are in parentheses. They are suppressed 
Table 4: Distribution of DC wealth at retirement by source and by race - Baseline model

Panel A: Quintiles (Q) & deciles (D) of the race-specifc income distribution

Q1 Q2 Q3 Q4 D9 D10

Wealth from employee White ($’000) 18.5 52.3 98.9 185.8 349.7 529.2

contributions Black ($’000) 5.5 14.9 27.5 51.1 95 262.3

Hispanic ($’000) 10.9 29.8 57.4 107.8 201.8 413.6

B-W Gap 70% 71.5% 72.2% 72.5% 72.8% 50.4%

H-W Gap 40.9% 43% 41.9% 42% 42.3% 21.8%

Wealth from employer White ($’000) 7.2 21.5 40.5 73.7 140.1 251.6

contributions Black ($’000) 2.9 7.5 14.3 26.4 44.8 119.5

Hispanic ($’000) 5 14.3 26.9 46.9 81.9 184.9

B-W Gap 59.6% 64.9% 64.7% 64.2% 68% 52.5%

H-W Gap 30.6% 33.7% 33.6% 36.4% 41.6% 26.5%

Wealth from tax White ($’000) 4.3 15.2 31.3 59.7 116.9 271.2

subsidies Black ($’000) 1.3 4.3 9.6 21 41.2 111.2

Hispanic ($’000) 2.6 8.8 19.4 38.7 66.3 174.1

B-W Gap 69.8% 71.5% 69.2% 64.7% 64.8% 59%

H-W Gap 40.4% 42.4% 38.1% 35.2% 43.3% 35.8%

Panel B: Quintiles (Q) & deciles (D) of the population income distribution

Q1 Q2 Q3 Q4 D9 D10

Wealth from employee White ($’000) 16.4 46 87.2 162.8 306.2 512.1

contributions Black ($’000) 8.6 24.9 49.2 101.2 229.8 416.3

Hispanic ($’000) 11.9 34 70.4 140.4 276.8 482

B-W Gap 47.7% 46% 43.6% 37.8% 25% 18.7%

H-W Gap 27.7% 26% 19.3% 13.8% 9.6% 5.9%

Wealth from employer White ($’000) 6.4 18.8 35.8 65 121.4 238.9

contributions Black ($’000) 4.4 12.9 25.4 47.8 102.3 193.4

Hispanic ($’000) 5.5 16.3 32.3 59 112 225.3

B-W Gap 30.5% 31.4% 29.3% 26.5% 15.7% 19%

H-W Gap 14.4% 13.5% 9.8% 9.3% 7.7% 5.7%

Wealth from tax White ($’000) 3.7 13.1 27.1 52.7 98.6 252

subsidies Black ($’000) 2.3 8.5 20 43.5 85.6 198.6

Hispanic ($’000) 2.9 10.4 24.2 49.1 90.2 224

B-W Gap 39.4% 35.1% 26.2% 17.4% 13.2% 21.2%

H-W Gap 23% 20.6% 10.6% 6.8% 8.5% 11.1%

Notes: This table shows simulated wealth at retirement fowing from each of employee contributions, employer

contributions, and the tax subsidies. For each component of wealth, we show means within lifetime earnings bins

by race. Also shown are the gaps between Black/Hispanic mean values with the corresponding White mean. The

two panels difer by how we form the lifetime earnings bins. In Panel A, we form lifetime earnings bins within

race. In Pane B, the bins represent population groups. In each case, lifetime earnings groups are divided into six

bins–the bottom four quintiles and the top two deciles.

51
Table 5: Change in DC wealth at retirement under the counterfactual tax and employer contribution

policy

Panel A: Quintiles (Q) & deciles (D) of the race-specifc income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +19.1 +25.9 +22.1 +10.1 -23.7 -72.2

DC Wealth ($’000) Black +16.3 +27.9 +35.4 +37 +32.1 -5.9

Hispanic +18.9 +27.5 +28.5 +21.9 +12.5 -39.8

Relative change in the B-W Gap -30.3% -25.1% -21.4% -14.9% -9.6% -5.4%

racial DC wealth gap H-W Gap -37.6% -26.1% -19.9% -12.2% -10.6% -5.1%

Relative change in the B-W Gap -2.8% -7.5% -9.9% -9.1% -8.5% -6.5%

racial consumption gap H-W Gap -5.9% -8.3% -9.1% -7.5% -9.7% -6.3%

Panel B: Quintiles (Q) & deciles (D) of the population income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +18.4 +25.6 +23.6 +12.9 -10.8 -69.1

DC Wealth ($’000) Black +20.3 +34.1 +37.3 +30.9 +10.1 -58.5

Hispanic +19.5 +28.2 +27.2 +17.8 +2.6 -64.3

Relative change in the B-W Gap -51.2% -45.1% -34.9% -24% -17.6% 1.6%

racial DC wealth gap H-W Gap -50.9% -36.1% -27% -19% -26.9% .2%

Relative change in the B-W Gap -18.3% -28.9% -25.9% -20.7% -18.2% -0.9%

racial consumption gap H-W Gap -62.4% -17.9% -16.8% -15.5% -26.6% -2.0%

Notes: This table illustrates the impact of our baseline counterfactual exercise on wealth on retirement and

consumption in retirement. This counterfactual exercise distributes the aggregate employer matches in each frm

so that all workers in that frm receive the same proportion of their earnings, and distributes the aggregate federal

tax expenditure so that all workers receive a contribution that is in proportion to their lifetime earnings. For each

race, and for diferent earnings bind, the table shows the absolute change in DC wealth induced by the reform.

Also shown are proportionate change in the Black-White and Hispanic-White wealth gaps. The two panels difer

by how we form the lifetime earnings bins. In Panel A, we form lifetime earnings bins within race. In Panel B,

the bins represent population groups. In each case, lifetime earnings groups are divided into six bins–the bottom

four quintiles and the top two deciles.

52
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57
A Variable and Sample Construction

A.1 Variables of interest

A.1.1 Data sources: ACS demographics, W-2, 1040, and 1099-R flings

We use Form W-2 data from 2005-2020 to measure earnings and deferred compensation. The W2 extracts available at the Census Bureau have information from Box 1 on taxable wages, tips,

and other compensation. Additionally, the W-2 extracts have a summary measure of deferred

compensation from Box 12 that primarily consists of employee tax-deferred contributions to DC

retirement plans. Specifcally, the IRS provides a deferred compensation variable that sums the

Box 12 values in codes D-H, but not the individual values by Box 12 code. These codes include

elective deferrals to plans under Box 12 codes D: 401(k), E: 403(b), F: 408(k)(6), G: 457(b), and

H: 501(c)(18)(D). The items in boxes E-F (403(b), 408(k), and 457(b) plans) are DC plans that

primarily difer from 401(k)s in which employers can provide them (such as nonprofts and local,

state, and federal governments). 501(c)(18)(D) contributions cover future payments under certain

Defned Beneft (DB) plans. From 2008 to 2018, an average of 51.6 million taxpayers made an

average of $255 billion of elective deferrals. The average share of those dollars by Box 12 Code

are D: 76 percent, E: 12 percent, F: 0.1 percent, G: 5.6 percent, and H: 0.02 percent. These boxes

cover 93.6 percent of all elective retirement contributions on W-2s over this period.33.

Crucially, since form W-2 is fled by frms, we are able to link workers to their employers through

the federal Employer Identifcation Number (EIN) of a worker’s employer. We assign each worker

to the EIN associated with the W-2 job in each tax year with the highest Box 1 earnings.

In addition, we use information from Form 1099-R flings (“Distributions From Pensions, Annuities, Retirement or Proft-Sharing Plans, IRAs, Insurance Contracts, etc.”). 1099-Rs contain

information on withdrawals from DC plans and payments from DB pensions. However, on the

1099-R extracts available to us, we only observe withdrawals and distributions in two categories:

1) gross distributions from employer-sponsored plans and 2) IRA withdrawals.34

33Source: IRS Statistics of Income Tax States for Individual Information Return Form W-2 Statistics, Table 7.A

at https://www.irs.gov/statistics/soi-tax-stats-individual-information-return-form-w2-statistics,

accessed 09/20/2023. 34The IRS also excludes distributions, such as direct rollovers, Section 1035 exchanges, and Roth conversions from

the 1099-R extract we use. For more information on the 1099-Rs, including separating DB and DC plans in the data,

see Bee and Mitchell (2017).

58
We also link individuals to 1040 tax flings, both contemporaneously (in the years we observe

their earnings) and for a subset of younger workers (under 42 in 2020), to the 1040 flings of their

parents when they were claimed as dependents. We include non-flers who do not receive W-2s.

From the contemporaneous 1040s of tax flers, we can observe marital status (from fling status)

and link individuals to their spouses through the PIK of the other fler on the tax return. We then

link the spouses to their W-2s to observe their earnings as well. Section A.1.3 provides a detailed

procedure.

To construct intergenerational linkages and observe parental resources (for the analysis in Section 5.1), we use the dependent information on 1040 tax returns, which is available in the years

1994, 1995, and from 1998 onwards. We create a dependent claiming history that identifes any

parent(s) that claimed each individual at all observed ages up to 18. Therefore, we can link individuals with their parents, conditional on the parents fling a 1040 in which they claim them as a

dependent at some point during their childhood.

We begin with the universe of individuals in the ACS who were born sometime from 1978-1992

and merge it with the universe of individuals from the dependent claiming history. We construct a

panel of these individuals, in which we observe the primary and secondary (when available) fler(s)

who claimed them as a dependent in a certain year. For our measure of parental income, we use the

parents that claimed the child at age 16 (or the nearest available age if the child was not claimed

on a tax return at 16). The birth cohorts are 1978-1992 because the lower bound allows us to

see parental income approximately when the individual is 16 during the 1994-2020 window, and

the higher bound ensures we observe at least one data point of the individual’s earnings, since we

restrict our overall sample to those between the ages of 25-59.5.

Afterwards, we merge on the earnings data for the primary and secondary (when available)

fler(s) for that year. The earnings data include the Adjusted Gross Income (AGI) reported in the

1040, and wage and deferred compensation as reported in the W-2. We use AGI while the child

was 16 as our measure of parental income because parents are more likely to be in the workforce

then (as opposed to when the child becomes a working adult and is as old as 42). Likewise, the

available W-2 records likely miss when the parents were in the workforce as they are not available

prior to 2005. We treat missing income information (i.e., for nonflers) as zero. Consequently, if

information is missing for both parents, we record parental income as zero, and if we have income

59
information for one but not the other, parental income matches the income of the one parent who

fles. If we have income information for both, parental income is simply the average of the two.

Lastly, we sort the individuals into decile-sized bins ranked by parental income and the observed

individual’s birth year, which we use for the basis of our analysis.

In addition, we construct a measure for parental awareness of DC contributions. From the

sample of individuals whom we can link to their parents when they are close to 16, we focus on the

subset for which at least one of their parents had a W-2 fled for them at some point during the

2005-2020 period. We create a dummy variable, which is turned on for those where at least one of

their parents contributed to a 401(k), i.e., had strictly positive deferred compensation, during the

window.

A.1.2 Outcome Variables

All variables in dollar terms are defated to base year 2017 using the Consumer Price Index provided

by the Bureau of Labor Statistics.35

Employee contributions This is deferred compensation reported in Box 12 of the W-2 tax

form. This amount generally corresponds to contributions to an employer-sponsored contribution

plan (such as a 401(k) plan).

Employee contribution rate The employee contribution rate is the percentage of salary, using

the ratio of the real employee contribution reported in Box 12 divided by the sum of the real

taxable wage reported in Box 1 of the W-2 and the real employee contribution. The formula

employee deferred compensation is . We additionally refer to this variable as “Own employee deferred compensation+employee W−2 wages

contrib. (% of inc.)” in output above.

Participation rate A dummy equal to one if the individual makes a positive contribution to a

retirement savings plan. This measures contributions on the extensive margin. We additionally

refer to this variable as “Positive contribution dummy (%)” in output above.

35https://www.bls.gov/cpi/research-series/r-cpi-u-rs-home.htm

60
Employee contribution rate (conditional on positive deferred compensation) The employee contribution rate conditional on positive deferred compensation. This measures contributions on the intensive margin. We additionally refer to this variable as “Own contribution (% of

income, contribution >0)” in output above.

Employee contribution plus employer matching contributions This is the sum of real

employee contributions and the imputed match contribution implied by the employer matching

formula collected from the employer’s Form 5500 fling. If an individual works more than 1 job,

we match the employer matching formula to the highest-salary job. We apply the match formula to the three highest-earning jobs separately. We then aggregate up the imputed contribution to generate the real employer match contribution. This is then added to the real employee

contribution for the combined employee and employer matching contributions. The formula is

employee deferred compensation+employer match . We additionally refer to this variable as “Employee employee deferred compensation+employee W−2 wages

plus employer matching contributions”, “Own plus match contribution (% of income)”, or “Employee contribution + employer match (% of income)” in output above.

Foregone employer matching (as a share of income) We measure the amount of potential

matching contributions as a fraction of income which are foregone by the worker by not exhausting

her employer’s matching contribution cap. This captures a fraction of foregone labor compensation

which is not received due to failure to fully exploit employer matching incentives. The formula

max employer match−employee deferred compensation is . We additionally refer to this variable as “Max employee deferred compensation+employee W−2 wages

match - own contribution (% of income)” in output above.

Early withdrawals We observe DC-plan withdrawals (and payments from pension plans) in

Form 1099-R flings from 1998-2020, which we treat as potential early withdrawals from DC plans.

We take early withdrawals from the year after individuals appear in the ACS survey. We apply

three key restrictions: 1) individuals must contribute more than $1000 in deferred compensation

in the four years prior to early withdrawal, 2) individuals must withdraw more than $1000 to

be classifed as an early withdrawal, and 3) individuals must be younger than 55 at the time

of early withdrawal. This should limit the number of false-positive early withdrawals that are

not from DC plans. We apply the frst and second restrictions as federal law allows employers

61
to automatically disburse individuals with under $1000 in deferred compensation upon separation.

The third restriction relates to the tax penalty for taking an early withdrawal—individuals 55 years

and older are allowed to take early withdrawals without incurring the tax penalty. We additionally

refer to this variable as “Positive withdrawal dummy (withdrawal >$1,000)” in output above.

Early withdrawal as a share of income Early withdrawal as a share of income is the real

early withdrawal amounts from retirement accounts reported in tax Form 1099-R divided by the

real income (the sum of real taxable wage reported in Box 1 of the W-2 and Box 12 of real deferred

compensation). The formula is

early withdrawal amount , employee deferred compensation+employee W−2 wages

winsorized at the 1% level after calculating the

share.

