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Federal Reserve Bank of Chicago

Retirement Savings Adequacy in U.S.
Defined Contribution Plans
Francisco Gomes, Kenton Hoyem, Wei-Yin Hu,
and Enrichetta Ravina

February 2020
WP 2022-40
https://doi.org/10.21033/wp-2022-40
Working papers are not edited, and all opinions and errors are the
responsibility of the author(s). The views expressed do not necessarily
reflect the views of the Federal Reserve Bank of Chicago or the Federal
Reserve System.
*

Retirement Savings Adequacy in U.S. Defined
Contribution Plans∗
Francisco Gomes†

Kenton Hoyem‡

Wei-Yin Hu§

Enrichetta Ravina¶
February 2020

Abstract
We evaluate retirement savings adequacy using a large panel of U.S. workers with
a 401(k) account. We model medical expenditures, longevity, investment risk, and the
likelihood of withdrawals due to hardship, job separation, and reaching age 59 1/2.
Based on their current account balances, income, saving, and investment behavior,
three in four workers in our sample are not saving enough for retirement. The dispersion
is related to plan features, account balances, but also worker saving behavior. A bequest
motive, lower housing equity, higher risk aversion, lower discount rates or lower future
returns worsen the shortfall. We examine various counterfactual policy interventions.
∗

We thank John Y. Campbell, Joao Cocco, Markku Kaustia, Bob McDonald, Olivia S. Mitchell, Kim
Peijnenburg, Giorgio Primiceri, Kathrin Schlafmann, seminar participants at Northwestern University, the
5th Cherry Blossom Financial Literacy Institute, the 4th European Workshop on Household Finance, and
the 9th Helsinki Finance Summit on Investor Behavior for their valuable comments and suggestions, and
Jingxiong Hu for very helpful research assistance. The views expressed in this paper are not necessarily
those of Edelman Financial Engines.
†
London Business School, fgomes@london.edu
‡
khoyem@gmail.com
§
Edelman Financial Engines, whu@edelmanfinancialengines.com
¶
Kellogg School of Management, enrichetta.ravina@kellogg.northwestern.edu

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1

Introduction

Defined contribution (DC) schemes are gradually replacing traditional defined benefit (DB)
pensions in several countries and, given the structural funding problems associated with the
latter, this phenomenon is likely to accelerate in the years to come. DC plans give workers the
freedom to choose the level and allocation of their retirement savings. However, in a world
where many individuals have limited financial literacy (e.g. Lusardi and Mitchell (2014),
and Clark, Lusardi and Mitchell (2015)), and several might suffer from time-inconsistent
preferences (e.g. Laibson (1997), and Harris and Laibson (2001)) or other behavioral biases,
these choices might leave them financially vulnerable at retirement.1
The National Retirement Risk Index computed by the Center for Retirement Research
at Boston College (Munnell, Webb, and Delorme (2006), and Munnell, Hou, Sanzenbacher
(2018)) suggests that a large fraction of the U.S. population is not saving enough for retirement. Yet, several other studies conclude that the vast majority of U.S. workers is actually
saving adequately (e.g. Engen, Gale, and Uccello (2005), Scholz, Seshadri, and Khitatrakun
(2006) and Hurd and Rohwedder (2012)).
In this paper we revisit this question using data on more than 350,000 U.S. workers
enrolled in defined contribution plans and evaluate whether, given their actual savings and
investment decisions, they are likely to accumulate enough wealth to maintain their standard
of living during retirement. Our data include worker’s age, current account balance, contribution rate, salary, portfolio allocations, and tenure at the company. Unlike the majority
of the previous literature, we do not assume workers save optimally over the remaining of
their working life. Rather, we estimate the evolution of their portfolio shares and contribution rates as functions of their past behavior and observable characteristics, and use these
evolution equations as inputs in our simulations. This approach has two main advantages.
1

Choi, Laibson and Madrian (2011) document the prevalence of highly suboptimal contribution rates
in 401(k) plans. Ahmed, Barber and Odean (2016) show that suboptimal asset allocation decisions by
individuals are likely to generate lower and more volatile retirement wealth compared to private accounts
without choice and to currently promised Social Security benefits. Using HRS data, Lusardi and Mitchell
(2018) find that fewer than 1/3 of individuals over the age of 50 have ever tried to devise a retirement plan,
and that this lack of planning is associated with low financial literacy. Fisch and Lusardi (20 20) find that
many individuals in 401(k) plans only invest through the workplace and have higher degrees of financial
illiteracy.

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First, to evaluate whether workers are saving optimally for retirement, we need a framework
that allows for the possibility they are making mistakes and capturing individual-specific
features such as the degree of time-inconsistency or inertia would make the modeling exercise very challenging, especially for features for which there is no modeling consensus (e.g.
limited financial literacy). Second, our approach allows us to match individual behavior as
accurately as possible without estimating and calibrating a separate version of the model for
each worker in the sample.
Our simulations of age-65 retirement wealth incorporate income shocks, the possibility
of early withdrawals due to job separations, hardship, and reaching age 59 1/2, employer
contributions and plan features, progressive taxation, and IRS limits on the amount the
worker and the employer can contribute. We measure the total resources available at retirement as the sum of simulated age-65 retirement wealth, Social Security income, non-DC
financial wealth, and net housing equity.2 We compute Social Security income based on the
simulated income profiles and the Social Security Administration formulas. We estimate
non-retirement financial wealth and net housing wealth using fitted coefficients from regressions of these two sources of wealth on retirement wealth and individual characteristics in
the Health and Retirement Study (HRS).
We check the predictive ability of our contribution and asset allocation evolution equations by estimating them on the first half of the sample and comparing the predicted and
actual values on the last sample date.3 We also use calculate unemployment rates, average
probabilities of withdrawal and fraction of the aggregate assets being withdrawn following
various life events in our sample, and find that they are comparable with the aggregate
statistics from the Bureau of Labor Statistics and Vanguard’s How America Saves. Finally,
in Section 2.1 we show that our sample is representative of the workers in the Current Population Survey (CPS) in terms of age and tenure at their firm, but comprises workers with
higher salary; and that it is similar to the Vanguard sample in terms of contribution rates
2

Since neither reverse mortgages not downsizing are commonly observed in the data (Caplin (2002), Venti
and Wise (2004), Poterba, Venti, and Wise (2011), Davidoff (2015)), we consider different scenarios regarding
the fraction of housing equity available/used to finance consumption during retirement.
3
We find that they are not statistically different from each other in 96.40% of the cases for the contribution
rates, in 93.04% of the cases for the bond share, and in 95.75% of the cases for the equity share.

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and asset allocations.
For each worker in our sample we run 10,000 simulations and compute the level of retirement consumption she can finance with her projected age-65 wealth and Social Security
Income. Retirement consumption is estimated from a model of optimal consumption and
savings decisions that incorporates medical expenditures, longevity, and investment risks,
and takes Medicare and Medicaid into account. Unlike in the wealth accumulation phase of
the worker’s life where we don’t take a stand on whether she is optimizing, at this stage we
focus on optimal consumption because we want to determine the best a worker can do with
the wealth she has accumulated.
We propose two measures of retirement adequacy. The first, which we label the consumption retirement replacement ratio (CRRR), is the ratio of retirement to adjusted current
consumption for each simulation. The second, which we label the certainty equivalent ratio
(CEQR), is the ratio of the certainty equivalent of future consumption across all simulations
to adjusted current consumption, and thus takes the worker’s risk aversion into account.
We estimate current consumption from the Current Expenditure Survey (CEX) based on
individual observable characteristics. We apply a 0.8 adjustment factor to current consumption because several expenditures such as housing, education, and children-related ones take
place early in life, but are enjoyed throughout. Moreover, upon retirement, work-related
expenses vanish, and individuals might turn to more home production.4
In our baseline specification, we find that close to three-quarters of the workers in our
sample are not saving enough for retirement. The median individual has more than a 40%
probability of having to decrease her consumption after age 65, even after taking the expenditure adjustment into account. Those at the 25th and 10th percentiles of the distribution
face a 50% probability of having to cut their standard of living by almost 9% and 22%,
respectively. Even those in the top 25th percentile of the distribution face approximately
a 25% probability of having to scale down their adjusted consumption upon retiring. The
under-saving problem is significantly worse if we consider a bequest motive, decrease the
fraction of home equity available to finance retirement consumption, or make more conser4

Academic studies and practitioners propose adjustment factors between 0.7 and 1. Our CRRR results
can easily be re-scaled to apply a different adjustment factor.

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vative assumptions about future average asset returns. In addition, when we back out the
relative risk aversion and discount factor parameters that would make all workers appear
adequately prepared, we find that they have in most cases the opposite relationship with
the worker demographics and allocation decisions than the ones predicted by theory and the
empirical literature.
We also explore how accumulated retirement wealth and preparedness relate to the initial characteristics of the workers in our sample. The results show the importance of the
initial contribution rates in explaining the variation in outcomes. A one percentage point
higher initial contribution rate is associated to a 2.67 ppt increase in the median CRRR,
corresponding to a consumption level 2.67 ppt higher in all retirement years. The size of the
account and the equity share have the expected positive and statistically significant coefficients, although their economic magnitudes is smaller: a $10,000 increase in initial account
balance corresponds to a 69 basis points increase in CRRR, while a 10 ppt increase in the
equity share corresponds, all else equal, to a 58 bps increase in CRRR. A more generous
employer match is associated with higher retirement consumption: each 1 ppt higher employer match generates a 29.5 bps higher annual retirement consumption. All else equal,
workers employed at companies that are older, privately held, invest more, and have higher
net income, tend to have more wealth by the time they reach retirement.The same is true for
those living in areas with higher financial literacy and a higher fraction of college educated
residents. Our results also indicate that once we take company features into account, the
dispersion of outcomes across income levels for workers of the same age increases, especially
for the young. Further, we observe a striking difference between those age 35 and below,
half of whom have median CRRRs of 1.25 or higher, and the older groups who have median
CRRRs of around 1. This result is partially explained by the young being enrolled in plans
with more generous employer contributions. In addition, the dispersion of outcomes rises
quite noticeably with age, primarily due to an increase in the left tail of the CRRR distribution, a particularly concerning result since those close to retirement have fewer years left
to benefit from possible changes in behavior or specific policy measures.
In the final section of the paper, we perform counter-factual experiments to assess the
impact of different retirement preparedness policies in the context of our framework. An im5