Employee share of contributions (individual-level) The employee share of contributions is

calculated diferently from the employee contribution rate. For each individual, we calculate

employee deferred compensation The employee contribution rate is calculated relative employee deferred compensation+employer match.

to total compensation; the employee share of contributions is the ratio of employee contributions

relative to total (employee plus employer) contributions. This is generally referred to as “employee

share of contributions.”

Employer share of contributions (individual-level) The employer share of contributions is

analogous to the employee share of contributions and difers from the employee match rate. The

formula is

employer match This is generally referred to as the “employer share of employee deferred compensation+employer match .

contributions.”

Firm-level employee share of contributions The frm-level employee share of contributions

difers from the employee share of contributions. Employee share of contributions are calculated at

the individual level. However, the frm-level employee share of contributions is the ratio of frm-level

aggregate employee match divided by the sum of frm-level aggregate employer match plus employee

f irm total employee deferred compensation deferred compensation. Hence, the formula is f irm total employee deferred compensation+f irm total employer match.

This is also defned as the average employee contribution as a percent of average income.

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Firm-level employer share of contributions The frm-level employer share of contributions is

analogous to the frm-level employee share of contributions. This is the ratio of frm-level aggregate

employer deferred compensation divided by the sum of frm-level aggregate employer match plus emf irm total employer match ployee deferred compensation. The formula is f irm total employee deferred compensation+f irm total employer match.

This is also defned as the average employer match as a percent of average income, as seen in Table

3.

A.1.3 Control Variables

Year The ACS provides the survey year.

Age bin We generate age from the ACS birth years and the ACS survey year. We bin people

into ages 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59.5.

Income bin Income is defned as the sum of total real Box 1 wages and Box 12 deferred compensation on W-2 flings. We generate income deciles from the total compensation distribution per

year and individual’s age, incorporating ACS weights.

Education We generate four educational categories from the ACS education variable—whether

a respondent has completed less than a high school degree, is a high school graduate, has some

college, a college degree, or a graduate degree.

Gender The ACS provides gender by male and female for the 2001-2019 surveys. We generate a

dummy for female.

Occupation The ACS provides several hundred occupational categories. The IPUMS 2010 crosswalk provides occupation codes that are consistent over time. We match the ACS occupation codes

with the consistent IPUMS 2010 codes, matching 12,260,000 out of 12,480,000 PIKs in our full

ACS sample.

County The ACS provides the county of residence.

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EIN W-2 flings provide EIN. We take the EIN for the highest-earning job if an individual worked

multiple jobs. Retirement plans are matched with the highest-earning EIN.

Tenure Tenure is constructed by matching all ACS individuals with their employers from 2005-

2020. Our W-2 flings report employers (EIN) in order of most wages earned. We take the earliest

known year for each individual-employer combination. We match the start year with the individual’s

frst EIN (employer from whom the individual earned the highest wages) during the ACS survey

year. Since our universe of W-2s begins in 2005 and our build begins in 2008, to avoid censoring

issues we classify tenure at the main employer into four main categories: 1) working less than one

year, 2) between 1-2 years, 3) between 2-3 years, and 4) at least 3 years.

Family structure We construct family structure from 1040 flings. The fve main groups include

single, no kids; single, with kids; dual, no kids; dual, with kids; and non-flers. We include non-flers

as individuals may receive W-2s but either forget or choose not to fle 1040s.

Spousal income Spousal income is linked using 1040 flings from the ACS observation year.

Spousal income is the sum of total real Box 1 wages and Box 12 deferred compensation from

W-2 flings. Spousal income bins are classifed by year and age using ACS weights into 12 main

indicators: i) 0 percentile (spouses who report $0 in earnings), ii) 10, 20, ..., 100 percentiles (spouses

for whom we have nonzero earnings), and iii) missing (individuals who are either single, non-flers,

or for whom we cannot match spousal income).

Auto-enrollment Auto-enrollment is taken from our universe of W-2 flings and matched frm

data. Our Form 5500 flings report whether a 401(k) plan ofers auto-enrollment in a given year. We

classify Form 5500 flings that do not report an auto-enrollment start date after 2005 as not ofering

auto-enrollment. Individuals who start at their main frm after frms enact an auto-enrollment

policy are classifed as having auto-enrollment. Individuals who start at their main frm before an

auto-enrollment policy begins or work at frms without auto-enrollment policies are classifed as not

having auto-enrollment. Due to censoring issues, individuals who are observed starting at a frm

in 2005 and work at frms where auto-enrollment begins either before or during 2005 are classifed

as unknown.

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Parental income Parental income is adjusted gross income for parents that we can link to ACS

respondents in 1040 flings. They are linked closest to when a person is claimed at age 16. We

generate parent income bins by year and child’s birth year (as a proxy for child age) from W-2s.

Note that we do not incorporate ACS weights in our calculation of parent income bins.

Parental awareness of 401(k) Parental 401(k) awareness is generated from positive deferred

compensation on fled parental W-2 flings.

A.1.4 Supplemental Variables

Health insurance The ACS provides health insurance status. Health insurance is pooled into

four main categories: 1) private, 2) public, 3) private and public, and 4) other or missing.

Housing share of income Housing costs as a share of household income are taken from W-2

flings and ACS reported household income. Housing costs are the sum of mortgage payments, rent,

and utilities as reported in the ACS. Some of the ACS reported household incomes are negative due

to debts. We sum individual and spousal income as an alternate household income. We take the

maximum household income from either the W-2 universe or the ACS to calculate housing costs.

Housing as a share of income is binned into quintiles by year and age and a “missing” category for

any individuals to whom we cannot match housing share of income.

Financial literacy We match the U.S. Department of Labor’s Occupational Information Network

Project (O*NET) with the ACS occupation codes for 2001-2009 and 2000-2019 using a bridge

provided by the FSU-UM Census Occupation Code-Occupational Information Network (O*NET)

Data Project. We are able to match 12,260,000 individuals (98.23%) in our sample. We generate

fnancial literacy for each occupation by averaging across mathematical, accounting, fnancial, and

economics knowledge and skills. Average fnancial literacy is binned into quintiles, with a “missing”

category for any observations to whom we cannot match fnancial literacy.

Maximum employer match Our Form 5500 hand-coded data provide the maximum percentage that employers match in contributions. Maximum employer matching is frst matched with

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individuals, then binned by year into quintiles. This represents the maximum employer match for

our sample of ACS-retirement-plan-matched employees.

Average frm match (% of average income) We calculate the average frm match (% of

average income) for each frm across our individuals. We frst match with individuals, then by year

into quintiles. This represents the average frm match rate as a percent of average income for our

sample of ACS-retirement-plan-matched employees.

A.1.5 Other Variables

Vesting status Vesting status is taken from our universe of W-2 flings and Form 5500 data.

Our retirement plan data provides information on the year in which employees are fully vested. We

generate indicators for being fully vested if an individual’s tenure meets or exceeds the fully vested

requirements.

DC Access We construct DC access from the universe of W-2 flings. We require at least 5% of

employees at a frm to have deferred compensation over the years 2005-2020.

A.2 Data Construction

This section covers our employee, employer, and merged employee-employer builds in more detail.

A.2.1 Employee data from the ACS

Our individual-level build begins with all ACS respondents from 2008-2017. Using protected identifcation keys (PIKs), respondents are matched with the universe of 1040, W-2, and 1099-R flings

from 2005-2020. The ACS provides age, education, gender, occupation, and county. 1040 and W-2

flings provide family structure, employer ID, tenure, spousal income, inter-generational linkages

(parental income and parental participation in DC plans), and direct contribution access (DC access). We further match individuals with frm-level data. From our initial build, we make several

restrictions. We require that i) individuals’ contributions to fall within federal tax limits for deferred compensation and ii) individuals earn more than a worker working at least 20 hours per

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week at the federal minimum wage. To ensure all individuals are within working age, we restrict

individuals to be between 25 to 59.5 years of age.

We restrict survey years from 2008-2017 due to censoring issues. While we have ACS respondents

from 2001-2019, our W-2 flings begin in 2005. Two key variables, job tenure and early withdrawals,

depend on having a panel of at least four years. Job tenure is categorized into < 1 year, 1 year,

2 years, and 3+ years. Early withdrawals condition on more than $1000 in nominal deferred

compensation over the four years prior to the early withdrawal. Both require W-2 Box 1 and

EIN information from the three years prior to appearing in the ACS survey. Including pre-2008

individuals would select for higher income employees who can contribute more in a given year and

would attenuate their tenure. We cap our observation years at 2017 due to our retirement planEIN crosswalk ending in 2017. This provides us with a repeated cross-sectional data set that is

representative of the United States from 2008-2017.

A.2.2 Employer data and sampling

The data set that we construct in this paper leverages the fact that that all retirement plans are

obligated to submit an annual regulatory form (Form 5500) to the federal government. For plans

with more than 100 participants, this form must include an attachment which contains a narrative

description of the retirement plan characteristics including, amongst many other details, the match

schedules (if any), vesting schedules (if any) and automatic features (if any). These descriptions

have been made publicly available by the Bureau of Labor, but in their original form (free-form

text) they are not amenable to empirical analysis.36 The data set that we use (described further

in Arnoud et al. (2021) on which this discussion is based, and in Choukhmane et al. (2023)) was

constructed from these fles for the largest 6,000 defned contribution plans, with their details

codifed in a consistent fashion.

The plan-level data that are constructed contain details on the full matching schedule, the

vesting schedule, and any automatic features (auto-enrollment or auto-escalation). These very

large frms cover a large number of employees - in 2017, 37 million employees were eligible to

contribute to one of these large plans and, collectively, they accounted for 55% of the population

36https://www.dol.gov/agencies/ebsa/about-ebsa/our-activities/public-disclosure/foia/

form-5500-datasets.

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of workers enrolled in private and non-proft sector defned contribution retirement plans. We link

these forms to the Census frm infrastructure via a multi-stage, fuzzy matching procedure which

incorporates information on numeric identifers such as EIN and telephone number as well as name

and address felds.

Public flings of Form 5500 plans provide information on retirement plans, including plan identifcation numbers, match formulas, and total number of participants. We begin with approximately 6,200 frms (92,500 unique retirement plan ID-year combinations), of varying company

and retirement plan participant sizes. We use the Hansen-Hurwitz estimator for single-stage cluster sampling. We match plan identifcation numbers with our employer identifcation numbers

(EIN). We are able to match around 5,000 plans and 35,500 plan-year combinations. We drop

frms that have diferent match formulas for diferent employees, that change match formulas

mid-year, or for whom we cannot fnd match formulas. Our fnal restriction is requiring internal consistency checks with our universe of W-2 flings. We require employer share of contributions

avg employee deferred compensation ( ) from Form 5500 flings to be within 15 percent- avg employee deferred compensation+avg employer match

age points of our estimates of employee share of contributions from the universe of W-2 flings.

This fnal restriction leaves us with about 3,800 unique plans and 21,500 plan-year combinations.

Finally, we match plans with our individual build, resulting in 3,800 unique plans and 21,000

plan-year combinations matched in our main matching sample.

To ensure a representative sample of frms in the United States, we use the Hansen-Hurwitz

estimator for single-stage cluster sampling. We collapse frm participation over all years in our

sample by frm plans. We then drop frms with less than 100 retirement plan participants. The

Nsample unconditional chance of being in the sample is We resize relative to the total number of US f irms .

average frm size. To account for large frms, we fag a certainty sample. We draw Nsample ≈ 3, 800

frms with replacement, allowing probability proportional to size. This implies the probability of

being drawn may be greater than 1 for larger frms. For all samples in our certainty samples, we

replace the probability with 1. Relative participant counts outside our certainty sample are rescaled

to [0, 1]. Finally, we apply the probability weights formula, 1−(1−p)n where p is the relative mean

and n is the number of frms not in the certainty sample, to produce our frm probability weights.

We calculate frm probability weights before restricting on match formulas and internal consistency checks. We do this for two main reasons: 1) frms were sampled without accounting for

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matching formula consistency, and 2) we apply a similar procedure to the ACS individual build.

This further allows us to match our frm sample with our individual sample.

A.2.3 Matched employee-employer data and sampling

We match the retirement plan build with individuals in the ACS individual-level build using federal

employer identifcation numbers (EIN). We match retirement plans by the frst listed EIN. EINs

are listed in descending order of total W-2 Box 1 wages. We match on the frst EIN and apply

the matching rules to any supplemental jobs. Out of 12,480,000 unique individuals in the ACS

individual-build, we are able to match 2,884,000 unique individuals with DC plans (accounting for

all individual- and frm-build restrictions).

The ACS person weights refect the US population. Firm weights refect the population of frm

employees for our 6000 sampled frms. However, frm weights do not cover the full ACS sample.

Our analysis, which uses individual-level observations, needs to refect the US population. Thus,

we calculate the combined probability of a person being sampled in the ACS and in the frms.

Our matched build can be considered a two-stage clustered sample. First, we sample 6000 frms

within the US, proportional to size. Then, from the representative sample of these frms, we sample

the US employee population. Each individual’s probability of appearing in our matched build is the

joint probability of being in a sampled frm and a sampled employee. Thus, the matched individual’s

probability weight is the product of the ACS probability weight with the frm probability weight.

Given that the ACS individual weight is a sample weight, we multiply the inverse of the ACS

sample weight by the frm probability weight. This is the matched individual probability weight;

the inverse is the matched individual analytic weight.

When constructing our matched build, defned as our “matching sample,” we begin with separate employee and employer builds. Our analysis uses fourteen key control variables in our main

regressions: race, year, age, income, education, gender, county, occupation, EIN, family structure,

spousal income, auto-enrollment, parent income, and parent awareness of (participation in) a DC

plan. These are listed under A.1.3. Supplemental analysis on the relationship between race with

wealth and fnancial literacy uses health insurance, housing as a share of income (in quintiles),

fnancial literacy (in quintiles), maximum employer match (in quintiles), and average employer

match (in quintiles). These are listed under A.1.4.

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The variables are generated from the employee, employer, and combined builds. Multiple variables depend on ranking individuals or frms relative to others in the employee or employer builds.

This afects when we apply restrictions to the sample and what weights we use to generate ranks.

Thus, we also preserve or generate the initial weights for both employee and employer builds, respectively. We calculate probability weights for our employer sample before applying our 15 percentage

point restrictions on the share of employer contributions, as the weights must refect the population

of U.S. frms.

This further applies to the variables we construct. After applying earnings and age restrictions,

as explained in A.2.1, we generate income deciles by year and age using the ACS sample weights.