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portant caveat is thatin our setting the parameters governing worker behaviorare backwardlooking and do not change in response to the policy. While this assumption might appear
very restrictive, it is worth noting that the empirical evidence overwhelmingly shows that
individuals often respond very passively to changes in the features of their 401(k) plan, both
in terms of contribution rates and investment decisions (e.g. Agnew, Balduzzi, and Sunden
(2003), Choi, Laibson and Madrian (2009), Choi, Laibson, Madrian, and Metrick (2003,
2004), Madrian and Shea (2001), Chetty et al. (2014)). Finally, we don’t attempt to measure the potential crowding out of outside savings induced by these policies, and thus our
estimates should be construed as an optmistic assessment of the effect of these policies.
We find that removing penalty-free early withdrawals for workers age 59 1/2 and older
would increase retirement consumption by at least 5% for those at the bottom of the distribution. By contrast, setting a minimal contribution rate of either 2% to 5% has negligible
effects, increasing the CRRRs by 1% or less. Only an age-dependent contribution rate that
starts from a low level of 4.5% and increases gradually to 15.5% before retirement, when
the individuals can presumably afford to save more, would generate sizable increases in retirement consumption for all age groups, and particularly for the workers at lower end of
the distribution. However, this policy corresponds to a 10% average contribution rate, way
above the 6.3% average and the 5.2% median in our sample, further evidence of the magnitude of the under-saving problem we find. Similarly, increasing every worker contribution
rate by 5 ppts would generate substantial increases in retirement consumption, but more
so for the workers who are already better off, leaving two thirds of the workers still falling
short. Finally, introducing automatic rollover of the account balances upon a job switch,
while effective, if implemented alone would only increase retirement consumption by 1 to 7
ppts, and more so for the workers who are already better off.
Related literature. Our paper is related to others who have also evaluated retirement
preparedness. Poterba (2015) and Skinner (2007) provide comprehensive surveys of the
literature and a discussion of the difficulties in evaluating retirement savings adequacy. The
paper more closely related to ours are Engen, Gale, and Uccello (2005) and Scholz, Seshadri,
and Khitatrakun (2006). Both solve an optimal life-cycle model of consumption and savings
decisions and compare the wealth accumulation implied by the model with that of HRS
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respondents born between 1931 and 1941. Scholz, Seshadri, and Khitatrakun (2006) find
that 84% of them are saving optimall y for retirement or close to it, while Engen, Gale, and
Uccello (2005) estimate that fraction to be between 56% and 65%. In addition to our more
comprehensive data, our study differs from theirs along several important dimensions. First,
we do not ask whether individuals behave optimally, but rather model future behavior by
projecting forward the estimates from the current data. Second, we study a very different
period and more recent age cohorts. The papers above focus on the late 1990s, and estimate
the private savings workers close to retirement need in order to supplement the Social Security
benefits and

DB pensions they are entitled to. They estimate that it is optimal that the

workers at the bottom of the wealth distribution finance retirement almost exclusively with
Social Security, and everyone else except the very top deciles mostly relies on Social Security
and defined benefit pensions. By contrast, in the more recent period we study, the bulk
of retirement savings is in the hands of the workers as opposed to the government and the
companies they work for, and DB plans are quickly being phased out in favor of DC ones
(Munnell and Chen, 2017). Such plans leave more latitiude to individual decisions and might
not provide the same level of retirement security. Moreover, we study the age cohorts who
are currently working, many of whom are decades away from retirement. Several studies
point to the fact that such cohorts might be more financially vulnerable than older ones.5
Finally, we exploit more granular information about the workers’ savings rates, investment
choices, plan menus, fees, employer contributions, and leakages, and are able to study the
effect of these features on retirement wealth accumulation.
Hurd and Rohwedder (2012) take consumption levels of new retirees in the HRS and
project them forward using evolution equations based on demographics and supplemented
with shocks. They find that 71% of the respondents can finance the present value of this
estimated consumption stream with their retirement wealth, as long as they can make full
use of their housing equity. While this approach sidesteps the need of estimating working-life
consumption, it has the drawback that the consumption level at the start of the estimation
might already reflect a decrease in standards of living that the retirees have put in place upon
5

For example, Lusardi, Mitchell, and Oggero (2017) document higher late-in-life financial vulnerability
of recent cohorts because they have taken on more debt early in life.

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reaching/getting closer to retirement. In addition, they focus only on retirees and study an
earlier period when retirees might have been better prepared.
Another strand of the literature measures retirement adequacy by estimating income
replacement ratios. Based on this approach and data from the Survey of Consumer Finances,
Munnell, Webb, and Delorme (2006) conclude that Poterba, Venti, and Wise (2012) take
a novel approach and study older retirees in the HRS. They find that almost half of them
died with no financial assets, living fully out of their social security income only 43% of
retirees are saving enough for retirement. By contrast, Purcell (2012) estimates the median
income retirement replacement ratio in the HRS at around 62%, which he views as not too
far below the recommended level. While easy to compute, income replacement ratios suffer
from several drawbacks, the main one being that they focus on the current period, ignoring
changes in income and expenses that might occur later in life. Finally, Poterba, Venti, and
Wise (2012) take a novel approach and study older retirees in the HRS. They find that almost
half of them died with no financial assets, living fully out of their social security income.
The remainder of the paper is organized as follows. In Section 2 we describe the data
and summarize our approach. In Sections 3 and 4 we describe the pre-retirement period
simulations, while in Section 5 we estimate optimal retirement consumption. In Section 6,
we report our baseline results and sensitivity analysis, while in Section 7 we examine the role
of the initial conditions in determining retirement adequacy of the workers in our sample.
In Section 8 we report a series of counter-factual experiments, and in Section 9 we conclude.

2
2.1

Data and methodology overview
Data

Our primary data is a proprietary dataset provided by Edelman Financial Engines, the
largest independent registered investment advisor in the U.S., which provides advice, and
investment management to participants in 401(k) plans. The dataset includes information on
worker 401(k) balances and contributions, salary, tenure at the firm, asset allocation over five
aggregated asset classes and company stock, demographic characteristics, and zip code over

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the period between 2005 and 2010. It also includes information on the returns, balance sheets,
and income statements of the firms the individuals work at, appended using information from
CRSP, Capital IQ, and Compustat; detailed information on plan characteristics, investment
options, and employer contributions, appended using information from DOL Forms 5500
that firms submit yearly to the Department of Labor; and fees for a more recent sub-period.
Our sample includes 1.6 million workers age 20 to 64 who have valid tenure data, earn
at least the minimum wage, and make their own saving and allocation decisions rather than
being enrolled in “managed accounts”.6 To avoid overfitting, we estimate the evolution
equations for the contribution rates, asset allocations, unemployment, job separation probabilities, and all the other parameters used in the paper based on this sample, regardless of
which subsample of workers we are focusing the analysis on. Panel A of Table 1 shows that,
compared to the workers in the 2010 Current Population Survey (CPS), the average worker
in our sample has similar age, 42.4 years, but has been working at her current employer for
longer, 9.9 vs 7.7 years, and earns a higher salary, $56,738 vs. $45,437. She also lives in
areas with similar house prices than the rest of the U.S. population ($256,413 on average in
our sample and $288,172 in the 2010 U.S. Census).
We compare the contribution rates and equity allocations of the workers in our sample
to those in Vanguard’s How America Saves and find that they are similar. The average
contribution rate is 6.9% in both datasets, while the medians are 5.6% and 6%, respectively.
The average equity allocation is 67% in our sample and 68% in Vanguard’s. By contrast,
the average account balance is somewhat lower in our sample, $56,592 vs. $79,077, and so
is the median, $14,562 vs. $26,926, consistent with the fact, highlighted by Munnell and
Chen (2017), that the Vanguard sample tends to have a disproportionate number of large
plans with higher earners (the average salary is $65,000) and older workers (46 years old on
average). Finally, we calculate plan-specific fees for each worker, based on their individual
exposure to equity, bonds, and cash, either directly or through target date funds, and the
fees charged by the mutual funds in their plan. We find that the average fees are 26.4 bps
6

The sample excludes individuals who have “managed accounts”, whereby Edelman Financial Engines
manages the portfolio on behalf of the client and charges a fee on the assets under management. The sample
does include workers employed at companies with automatic enrollment and who are auto-enrolled.

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for bond funds, and 33.4 bps for the equity ones.
Bekaert, Hoyem, Hu and Ravina (2017) study a larger sample of approximately 3.8
million individuals and 296 firms. They show that the firms our workers are employed at
are, on average, larger than those in Compustat, with a median number of employees of
4,600, compared to only 475 in the Compustat sample, have higher ROA, have an average
age of 65 years, and are approximately half publicly listed and half privately held. They also
display more variety, with very large public firms next to smaller private ones. The same
is true for our estimation sample. Panel B of Table 1 shows that about 44% of the firms
are public, and they employ 62% of the workers. The median number of employees is 6,948,
and the average firm age is 74 years. Firms in both the full sample and our sample tend
to be more similar to the S&P500 fir ms: they have similar leverage (23.5% vs. 23.93%)
and investment intensity (4.70% vs. 4.17%), defined as capital expenditures over assets, but
slightly lower profitability (3.43% vs. 5.84%).
While we use the sample above to estimate our parameters, in the current analysis we
focus on the retirement preparedness of the subsample of workers employed at firms that offer
only defined contributions plans, rather than both defined benefit and defined contribution
ones. This sample includes a total of 350,859 workers. It is more straightforward to analyze
and reflects the increasingly common situation of workers having access only to DC plans
and being responsible for saving enough for retirement themselves. Indeed, based on data
from the Survey of Consumer Finances (SCF), Munnell and Chen (2017) find that between
1983 and 2016 the proportion of workers who only have a 401(k) has risen from 12% to 73%,
the proportion of workers who only have a defined benefit plan has decreased from 62% to
17%, and the proportion of workers with both has dropped from 26% to 10%.
Panel C of Table 1 contains the summary statistics for this subsample and shows that
the average worker is very similar to the one in the CPS: she is 41.3 years old, and has
worked at her firm for 7.9 years. She has however a higher salary ($56,464), like in the
larger estimation sample. Compared to the estimation sample, she contributes slightly less
to the plan (6.3% of salary vs. 6.9%), invests more conservatively, with a risky share of
62.44%, and pays similar fees. Finally, Panel D of Table 1 presents summary statistics for
the firms at which these workers are employed. It shows that the DC-only firms are on
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average 59 years old, have 13,674 employees, have similar leverage and investment intensity
as the estimation sample, but have slightly higher profitability, and are slightly more likely
to be private (62.79%). These similarities are comforting, given the further constraints we
have imposed on the sample.

2.2

Methodology overview

Our analysis consists of the three main steps which we outline below and describe in detail
in Sections 3 to 5.
First, we use simulations to compute, for each worker, the joint expected distribution of
T
, and social security income, YSi65 , assuming a retirement
total wealth at retirement, Wi65

age of 65.7
We decompose total wealth at retirement into four components:
- Retirement wealth associated to the current job and all future jobs (Wi65 )
other
- Wealth in the retirement accounts associated to previous jobs (Wi65
)
FW
)
- Wealth in non-retirement accounts available at retirement age (Wi65
HW 8
)
- Net housing wealth at retirement age (Wi65

For each worker, we obtain the distribution of Wi65 by starting from her current account
balance and simulating forward until age 65 based on the saving and investment behavior we
observe in the data. We run 10,000 simulations for each worker in the sample. The evolution
of employee contribution rates is estimated as a flexible function of the employee’s own lagged
contribution rate, age, salary, tenure at the firm, and their interactions, while the evolution of
employer contributions is based on the plan-specific rules reported by each firm in the Form
5500 filed yearly with the Department of Labor (DOL) and on the worker’s characteristics.
Our simulations take into account the IRS limits on employee and employer contributions,
and the fact that, upon turning 50, workers can elect to contribute more. The evolution
of the equity, bond, and cash portfolio allocations are estimated based on the worker’s
own lagged allocation, age, salary, tenure, and their interactions. Consistent with Madrian
7

Medicare and Medicaid are also taken into account and discussed below.
We consider different scenarios regarding the fraction of net housing wealth accessed during retirement
and provide additional details in Section 4.3.
8

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and Shea (2001), Agnew, Balduzzi, and Sunden (2003), and the subsequent literature on
401(k) accounts, we find significant inertia in both employee contribution rates and asset
allocations. Finally, based on the worker’s age, salary, industry, and other characteristics,
we also estimate the probability that in any period she becomes unemployed for some time,
switches jobs, or faces economic hardship, and that, as a result, with some probability, she
withdraws funds from her retirement account.
We follow a similar procedure to estimate the retirement wealth the worker has acother
). Assuming she started working at age 20 and using
cumulated at previous jobs (Wi65

information on her tenure in the current job, we calculate how long she has worked for preother
vious employers and compute Wi65
by simulating backward based on the same evolution

rules for contribution rates, portfolio allocations, and probabilities of withdrawing due to
unemployment, job changes, or hardship that we use to compute Wi65 . Finally, we obtain
FW
) and of net housing
measures of wealth accumulation in non-retirement accounts (Wi65
HW
) from estimates based on the Health and Retirement Study and the median
wealth (Wi65

house price in the area where the worker lives. This approach allows us to assign a different
FW
HW
value of Wi65
and Wi65
to each worker in each simulation, instead of assigning the average

value to all the individuals in our sample and across all simulations.
In the second step of the analysis we compute the optimal level of retirement-age consumption that can be sustained by each combination of total wealth and social security
income generated by our simulations. We use a consumption and savings model that incorporates investment, longevity, and out-of-pocket medical expenditure risk.9
Finally, in the third step, we evaluate each worker’s degree of retirement preparedness by
comparing the retirement consumption computed in the second step with an estimate of the
consumption during her working life. We estimate working-life consumption for each worker
based on the Consumer Expenditure Survey (CEX) and we account for the fact that upon
retirement individuals decrease work-related and other types of expenses and also turn to
9

While we don’t take a stand on whether the workers are optimizing during the asset accumulation phase
of their life, but rather we simulate the contribution rates and portfolio allocations based on the behavior
observed in the sample, when we estimate the consumption stream that can be financed by the wealth
accumulated at age 65, we compute the optimal consumption to determine the best the workers can do with
that wealth.

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home production for a larger fraction of their consumption needs.

3

Wealth accumulation in current and future DC accounts

We start the simulations at the oldest age for which we observe each worker in the sample,
take her current account balance as the starting point, and simulate forward until retirement
age.

3.1

Wealth evolution without leakages

To facilitate the exposition, we first describe the evolution of retirement wealth in the absence
of pre-retirement withdrawals (”leakages”).
3.1.1

Asset returns and fees

In our baseline analysis, retirement wealth can be invested in three asset classes: stocks,
bonds, and cash, with gross returns RtS , RtB , and Rf , respectively.10 The real return on cash
(Rf ) is assumed to be constant and calibrated to 0.5%, based on the historical mean real
return of 30-day T-Bills from 1926 to 2016. The returns on bonds and stocks are assumed
to be normally distributed and i.i.d. over time:
RtS ∼ N (µS , σ S )

(1)

RtB ∼ N (µB , σ B )

(2)

The equity return is set equal to the historical real return on the CRSP value-weighted index, with an annual standard deviation of 20%, and an equity premium of 6%. The bond
portfolio is a combination of five different types of bonds, each matched to a specific index:
the Barclays Capital Intermediate Government Bond Index, the Barclays Capital Long Term
10

We aggregate the investments in small and mid-cap funds, large cap funds, international equity funds,
and company stock into a general equity asset class; investments in bonds into a bond asset class; and
short-term treasury bills and cash-like investments in a cash asset class.

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Government Bond Index, the Salomon Brothers Non-US Government Bond Index, the Barclays Capital Corporate Bond Index, and the Barclays Capital Mortgage Backed Securities
Index. Each index is weighted based on the average monthly holdings by American investors
as reported in the ICI Fact Books. The historical return of such bond portfolio is 3.85. We
set the standard deviation to 0.08, since the weighted average standard deviation is 8.5%,
and the average correlation between the different indices is close to 1 (0.85).
Finally, our simulations also include the fees each worker pays on her stock and bond
portfolios, τ Si and τ B
i , respectively. Such fees are calculated based on the fees charged by the
mutual funds available in worker’s plan menu, and on her exposure to equity, bonds, and
cash, either directly or through target date funds. We find that fees vary significantly across
plans and investment vehicles, and across workers and firms (Panels A and C of Table 1).
3.1.2

Asset allocations and employee contributions

In the absence of pre-retirement withdrawals, retirement wealth Wit evolves based on the
net-of-fee returns on previous account balances, and employee and employer contributions,
according to the following equation:
B
B
S
B
f
e
Wit = [αSi,t−1 RtS (1 − τ Si ) + αB
i,t−1 Rt (1 − τ i ) + (1 − αi,t−1 − αi,t−1 )R ]Wi,t−1 + kit Yit + Kit (3)

where ki denotes the employee contribution rate, Kite denotes the employer contribution, and
αSit and αB
it denote the shares of her portfolio invested in stocks and bonds, respectively.
In the first year of the simulations, each worker’s contribution rate (kit ) and portfolio
shares (αSit and αB
it ) are set at their most recent sample values, and in the following years
they evolve according to the worker’s characteristics and the evolution equations estimated
from our panel. The employer contribution rates are calculated based on the rules reported
by each firm in the DOL Form 5500, and are described in more detail in the next subsection.
Panel A of Table 2 reports the estimation of the worker’s contribution rate as a function
of its own lag, the worker’s demographic characteristics, and their interactions. The specifications in Columns (1) and (3) include age and age squared, the worker’s annual salary,
and her tenure. The coefficients indicate that workers of higher age, salary, and tenure have
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on average higher contribution rates. The low R2 of these regressions points to the fact that
demographic characteristics explain a very small amount of the variation in contribution
rates across workers, similar to the results in the consumption and investment literature
(Browning and Lusardi, 1996; Giglio, Maggiori, Stroebel, and Utkus, 2019). To capture the
effect of firm characteristics, plan quality, fees, employer contribution rules, and any time
invariant firm characteristics that might affect workers’ contribution rates, Columns (2) and
(4) include firm fixed effects in the regressions. The coefficients are similar to the ones in
Columns (1) and (3), and the R2 only increases to about 10%. By contrast, Columns (5)
to (8) show that including the lagged contribution rate in the regressions increases the R2
dramatically, to about 70%, and that adding firm fixed effects to such regressions does not
further increase their explanatory power (Columns (6) and (8)). We find that contribution
rates are a concave and increasing function of age, and that they are very persistent, consistent with prior evidence that individuals don’t change their saving behavior by much from
one year to the next. Adding zip code fixed effects to better capture the socio-economic
background of the worker and the general economic conditions of the area she lives in, winsorizing the dependent variable at the 1st and 99th percentiles, or restricting the sample to
cases with positive contribution rates yield qualitatively and quantitatively similar results
(available upon request). We choose the evolution equation in Column (5) as an input to
our simulations, because of the high R2 and the parsimonious specification. We thus model
the evolution of the worker’s contribution rate as
kit = −0.0096 + 0.851 ∗ ki,t−1 + 0.000692 ∗ ait − 0.00000628 ∗ a2it

(4)

where ait represents the worker’s age.11 In addition, every year the IRS sets the maximum
dollar amount that can be contributed to tax deferred retirement accounts, caps the catch-up
contributions for workers older than 50, and sets limits on the base salary used to calculate
the employer’s contributions. Our simulations take these limits into account, and assume
they increase with inflation.12
11