This refects all people in the ACS who match our sample requirements. We then match the

employee data with the restricted version of our employer data by their frst EIN and year. After

matching the employee data, we then restrict on years 2008-2017. This provides a repeated crosssection.

In parallel, we match each ACS individual with their spouse’s income in the same year and

generate intergenerational linkages with parents. Spousal income is defned as the sum of real Box

1 wage and deferred compensation across all the spouse’s jobs. For parent income, we generate

rankings for real adjusted gross income (AGI) by year by the ACS individual’s birth year without

incorporating weights. We merge spousal income, parent income (real AGI), and parent income

deciles to the employee data using PIK. We then generate spousal income deciles by year and

the ACS individual’s age, using ACS weights. All income deciles are defned relative to the ACS

individual’s age as we observe the outcomes for the ACS individual.

Our supplemental variables that require rankings use both ACS weights and combined weights.

Housing share of income is defned relative to the full ACS sample with ACS weights, by year

and age, as we observe it for the full ACS sample. Financial literacy, which is modeled for each

occupation and matched via occupation codes, is similarly weighted by year, using ACS weights.

This is because the ranking needs to refect the ACS sample. However, employer generosity (maximum and average employer matching) must refect the population of both frms and individuals

and be accurate. Hence, employer generosity variables are ranked using the combined weights after

restricting for inaccuracies in match formulas.

We apply two fnal restrictions to compensation and control variables before running regressions.

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For compensation, we require the nominal sum of Box 1 wages and deferred compensation to be

greater than $8000 and require wages to be strictly greater than $0. This eliminates people who

have zero wages but have deferred compensation (likely people with high wealth who are exploiting

employer matches). We require control variables to be nonmissing (except for parental awareness

of DC plans) to ensure consistency across all regressions. Table D.2 shows the racial and age

composition for our matching sample as we restrict on nonmissing control variables.

A.3 Samples

Our analysis covers eight main samples, taken from the individual, frm, and combined frm builds.

Our main samples are our matching sample, parent-matching sample, and full sample. Supplemental samples include our vesting sample and defned contribution (DC) samples. Our vesting sample

is the subset of individuals from the matching sample whom we know are fully vested. Our DC

sample is the subset of all ACS individuals from the full sample who have DC plan access. We

construct access to DC plans from the universe of W-2s. Any frm where at least half of employees

from 2005-2020 report deferred compensation is defned as providing DC plan access. We split our

DC access samples into the raw DC access sample and a sample that has more than 100 employees.

The restricted version of the DC access sample is comparable to our matching sample. Appendix

A.4 discusses our sample’s representativeness of the U.S. population.

A.3.1 Samples from the combined individual and frm builds

Matching sample This is our main sample for analysis. It contains all individuals in the ACS for

whom we match Form 5500 flings that meet our match formula and internal consistency restrictions.

Individuals are required to have an auto-enrollment status. This sample uses combined ACS and

frm-level analytic weights. The total number of unique individuals (after dropping missing control

variables) is 1,722,000.

Parent-matching sample This is our secondary sample. It contains all individuals in the matching sample that are born after 1978 and to whom we can match parent income. We require nonmissing parent income and auto-enrollment statuses. This sample uses combined ACS and frm-level

analytic weights. The total number of unique individuals (after dropping missing control variables)

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is 447,500.

Vesting sample The vesting sample contains all individuals in the matching sample who are fully

vested in their ACS year. We require auto-enrollment status. This sample uses combined ACS and

frm-level analytic weights. The total number of unique individuals (after dropping missing control

variables) is 1,243,000.

A.3.2 Samples from the individual build

Full sample This is the basis for all samples. It contains all individuals in the ACS. This sample

uses ACS analytic weights. The total number of unique individuals (after dropping missing control

variables) is 12,140,000.

Parent sample This is a supplemental sample, included for representativeness. It is the subset

of individuals in the ACS who are born after 1978 and to whom we can match parent income. This

sample uses ACS weights. The total number of unique individuals (after dropping missing control

variables) is 3,154,000.

DC access sample This is a supplemental sample. It is the subset of individuals in the ACS who

have DC access. This sample uses ACS analytic weights. The total number of unique individuals

(after dropping missing control variables) is 9,595,000.

Restricted DC access sample This is a supplemental sample. It is the subset of individuals

in the ACS who have DC access and more than 100 employees. This sample uses ACS analytic

weights and is comparable to our matching sample. The total number of unique individuals (after

dropping missing control variables) is 2,699,000.

A.3.3 Samples from the frm build

Matched Form 5500-W-2 sample This is the sample of Form 5500 frms for whom we can

match employer ID numbers from our universe of W-2 flings. To ensure consistency between our

collected retirement plan data and our W-2 flings, we require each frm’s share of contributions

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to deferred compensation from the Form 5500 data to be within 15 percentage points of our W-2-

imputed frm share of contributions. This ensures that our imputed employer matches are accurate

and consistent. Figure C.31 shows our W-2 imputations and reported Form 5500 data have a

correlation of .896 and R2 of 0.96.

A.4 Data representativeness

This section addresses concerns with the representativeness of our results. The frst concern, in

relation to our retirement plan data, is whether the matching sample represents the employed

population of the U.S. that has access to deferred compensation plans. The second concern, related

to sample restrictions, is whether dropping individuals with missing demographics skews the racial

and age compositions of our samples.

A.4.1 Representativeness across samples

We frst address whether matching ACS individuals with our retirement-plan data biases our results,

given that our matching sample is efectively a two-stage clustered sample. Table D.1 provides the

distribution of key retirement savings outcomes. Appendix A.1.2 provides variable defnitions.

The three key comparison samples are the full sample of ACS employees, the restricted DC

access sample, and the matching sample that merges the full individual and retirement plan builds.

All three samples show the distribution conditional on nonmissing individual and household demographics. We compare the restricted DC access sample with the full and matching samples, as the

matching sample samples from the largest 6000 frms in the US; public flings are only required

for frms with over 100 employees. The restricted DC access sample carries the same 100-employee

restriction. We thus compare the DC access and matching sample, as the DC access sample is the

subset of all ACS individuals at large frms with access to retirement plans; the matching sample

is the subset of ACS individuals to whom we match large frms and retirement plans.

As Table D.1 shows, employees in our matching sample have an average real compensation of

$72,810 while employees in our restricted DC access sample have an average real wage of $74,330.

Median real compensation is respectively $49,260 and $51,240, while the 90th percentile of real

compensation is respectively $133,500 and $135,600. All values are within $2,000 of each other.

Average deferred compensation is respectively $3,351 and $3,495. Participation rates are respec73
tively 65.23% and 66.29%. Early withdrawal rates (conditional on > $1,000 in withdrawals) are

respectively 13.5% and 12.96%. Even household demographics are similar—average real spousal

income is, respectively, $9,842 and $9,931.

Since our analysis focuses on employees who have access to deferred compensation plans, we

expect real compensation, real deferred compensation rates, and participation to be signifcantly

higher than our full sample. The fact that our DC access and matching samples are so similar

while displaying expected gaps relative to our full sample indicate that our matching sample is

representative of the US labor force working at large frms.

A.4.2 Representativeness in racial composition

Another concern is representativeness in racial and age composition as we control for individual and

household demographics. Table D.2 shows how the composition of the full individual sample, the

restricted DC access sample, the main matching sample, and the parent-matching sample change

by race as we restrict for individual and household demographics. The sample composition by

race is similar across race and age for both the matching and parent-matching sample. Sample

compositions by race are similar across race for all samples, even as we restrict for nonmissing

individual and household demographics.

A.5 Patterns of heterogeneity

In this subsection, we discuss in further detail the heterogeneity results referenced in Section 4.4.

Education. Racial gaps between Black (Hispanic) workers and White workers increase with

education from 0.62 p.p. (0.01 p.p.) lower contributions for high-school graduates to 1.5 p.p. (0.80

p.p.) lower contribution rates for graduate-degree holders. Please see Figure C.10.

Gender. White women contribute 0.58% more than White men with similar characteristics

and, consistent with the broad pattern in Figure 4, the Black-White savings gap is larger for women

(-1.1%) than for men (-0.64%). For Hispanic workers, gaps are similar across genders. Please see

Figure C.11.

Tenure. White workers with three or more years of tenure save nearly 2.0 p.p. more than White

workers in their frst year of tenure. The Black–White (Hispanic–White) contribution gap increases

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from -0.34 p.p. (-0.16 p.p.) for workers in their frst year of tenure to -1.2 p.p. (-0.55 p.p.) for

those with at least three years of tenure. Please see Figure C.12.

Financial Literacy: We create a proxy for fnancial literacy using data from O*NET on the

level of knowledge in mathematics, accounting, economics, and fnance across occupation codes

(see Appendix A.1.3 for details). Retirement contribution rates are increasing in our measure

of fnancial literacy and so are the racial contribution gaps. The Black-White (Hispanic-White)

savings gap increases from -0.69 p.p. (-0.56 p.p.) in the bottom quintile to -1.3 p.p. (-0.66 p.p.) in

the top quintile of our fnancial literacy measure. Please see Figure C.18.

Employer Generosity. We defne employer matching generosity as the maximum employer match

as a percentage of salary that one could receive by fully exploiting the matching formula. Across all

racial groups, contribution rates are increasing in our measure of employer generosity: for instance,

White workers with an employer in the top quintile of matching generosity contribute 2.2 p.p.

more than those with employers in the bottom quintile. Racial contribution gaps also grow with

matching generosity, the Black–White (Hispanic–White) gap for employees increases from -0.42

p.p. (-0.20 p.p.) in the bottom quintile to -1.3 p.p. (-0.72 p.p.) in the top quintile. Please see

Figure C.17.

Health Insurance. Contribution rates are uniformly low among those with no access or only

public access to health insurance, while racial gaps are larger for workers covered by private health

insurance: Black (Hispanic) workers with a private health care plan contribute 1.1 p.p. (0.50 p.p.)

less than their White counterparts. Please see Figure C.16.

B Microsimulation Model

B.1 Overview

Our analysis is in two parts. The frst confronts the fact that, to understand the implications of

diferential saving and match patterns over the whole lifecycle, we need full lifecycles of data on

retirement plan access and DC plan withdrawals in the population. However, we have a maximum

of 13 years of observations per individual. We use these partial lifecycles and a simple hot deck

imputation strategy to construct panels of synthetic lifecycles, described in Section B.2.

The second is a development of a microsimulation model, described in Section B.4, which has

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three objectives. The frst objective is to use the data on the fows that we observe (earnings;

contributions to, and withdrawals from, DC accounts) and a model of the economic and policy

environment to generate simulated data for objects that we do not directly observe: the stock of resources for retirement, Social Security entitlements in retirement, and the trajectory of withdrawals

from retirement accounts.

The second objective is to evaluate what would be the diferences in wealth at retirement if the

individual saved in a taxable brokerage account rather than the tax-advantaged defned contribution

account. This allows us to build a measure of the value of tax expenditure at the individual level

and to measure its distributional incidence.

The third is to evaluate what would be the distributional impact of changes to retirement

savings institutions in the US. We consider three counterfactual policies. In the frst, we break

the link between saving and remuneration by calculating the counterfactual employer contribution

for each frm which, if paid to every employee in proportion to their earnings, would cost the

same to the employer as their current matching contributions. We evaluate what would be the

distributional impact of moving from the status quo to a system where all employees received that

contribution. The second counterfactual setting that we study breaks the link between government

contributions to retirement accounts and savings choices by redistributing the tax expenditure so

that it is proportional to lifetime income, once again regardless of the taxpayer’s retirement savings

choice. The third combines both reforms.

B.2 Modeled Lifetime Paths of Earnings, Retirement Plans, and Withdrawals

In order to estimate our microsimulation model and evaluate the distribution of tax and wealth

impacts of Defned Contribution (DC) retirement plans, we need to capture the distribution of paths

of earnings, retirement plan access, and DC plan withdrawals in the population. However, our data

is limited in several respects. First, for many workers entering now close to retirement, DC plans

were not in wide use at the onset of the working career. Furthermore, Form W-2s, our data source

for individual wage and salary earnings and contributions to DC plans, are only available starting

in 2005. Our information on plan characteristics from the Form 5500 is only available through

2017. That leaves us with up to 13 years in the period from 2005 to 2017 to simultaneously observe

earnings and DC contributions from W-2s, plan characteristics and matching from the Form 5500s,

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and withdrawals on Form 1099-Rs. Our aim is to convert these shorter windows of information

into plausible lifetime trajectories spanning working ages from 25 to 65.

To construct the plausible lifetime trajectories, we use a simple hot deck imputation strategy.

We partition ages starting at age 25 into overlapping bins of 4 years (25-28, 27-30, 29-32..., 63-66).

For a given age bin b, we observe their ages at t, t + 1, t + 2, and t + 3. For individuals in bin

b+1, we observe their ages in t+2, t+3, t+4, and t+5. We use the information from individuals

in bin b + 1 to impute earnings, DC plan access, contributions, characteristics, and withdrawals to

individuals in bin b. We do so by matching individuals in bin b to similar individuals in b + 1 using

the information observed at the overlapping ages (t + 2 and t + 3) and appending the information

from the later non-overlapping age (t + 4 and t + 5) to bin b individuals.

As an example, suppose Person A had earnings increasing at $1,000 a year from $25,000 at

25 to $28,000 at 28. This person’s frm did not ofer a 401(k) plan and thus the person made no

contributions to or withdrawals from a plan. Now suppose Person B had earnings increasing from

$26,500 at 27 to $1,500 a year to $31,500 at 30, and likewise had no access to a DC plan. Persons

A and B had similar earnings and plan access in the observed overlapping ages - yA,27 = 27, 000

and yA,28 = 28, 000 compared to yB,27 = 26, 500 and yB,28 = 28, 000. As these workers had similar

observable characteristics in the overlapping years, we impute to person A the information from

person B at ages 29 and 30 to lengthen the number of years of earnings for Person A to cover ages

25 to 30. We can then repeat this process by imputing earnings for person A at ages 31 and 32

using individuals in the next age bin covering ages 29 to 32. For a visual representation of how

this would work, refer to Figure C.32. By repeating this process, we construct lifetime histories of

earnings, DC plan access, and employee and employer plan contributions.

For early retirement withdrawals of working-age individuals, we do an additional imputation

step to impute withdrawals relative to contributions in the prior years to better align withdrawal

amounts to contributions. This helps reduce the number of cases in the model where the withdrawals exceed recent contributions substantially. However, because we do not observe returns or

contributions in the distant past, there will be many cases in the data where withdrawals exceed

recent contributions, even with contributions observed over a longer time horizon than we use in

the imputation.

77
B.2.1 Imputing DC Plan Access and Matching Rules for All Firms

A necessary input into the hot deck model described in Section B.2 is information on frm matching

rules and DC plan availability for all frms. However, our data set of frm matching schedules from

publicly available Form 5500 flings covers a subset of frms, including the largest 4,200 frms and

a random sample of smaller frms. We use this data to impute DC access and plan matching rules

to all frms. First, because we are interested in simulating lifetime trajectories for workers under

the current system, we restrict to the plan characteristics in the most recent year for each frm

linked to the form 5500. For all frms, we summarize the distribution of deferred contributions

across their workers. As an example, suppose in a given frm, 90 percent of workers have 0 deferred

compensation and 10 percent contribute exactly 3 percent of their earnings to a DC plan. We

summarize the share of workers in each frm that contribute in 10 bins between 0 and 10 percent

of their earnings to DC plans with separate bins for 0 contribution and > 10 percent, i.e. bins of

0, (0-1) percent, [1-2) percent, [2-3) percent, etc. We use kmeans clustering to separate frms into

10 distinct groups based on the distribution of worker deferred contributions in these bins. Finally,

we impute DC plan access and frm match schedules to the frms without available Form 5500 data

using a hot deck matching on the worker DC contribution clusters, frm size, and average earnings

for workers at a frm. This means that if two frms, A and B, have a mass of contributions at

around 3 percent of earnings, they are likely to be in the same worker contribution cluster. If frm

A has plan details available from Form 5500, with matching contributions of 100 percent up to 3

percent of earnings and 0 percent thereafter. Firm A would then be a likely donor of its match

schedule to frm B, which does not have available Form 5500-based plan information.

B.3 Summary and Output

The result of this procedure is a simulated data set for individuals i aged from t ∈ {25, . . . , 90},

where 90 is assumed to be the last age of life and in which mortality is deterministic.

Variables that we observe (with the associated notation given for objects that will feature in

the treatment below) are:

• Demographic measures: age (t) and race,

• Compensation measures: earnings (e) and contributions the employee elects to make to their

78
employer-sponsored defned contribution account (dcee),

• Whether the individual works in a frm ofering a DC plan and, if so, the match schedule

(dcf (.)), and

• Withdrawals from DC accounts before retirement (w).

B.4 Model Description

B.4.1 Savings Vehicles

Central to the exercise is to compare outcomes under the status quo, in which the deferred compensation we observe is paid into a tax-deferred defned contribution account, with a counterfactual

setting–in which accounts with that tax treatment are not available, and those same contributions

are instead paid into a (taxable) brokerage account. We will evaluate each individual’s savings

trajectory under two systems of taxation, indexed by j ∈ {DC, BK}. The superscript j = DC

indicates that the individual is saving in a tax-deferred 401(k) account, and j = BK indicates that

they are saving in a brokerage account. Savings in the tax-deferred (DC) account beneft from

the fact that income tax is deferred until the funds are withdrawn and that investment returns

accumulate free from income and capital gains taxes. Saving in the brokerage account is made out

of taxed income and has returns that are subject to tax, but withdrawals are made free of income

tax.

Below we refer to the ‘DC saver’ and the ‘brokerage saver’ as shorthand for the saver in a setting

where DC accounts are available and not, respectively.

B.4.2 Observable: Earnings, Contributions and Withdrawals

Employees receive compensation that can be divided into earnings ei,t and deferred compensation

dcee Employees may also receive an employer match, which is a frm-varying function indexed i,t.

by f: f dc (eei,t). In the below, for notational ease, we suppress the dependence of the employer er

contribution on the employee contribution and denote the employer contribution made on behalf

of individual i at age t as dcer

i,t.

Withdrawals j from retirement accounts are denoted by wi,t, with j indexing the nature of the

account (DC or brokerage). We observe withdrawals made by our agents up to the age of 65. These

79
observed withdrawals in the data are withdrawals from the DC account and are recorded before

the deduction of income tax.

B.4.3 Wealth

Wealth j balance at beginning-of-period is given by Bi,t and is initialized to zero at age 25. Net fows

j into the wealth vehicle are denoted by fi,t:

j c,j j = dcee f i,t + dcer − w (4) i,t i,t − τi,t i,t,

where dcee and dcer are, respectively, deferred compensation by the employer and the employermatch contributions. There are two deductions from these gross fows. The frst (τ c,j ) are taxes

on these contributions. This object will be defned in detail below, but, in brief, note that dcee

and dcer are measured as gross-of-tax. For the DC saver, no income tax is owed on these and so

τi,t

c,DC = 0. For the brokerage saver, income tax must be paid before contributions are made. The

j second deduction is wi,t, which are withdrawals from the account. These are observed before the

age of 65; in Section X, we propose a model of withdrawals which flls these in for after the age of

65.

The law of motion for wealth balance is given by:

j j j r,j B = (B i,t)(1 + ρt) − τ , (5) i,t+1 i,t + f t

where ρt is a rate of return that depends on age (with the time-dependence due to the changing

r,j mix of assets in the portfolio), and τ represents the taxes paid on that return in that period. This t

will be zero for the DC saver, and we will describe it for the brokerage saver in the next subsection.

B.4.4 Investment Returns

Two comments are needed on the investment returns. The frst is that they vary with age. Each

age t is associated with a portfolio composition between equities, bonds, and bills, with shares given

k b m by st , st, and s . During working years, these shares are interpolated from Fidelity target date t

80
funds.37 In retirement, we assume exclusive investment in bonds. The age profle of investment

composition is shown in Figure C.33a, and the associated age profle of real rate of return is shown

in Figure C.33b. Real rates of return for these asset types (ρk, ρb, and ρm, respectively) are taken

from Jord`a et al. (2019). The combination of these assumptions yields age-specifc rates of return

ρt:

k b m ρt = ρk · st + ρb · st + ρm · st . (6)

The second comment on returns is the division of returns into unrealized capital gains, distributions taxed as long-term capital gains, and returns taxed as income (e.g. ordinary dividend

income).38 Distinguishing between the nature of the return will be important in our treatment of

the taxation of the return for the brokerage saver. The share of returns represented by each of

these is given respectively by χg, χk, and χi

, which sum to 1. The dollar fows associated with each

of these three types of return are given below:

  g,j j j r = B · χg · ρt, (7) i,t i,t + fi,t

  k,j j j r = B + f · χk · ρt, (8) i,t i,t i,t

  i,j j j r = B · χi · ρt. (9) i,t i,t + fi,t

Accumulation and withdrawal of untaxed capital gains When individuals withdraw funds

from their accounts, they will need to realize some, previously unrealized, capital gains. This will

have tax implications for the brokerage saver, and it will be necessary, therefore, for us to keep

track of that part of the account balance formed of unrealized capital gains. We divide the account

j p,j g,j balance B into principal B and (thus far untaxed) capital gains: B We defne the latter i,t i,t i,t .

37We used asset allocations of the Fidelity Freedom Funds ranging from retirement years 2005 to 2065 between

equities, bonds, and short-term debt as of year-end 2022. Distance to retirement is thus the target date minus 2023.

A one-dimensional Akima interpolator was used to calculate shares between observed age distances to retirement.

Our shares may be compared to Fidelity’s own description of their glide path, such as in Fidelity (2023). 38The second component – distributions taxed as long-term capital gains – do not represent returns which are realized for a withdrawal. Rather they are the gains, realized as mutual fund managers trade assets, which are passed on

to investors. See Fidelity’s description of these distribution types at https://www.fidelity.com/learning-center/

investment-products/mutual-funds/taxes.

81
recursively as:

g,j g,j g,j k,j B = B + r − w (10) i,t+1 i,t i,t i,t ,

g,j where Bg,j is the cash value of the stock of unrealized capital gains in the account balance, ri,t are

k,j additional untaxed gains attained in year t, and wi,t are gains actually realized when a withdrawal

is made.

Whenever j a withdrawal (wi,t) is made, we assume that the withdrawal comprises untaxed capital

k,j p,j gains w and principal w in proportions that equal their share of the stock of wealth. That is, i,t i,t

the share of any withdrawal by the brokerage saver which is subject to capital gains tax is equal

to the share of unrealized capital gains in wealth:

k,j g,j wi,t Bi,t = . (11) j j w B i,t i,t

B.4.5 Social Security Income

We assume all individuals stop earning when they turn 66 and that they begin claiming Social

Security benefts. Central to the determination of Social Security benefts is ‘Average Indexed

Monthly Earnings’ (aime) which is the average of the best 35 years of total compensation:39

 max  X min(e+dc ) ee 1 i,t, e aimei = (12) 35 12

k∈best 35

Monthly Social Security benefts are equal to 90% of aime up to the frst ‘bend point’ ($895 in

2018), 32% of any aime above the frst bend point and below the second point ($5,397 in 2018)

and 15% of any aime above the second bend point.

B.4.6 Withdrawals

We distinguish between ‘early withdrawals’ and ‘retirement withdrawals.’ The former are those

taken before the age of 65, and we observe these in our data. The latter are after the age of 65, are

not observed, and so must be modeled.

39Recall from Section X that we are assuming an environment with zero infation and zero real wage growth, and

so there is no indexation of the earnings in equation (12) where the measure of earnings that enters the calculation

is capped at a value given by emax.

82
Early withdrawals We defne early withdrawals as all withdrawals before the age of 65.40 The

measure that we observe in our data (denoted by wDC) is that before income taxation, which must i,t

be paid on all withdrawals from DC accounts – for the equivalent withdrawal which will be applied

to the brokerage saver (denoted by wBK

i,t ), we calculate the after-tax quantity retained by the DC

saver.

One complication arises when the early withdrawal that we see would lead to the brokerage

saver having a negative balance. This occurs in only a small share of cases (14.2%). In these cases,

we adjust the measure we see in our data to be the largest number that avoids the brokerage saver

going negative. This adjustment reduces the withdrawal by approximately 17.6% for that share of

savers.

Retirement withdrawals Individuals retire at the beginning of age 66 with balance in their

j account of Bi,66. They employ a consumption rule each year to determine how much to withdraw

each period t. We set this rule such that consumption for the DC saver is constant each period.

In particular, the withdrawal each period is equal to:

j 1 − α j w = B (13) t 1 − α90−t+1 i,t.

1 41 where α = is defned using the return on bonds ρb. This rule keeps pre-tax withdrawals (1+ρb)

constant. We assume that individuals consume their withdrawal, net of taxes:

j j w,j c = w − τ , (14) t t i,t

where τi,t

w,j are taxes incurred by withdrawing money from account j and will be defned in the next

section. Constant (pre-tax) withdrawals keep post-tax consumption constant for the DC saver (as

income does not change in retirement) and close to constant for the brokerage saver (for whom

small changes in average tax rates will occur as wealth is decumulated).

40Not all of these will be subject to an early withdrawal penalty, which only applies to some withdrawals made

before the age of 59.5. We return to this when we discuss the taxation of withdrawals in Section B.6.1. 41This consumption rule is that which would be obtained from a cake-eating problem in which life-span is deterministic and in which the discount rate is set equal to the interest rate.

83
B.5 Summary

The data that we construct, together with the features outlined above, yield two parallel data sets:

one representing the earnings, savings, account balance, and withdrawals of the DC saver, and one

representing the same objects for the brokerage saver. We represent these by the following:

( ) ( )

i,t, dcer , wDC}90 DC}90 {ei,t, dcee i,t, BBK BK}90 BK}90 {ei,t, dcee i,t, Bi,t

DC

i,t t=25; {ci,t t=66 i,t, dcer i,t , wi,t t=25; {ci,t t=66

where the frst three objects are common across the two tuples, but the balances, withdrawals and

consumption profles difer, due exclusively to the diferent forms of taxation the two savers face.

B.6 Taxation

The previous section concludes by noting our data and microsimulation model yield, for each

individual in our data, two trajectories of wealth accumulation and decumulation – one if they save

in a DC account and one if they saved the same quantities in a taxable brokerage account. The

DC saver will have, due to their access to preferential taxation, higher consumption in retirement.

This section shows how we measure these diferences in tax treatment across the life cycle.

At the most general level, we take the fow of income, saving and return that we measure and

use TAXSIM to evaluate the taxes. This allows us to construct our summary measure of wealth at

retirement: which is the present discounted value of consumption facilitated by accumulated wealth

at retirement. This section provides, for the interested reader, full details on how we measure that.

B.6.1 Decomposing the overall tax burden into components

We denote our modelled tax function, which distinguishes between the three forms of income that

agents in our model earn, as T(N, K, S). N denotes infows taxed according to the income tax

schedule (e.g., wage income during working life and 401(k) distributions in retirement); K denotes

income taxed as long-term capital gains; and S denotes Social Security benefts.42

42Note that efective tax rates in retirement are usually very low (see Chen and Munnell (2020)), due in part to

the favorable tax treatment of Social Security benefts, on which many households pay no tax at all (see also Joint

Committee on Taxation (2019)).

84




We wish to decompose the total tax burden (denoted by T) into shares that can be ascribed

to earnings (τ e), contributions to retirement accounts (τ c), investment returns (τ r), taxes owed on

Social Security benefts (τ s), and withdrawals from retirement accounts (τ w). Earnings, contributions, returns and withdrawals, of course, interact in a non-linear (and quite complex) manner to

generate overall tax liability. This means that there is no unique decomposition such that the total

tax burden T can written as the sum of these components. This section explains how we obtain

one such decomposition.

We use rules for tax year 2018 according to NBER’s TAXSIM 32 tool to calculate federal income

tax owed by each simulated individual.43

e,j Taxation of Earnings We frst defne taxes on earnings (τi,t ) as follows:



 � 

e,j T ei,t, 0, 0 if t < 66 for j = DC, BK;

τi,t = (15) 0 if t ≥ 66 for j = DC, BK.

This does not difer by the type of saver, and the second equality follows from our assumption of

no earnings from the age of 66.

Taxation of Social Security We defne the tax on Social Security as the tax that would be

paid if an agent had their Social Security income and no other income as:

�  τi,t

ss,j = T 0, 0, ssi,t if t ≥ 66 and j = DC, BK, (16)

which also does not difer by type of saver.44

Taxation of Contributions Our defnition of taxable earnings excluded that part of earnings

which was saved for retirement: an employee’s choice of deferred compensation and any associated

43The N, K, and S income sources are fed into the pwages, ltcg, and gssi felds in TAXSIM, respectively. We assume

that all individuals take the standard deduction and do not claim any other credits or deductions. See Feenberg and

Coutts (1993) for a description of the TAXSIM model. 44As it happens τ ss,j will be zero for everyone in our sample – an individual with maximum Social Security income i,t

and no other income will not face any income tax. We retain the variable for completeness and because its exclusion

may obscure some features of the exposition.