In the simulations, we constrain the contribution rates to be non-negative and below 30%, which is
higher than the 99th percentile in our sample.
12
Details about the IRS limits on contributions can be found at https://www.irs.gov/retirement-

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In Columns (9) and (10) we model worker contribution rates as a more complex function
of their own lag, worker’s salary, tenure at the firm, account value, a cubic polynomial in
age, and their interactions. The objective is to check whether, as the worker ages, she plays
catch up and contributes more if she realizes her account balance is low. Columns (9) and
(10) show this is not the case: as the worker ages she contributes more than before if, all
else equal, her account balance and past contribution rates are higher, not lower. In Section
6.2.4 we show that our findings are unchanged if use this more complex evolution equation
as input for our simulations.
Panel B of Table 2 reports the estimation of the evolution of the portfolio allocations as a
function of their own lag, the worker’s characteristics, and their interactions. For brevity, we
only report the specifications including lagged portfolio shares, as both the bond and equity
share display significant persistence. Columns (1) and (3) report the coefficients on age and
annual salary, their squared values, and their interactions, while Columns (2) and (4) report
the results of running the same specifications with firm fixed effects. Column (1) shows that
the most important determinant of the equity share is its own lag, with a coefficient on the
lagged share of 0.92, and that the other coefficients are not statistically significant. Column
(2) shows that when we add firm fixed effects more coefficients become significant, but that
the explanatory power of the regressions does not increase. Column (3) shows that the most
important determinant of the bond share is also its own lag, but that age and salary also
matter. The coefficient on the lagged bond share is 0.91. All else equal, the bond share in the
worker’s portfolio increases with age and more so at higher levels of salary, and it decreases
with salary, although this effect is economically small. Similar to the case of equity, adding
firm fixed effects doesn’t increase the explanatory power of the regressions. Thus, we choose
the specifications in Columns (1) and (3) as the input for our simulations:
αSit = 0.081880053 + 0.91617255αSi,t−1

(5)

B
2
αB
it = 0.91410212αi,t−1 + (3.467069E − 4)ait − (4.088E − 8)Yit + (1.199E − 11)ait Yit

(6)

plans/cola-increases-for-dollar-limitations-on-benefits-and-contributions. We verify in the data that such
limits do indeed closely track inflation.

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where ait represents the worker’s age, and Yit her salary.
Finally, we check the predictive ability of our evolution equations by repeating the estimation using only the first half of the sample, and using the estimated coefficients to predict,
for each worker, the contribution rate and the asset allocations on the last date she appears
in the sample. We find that the predicted and actual values at the last sample date are not
statistically different from each other in 96.40% of the cases for the contribution rates, in
93.04% of the cases for the bond share, and in 95.75% of the cases for the equity share.
3.1.3

Employer contributions

We capture the employer contribution schemes with the following flexible specification
0

T ot

Kite (Yit ) = M in{M in{kie0 Yit , K i } + Kimatch , K i }

(7)

where kie0 is the portion of the employer contribution independent of the employee’s own con0

tribution, expressed as a percentage of her current salary, and capped at K i , while Kimatch is
the employer’s matching contribution, described below. The total employer contribution is
T ot

capped at K i .
The matching contribution rules usually have multiple tiers. For example, the company
might match 100% of the employee’s contribution up to 3% of her salary, and 50% of the
contribution up to an additional 2% of her salary. Therefore, we specify a fairly general
formulation below:

Kimatch


e1


κe1 ∗ kit
if kit ≤ k i

 i
e1
e1
e1
e2
e1
= Yit ∗ κe1
∗ (kit − k i )
if k i < kit ≤ k i + k i
∗ k i + κe2
i
i



 κe1 ∗ k e1 + κe2 ∗ k e2 + κe3 ∗ M in{k − (k e2 + k e1 ), k e3 } if k > k e2 + k e1
it
it
i
i
i
i
i
i
i
i
i
i
(8)

where kit is the employee contribution rate, defined in Section 3.1.2. In the example above
we would have
e1

e2

e2
e3
κe1
i = 100%, k i = 3%, κi = 50%, k i = 2%, κi = 0%

The features of each pension plan are then represented in our simulations by the following
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vector of parameters:
0

e1

e2

e3

T ot

e2
e3
{kie0 , K i , κe1
i , k i , κi , k i , κi , k i , K i }

Panel C of Table 2 provides descriptive statistics for these parameters. For comparison,
we report values for both the estimation and DC-only samples. The average non-matching
employer contribution (kie0 ) is 1.83% of salary for the full sample, and 1.57% for the DC-only
sample. The median is 0% in both samples, as only one-third of firms provide non-matching
contributions. The median (average) firm matching contribution is 60% (72.08%) of the
employee’s contributions up to a median (average) limit of 4% (3.82%) for the estimation
sample. The median (average) firm matching contribution is 100% (62.77%) of the employee’s
contributions up to a median (average) limit of 4.5% (3.20%) for the DC-only sample. The
averages show that overall the employer contributions in the DC-only sample tend to be less
generous than those in the full sample, indicating that firms that are substituting generous
defined benefit plans with defined contribution ones also tend to provide better terms in
their 401(k) plans. However, the medians tell a different story, making it unclear which set
of plans is overall better.
Finally, more than two-thirds of the firms don’t make further contributions (i.e. κe2
i =
e3
κe3
i = 0), and only 1% of the workers have a third tier (κi > 0). For this reason, we do not

consider additional tiers in our simulations.

3.2

Wealth evolution with leakages

Workers can withdraw funds from their retirement accounts because of a job separation,
either due to unemployment or a voluntary job switch, in case of hardship, and upon reaching
age 59 1/2.13 Munnell and Webb (2015) estimate that these “leakages” reduce “aggregate
401(k)/IRA wealth at retirement by about 25 percent.”
In the next four subsections we describe how we model such withdrawals in our simulations, and in subsection 3.2.5 we provide details on the empirical estimation of the withdrawal
probabilities and amounts for different types of worker.
13

Hardship includes health care expenditures larger than 10% of the worker’s income, permanent and
total disability, outlays incurred to prevent foreclosure, costs related to purchasing the principal residence,
excluding mortgage payments, and the cost of post-secondary education.

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3.2.1

Withdrawal following a voluntary job switch

With probability π s (.) a worker voluntarily switches jobs, and, upon that happening, with
probability π sW (..), she withdraws a fraction ls (.) of her account balance. The corresponding
retirement wealth accumulation equation is given by

e
 RW W
i,t−1 + kit Yit + Kit
it
Wit =
 RW W
+ k Y + K e − ls (.)W
it

i,t−1

it it

it

with probability 1 − π sW (.)
i,t−1

(9)

with probability π sW (.)

where
f
B
S
B
B
RitW = αi,t−1 RtS (1 − τ Si ) + αB
i,t−1 Rt (1 − τ i ) + (1 − αi,t−1 − αi,t−1 )R

and

π sW (.) :

probability of withdrawal, conditional on a job switch

ls (.) :
3.2.2

fraction of the account balance withdrawn, conditional on a job switch

Withdrawal following a job loss

Workers face a probability π u (.) of becoming unemployed, which is reflected in the evolution
of retirement wealth by

e
 RW W
i,t−1 + (1 − u(.))(kit Yi + Kit )
it
Wit =
 RW W
+ (1 − u(.))(k Y + K e ) − lu (.)W
it

i,t−1

it it

it

with probability 1 − π uW (.)
i,t−1

with probability π uW (.)
(10)

where
u(.) :

duration of the unemployment spell (in a fraction of a year)

π uW (.) :

probability of withdrawal, conditional on unemployment

lu (.) :

fraction of the account balance withdrawn, conditional on unemployment

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Notice that in this case the contributions only take place while the individual is employed,
for a fraction (1 − u(.)) of the year.
Following a job loss, we consider three different scenarios regarding the worker’s new
pension plan. In the first, we assume that her new DC plan is identical to the current one.
In the second and third, we assign her to a new DC plan randomly drawn from the plans of
workers in the same income decile, or from all the plans in the sample. Appendix 1 shows
that the results are almost identical across these scenarios.14
3.2.3

Withdrawal due to hardship

A hardship withdrawal occurs with probability π h and, in such case, no contribution is made
for that period. Wealth accumulation is given by
Wit = RitW Wi,t−1 − lh (.)Wi,t−1

(11)

where lh (.) is the fraction of the worker’s account balance that is withdrawn.15
3.2.4

Withdrawal upon reaching age 59 1/2

Starting at age 59 and a half, workers can withdraw funds from their retirement account
without penalty. In our simulations this occurs with probability π 60
W . In such an event, no
contribution is made to the retirement account, and wealth accumulation is given by
Wit = RitW Wi,t−1 − l60 (.)Wi,t−1

(12)

where l60 (.) is the fraction of the account balance that is withdrawn.
14

We are implicitly assuming that if a worker at some points joins a firm with a DB plan she is immediately
vested and that the wealth accumulated through this plan is the same as what she accumulates in the DC
plan.
15
In this case, by definition, funds are withdrawn from the retirement account with certainty, π hW = 1 .

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3.2.5

Estimation of the leakages parameters

Job Separations. Unemployment rates and durations are estimated as a function of industry, age, salary, and education based on the Current Population Survey Merged Outgoing
Rotation Groups (MORG), a monthly survey conducted by the Bureau of Labor Statistics
to measure labor force participation and employment. In these estimations, we assume the
workers enter the labor force at age 23, get no additional education once they start working, and, when changing jobs, stay in the same industry. The coefficients we obtain for the
probability of unemployment (π u ) and its expected duration (u) are given by

π ui = constantprobi − 0.0248848 ∗ ai + 0.00024636 ∗ a2i

(13)

ui = constantduri + 1.0450717 ∗ ai − 0.0078187 ∗ a2i

(14)

where the constant term is worker-specific and includes industry fixed effects, and education effects estimated for each individual based on her industry, age, and salary. As a
consistency check, we find that applying the estimates above to our own sample of workers
yields an average unemployment rate of 4.73%, and a duration of 28 weeks, in line with the
recent aggregate statistics.
We obtain industry-level separation ratios due to voluntary job changes from the Job
Openings and Labor Turnover Survey (JOLTS), conducted monthly by the Bureau of Labor
Statistics.
π si =

U nemploymentRate
− U nemploymentRate
SeparationRatio

(15)

The fraction of plan participants cashing out upon a voluntary or involuntary job separation and the average fraction of funds withdrawn by such workers in each age bracket are
estimated based on the equations above, data from Munnell and Webb (2015), tabulations
from the 2008 and 2013 editions of Vanguard’s How America Saves, and our own data. According to Vanguard data, 9% of workers changed or lost their jobs in 2008. Of these, 28.8%
took money out of their retirement accounts, although the fraction of the account balance
being withdrawn varied significantly by age and account size, with young and low-balance
account holders being more likely to withdraw and withdrawing larger fractions (see Table
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2 in Munnell and Webb, 2015). Vanguard estimates that 0.5% of all its 401(k) assets were
withdrawn because of this reason.
Panel A of Table 3 reports our calculations. The first two columns reproduce Table 2
from Munnell and Webb (2015). For each age group, the first column reports the percent
of plan participants cashing out upon a job separation, either voluntary or involuntary,
while the second column reports the fraction of that cohort’s aggregate account balance
that is being cashed out. Columns (3) and (4) report the probability of losing one’s job or
switching voluntarily, based on equations (13) and (15) above. Columns (5) and (6) report
the fraction of participants cashing out upon unemployment and a voluntary job switch,
respectively. They are based on estimates from Engelhardt (2003), who finds that, in case of
unemployment, the probability of cashing out is 46.7% higher than for voluntary job switches.
For example, a worker in her 20s who leaves her firm has a probability of cashing out equal to
43.84%, if she lost her job (Column (5)), and equal to 30.03%, if she switched jobs voluntarily
(Column (6)). These probabilities are calculated to make the overall probability of cashing
out equal to 35%, as reported in Column (1).
The other columns in Panel A outline in detail our computations of the average fraction
of the worker’s account being withdrawn, by age and reason for the separation, based on
the total amount of funds available to each age group in our data, the average account
value, and the probabilities calculated above. Column (7) reports the total dollar balance
available to each age cohort in our dataset, Column (8) the number of people in each age
group, and Column (9) their average account value. Columns (10) and (11) calculate the
number of workers in our dataset becoming unemployed or switching to another firm, based
on the probabilities in Columns (3) and (4). Column (12) reports the aggregate account
balance available to such workers, based on the average account value calculated in Column
(9). Column (13) reports the total funds withdrawn by those who leave the firm, based on
the aggregate balances in Column (12) and the withdrawal fraction estimated by Munnell
and Webb (2015) and reported in Column (2). Based on this information, Columns (14)
and (15) report the number of workers withdrawing funds because of unemployment and
voluntary job switches, respectively. Column (16) report the average amount withdrawn by
each worker, as a fraction of the total asset withdrawn (Colum (13)) and the number of
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people leaving the firm (the sum of Columns (14) and (15)). Finally, Column (17) reports
the fraction of the worker’s account balance that is being withdrawn, as the ratio of the
average amount withdrawn reported in Column (16) and the average account value in that
age cohort (Column (9)). The inputs for our simulations are the probability of cashing out
due to unemployment (Column (3)) or a voluntary job switch (Column (4)), and the fraction
of the worker’s own account that she withdraws (Column (17)) given by
π uW = 0.4384Ia∈[20,29] + 0.3997Ia∈[30,39] + 0.3983Ia∈[40,49] + 0.2982Ia∈[50,59] + 02361Ia∈[60,69]
(16)
π sW = 0.3003Ia∈[20,29] + 0.2738Ia∈[30,39] + 0.2728Ia∈[40,49] + 0.2042Ia∈[50,59] + 0.1617Ia∈[60,69]
(17)
ls = lu = 0.4286Ia∈[20,29] + 0.3438Ia∈[30,39] + 0.3125Ia∈[40,49] + 0.2917Ia∈[50,59] + 0.2105Ia∈[60,69]
(18)
As a consistency check, we use the estimates above to calculate the average fraction withdrawn across all cohorts, and find that it is 30.3%, compared to 28.8% reported by Munnell
and Webb (2015).16 We also calculate the percentage of the total assets being withdrawn
and find that it is about 7%, both in our sample and in Munnell and Webb’s.
Hardship withdrawals. Based on data from the Survey of Consumer Finances and from
Vanguard’s How America Saves, Munnell and Webb (2015) estimate that people taking
hardship withdrawals are 1.2% of the total (see Fig. 3 in their paper) and withdraw 0.3% of
total aggregate assets. Based on this information, the fact that in our sample workers age
59 or less are 90.17% of our sample, own 81.67% of the assets, and have an average account
value of $55,462, we estimate that 1.33% of them will make a hardship withdrawal and they
will withdraw 0.37% of the total assets belonging to their age group. This corresponds to
withdrawing on average 27.6% of the funds in their individual accounts. As a consistency
check, Vanguard estimates that, on average, people who make hardship withdrawals withdraw 0.28% of the funds available to those younger than 60, and 25% of the funds in their
16

Taking a weighted average yields a withdrawal fraction equal to 24.31%, as reported at the bottom of
Column (17) of Panel A of Table 3.

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individual accounts.
Age 59 1/2 withdrawals. Munnell and Webb (2015) estimate that 0.93% of the workers
make withdrawals upon reaching 59 1/2 years of age, and cash out 0.2% of the total assets in
the system. Since in our sample workers age 60 and higher are 9.83% of the total, own 18.33%
of the assets, and have an average account value of $114,081, we estimate that the probability
of making a withdrawal conditional on reaching age 60 is 9.49%, the average fraction of the
total assets withdrawn is 1.09%, and the fraction of the worker’s balance being withdrawn
is 11.49%. Both the probability of withdrawing and the fraction withdrawn are estimated
as a (negative) function of the worker’s salary decile. The estimates are reported in Panel B
of Table 3.
It is worth noting that loans are excluded from the analysis, despite being an increasingly
important phenomenon, because based on the estimates in Munnell and Webb (2015) they
don’t affect asset accumulation by much, since the great majority of them is repaid.

3.3

Labor income process

Following the life-cycle consumption and savings literature, we model labor income as

 f Y (t, Z ) + P + U
with probability 1 − π ui (.)
it
it
it
Ln(Yit ) =
 (1 − ϕ)(f (t, Z ) + P + U ) with probability π u (.)
it
it
it
i

(19)

where f Y (t, Zit ) is a deterministic polynomial of age and individual characteristics, ϕ is the
fraction of income lost during an unemployment spell, π ui (.) is the probability of unemployment, defined above, and
Uit ∼ N (0, σ 2U )

(20)

Pit = Pit−1 + Nit , Nit ∼ N (0, σ 2N )

(21)

We set both σ N and σ U to 0.1, as it is standard in the literature (Gourinchas and Parker
(2002), Carroll (1997), Cocco, Gomes and Maenhout (2005)). The probability of unemployment is worker-specific, and discussed in Section 3.2.5, while the fraction of yearly income

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lost during an unemployment spell is taken from Brown, Fang, and Gomes (2012). We initialize our simulations with the actual observed wage income for each worker, and use the
stochastic process above to simulate the evolution of income going forward.

4

Other sources of wealth

Most individuals in our sample have worked in at least one previous job before joining their
current employer. It is therefore important to estimate the retirement wealth accumulated
other
). In addition, they might also have accuduring any previous employment spells (Wi65
FW
mulated financial wealth outside of their retirement accounts (Wi65
), and they might have
HW
access to home equity (Wi65
) they can use to finance consumption in retirement either by

downsizing to a smaller house or by entering into a reverse mortgage. Combining all these
sources, wealth accumulation at retirement is given by
T
other
FW
HW
Wi65
= Wi65 + Wi65
+ Wi65
+ θWi65

(22)

where θ is the fraction of housing wealth spent during retirement.
As a preview of our results, we find that, except for scenarios with very high θ, total wealth
at retirement is largely determined by the worker’s retirement account balances (Wi65 +
other
Wi65
), which constitute the primary output of our simulations. In our baseline case, where
T
other
is 0.66, i.e. two-thirds of the total wealth
)/Wi65
θ = 0.5, the median value of (Wi65 + Wi65

available to finance retirement is coming from the retirement accounts. Moreover, even at
the 25th percentile of the wealth distribution, this ratio is still larger than 0.50.

4.1

Retirement wealth from previous employment spells

In order to estimate retirement wealth accumulation at previous employers, we first compute
the total length of those employment spells by combining information on the worker’s age at
the start of our simulations (a0 ) and her tenure on the current job (t). In our baseline analysis,
we assume that everyone starts working at age 20 (t0 ). We then make the same assumptions
as above regarding the evolution of wage income, asset returns and fees, the probability
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of unemployment, voluntary job switches, and leakages. We also assume that during any
previous employment spell(s), each worker had access to a retirement plan identical to the
current one, or to one drawn at random either from the full sample, or from the plans
available to the workers in her income decile. Under these assumptions, the evolution of
retirement wealth from earlier employment spells is given by

Witother


 RP W other + K e + k Y
it it
i,t−1 i,t−1
it
=
 RP W other
i,t−1

i,t−1

t ∈ [t0 , a0 − t]

(23)

t ≥ a0 − t

where
P
B
B
S
B
f
Ri,t−1
≡ αSi,t−1 RtS (1 − τ Si ) + αB
i,t−1 Rt (1 − τ i ) − (1 − αi,t−1 − αi,t−1 )R

(24)

The first branch of the formula captures the wealth evolution while the worker was enrolled
in the plan, and includes both worker and employer annual contributions. Labor income is
simulated backwards for these years based on the stochastic process in (19). The second
branch captures the evolution of the account balances from the time the worker started
her current job, at which point no additional contributions were made to these plans. The
contribution parameters kit and Kite are derived in Sections 3.1.2 and 3.1.3, respectively,
B
S
while the returns, the fees, τ Si and τ B
i , and the asset allocations, αi,t and αi,t , are described

in Sections 3.1.1 and 3.1.2.