85








employer match dcee For the DC saver, income which is contributed to the account is i,t + dcer

i,t.

untaxed, so τ c,DC = 0. For the brokerage saver, the tax we ascribe to contributions is equal to the i,t

additional income tax the saver would have paid by taking compensation as earnings. This is given

by the second line in:



 c,j 0 for j = DC,

τ = (17) i,t   

e,BK T ei,t + dcee − τ for j = BK. i,t + dcer

i,t i,t , 0, 0

where the positive term in the second line gives the income tax owed from earnings that include

deferred compensation and the negative term nets of that tax already ascribed to earnings, defned

in equation (15).

As we assume that there are neither earnings nor contributions after retirement age, for both

c,j savers we obtain that τ = 0 for all t ≥ 66. i,t

Taxation of withdrawals The taxation of withdrawals depends on whether they are ‘early

withdrawals’ (those up to the age of 65) or ‘retirement withdrawals’ (from the age of 65). Taking

the former case frst, the DC saver must pay income tax and may face a tax penalty. This penalty is

incurred at a rate pt, which is equal to 10% for non-exempt withdrawals before the age of 59.5 and

is equal to 0 for withdrawals after the age of 65. The frst line of equation (18) gives this quantity,

the positive terms are respectively the regular income tax on earnings and DC withdrawals and the

tax penalty; the negative term subtracts taxes already ascribed to earnings.

The brokerage saver need not pay income tax on withdrawals but must pay capital gains taxes

on gains realized to withdraw their funds (wk,BK). This quantity is defned in the second line in i,t

equation (18), where the frst term gives the tax liability from earnings, contributions and capital

gains and the negative term subtracts taxes already ascribed to earnings and contributions.

   

DC DC e,T D

w,j T ei,t + w , 0, 0 + ptw ⊮(t < 60) − τ if j = DC and t < 66, i,t i,t i,t

τ = (18) i,t     

k,BK e,BK c,BK T ei,t + dcee i,t, w , 0 − τ + τ if j = BK and t < 66. i,t + dcer i,t i,t i,t

86








In retirement, the DC saver pays regular income taxes on withdrawals (see the frst line of

equation (19), while the brokerage saver pays capital gains taxes on that share of withdrawals

k,BK which represent previously unrealized gains (wi,t ). Both savers are, at this point in their lifecycle,

claiming their Social Security payments, which enter as the third argument of the tax function:



 DC ss,DC T

�

w − τ if t ≥ 66 and j = DC, w,j i,t , 0, ssi,t i,t

τi,t = (19)  �  

k,BK ss,BK T 0, wi,t , ssi,t − τi,t if t ≥ 66 and j = BK.

Taxes on Investment Returns All returns on funds in DC accounts are untaxed. That is,

g,j i,j there is no taxation of unrealized gains (r ), there is no income tax on dividend income (r ), and i,t i,t

k,j there is no capital gains tax for distributions (ri,t ). So the taxes paid by the DC saver on returns

are zero.

g,j For the brokerage saver, while the unrealized capital gains (ri,t ) incur no immediate tax liability,

i,j income tax is paid on dividend income (ri,t), and capital gains tax is paid on realized gains. As

described in Section B.4.4, the latter come in two parts – that part of the return which is distributed

k,j even in the absence of a withdrawal (ri,t ), and that part of the return which is realized when a

k,j withdrawals is made (wi,t ).

Taxes on portfolio returns for the brokerage saver are given in (20). In both lines (representing,

respectively, taxes before and after retirement), the frst term gives all taxes due in a particular

period (on earnings, contributions, withdrawals and returns), and the second term nets of those

taxes already ascribed to earnings, contributions, and withdrawals.

   i,BK k,BK k,BK T ei,t + dcee i,t + r , r + w , 0 i,t + i,t dcer

 i,t i,t

  

if t < 66, r,BK e,BK c,BK w,BK τ = − τ + τ + τ (20) i,t i,t i,t i,t

  

i,BK k,BK k,BK ss,BK w,BK T r , r + w − (τ + τ ) if t ≥ 66. i,t i,t i,t , ssi,t i,t i,t

87




B.7 Lifetime Measures

B.7.1 Implied Post-Tax Interest Rate

Our model contains multiple interest rates which could be used to evaluate the present value of

future fows. To do this, we defne an interest rate rˆi,t as the post-tax rate of return that the

brokerage saver would pay if their deferred gains each period were realized as long-term capital

gains.45 We frst defne the hypothetical taxes on portfolio returns in this case as:

   i,BK g,BK k,BK k,BK T ei,t + dc , r + r + w , 0 ee i,t + r i,t + i,t i,t dcer

 i,t i,t

\   

if t < 66, r,BK e,BK c,BK w,BK τ = − τ + τ + τ (21) i,t i,t i,t i,t

  

i,BK g,BK k,BK k,BK ss,BK w,BK T r , r + r + w , ssi,t − (τ + τ ) if t ≥ 66. i,t i,t i,t i,t i,t i,t

g,BK where this expression is the same as that in equation (20) except for the inclusion of ri,t each

period in the second argument. The implied, post-tax interest rate is then

\r,BK τ

rˆi,t = rt − i,t . (22) BBK + f BK

i,t i,t

This rate is used across all counterfactuals.

B.7.2 Wealth

We have two measures of resources in retirement: a) Wealth which just takes account of the value in

DC accounts and b) Consumption – a broader measures which also includes Social Security wealth.

Wealth Our measure of wealth is the present discounted value of after-tax withdrawals facilitated

by the account balance. We can express this as recursively, backwards from age 90. With Ai,

j

90 = 0,

we defne:

45This assumption ensures that interest rate we choose for discounting does not depend on patterns of withdrawals

that we observe in our data.

88




     ADC

 i,t+1 w,DC c,BK

1+ˆri,t+1

+ wDC − τi,t+1 − dcee i,t+1 − τi,t+1 for j = DC,

j i,t+1 i,t+1 + dcer

Ai,t =     (23)

ABK

 i,t+1 BK \r,BK c,BK dcee 1+ˆri,t+1

+ w − τi,t+1 − i,t+1 + dcer − τ for j = BK. i,t+1 i,t+1 i,t+1

as the present value of future post-tax withdrawals less future post-tax contributions.

This is private retirement wealth and does not include wealth held in the form of Social Security

benefts. We defne Social Security wealth as:

  SSi,t+1 SSi,t = + ssi,t+1 − τi,t

ss

+1 . (24) 1 + rˆi,t+1

Our broad measure of wealth – which we refer to as consumption – takes into account both

wealth in private accounts and Social Security wealth,

= ADC + CSS Ci,t (25) i,t i,t ,

B.8 Decomposing Retirement Wealth into its components

In this subsection we defne how we decompose retirement wealth into three components: that

which fows from employee contributions, that which can be ascribed to employer contributions,

and that which is due to the favorable tax treatment of DC accounts.

B.8.1 Value of DC Tax Treatment

The total tax beneft to an individual i is defned as the diference between the retirement wealth

of the DC saver and that of the brokerage saver.

AT = ADC

i,65 − ABK (26) i i,65 .

To fnd the retirement wealth concept attributable to the employee alone, we need to fnd, for each

individual in our data, the proportion of contributions that are from the employee. The value at

retirement of the contributions made by each of the employee and the employer are, respectively:

89
X Y

65  65  X Y65  65 

DCee dcee DCer dcer = (1 + rˆτ ) = (1 + rˆτ ) . (27) i,t i,t

t=25 τ=t t=25 τ=t

These can then be used to calculate the proportion of retirement wealth for the brokerage saver (i.e.

after the tax benefts have been removed) which comes from employee contributions and employer

contributions. These are, respectively:

DCee DCer

AEE · ABK AER · ABK = = (28) i i,65 i i,65 . (DCee + DCer) (DCee + DCer)

The Treasury Department estimates the aggregate tax beneft given to DC savers in 2021 was $119

billion in 2021 (US Department of the Treasury (2023)). As a check on our model, we would like to

compare our estimate of the tax beneft to the ofcial estimate. Using an annuitization factor based

on our model interest rate, we transform the mean lifetime tax beneft AT = $52, 936 to an annual i

measure by dividing it by a factor of approximately 50. This results in a mean annual tax beneft

of about $1,054. This estimate is for the population represented by our simulated data, where

population DC coverage is estimated to be that for those currently in their 20s.46 To convert our

number to one which can be considered refective of the current US population (who are the basis

for the Treasury’s numbers), we multiply our average annual tax beneft by the ratio of the DC

savings rate in the population to the DC savings rate in the hotdeck sample. This ratio is around

1.5 and yields a comparable mean annual tax beneft to $694 per worker. Finally, we multiply this

by an estimate of the civilian population engaged in work at any time in 2018 from the public

CPS-ASEC, around 168 million people. Our model estimate of aggregate annual tax beneft to DC

savers is then $117 billion.

B.9 Tax Counterfactual

The tax counterfactual considers the efect on retirement wealth and consumption if the aggregate

associated tax expenditure were distributed proportionally to lifetime earnings. This would break

the link between saving decisions and a worker’s share of this tax expenditure but would not

otherwise increase redistribution across lifetime income groups. That is, every individual would

46Our hotdeck imputation model matches younger people to older people based in part on DC access, the fact that

younger people are more likely to have access to DC plans will make DC access more prevalent in our sample than

in the population.

90
receive a government contribution to her DC account calculated as a proportion of her lifetime

earnings. This proportion is uniform across all individuals and chosen so that the total cost of

these government contributions matches the total cost incurred under the existing tax-favored

system.

Let the value of lifetime total earnings be:

X Y

65  65 

LEi = (compi,t) (1 + rˆτ ) (29)

t=25 τ=t

where compi,t = ei,t + dcee is the sum of earnings and deferred compensation. We defne a redis- i,t

tributed tax advantage that allocates the total tax beneft in the economy so that it is proportional

to lifetime income:

LEi X A′

i

T = P LEn

· AT

n (30) n n

where the frst term is an individual’s share of aggregate lifetime earnings and the second term

is the aggregate tax expenditure. We assume no behavioral response to the change in the tax

treatment of retirement contributions so that employee and employer contributions are unchanged.

We indicate with a ′ superscript aggregates under this counterfactual. Retirement wealth and

retirement consumption in this counterfactual are therefore equal to:

A′DC = AEE + AER + A′T C′ = SSi + A′DC

i i i i i i

B.10 Match Counterfactual

In the presence of an employer match for retirement contributions, those who save more receive

higher total compensation from their employer. Our employer match counterfactual breaks this link

and considers the efect of a noncontingent employer contribution that is proportional to employee

earnings. Every worker would receive an employer contribution to her DC account proportional to

her current earnings, regardless of whether she makes a contribution. This percentage would be

the same for all workers under the same employer but would vary across employers. It is selected

91
so that the total cost of employer contributions for a given employer equals the total cost that this

employer incurs under its existing matching formula.

For our employer-match counterfactual, we calculate the proportional contribution that, if given

to all employees in the frm, would cost the same to the frm as their actual matching contributions.

That is, for each time period t we calculate the ratio of total matching contributions to total income

for each frm and multiply that by individual income. Denoting as i an employee working in frm

f with an employer match of dcer 47 instead of receiving dcer in period t, the employee receives: i,t, i,t

compi,t X dc∗er = P · dcer (31) i,t n,t

n∈f compi,t n∈f

where the frst term is individual i’s share of compensation in their frm in period t and the second

term is the aggregate matching contributions made by their employer in period t. We then calculate

all modeled objects as described above assuming that, instead of their actual employer match

contributions (dcer ) each period, employees receive the counterfactual match dci,t

∗,er. Accounting for i,t

this and for the fact that trajectories of taxation will be diferent, will yield diferent levels of wealth

at retirement. All stocks in this model are denoted as in the baseline model but with the addition

of a ∗ superscript. We denote the counterfactual contributions from employers and due to the tax

expenditure as (A∗,ER and A∗T ), respectively., so that the new levels of wealth and consumption i i

in retirement are equal to:

A∗DC = AEE + A∗ER + A∗T C∗ = SSi + A∗DC (32) i i i i i i

B.11 Combined Counterfactual

Our combined counterfactual equalizes both the employer match contribution and the tax subsidy.

To do this frst obtain the brokerage saver’s wealth under the employer match counterfactual

†BK †ER C . We add to the redistributive tax subsidy calculated in tax counterfactual (A ). Denoting i,t i

dc 47 er This will be linked to the employee’s contribution (dcee

i,t) by a function that gives the employer match: i,t =

mf (dcee

i,t).

92
i all aggregates under the combined counterfactual with an † superscript (though note that A†ER =

A∗ER

i ), we obtain:

†DC = AEE †ER †T † †DC A + A + A C = SSi + A (33) i i i i i i

B.12 Parameterization

B.12.1 Rates of return

Total investment return is given by an age-varying interest rate rt. Each age t is associated with a

portfolio composition between equities, bonds, and bills, parameterized by σt

k, σtb, and σm

t . During

working years, these shares are interpolated from Fidelity target date funds (see, for example, the

2040 Target Date Fund in Fidelity (2023)). In retirement, we assume exclusive investment in bonds.

The age-profle of investment composition is shown in Figure C.33a, and the associated age-profle

of real rate of return is shown in Figure C.33b. Real rates of return for these asset types (ρk, ρb,

and ρm, respectively) are taken from Jord`a et al. (2019). The combination of these assumptions

yields age-specifc rates of return rt according to

rt = ρk · σk + ρb · σb + ρm · σm. (34) t t t

Note in retirement that rt = ρb. We derived the decomposition of returns into these shares by studying the historical price trends and distributions of the Fidelity Freedom Funds Fidelity (2023).48

48Our breakdown of 50% price change, 40% distribution taxed as long-term capital gains, and 10% taxed as income

is very similar to the 48/43/9 breakdown found by Sialm and Zhang (2020), under the assumption that 95% of

dividends are non-qualifed.

93
Appendix Figures

C Appendix Figures

C.1 Supplemental Figures to Section 2

Figure C.1: Matching schedules

Notes: The sample is all employer match schedules for plans in a particular year. Each line represents a match

schedule, and the depth of shade represents the frequency of the match schedule.