4.2

Financial wealth outside retirement accounts

Throughout their lives, workers might also save outside their retirement accounts, to finance
both pre-retirement and retirement consumption. To measure the wealth saved for retirement
purposes outside of retirement accounts, we turn to the Health and Retirement Study, and
estimate the relationship between retirement and non-retirement financial wealth at age 65.
More precisely, we fit the following regression and use the resulting mapping from retirement
to non-retirement wealth in our simulations:
FW
Wi65
= αF W + β F W ∗ Wi65 + εFi W

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(25)

Focusing on the sub-sample of married individuals between age 62 and 67 in the 2010
Wave of the HRS, we estimate the relationship between household net wealth excluding
retirement and housing wealth, and the balance in the respondent’s DC plans, controlling
for her salary in the current job or the last job prior to retirement. This wealth measure
is computed as the sum of the value of stocks, mutual funds, investment trusts, checking,
savings and money market accounts, certificates of deposit, government savings bonds, Tbills, bonds and bond funds, and all other savings, less non-real estate debt. We restrict
the estimation to married people, who constitute 67% of the respondents in the 62-67 age
bracket, to avoid underestimating households’ outside wealth by including single individuals
in the regression. Nevertheless, we confirm that in our sample the net wealth of single
individuals as defined above is about half of that of married ones.
As a consistency check, Panel A of Table 4 shows that the DC account balance of married
respondents between 62 and 67 in the HRS, both overall, from their last job, or measured as
total retirement wealth is very similar to the account balances for the workers between age
62 and 67 in our 401 (k) sample, both in terms of their mean and median, and of their overall
distribution. The exception is the unconditional total retirement wealth, which is zero for
the bottom quartile of the HRS sample, due to non-participation and possibly to issues with
this survey question (see Gustman et al. (2014) for a detailed analysis of the issues with the
pension wealth data files in the HRS). Because of the findings in Gustman et al. (2014), we
estimate outside financial wealth as a function of total DC account balance, rather than total
retirement wealth. Finally, Panel A of Table 4 also shows that the balance from the main
account, or the account connected to last job, is very similar to the total balance, suggesting
that most people close to retirement, or already retired, have consolidated their balances
into one account.
The estimates from the regression of outside financial wealth on DC account balance are
reported in Panel B of Table 4, both including and excluding salary. We pick specification
(1) as an input for our simulations because of its simplicity, and note that the coefficients
do not depend much on conditioning on the respondents having positive retirement wealth.

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4.3

Housing wealth

During retirement, individuals can use part or all of their home equity by downsizing to a
smaller house or entering into a reverse mortgage.
Since worker-level information about housing equity is not available in our sample, we
compute it using a three-step procedure. First, we estimate the probability that each worker
is a homeowner at age 65 (phi65 ). Second, we estimate her house value at age 65 by projecting
forward the Zillow median house value Hi in the zip code where she currently lives, using an
expected housing price appreciation rate (rH ) of 1%, taken from Cocco (2005).17 We then
combine these values with an estimate of the loan-to-value ratio at age 65 from the Health
and Retirement Study. Our estimate of housing wealth is thus given by:
HW
Wi65
= phi65 (1 + rH )65−a Hi (1 − LT Vi65 )

The probability of being a homeowner is estimated with a probit model based on the
subsample of married individuals between the ages of 62 and 67 in the HRS.18 Panel A of
Table 5 presents the summary statistics. The first four rows of the Panel show that most
people in this age group don’t own additional real estate beyond their first residence, and
that the house values from the HRS and those from Zillow are quite similar over our sample
period. The last two rows show that for this sample the average (median) loan to value ratio
on the first residence is 27.4% (5.7%), indicating that most people have paid down their
mortgages almost completely by the time they have reached retirement age. The values
including other real estate are similar.
Panel B of Table 5 reports the regression coefficients. Columns (1) and (2) show the
probability of being a homeowner as a function of retirement wealth and salary, overall and
conditional on positive retirement wealth, while Columns (3) and (4) show the LTV on the
first residence and overall as a function of the same variables. We base our simulations on the
17

Yao and Zhang (2005) use a 0% appreciation rate. This lower value would decrease estimated housing
wealth and exacerbate the retirement shortfall we find in the study.
18
The data indicate that single individuals in this age bracket are more likely to be renters, and, when
they are homeowners, they tend to own cheaper houses and have about half the housing wealth of married
couples.

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estimates in Columns (1) because of the higher R2 , and, for consistency, on the estimates in
Column (3), noting that the LTV coefficients are quite similar across the two specifications.

4.4

Social Security income

During retirement, the workers’ accumulated wealth is supplemented by Social Security
income. For each simulation, we apply the Social Security formulas to the worker’s lifetime
income profile estimated based on the stochastic process given by (19). The amount of Social
Security income a retiree receives is calculated based on a piece-wise linear function of the
average indexed monthly earnings. The formula implies a replacement ratio of 90% up to a
certain amount, of 32% for the portion of earnings between that amount and the next kink
point, and of 15% for the rest.19 We let the kink points grow over time at the inflation rate,
after verifying the reasonableness of this approach in the data.

5

Consumption during retirement and retirement preparedness

For each simulation, we compute the consumption level that can be financed by the worker’s
wealth at age 65 and her Social Security benefits. Our approach is to calculate the optimal
consumption the worker can sustain with the simulated resources she has at the time she
retires. While actual consumption patterns during retirement might differ from the optimal
path, they would make the worker worse off in terms of expected utility maximization and
thus imply worse expected outcomes than the ones we analyze.
We compute optimal consumption during retirement as the solution to an intertemporal
consumption and savings problem starting at age 66. Our model includes longevity risk, investment return risk, uncertain out-of-pocket medical expenditures, federal and local taxes,
and realistic Social Security rules. By explicitly including out-of-pocket medical expenditures, the model also takes the financial support provided by the Medicaid and Medicare
19

Details
of
the
Social
Security
benefit
formula
can
be
found
at
https://www.ssa.gov/policy/docs/chartbooks/fast facts/2010/fast facts10.html. For 2010 the kink points
were $761 and $4,586.

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programs into account.

5.1

Preferences and budget constraint

Individual preferences are given by a time-separable power utility function:

U =E

100
X

β

t−65

t=65

t−1
Y

!
pj

j=0

(Cit )1−γ
1−γ

(26)

where pt denotes the probability that the individual survives to age t + 1, conditional on
being alive at age t. As we explain in more detail below, these probabilities are stochastic,
allowing us to incorporate longevity risk in the model. To avoid carrying around an additional
preference parameter, we address bequest motives when evaluating retirement adequacy,
rather than including them directly in the optimization problem.20
We assume retirees have access to a risky asset, stocks, and a riskless asset, T-bills.
Based on the extensive evidence that individuals rebalance their 401(k) portfolios only very
infrequently (Section 3.1.2 of this paper, but also Agnew, Balduzzi, and Sunden (2003),
Brunnermeier and Nagel (2008), and Bilias, Georgarakos, and Haliassos (2010) among others), we assume each individual keeps constant portfolio shares throughout retirement, and
present results for different hypothetical allocations. By contrast, a model of optimal portfolio allocation would imply counterfactually high changes in individual allocations over the
life cycle for most combinations of the preference parameters. We also note that given that
we assume an exogenous portfolio rule and vary the weight in the risky asset to generate
different values of the expected return and standard deviation of the retiree’s portfolio, our
two-asset specification is equivalent to one with a larger set of assets, as long as all risky
assets have the same Sharpe ratio.21 Further, the sensitivity analysis reported in Section
6.2.2 confirms that the main conclusions about retirement preparedness are unchanged under
different assumptions about the retiree’s asset allocation. Finally, we do not include annuity
20

Love, Palumbo, and Smith (2008) and DeNardi, French, and Jones (2010), among others, nicely illustrate
the role of longevity risk, mortality risk, medical expenditure risk, and bequest motives in explaining wealth
evolution during retirement.
21
Section 3.1.1 shows that the historical Sharpe ratio on stocks is 0.30, and the one on bonds is similar
(0.28).

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products in our model, as they are not widely used despite having been shown to potentially
generate substantial welfare gains at retirement if individuals were to invest (more) in them
(e.g. Horneff, Maurer, Mitchell and Stamos (2010)).
The dynamic budget constraint is:
T
Wi,t+1
= Rt+1 WitT − Cit − Mit + YS

(27)

where Mit denotes the medical expenditure shocks, Rt+1 is the return on the fixed retirement
portfolio, and Y S is social security income.

5.2

Longevity risk and medical expenditures

We model longevity risk following Lee and Carter (1992), who specify death rates for age t
and calendar time x (dt,x = 1 − pt,x ) as:
ln(dt,x ) = at + bt × φx

(28)

The at coefficients capture the average shape of ln(dt,x ) over the life-cycle, while the bt
coefficients reflect how mortality rates at different ages respond to mortality shocks over
time, φx .22 The random variable φx is given by:
φx = µφ + φx−1 + εφx

(29)

where µφ is the drift parameter, and εφx is normally distributed with mean zero and standard
deviation σ φ . We take the values for at , bt , µφ and σ φ from Cocco and Gomes (2012).
We estimate the process for out-of-pocket medical expenditures using data from the HRS
on the subsample of retirees older than 65. These expenditures reflect what the retirees have
to pay beyond any Medicare and Medicaid benefits, thus incorporating the social insurance
provided by these programs into our analysis. Since in the data medical expenditures are
22

The bt coefficients are a relative measure, normalized to sum to one.