94
C.2 Supplemental Figures to Section 4

Figure C.2: Decomposing DC plan accessibility and savings by race

-10

-5

0

5

10 Raw +Year+Age +Income +Education +Gender +Occupation +County +Tenure +Fam. Struc. +Spouse Inc.

Panel A: DC Access dummy

(full sample of ACS respondents)

-.3

-.2

-.1

0

.1 Raw +Year+Age +Income +Education +Gender +Occupation +County +Tenure +Fam. Struc. +Spouse Inc.+AE

Panel B: Ratio of firm-level aggregate

employer contributions / aggregate wages 

0

1

2

3

4 Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.+AE

Panel C: share of total contributions from

employers (401k participants only) 0

.2

.4

.6 Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.+AE

Panel D: Foregone employer matching

contributions (as share of income) Share (p.p.) diff relative to White

Black Hispanic 95% CI

Notes: Panel A presents accessibility to DC plans by race. Panel B shows the ratio of

frm-level aggregate employer contributions divided by total employee compensation for each frm

aggregate employer match ( ). Panel C shows the share of total contributions aggregate employer match+aggregate employee deferred compensation

employer match at the individual-level ( ). Panel D shows the foregone employer matching contribu- employer match+employee DC

tions (as a share of total income). We use the specifcation defned in Equation 1, omitting EIN for Panels A and

B due to perfect collinearity.

95
Figure C.3: Racial gap estimates re-weighted using the characteristic shares of White employees

-3

-2

-1

0

Raw+ Year + Age + Income+ Education

Reweighted

-3

-2

-1

0

Raw+ Year + Age + Income+ Education

Baseline

Panel A: Employee contrib. + employer match (% of inc.)

0

5

10

15

Raw+ Year + Age + Income+ Education

Reweighted

0

5

10

15

Raw+ Year + Age + Income+ Education

Baseline

Panel B: Early withdrawal (withdr. >$1000) Share (p.p.) difference

Black Hispanic 95% CI

Notes: This fgure presents a robustness check of our main results. We re-weight the Black and Hispanic

worker distributions according to the White worker distribution. The left column of fgures presents gaps for our

reweighted matching sample gaps; the right column of fgures presents gaps for our matching sample results, as

presented in Figure 2. We use the progressive specifcation defned in Equation 1. Due to cell size constraints

in U.S. Census disclosure requirements, we present estimates for the frst fve regression controls, from raw gaps

through gender. Panel A shows the employee contribution in opaque bars and overlays the employer match in

transparent bars. Panel B shows the early withdrawal rates.

96
Figure C.4: Racial gap estimates across samples

-2

-1.5

-1

-.5

0

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.

Full ACS

-2

-1.5

-1

-.5

0

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc. + Par. Inc. + Par. Aware.

Parent

-2

-1.5

-1

-.5

0

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.+AE

Fully Vested

Panel A: Own contrib. (% of income)

0

5

10

15

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.

Full ACS

0

5

10

15

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc. + Par. Inc. + Par. Aware.

Parent

0

5

10

15

Raw +Year+Age +Income +Education +Gender +Occupation +County+EIN +Tenure +Fam. Struc. + Spouse Inc.+AE

Fully Vested

Panel B: Early withdrawal (withdr. >$1000) Share (p.p.) difference relative to White

Black Hispanic 95% CI

Notes: This fgure presents robustness checks for our main results (Figure 2). We use the progressive specifcation

(Equation 1) for our full ACS sample of employees, our parent sample (without retirement plan matches), and our

vesting sample (restricting on fully-vested employees). Panel A presents the employee contribution rate; Panel B

presents early withdrawals. Coefcients are relative to White.

97
Figure C.5: Regression coefcients and groups shares 0

1

2

3 Share (p.p.) diff. relative to Age 25-30

.6

.8

1

1.2

1.4 Group share rel. to pop. shares 25-30 30-35 35-40 40-45 45-50 50-55 55-59.5 Age Bins

Panel A: Age

-2

-1

0

1

2 Share (p.p.) diff. relative to Income Decile 5

0

.5

1

1.5 Group share rel. to pop. shares 1 2 3 4 5 6 7 8 9 10

Income Deciles Panel B: Income

0

.5

1

1.5 Share (p.p.) diff. relative to No HS

0

1

2

3 Group share rel. to pop. shares No HS Graduated HS Graduated

college Graduate degree Education Bins Panel C: Education

-1

-.5

0

.5

1 Share (p.p.) diff. relative to Spousal Income Decile 5

0

.25

.5

.75

1

1.25

1.5 Group share rel. to pop. shares Missing

0 1 2 3 4 5 6 7 8 9 10 Spousal Income Deciles

Panel D: Spousal Income White Black Hispanic 95% CI

Notes: This fgure presents i) the racial composition (bars, right axes) and ii) the regression coefcients (dots, left

axes), from our fully saturated model (defned in Equation 1) for four important mediating channels: age (Panel

A), income (Panel B), education (Panel C), and spousal income (Panel D). The regression outcome is employee

contribution plus employer matching rate (% of income). Appendix A.1.3 provides defnitions for the outcome

and mediating channels. The racial composition for each bin corresponds to Panel B in 6, while the coefcient

estimates correspond to Panel C in 6. The coefcients are provided in column 1 of Table 3.

98
Figure C.6: Share of workers who stay at their frm across the income growth distribution

0

10

20

30

40

50

60

70

80

Share (p.p.) who remain at the same main firm in years t-1, t, and t+1

0 10 20 30 40 50 60 70 80 90 100

Income Growth Bins (Ventiles)

Notes: Of the ACS respondents we observe in year t and who satisfy our requirements to be in the early withdrawal

sample, we plot the share of workers who remain at the same main frm (i.e., the frm who pays them the most)

in years t − 1, t, and t + 1.

99
Figure C.7: Racial savings gaps by year

-3

-2

-1

0

1

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Year

Raw

-3

-2

-1

0

1

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Year

All Controls Share (p.p.) difference

Panel A: Employee contrib. + employer match (% of inc.)

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in employee contribution plus employer match rates for each year

from 2008-2017. The left column shows disparities for our raw specifcation without independent variables. The

model is yit = α + β1yeart + ζ(yeart · racei) + εit. The right column shows the disparities for our fully-saturated

model. Regression variables include dummies for year, age, income, education, gender, occupation, county, EIN,

and tenure. Our model is yit = α+β1yeart +β2agebini +β3incomebini +β4educbini +β5femalei +γoccupation +

δcounty +λEIN +β6tenurei +ζ(yeart · racei)+εit. ζ provides our coefcients of interest. 95% confdence intervals

are included; standard errors are clustered by EIN. See Figure 3 for more details.

100
Figure C.8: Racial savings gaps and leakage by age

-2

0

2

4

25-29 30-34 35-39 40-44 45-49 50-54 55-59.5

Age Bins

Raw

-2

0

2

4

25-29 30-34 35-39 40-44 45-49 50-54 55-59.5

Age Bins

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

0

5

10

15

20

25-29 30-34 35-39 40-44 45-49 50-54

Age Bins

Raw

0

5

10

15

20

25-29 30-34 35-39 40-44 45-49 50-54

Age Bins

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by age. Panel A shows disparities in employee

contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional on

withdrawals >$1,000). The left column shows disparities for our raw specifcation without other mediating

channels. The model is yit = α + β1age i + ζ(age i · racei) + εit. The right column shows the disparities for

our fully-saturated model. Regressions include mediating channels that interact with race. These are year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini + β4educbini + β5femalei + γoccupation + δcounty + λEIN + β6tenurei + ζ(yeart · racei) + εit. ζ

provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by EIN.

See Figure 3 for more details.

101
Figure C.9: Racial savings gaps and leakage by income

-4

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Income Deciles

Raw

-4

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Income Deciles

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Income Deciles

Raw

-5

0

5

10

15

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Income Deciles

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by income. Panel A shows disparities in employee

contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional on

withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables.

The model is yit = α + β1incomebin i + ζ(incomebin i · racei) + εit. The right column shows the disparities

for our fully-saturated model. Regression variables include dummies for year, age, income, education, gender,

occupation, county, EIN, and tenure. Our model is yit = α+β1yeart +β2agebini +β3incomebini +β4educbini +

β5femalei + γoccupation + δcounty + λEIN + β6tenurei + ζ(incomebin i · racei) + εit. ζ provides our coefcients

of interest. 95% confdence intervals are included; standard errors are clustered by EIN. See Figure 3 for more

details.

102
Figure C.10: Racial savings gaps and leakage by education

-2

0

2

4

6

No HS Graduated

HS

College

graduate

Graduate

degree

Education Bins

Raw

-2

0

2

4

6

No HS Graduated

HS

College

graduate

Graduate

degree

Education Bins

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

No HS Graduated

HS

College

graduate

Graduate

degree

Education Bins

Raw

-5

0

5

10

No HS Graduated

HS

College

graduate

Graduate

degree

Education Bins

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by education. Panel A shows disparities in

employee contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional

on withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent

variables. The model is yit = α + β1educ i + ζ(educ i · racei) + εit. The right column shows the disparities

for our fully-saturated model. Regression variables include dummies for year, age, income, education, gender,

occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini + β3incomebini + β4educi +

β5femalei+γoccupation+δcounty +λEIN +β6tenurei+ζ(educ i·racei)+εit. ζ provides our coefcients of interest.

95% confdence intervals are included; standard errors are clustered by EIN. See Figure 3 for more details.

103
Figure C.11: Racial savings gaps and leakage by gender

-3

-2

-1

0

1

Male Female

Gender

Raw

-3

-2

-1

0

1

Male Female

Gender

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

Male Female

Gender

Raw

-5

0

5

10

15

Male Female

Gender

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by gender. Panel A shows disparities in employee

contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional on

withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables.

The model is yit = α + β1female i + ζ(female i · racei) + εit. The right column shows the disparities for our

fully-saturated model. Regression variables include dummies for year, age, income, education, gender, occupation,

county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini + β3incomebini + β4educi + β5femalei +

γoccupation + δcounty + λEIN + β6tenurei + ζ(female i · racei) + εit. ζ provides our coefcients of interest. 95%

confdence intervals are included; standard errors are clustered by EIN. See Figure 3 for more details.

104
Figure C.12: Racial savings gaps and leakage by tenure

-2

0

2

4

<1 year 1 year 2 years 3+ years

Tenure Bins

Raw

-2

0

2

4

<1 year 1 year 2 years 3+ years

Tenure Bins

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

<1 year 1 year 2 years 3+ years

Tenure Bins

Raw

-5

0

5

10

15

<1 year 1 year 2 years 3+ years

Tenure Bins

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by tenure. Panel A shows disparities in employee

contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional on

withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables.

The model is yit = α+β1tenure i+ζ(tenure i· racei) +εit. The right column shows the disparities for our fullysaturated model. Regression variables include dummies for year, age, income, education, gender, occupation,

county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini + β3incomebini + β4educi + β5femalei +

γoccupation + δcounty + λEIN + β6tenurei + ζ(tenure i · racei) + εit. ζ provides our coefcients of interest. 95%

confdence intervals are included; standard errors are clustered by EIN. See Figure 3 for more details.

105
Figure C.13: Racial savings gaps and leakage by family structure

-3

-2

-1

0

1

2

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

Raw

-3

-2

-1

0

1

2

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

0

5

10

15

20

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

Raw

0

5

10

15

20

Non-filers Single,

Kids

Single,

No Kids

Dual,

Kids

Dual,

No Kids

Family Structure Bins

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by family structure. Panel A shows disparities in employee contribution plus employer match rates. Panel B shows disparities in early withdrawal rates

(conditional on withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables. The model is yit = α + β1f amilystructure i + ζ(f amilystructure i · racei) + εit. The right

column shows the disparities for our fully-saturated model. Regression variables include dummies for year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini+β4educi+β5femalei+γoccupation+δcounty +λEIN +β6tenurei+ζ(f amilystructure i·racei)+εit.

ζ provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by

EIN. See Figure 3 for more details.

106
Figure C.14: Racial savings gaps and leakage by parent income

-2

-1

0

1

2

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Parent Income Deciles

Raw

-2

-1

0

1

2

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Parent Income Deciles

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Parent Income Deciles

Raw

-5

0

5

10

15

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Parent Income Deciles

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by parent income. Panel A shows disparities in employee contribution plus employer match rates. Panel B shows disparities in early withdrawal rates

(conditional on withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables. The model is yit = α + β1parentincomebin i + ζ(parentincomebin i · racei) + εit. The right

column shows the disparities for our fully-saturated model. Regression variables include dummies for year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini+β4educi+β5femalei+γoccupation+δcounty+λEIN +β6tenurei+ζ(parentincomebin i·racei)+εit.

ζ provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by

EIN. See Figure 3 for more details.

107
Figure C.15: Racial savings gaps and leakage by housing as a share of income

-4

-3

-2

-1

0

1

Q1 Q2 Q3 Q4 Q5

Housing Share Quintiles

Raw

-4

-3

-2

-1

0

1

Q1 Q2 Q3 Q4 Q5

Housing Share Quintiles

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

Q1 Q2 Q3 Q4 Q5

Housing Share Quintiles

Raw

-5

0

5

10

15

Q1 Q2 Q3 Q4 Q5

Housing Share Quintiles

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by housing as a share of income. Panel A shows

disparities in employee contribution plus employer match rates. Panel B shows disparities in early withdrawal

rates (conditional on withdrawals >$1,000). The left column shows disparities for our raw specifcation without

independent variables. The model is yit = α+β1housingsharebin i+ζ(housingsharebin i·racei)+εit. The right

column shows the disparities for our fully-saturated model. Regression variables include dummies for year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini+β4educi+β5femalei+γoccupation+δcounty +λEIN +β6tenurei+ζ(housingsharebin i·racei)+εit.

ζ provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by

EIN. See Figure 3 for more details.

108
Figure C.16: Racial savings gaps and leakage by health insurance

-6

-4

-2

0

Private Private +

Public

Public None

Health Insurance Bins

Raw

-6

-4

-2

0

Private Private +

Public

Public None

Health Insurance Bins

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

0

5

10

15

20

Private Private +

Public

Public None

Health Insurance Bins

Raw

0

5

10

15

20

Private Private +

Public

Public None

Health Insurance Bins

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by health insurance. Panel A shows disparities in employee contribution plus employer match rates. Panel B shows disparities in early withdrawal rates

(conditional on withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent variables. The model is yit = α + β1healthinsurance i + ζ(healthinsurance i · racei) + εit. The right

column shows the disparities for our fully-saturated model. Regression variables include dummies for year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini+β4educi+β5femalei+γoccupation+δcounty +λEIN +β6tenurei+ζ(healthinsurance i·racei)+εit.

ζ provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by

EIN. See Figure 3 for more details.

109
Figure C.17: Racial savings gaps and leakage by maximum employer match

-4

-2

0

2

4 Q1 Q2 Q3 Q4 Q5

Raw

-4

-2

0

2

4 Q1 Q2 Q3 Q4 Q5

All Controls Share (p.p.) difference

Panel A: Employee contrib. + employer match (% of inc.)

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by the maximum employer match. Panel A shows

disparities in employee contribution plus employer match rates. Panel B shows disparities in early withdrawal

rates (conditional on withdrawals >$1,000). The left column shows disparities for our raw specifcation without

independent variables. The model is yit = α + β1max employer match bin i + ζ(max employer match bin i ·

racei) + εit. The right column shows the disparities for our fully-saturated model. Regression variables include

dummies for year, age, income, education, gender, occupation, county, EIN, and tenure. Our model is yit =

α + β1yeart + β2agebini + β3incomebini + β4educi + β5femalei + γoccupation + δcounty + λEIN + β6tenurei +

ζ(max employer match bin i · racei) + εit. ζ provides our coefcients of interest. 95% confdence intervals are

included; standard errors are clustered by EIN. See Figure 3 for more details.

110
Figure C.18: Racial savings gaps and leakage by fnancial literacy

-4

-2

0

2

Q1 Q2 Q3 Q4 Q5

Financial Literacy Quintiles

Raw

-4

-2

0

2

Q1 Q2 Q3 Q4 Q5

Financial Literacy Quintiles

All Controls

Panel A: Employee contrib. + employer match (% of inc.)

-5

0

5

10

15

Q1 Q2 Q3 Q4 Q5

Financial Literacy Quintiles

Raw

-5

0

5

10

15

Q1 Q2 Q3 Q4 Q5

Financial Literacy Quintiles

All Controls

Panel B: Early withdrawal (withdr. >$1000) Share (p.p) difference

White Black Hispanic 95% CI

Notes: This fgure presents the racial gaps in savings and leakage by fnancial literacy. Panel A shows disparities in

employee contribution plus employer match rates. Panel B shows disparities in early withdrawal rates (conditional

on withdrawals >$1,000). The left column shows disparities for our raw specifcation without independent

variables. The model is yit = α + β1f inancial literacy bin i + ζ(f inancial literacy bin i· racei) + εit. The right

column shows the disparities for our fully-saturated model. Regression variables include dummies for year, age,

income, education, gender, occupation, county, EIN, and tenure. Our model is yit = α + β1yeart + β2agebini +

β3incomebini + β4educi + β5femalei + δcounty + λEIN + β6tenurei + ζ(f inancial literacy bin i · racei) + εit. ζ

provides our coefcients of interest. 95% confdence intervals are included; standard errors are clustered by EIN.

We drop occupation fxed efects due to perfect collinearity. See Figure 3 for more details.

111
Figure C.19: Savings gaps by income interacted with demographics, raw

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

No HS Graduated HS

Graduated college Graduate degree

Education

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

<1 year 1 year

2 years 3+ years

Tenure

-4

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Non-filer Single, Kids Single, No Kids

Dual, Kids Dual, No Kids

Family Structure

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Parent Income Gap

Notes: This panel is the raw version of Figure 8, excluding all dummies. It shows gaps in employee plus employer

matched contribution rates by diferent covariates and income deciles, relative to individuals in the 5th income

decile who are in our selected base category (e.g., education bin “No HS” for our education variable). The dashed

line indicates the base category. Beginning clockwise from the top left, we have age, education, family structure,

parent income, tenure, and maximum employer match. Each group of bars corresponds with an income decile.

Each individual bar represents the group of people in that income decile. The legend defnes each category. Our

model resembles our main specifcation, but includes an interaction between income and our control variable of

choice. Our model is yit = α + ζ(variablei · incomebini) + εit

112
Figure C.20: Savings gaps by income interacted with demographics, fully saturated

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

25-29 30-34 35-39 40-44

45-49 50-54 55-59.5

Age

-2

-1

0

1

2

3

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Male

Female

Gender

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Maximum employer match

-4

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Financial Literacy Gap

Notes: This fgure presents other important mediation channels, using the same model as Figure 8. It shows

gaps in employee plus employer matched contribution rates by diferent covariates and income deciles, relative

to individuals in the 4th income decile who are in our selected base category (e.g., age bin “25-30” for our age

variable). Important mediation channels, in counter-clockwise direction, are age, gender, fnancial literacy, and

maximum employer match. Our model includes an interaction between income and our mediating channel of

choice. We include dummies for year, age, education, gender, occupation, county, EIN, and tenure. It omits

occupation fxed efects for fnancial literacy due to the that our fnancial literacy measure is at the frm level.

113
Figure C.21: Savings gaps by important mediation channels, raw

-2

0

2

4

6

8

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

25-29 30-34 35-39 40-44

45-49 50-54 55-59.5

Age

-4

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Male

Female

Gender

-4

-2

0

2

4

6

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Maximum employer match

-4

-2

0

2

4

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Quintile 1 Quintile 2 Quintile 3

Quintile 4 Quintile 5

Financial Literacy Gap

Notes: This panel is the raw version of Figure C.20, excluding all dummies. It shows gaps in employee plus

employer matched contribution rates by diferent covariates and income deciles, relative to individuals in the 4th

income decile who are in our selected base category (e.g., age bin “25-30” for our age variable). The dashed

line indicates the base category. Beginning clockwise from the top left, we have age, education, family structure,

parent income, tenure, and maximum employer match. Each group of bars corresponds with an income decile.

Each individual bar represents the group of people in that income decile. The legend defnes each category. Our

model includes an interaction between income and our mediating channel of choice. It omits occupation fxed

efects for fnancial literacy due to perfect collinearity.

114
Figure C.22: Value of withdrawals at retirement by race and earnings 50 100 150 200 250 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Race Earnings Bin

White Black Hispanic 50 100 150 200 250 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) By own-group quintiles (b) By population quintiles

This fgure shows the future value at retirement of all pre-retirement withdrawals as a percentage of average

annual lifetime earnings. These amounts are graphed by race and earnings quintiles calculated on the entire

population, with the top quintile split into two deciles.

C.3 Supplemental Figures to Section 7

Figure C.23: Contrib. of employer and tax subsidies to retirement wealth, by education

0 100 200 300 400 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

N H C G N H C G N H C G N H C G N H C G N H C G

Group Earnings Bin (Outside Axis), Own Education (Inside Axis)

Employer Subsidy Tax Subsidy

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

N H C G N H C G N H C G N H C G N H C G N H C G

Population Earnings Bin (Outside Axis), Own Education (Inside Axis)

Employer Subsidy Tax Subsidy

(a) By own-group quintiles (b) By population quintiles

Notes: This fgure follows the format as Figures 11 and 12, but by own education instead of race or parental

income. Education levels are no high school, graduated high school, graduated college, or graduate degree. The

darker bars are the value at retirement of all employer matches, accounting for any pre-retirement withdrawals.

The lighter bars are the value at retirement of the various tax advantages given to DC accounts throughout the

life cycle. These amounts are divided by average annual lifetime earnings in order to standardize comparisons

across earnings levels. Education levels are graphed by earnings quintiles, with the top quintile split into two

deciles. Panel A has quintiles calculated within each race group, while Panel B’s quintiles are calculated across

own-education groups.

115
Figure C.24: Contrib. of employer and tax subsidies to retirement wealth

0 200 400 600 Percent of Average Annual Lifetime Earnings 20 40 60 80 90 100

Population Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

White EE Contrib. Black EE Contrib. Hispanic EE Contrib.

0 20 40 60 80 100 Percent of Average Annual Lifetime Earnings 20 40 60 80 90 100

Population Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

White EE Contrib. Black EE Contrib. Hispanic EE Contrib.

(a) By race and population income group, $ (b) By race and population income group, %

0 200 400 600 800 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Employer Subsidy Tax Subsidy Employee Contribution

(c) By parental income and own pop. income group,

$

0 20 40 60 80 100 Percent of DC Wealth

Q1 Q2 Q3 Q4 D9 D10

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Employer Subsidy Tax Subsidy Employee Contribution

(d) By parental income and own pop. income group,

%

Notes: This fgure follows the format as Figures 11 and 12, but with the addition of employee contribution to

wealth at retirement. The bottom (darkest) bars are employer match, then tax subsidy, then employee contribution, representing all the components of wealth at retirement. All panels show splits by quintiles calculated on

population lifetime earnings, with the last quintile split into two deciles. Panels A and B show subsidies by race,

while Panels C and D show splits by parental income quintile. Panels A and C show all variables as a percentage

of average annual lifetime earnings, while Panels B and D show variables as a percentage of wealth at retirement

(which sum to 100).

116
Figure C.25: Change in retirement wealth and consumption, by education -100 -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

No HS Graduated HS

Graduated College Grad Degree -50

0 50 100 150 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

No HS Graduated HS

Graduated College Grad Degree

(a) ∆ wealth, by education, own group quintiles (b) ∆ wealth, by education, pop. quintiles -10 -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

No HS Graduated HS

Graduated College Grad Degree -10 -5

0

5 10 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

No HS Graduated HS

Graduated College Grad Degree

(c) ∆ cons., by education, own group quintiles (d) ∆ cons., by education, pop. quintiles

Notes: This fgure is in the same format as Figures 13 and 14, but by own education instead of race or parental

income. Education levels are no high school, graduated high school, graduated college, or graduate degree. This

fgure illustrates the impact of our baseline counterfactual exercise on wealth on retirement and consumption

in retirement. This counterfactual exercise distributes the aggregate employer matches in each frm so that all

workers in that frm receive the same proportion of their earnings, and distributes the aggregate federal tax

expenditure so that all workers receive a contribution that is in proportion to their lifetime earnings. We show

the efect on two outcomes: the top two panels (A and B) show the change in DC wealth on retirement, with

wealth expressed as a proportion of average annual working life earnings. The bottom two panels (C and D)

show proportionate change in consumption in retirement (where consumption is the sum of DC wealth and Social

Security). For both DC wealth and consumption, we show results by two diferent types of lifetime earnings bins.

The graphs on the left (Panels A and C) form lifetime earnings bins within education group. In the graphs on the

right (Panels B and D) the bins represent population groups. In each case, lifetime earnings groups are divided

into six bins–the bottom four quintiles and the top two deciles.

117
Figure C.26: Change in retirement wealth and consumption under tax counterfactual, by race -50

0 50 100 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -50

0 50 100 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) Change in ret. wealth, own race quintiles (b) Change in ret. wealth, pop. quintiles -4 -2

0

2

4

6 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -4 -2

0

2

4

6 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(c) Change in ret. consumption, own race quintiles (d) Change in ret. consumption, pop. quintiles

Notes: This fgure illustrates the impact of our tax counterfactual exercise on wealth on retirement and consumption in retirement. This counterfactual exercise distributes the aggregate federal tax expenditure so that

all workers receive a contribution that is in proportion to their lifetime earnings. We show the efect on two

outcomes: the top two panels (A and B) show the change in DC wealth on retirement, with wealth expressed

as a proportion of average annual working life earnings. The bottom two panels (C and D) show proportionate

change in consumption in retirement (where consumption is the sum of DC wealth and Social Security). For

both DC wealth and consumption, we show results by two diferent types of lifetime earnings bins. The graphs

on the left (Panels A and C) form lifetime earnings bins within race. In the graphs on the right (Panels B and D)

the bins represent population groups. In each case, lifetime earnings groups are divided into six bins–the bottom

four quintiles and the top two deciles.

118
Figure C.27: Change in retirement wealth and consumption under match counterfactual, by race -20

0 20 40 60 80 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -20

0 20 40 60 80 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(a) Change in ret. wealth, own race quintiles (b) Change in ret. wealth, pop. quintiles -2

0

2

4

6 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White Black Hispanic -2

0

2

4

6 Percent of Retirement Consumption

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White Black Hispanic

(c) Change in ret. consumption, own race quintiles (d) Change in ret. consumption, pop. quintiles

Notes: This fgure illustrates the impact of our match counterfactual exercise on wealth on retirement and

consumption in retirement. This counterfactual exercise distributes the aggregate employer matches in each

frm so that all workers in that frm receive the same proportion of their earnings. We show the efect on two

outcomes: the top two panels (A and B) show the change in DC wealth on retirement, with wealth expressed

as a proportion of average annual working life earnings. The bottom two panels (C and D) show proportionate

change in consumption in retirement (where consumption is the sum of DC wealth and Social Security). For

both DC wealth and consumption, we show results by two diferent types of lifetime earnings bins. The graphs

on the left (Panels A and C) form lifetime earnings bins within race. In the graphs on the right (Panels B and D)

the bins represent population groups. In each case, lifetime earnings groups are divided into six bins–the bottom

four quintiles and the top two deciles.

119
Figure C.28: Change in retirement wealth and consumption with behavioral response, by race and

population income bins

-100

-50

0

50

100

150

200

20 40 60 80 90 100

Percent of Average Annual Lifetime Earnings

Population Earnings Bin

White, Baseline Black, Baseline Hispanic, Baseline

White, with Response Black, with Response Hispanic, with Response

-150

-100

-50

0

50

100

150

200

20 40 60 80 90 100

Percent of Average Annual Lifetime Earnings

Population Earnings Bin

White, Baseline Black, Baseline Hispanic, Baseline

White, with Response Black, with Response Hispanic, with Response

(a) 10c saving efect per dollar of incentives (b) 20c saving efect per dollar of incentives

-150

-100

-50

0

50

100

150

200

20 40 60 80 90 100

Percent of Average Annual Lifetime Earnings

Population Earnings Bin

White, Baseline Black, Baseline Hispanic, Baseline

White, with Response Black, with Response Hispanic, with Response

-200

-150

-100

-50

0

50

100

150

200

20 40 60 80 90 100

Percent of Average Annual Lifetime Earnings

Population Earnings Bin

White, Baseline Black, Baseline Hispanic, Baseline

White, with Response Black, with Response Hispanic, with Response

(c) 30c saving efect per dollar of incentives (d) 40c saving efect per dollar of incentives

Notes: This fgure shows alternate versions of Figure 13, Panel B, under diferent assumptions of behavioral

response to a reduction in savings incentives. We assume that if the combined subsidy in baseline is X, then

the employee wealth at retirement decreases by Y % · X under the combined counterfactual, refecting the loss

of savings incentive. Panels A, B, C, and D assume incentive efects of 10%, 20%, 30%, and 40%, respectively.

All panels express change in wealth concept at retirement as a percentage of average annual lifetime earnings

by race and population lifetime earnings quintiles (with the top quintile split into two deciles). In all panels,

the transparent bars show the level of change without behavioral response, while the solid bars show the level of

change with the specifed incentive efect.