31

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highly correlated with income, we model them as a ratio of disposable income at age 65
Mit
= f M (t) + Vit
Y65

(30)

Vit = ρVit + εit , Vit ∼ N (0, σ 2V )

(31)

where t denotes age and

We experiment with estimating equation (30) both in logs and in levels and find that the
latter better fits the data.23 We fit f M (t) as a third order polynomial and estimate ρ = 0.4377
and σ = 0.2842.24

5.3

Optimization problem

The full optimization problem is given by:

E
M ax
100

{Ct }65

100
X

β

t−65

t=65

t−1
Y

!
pj

j=0

(Cit )1−γ
1−γ

(32)

subject to the budget constraint in equation (27), to the stochastic process for the survival
probabilities in equations (28) and (29), and the process for medical expenditures in equations
(30) and (31). We scale wealth by Y S , and we are left with four state variables: scaled
T
/Y S ), age (t), a persistent medical expenditure shock (Vi,t ), and the current
wealth (Wi,t

survival probability (pt ). The model is initialized at the wealth level available at the start
T
T
. Thus, the optimal consumption path for a given value of Wi65
/Y S is:
of retirement, Wi65

T
T
/Y S ), . . .}
{Ci65 (Wi65
/Y S ), Ci,66 (Wi65

T
We solve the model for a grid of potential values of Wi65
/Y S , and, using interpolation, we

obtain the implied optimal consumption sequence for each of the 10,000*350,859 paths we
23
Both in the model and in the simulations we restrict Mit to be positive, and we cap Mit /Y65 at 2.0.
Since there are no observations in the HRS for which this ratio exceeded 200%, this constraint is strongly
motivated by the data and does not affect the validity of the estimation.
24
The coefficients of the age polynomial are 0.1463164, 0.0025844, −0.0001708, and 0.0000174, for the
constant, linear, quadratic, and cubic term, respectively.

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simulate.

5.4

Evaluating retirement adequacy

In the final step of our analysis, we evaluate to what extent, and for which workers, wealth
accumulation at age 65 can sustain an optimal consumption level during retirement that is
comparable, after making some adjustments, to the pre-retirement one. Below we discuss
the methodology used to perform this evaluation.
5.4.1

Our approach

From a utility maximization perspective, the discounted marginal utility of consuming one
more dollar today should be equal to the marginal utility of saving that dollar for the future,
i.e. the optimal consumption path should satisfy
U 0 (Cia0 ) = β (65−a0 )

64
Y

!
pj

p
)(65−a0 ) ]
E[U 0 (Ci65 )(Ri,a
0 ,65

(33)

j=a0

where Cia0 denotes current consumption, Ci65 denotes consumption at retirement age, and
p
Ri,a
is the return on a feasible investment portfolio from age a0 till retirement. While
0 ,65

this equality holds for all ages, both pre- and post-retirement, we focus on ages a0 and 65
because we observe a0 in our data, and because if the optimal consumption at the beginning
of retirement, Ci65 , is too low, the same is true for the optimal consumption in all future
years.
Equation (33) implies that optimal consumption is a smooth, although not necessarily
constant, function of age. Indeed, in most life-cycle models consumption is a mildly humpshaped function of age. The hump-shaped pattern is concentrated very early in life, when
the precautionary savings motive and liquidity constraints are most prominent, and, absent
a strong bequest motive, very late in life, when the survival probabilities drop significantly
(e.g. Gourinchas and Parker (2002), and Cocco, Gomes and Maenhout (2005)). For this
reason, we assume that optimal consumption smoothing implies

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U 0 (Cia0 ) = E[U 0 (Ci65 )]

(34)

i.e. the level of retirement savings is adequate if, in expectation, the worker will be able to
maintain her current standard-of-living when she retires.25
It is important to emphasize that several expenditures, e.g. housing, education, and
children-related expenses, are incurred early in life, but generate consumption over the entire
life cycle. Moreover, during retirement, individuals partially substitute marketplace goods
for home production, which has lower financial costs (Aguiar and Hurst, 2005 and 2013).26
Therefore, we expect that expenditures during retirement will be lower than before even if
the individual saved enough and she is actually enjoying the same standard of living. More
explicitly, we can rewrite Equation (34) as

U 0 (Cia0 ) = U 0 (ϕExpendituresia0 ) = E[U 0 (Ci65 )]

(35)

where ϕ is an adjustment factor that based on both academic studies and practitioners’
guidelines ranges from 0.7 to close to 1. Since lower values of ϕ are associated to lower
thresholds for retirement preparedness, we start with a conservative baseline value of ϕ =
0.8.27
Finally, our approach focuses on direct comparisons of consumption rather than income
levels. The limitations of evaluating retirement adequacy solely based on income measures
are discussed in detail in Poterba (2015) and Biggs (2016), and acknowledged by most of
the studies using them (e.g. Munnell, Webb and Delorme (2006), VanDerhei (2006), Brady
(2010), and Pang and Schieber (2014), among others). The main one is that, unlike (35),
25

Since at young ages consumption might actually be lower than in (34) because of precautionary savings
and borrowing constraints, our approach understates young workers’ retirement preparedness. It is worth
noting however that our finding that 75% of the workers are likely to fall short does not depend on the younger
cohorts. To the contrary, based on our simulations, younger workers appear to be the best prepared.
26
Medical expenditures increase substantially after-retirement, and indeed they are directly incorporated
in our model of optimal retirement consumption.
27
One of the measures of retirement adequacy we report below, the consumption replacement ratio, can
be easily recomputed for different values of ϕ by multiplying it by the ratio of 0.8 to the new adjustment
factor. For example, results for ϕ = 0.9 can be computed by multiplying the consumption replacement ratios
reported in Sections 6 and 8 by 0.8/0.9.

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which is the result of an optimization problem over the entire retirement period, focusing on
income replacement ratios at the date of retirement ignores changes in income and expenses
that may occur later in life. Also, target income replacement ratios do not consider the heterogeneity in individual circumstances. Finally, the way both the pre- and post- retirement
income is measured can sometimes substantially affect the fraction of households deemed
adequately prepared for retirement.
5.4.2

Certainty equivalent ratio and consumption replacement ratios

Following the approach outlined above, we calculate two measures of retirement preparedness: the certainty equivalent ratio (CEQR), and the distribution of the consumption retirement replacement ratios (CRRRs).
The certainty equivalent ratio (CEQR) is obtained by computing the certainty equivalent
of consumption from the right-hand-side of (35) after imposing a specific functional form
(power utility in our case):
CEQR ≡

C i65
C i65
=
ϕExpendituresia0
Cia0

(36)

where C i65 is obtained from:
E[U 0 (Ci65 )] = U 0 (C i65 )
By contrast, for each worker, the consumption retirement replacement ratios (CRRRs)
are the percentiles of the distribution of the ratio of post- to pre-retirement consumption
across the 10,000 simulation paths:
CRRR(ω) ≡

Ci65 (ω)
Ci65 (ω)
=
, ω = 1, . . . , 10, 000
ϕExpendituresia0
Cia0

(37)

A risk-neutral worker will aim for an average CRRR = Ci65 /Cia0 of 1. For such an
individual, a value less than 1 represents a shortfall in retirement savings, with the actual
distance between 1 and her CRRR measuring the shortfall percentage expressed in consumption units. A risk averse worker would instead aim for a CRRR greater than 1 and a CEQR
of 1.
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Retirement consumption, Ci65 , is computed, for each simulation path, by inputting the
T
total wealth at retirement, Wi65
, and social security income, Y S , into the model of retirement

consumption described in Section 5.3, after choosing the parameters of the retirement model
Z ≡ {αR , γ, β}. Consumption during working years, Cia0 , is estimated based on Consumer
Expenditure Survey (CEX) data, following the procedure described in the next section.
5.4.3

Estimating current expenditures

We use the CEX to estimate expenditures during the individual’s working life as a function
of the workers’ observable characteristics in our dataset, just as we used the HRS to estimate
other forms of wealth. Total expenditure is defined as the sum of food, alcohol, and tobacco,
apparel and services, entertainment, personal care, housing and shelter, health, reading and
education, transportation, and miscellaneous. We use the methodology proposed by Deaton
and Zaidi (2002) to calculate adult equivalents for each household and convert householdlevel expenditures into individual-level ones.
Table 6 reports the coefficients of the regression of total annual expenditures on age and
salary, for respondents between age 20 and 65 who were interviewed by the CEX between
2006 and 2011, and whose ratio of total expenditures over salary falls in the interquartile
range.28 We explore various specifications in which age enters the regressions both linearly
and as a set of dummy variables, and both as a stand-alone variable and interacted with
salary and salary squared. The regression in Column (1) estimates total expenditure as
50.4% of pre-tax salary, plus a term dependent on the respondent’s age. For example, a 42
year old worker earning the median salary, $50,000, would have annual total expenditures
of $30,045, equal to 60% of her pre-tax salary. The more flexible specifications in Columns
(2) to (5) yield similar results. We pick the specification in Column (4) as input for our
analysis because of the high R2 and the flexible specification.29 Based on these coefficients,
we calculate total expenditure in our 401(k) dataset as a function of worker age and salary.
28

This corresponds to a ratio of expenditures over salary ranging between 0.4 and 1. We impose this
restriction to avoid the effect of outliers and unusual circumstances.
29
According to this specification, a 42 year old worker with $50,000 salary would spend 61% of her pre-tax
salary.