120
Figure C.29: Median subsidies relative to white under withdrawal assumptions 100

53

69 0 20 40 60 80 100

ER Subsidy

100

31

62 0 20 40 60 80 100

Tax Subsidy

100

45

67 0 20 40 60 80 100

Total Subsidy Percent of White Median Value

White Black Hispanic

100

35

66 0 20 40 60 80 100

ER Subsidy

100

31

62 0 20 40 60 80 100

Tax Subsidy

100

33

64 0 20 40 60 80 100

Total Subsidy Percent of White Median Value

White Black Hispanic

(a) Subs. rel. to White, withdrawals from EE (b) Subs. rel. to White, withdrawals from EE + ER

Notes: This fgure shows employer, tax, and total subsidy to groups relative to a base group under diferent

assumptions relating to early withdrawals. Panel A shows subsidies by race, relative to the White value, under

the assumption that all early withdrawals are “deducted” from employee wealth balance. These estimates can

be compared to Figure 1, showing a similar measure in the matching sample. By contrast, Panel B employs the

assumption used throughout the microsimulation model, that early withdrawals are taken out of both employee

and employee wealth balances in a proportional manner.

Figure C.30: Contrib. of employer and tax subsidies to retirement wealth, by race, all withdrawals

from EE

0 100 200 300 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Group Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

0 100 200 300 400 Percent of Average Annual Lifetime Earnings

Q1 Q2 Q3 Q4 D9 D10

Population Earnings Bin

White ER Subsidy Black ER Subsidy Hispanic ER Subsidy

White Tax Subsidy Black Tax Subsidy Hispanic Tax Subsidy

(a) By Own Race Quintiles (b) By Population Quintiles

Notes: This fgure is analagous to Figure 11, quantifying the efect of employer matching and tax subsidies on

wealth at retirement by race and earnings. It difers from that graph in its treatment of how early withdrawals

afect employee and employer shares of wealth at retirement, which are used to calculate the employer match

subsidy. In the main model, early withdrawals are taken proportionally out of both the employee and employer

wealth balances. In this fgure, however, early withdrawals are taken exclusively out of the employee balance. The

darker bars are the value at retirement of all employer matches, accounting for any pre-retirement withdrawals.

The lighter bars are the value at retirement of the various tax advantages given to DC accounts throughout the

life cycle. These amounts are divided by average annual lifetime earnings in order to standardize comparisons

across earnings levels. Non-Hispanic White, Black, and Hispanic values are graphed by earnings quintiles, with

the top quintile split into two deciles. Panel A has quintiles calculated within each race group, while Panel B’s

quintiles are calculated across racial groups.

121
C.4 Supplemental Figures to Appendix A.2

Figure C.31: Bin scatter of W2-imputed vs. Form 5500-reported employee contribution share

y = .896x

R2 = .96

.5

.6

.7

.8

.9

1 W2 employee share

.5 .6 .7 .8 .9 1

F5500 employee share

Bin averages Line of best fit

This binscatter shows the W2-imputed frm-level employee share of contributions total employee deferred compensation ( ) against the publicly-fled Form 5500 average em- total employee deferred compensation+total employer match

ployee share of contributions.

C.5 Supplemental Figures to Appendix B

122
Figure C.32: Simulating Lifetime Trajectories from Shorter Panels

123

Notes: This fgure shows a schematic of the imputation model used to simulate lifetime trajectories of earnings, deferred comwithdrawals for workers aged 25 to 65 from the shorter panels available to us for individual workers. We construct full lifetime matching individuals across overlapping age bins. For example, in 1. Persons A and B have similar earnings and job characterist(27 and 28) so we append Person B’s information at 29 and 30 to Person A that adds two additional years to the trajectory of process at increasing ages (31-32, 33-34, ..., 65-66) to create a full lifetime path of earnings, employee and employer contributio

withdrawals from ages 25 to 65.
Figure C.33: Portfolio shares and rate of return

0 .2 .4 .6 .8 1 Proportion of Portfolio

20 40 60 80 100

Age

Stocks, Fidelity Bonds, Fidelity Money, Fidelity

Stocks, Interpolated Bonds, Interpolated Money, Interpolated .02 .03 .04 .05 .06 .07 Real Rate of Return

20 40 60 80 100

Age

(a) Interpolated Portfolio Shares (b) Real Rate of Return over the Lifecycle

Notes: This fgure shows underlying parameterizations for portfolio composition and returns in the microsimulation model described in Appendix B. The points of Panel A show actual portfolio shares for Fidelity Freedom

Funds for each age. We interpolate shares between these observations for each integer age, given by the lines in

Panel A, although we assume exclusive investment in bonds at retirement. Panel B shows the real rate of return,

which is determined by the portfolio composition and the associated returns of each component, by age.

Figure C.34: Withdrawal Path

0 .2 .4 .6 .8 1 Proportion0 20 40 60 80 100 Thousands Dollars

65 70 75 80 85 90

Age

Balance at Start of Period Portion of Balance Withdrawn

Notes: This fgure shows the process for estimating withdrawals in retirement in the microsimulation model

described in Appendix B. For the purposes of illustration, we suppose an individual retires with wealth balance

of $100,000, which they draw down until their last year of life at age 90. The left axis corresponds to the green line,

showing the wealth balance at the start of each period. The right axis corresponds to the blue line, showing the

proportion of remaining wealth balance that is withdrawn each period. This process ensures constant withdrawals

each period and a smooth draw-down of wealth in retirement.

124
D Appendix Tables

D.1 Supplemental Tables to Appendix A.2

125
Table D.1: Summary statistics by sample

126

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

Variable Full, Full (ACS DC Access DC Access Matc

unrestricted employees) (ACS (ACS 

Employees) Employees

at Large

Firms)

Average age 41.63 41.66 41.81 41.41 41.

Employee contribution ($) $2,213 $2,248 $2,855 $3,495 $3,3Box 1 W-2 total compensation $61,140 $61,880 $67,780 $74,330 $72,

Spousal Box 1 W-2 total compensation $9,915 $9,914 $10,000 $9,931 $9,8

Own contrib. (% of inc.) 2.7% 2.7% 3.4% 3.9% 3.8Own contrib. (% of inc., contrib. >0) 5.9% 5.9% 6% 5.9% 5.8

Positive contrib. dummy (%) 45% 45.6% 57.3% 66.3% 65.2Match contrib. (% of inc.) 1.9Own + match contrib. (% of inc.) 5.7Max match - own contrib. (% of inc.) 1.7Positive withdr. dummy 14.3% 14.2% 14.2% 15.7% 16.5Positive withdr. dummy (withdr. >1000) 11.8% 11.8% 11.8% 13% 13.5

This table presents from left to right, the progression from our full unrestricted ACS employee sample (before dropping missing csample (restricted on nonmissing controls), our full DC access sample, our DC access sample (>100 employees per frm), our 

parent-matching sample. This refects the order of our US population and frm sampling. Spousal income includes spouses claime$0 in earnings (41% of our matching sample).
Table D.2: Racial and Age Composition by Controls

Control Variable N White Black Hispanic Asian Ages Ages 

(%) (%) (%) (%) 25-34 35-44 

Panel A: Matching SampleRace, year, age, income, educationFemaleOccupation, county, EIN, tenureFamily, spousal income, autoenrollment

Panel B: Parent, Matching Sample

Race, year, age, income, educationFemaleOccupation, county, EIN, tenureFamily, spousal income, parent income

Parent awareness

1753000 71% 11% 12% 6% 28% 28% 

1751000 71% 11% 11% 6% 28% 28% 

1723000 71% 11% 11% 6% 28% 28% 

1722000 71% 11% 11% 6% 28% 28% 

479800 69% 11% 13% 4% 85% 15%

479700 69% 11% 13% 4% 85% 15%

471300 70% 11% 13% 4% 85% 15%

471200 70% 11% 13% 4% 85% 15%

447500 70% 11% 13% 4% 86% 14%

127Notes: This table presents the racial and age composition of our matching and parent-matching samples as w
Table D.3: Change in DC wealth at retirement under the counterfactual tax policy

Panel A: Quintiles (Q) & deciles (D) of the race-specifc income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +10.5 +12.8 +9.3 +0.1 -25.2 -68.6

DC Wealth ($’000) Black +9.1 +14.7 +17.4 +16.4 +11.1 -15.9

Hispanic +11 +14.9 +13.9 +8.3 +1.0 -43.7

Relative change in the B-W Gap -20.8% -15.3% -11.6% -7.4% -4.6% -3.1%

racial DC wealth gap H-W Gap -29.1% -17.7% -11.7% -6.5% -6.3% -2.6%

Relative change in the B-W Gap -1.8% -4.5% -5.4% -4.8% -4.7% -4.4%

racial consumption gap H-W Gap -6.5% -6.1% -5.6% -4.4% -6.4% -4.0%

Panel B: Quintiles (Q) & deciles (D) of the population income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +10.2 +12.9 +10.5 +2.3 -15.3 -65.3

DC Wealth ($’000) Black +11.1 +17 +16.8 +10.1 -4.5 -52.9

Hispanic +11.3 +15.0 +12.7 +5.1 -7.6 -64.8

Relative change in the B-W Gap -33.5% -25.3% -17.1% -9.6% -7.3% +0.2%

racial DC wealth gap H-W Gap -40.6% -24.9% -15.4% -9.5% -13.8% +6.2%

Relative change in the B-W Gap -9.4% -14.4% -12.1% -8.7% -8.5% -2.1%

racial consumption gap H-W Gap -64.3% -13.2% -9.8% -8.3% -14.5% +3.5%

Notes: This table shows the efect of the tax counterfactual on wealth at retirement by race and income bin,

as well as the corresponding efect on the wealth gaps between White and Black/Hispanic savers. Changes are

given by group-specifc (Panel A) and population (Panel B) income quintiles, with the top quintile split into two

deciles.

128
Table D.4: Change in DC wealth at retirement under the counterfactual employer contribution

policy

Panel A: Quintiles (Q) & deciles (D) of the race-specifc income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +9.3 +14.6 +15.1 +12 -2.3 -18.0

DC Wealth ($’000) Black +7.6 +14.5 +20.4 +24.2 +26.2 +8.9

Hispanic +8.4 +13.9 +16.6 +16.5 +14.1 -2.4

Relative change in the B-W Gap -17.2% -13.9% -12.2% -9% -6.3% -3.2%

racial DC wealth gap H-W Gap -17.7% -12.5% -10.2% -7.1% -6.0% -3.9%

Relative change in the B-W Gap -0.9% -3.4% -5.1% -5.0% -5.1% -3.2%

racial consumption gap H-W Gap +0.7% -2.5% -3.9% -3.8% -5.0% -3.9%

Panel B: Quintiles (Q) & deciles (D) of the population income distribution

Q1 Q2 Q3 Q4 D9 D10

Absolute change in White +8.8 +14.1 +15.2 +12.9 +3.0 -17.0

DC Wealth ($’000) Black +9.9 +19.3 +24.1 +25.8 +16.1 -16.3

Hispanic +8.7 +14.6 +16.8 +15.6 +10.9 -9.6

Relative change in the B-W Gap -32.8% -29.2% -23.7% -18.4% -12.6% 1.4%

racial DC wealth gap H-W Gap -23.9% -17.5% -15.5% -12.5% -17.2% -8.8%

Relative change in the B-W Gap -10.6% -17.7% -17.0% -15.3% -12.1% +0.7%

racial consumption gap H-W Gap +0.7% -5.6% -8.4% -9.3% -16.4% -8.4%

Notes: This table shows the efect of the employer-match counterfactual on wealth at retirement by race and

income bin, as well as the corresponding efect on the wealth gaps between White and Black/Hispanic savers.

Changes are given by group-specifc (Panel A) and population (Panel B) income quintiles, with the top quintile

split into two deciles.

129
D.2 Supplemental Table to Appendix B

Table D.5: Parameter and Variable Defnitions

Earnings, Consumption, Social Security

ei,t Earnings

α Discount rate in retirement

j

ct Consumption in retirement

aimei Average indexed monthly earnings max e Social Security taxable maximum

δ1 First PIA bend point

δ2 Second PIA bend point

ssi,t Annual Social Security benefts

Wealth Flows

dcee Employee savings i,t

dcer Employer savings i,t

j w Savings account withdrawals i,t

j f Flow into retirement account i,t

j B Wealth balance i,t

p,j B Principal part of wealth balance i,t

g,j B LTCG part of wealth balance i,t

k,j w LTCG portion of withdrawal i,t

Rate of Return

ρt Rate of return at age t

g,j r Return from unrealized capital gain i,t

k,j r Return from LTCG distributions i,t

i,j r Return from interest distributions i,t

kst Portion of assets invested in stocks bst Portion of assets invested in bonds

sm Portion of assets invested in money t

ρk Real rate of return on stocks

ρb Real rate of return on bonds

ρm Real rate of return on money

χg Share from unrealized capital gain

χk Share from LTCG distributions

χi Share from interest distributions

rˆi,t Implied post-tax rate of return

i

t ∈ {25, . . . , 90}

j ∈ {DC, BK}

T(· , · , ·)

e,j τi,t

ss,j τi,t

c,j τi,t

r,j τi,t

w,j τi,t

r,j τˆi,t

ADC

i,t

SSi,t

Ci,t

CBK+SS

i,t

AT

i

DCEE

i

DCER

i

AEE

i

AER

i

LEi

C′T

i

A′DC

i

C′DC

i

dc∗

A∗DC

i,t

C∗DC+SS

i,t†DC Ai,t

† Ci,t

State Variables

Individual

Age

Type of savings vehicle

Taxes

Federal income tax function

Taxes owed on earnings

Taxes owed on Social Security Benefts

Taxes owed on savings

Taxes owed on returns

Taxes owed on withdrawals

Hypothetical taxes owed on returns

Lifetime Measures

DC Wealth

Social Security Wealth

Consumption

Consumption brokerage WC

DC tax subsidy

Value of employee contributions

Value of employer contributions

Wealth attributable to employee

Employer subsidy

Value of lifetime income

Counterfactuals

Counterfactual tax subsidy

DC Wealth under tax CF

Consumption under tax CF

Counterfactual employer match

DC wealth under ER CF

Consumption under ER CF

DC Wealth under combined (CB) CF

Consumption under CB CF

Table D.6: Parameters Values and Sources

Parameter Value Source max e $128,400 Social Security Administration (2023b)

δ1 $895 Social Security Administration (2023a)

δ2 $5,397 Social Security Administration (2023a)

ρk 0.0688 Jord`a et al. (2019)

ρb 0.0253 Jord`a et al. (2019)

ρm 0.0103 Jord`a et al. (2019)

σk

t , σbt, σmt Figure C.33a Fidelity (2023)

χg 0.5 Yahoo Finance, Sialm and Zhang (2020)

χk 0.4 Yahoo Finance, Sialm and Zhang (2020)

χi 0.1 Yahoo Finance, Sialm and Zhang (2020)

130