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5.4.4

Adjusting for taxes

Since expenditures in the CEX are financed by after-tax income, we convert the retirement
consumption obtained from each simulation into its after-tax equivalent by taking both
federal and local taxes into account.
We also account for differences in taxes during working life and retirement by taking tax
brackets into account. In addition, for each individual, we calculate state-specific taxes based
on the zip code where she currently lives, and, to economize on computations, her median
simulated income.30 For simplicity, we assume that after retirement both Social Security
T
payments (Y S ) and dis-saving from existing financial wealth (Rt+1 WitT − Wi,t+1
) are taxed

at the same rate, and apply the appropriate tax rates directly to each simulated value of
consumption:31

T
Cit = Rt+1 WitT − Wi,t+1
− Mit + Y

6

Baseline results and sensitivity analysis

6.1

Baseline results

Table 7 shows the distribution of the consumption replacement ratios (CRRRs) the certainty
equivalent ratio (CEQR), and the distribution of age-65 total simulated wealth for a baseline
case where we assume power utility, risk aversion of 5, a discount factor of 0.95, and a 50%
equity allocation at retirement, i.e.
Z ≡ {αR , γ, β} = {50%, 5, 0.95}
We pick these parameter values because they are commonly used in the literature on
portfolio choice over the life-cycle (see for example Brown (2001), and Horneff, Maurer,
30

This approach assumes, for lack of a better alternative, that the individual remains in the same state
until retirement. If he moves to a state with lower taxes upon retirement, our approach conservatively
overestimates the degree of retirement preparedness.
31
This approach will slightly overstate the individual’s tax burden since it assumes Mit = 0. Note however
that at age 65, the time of our analysis, the expected value of medical expenditures is very low.

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and Mitchell (2018)). In Section 6.2.2 we illustrate how changing these parameters affects
the results and also re-examine our findings in light of the well documented cross-sectional
heterogeneity in risk aversion and discount factors (Harrison, Lau and Rutstrom (2007) and
Paravisini, Rappoport, and Ravina (2016)).
Columns (1) through (6) of Table 7 present the consumption replacement ratio (CRRR)
results.32 The rows refer to workers ranking at different percentiles in the worker population,
and display, for each individual, the CRRRs corresponding to different percentiles of the
distribution across her 10,000 simulations. For example, the row labelled ”50th percentile”
refers to the worker with the median CRRR in the population. Based on our simulations, she
has a 50% probability of obtaining a CRRR of 1.11, i.e. of being well prepared and having
retirement consumption equal 1.11 times her adjusted pre-retirement consumption, where
the adjustment factor is ϕ = 0.8. However, with 40% probability her CRRR at retirement
will be 1, i.e. her accumulated wealth will be just enough to maintain her standard of living.
With 30% probability her CRRR will only be 0.90, and she will be falling short by 10%, i.e.
each retirement year her consumption will be 10% lower than the one preserving her standard
of living; and with 10% probability her CRRR will be as low as 0.69, a 31% shortfall. The
prospects are worse for the worker in the second row, the 25th percentile of the distribution
of CRRRs in the population. His probability of falling short is more than 50%: the CRRRs
are only 0.91, 0.84, 0.76, and 0.60, respectively. Column (6) reports the mean CRRR for
the same workers and shows that, if all workers were risk neutral, the worker at the 25th
percentile and above would be saving enough for retirement. However, the results worsen if
we take risk aversion into account.
Column (7) reports the certainty equivalent ratio (CEQR), which integrates over the full
distribution of outcomes using the baseline utility function, and thus measures the shortfall
taking risk aversion into account. It shows that for the baseline risk aversion coefficient of
5, the certainty equivalent ratio is only 0.76 for the 25th percentile worker and 0.86 for the
median one, indicating that, in risk-adjusted terms, their wealth accumulation falls short by
32

We report the results for the case in which, following unemployment, the worker joins a company with
the same DC plan as her current firm. Appendix 1 shows the results are quantitatively indistinguishable
when we assign her to a new plan drawn randomly from our sample, or from the set of plans of workers in
her income decile.

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24% and 14%, respectively. Indeed, Column (7) shows that more than 75% of the workers
are not saving enough for retirement, with the CEQR at the 75th percentile falling just below
1 (0.99). The picture is much worse for the worker at the 10th percentile of the distribution,
with a CEQR of 0.68, but even the worker at the 90th percentile, despite saving adequately
in risk-adjusted terms (CEQR greater than 1), still faces close to 10% probability of not
having accumulated enough wealth by age 65, with a CRRR of 0.92 at the 10th percentile
of her CRRR distribution.
Finally, Columns (8) to (12) report the simulated age-65 total wealth in 2010 constant
dollar terms corresponding to each of the CRRRs in the first five columns.

6.2
6.2.1

Sensitivity analysis
Bequest motive and housing wealth availability

The baseline results in the previous section assume no bequest motive, apart from the remaining housing equity.33 If the workers in our sample wished to leave an additional bequest,
then their retirement savings would be even less adequate. Panel A of Table 8 reports the
results from introducing a target bequest equal to 10% of age-65 wealth, and assuming that
only savings in excess of this amount can be used to finance consumption during retirement.
By contrast, Panel B of Table 8 reports the results when we assume that all of housing equity
is left unused.34
Panel A of Table 8 shows that, relative to the baseline results reported in Table 7, a
bequest motive affects the CRRRs of a given individual more in the good scenarios than
in the bad ones. The reason is that, regardless of her ranking in the population, when a
worker gets a bad draw and ends up in the bottom 10th or 20th percentile of her CRRR
distribution, a larger fraction of her consumption will be financed by Social Security, and
thus setting 10% of her remaining wealth aside for a bequest has a smaller impact on her
33

Since the baseline results only allow for 50% of home equity to be used to finance retirement consumption,
the remaining 50% is available to bequeath.
34
This could happen because of bequest motives, but also because of lack of access or information about
reverse mortgages and other financial products that allow for home equity release. The costs of accessing
housing equity can be both direct financial costs and indirect ones like obtaining and processing the necessary
information.

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consumption. Similarly, a bequest proportional to the total wealth accumulated at age 65
affects the CRRRs of wealthier workers disproportionately more, as they rely less on Social
Security to finance consumption during retirement. Compared to the baseline specification,
the reduction in CRRRs ranges from 3 percentage points for the worker at the 10th percentile
of the distribution and facing a worst case scenario, to 12 percentage points for the 90th percentile worker getting the median draw from her CRRR distribution. Similarly, the CEQRs
are 4 percentage points lower for those at the 10th percentile of the worker distribution, and
7 percentage points lower for those in the 90th.
Similarly, Panel B of Table 8 shows that restricting access to housing equity hits the
right tail of the distribution more strongly, since both wealthier workers, and, for any given
worker, better draws from their own wealth distribution, tend to be associated with more
housing wealth. This pattern reverses for workers in the 75th percentile and above for whom
housing equity is a larger fraction of their total accumulated wealth when they get a bad
draw compared to cases when they get a good one and have proportionally more financial
wealth. Yet, unlike in the bequest analysis above, compared to the baseline results in Table
7, the drop in consumption replacement ratios and in CEQRs is substantial regardless of the
worker’s ranking, or the draw from her CRRR distribution. The workers at the 10th and
25th percentiles suffer drops in their CEQRs of 10 and 13 percentage points, respectively.
This result is quite worrisome, since poorer workers are more likely to lack access to home
equity release products or to be deterred by their high costs, and thus to end up in this
scenario. By contrast, while individuals in the 90th percentile face a larger drop in their
CEQR, 27 percentage points, and end up with a CEQR below 1, they are also substantially
more likely to have access to housing equity and not end up in this situation.
6.2.2

Alternative preference parameters and asset allocations during retirement

As discussed in Section 5, retirement consumption is obtained from a structural model which
computes the optimal consumption that can be sustained by the worker’s simulated wealth
and Social Security income. For this reason, the level of retirement consumption depends on
the choice of risk aversion γ, subjective discount factor β, and retirement-period portfolio

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allocation (αR ).
Table 9 shows the median worker’s CEQR and her median CRRR for different values of
these parameters.35 Panel A reports the CEQR for the baseline equity allocation of 50%,
and risk aversion parameters of 2, 5, and 8, respectively. Panel B reports the median CRRR
for the same combination of parameters. Panel C reports the CEQRs for the baseline risk
aversion coefficient of 5, and equity allocations during retirement ranging from 0 to 100%.
The rows refer to values of the discount factor, ranging from 0.925 to 0.975. Panel A and B
show that as risk aversion falls both CEQRs and CRRRs increase, as individuals with lower
risk aversion care less about medical expenditures, longevity risk, and investment returns
risk, and thus need to save less for retirement. Based on our simulations, a risk aversion
parameter of 2 generates enough retirement savings for the median worker regardless of
her discount factor, and will likely allow her to leave a bequest or avoid accessing home
equity. By contrast, higher risk aversion than our baseline value generates an even more
severe retirement under-saving problem. Notice that since the distribution of age-65 wealth
is independent of risk aversion, the variation in the median CRRR across values of risk
aversion reportedl in Panel B reflects how strongly the worker cares about retirement period
risks, i.e. medical expenditure, longevity, and investment risk during retirement. Panel B
shows that such variation is substantial, highlighting that our finding that in the low risk
aversion scenario most workers are saving enough for retirement relies heavily on them not
caring much about post-retirement risks.
Panel C shows that the median CEQR doesn’t vary much with the retirement portfolio
equity share. Our baseline assumption of αR =50% yields the highest CEQR, as a no equity
exposure investment strategy forgoes the equity premium and results in low wealth accumulation, and a 100% equity exposure generates excessive risk-taking. For each discount factor,
the different equity allocations we consider generate a difference in average yearly consumption of only a few percentage points, indirectly confirming that our approach of keeping
retirees’ equity shares constant in the optimization problem in Section 5 is reasonable given
the limited effect of retirement-period equity shares on replacement ratios.
Finally, an increase in the discount rate corresponds to higher CRRRs and CEQRs,
35

The full set of results, including other CRRR percentiles, is available upon request.

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although the effect is smaller than that of changing risk aversion. Indeed, even with a
discount factor of 0.925, the median CEQR is still below 1, indicating that more than half
of the workers is not saving enough for retirement.
In Fig. 1 we further illustrate how the fraction of workers adequately saving for retirement
varies with the risk aversion and the discount factor parameters. Panel A shows that, when
we hold the discount factor constant at 0.95, for values of risk aversion above 3.6 more than
half of the workers in our sample have a CEQR lower than 1, i.e. are not be adequately
prepared for retirement. For values of 2.8 and above, about 1/3 of the workers fall short.
Similarly, Panel B of Fig 1 shows the fraction of workers adequately saving for retirement
as a function of the discount factor. In this case, the curve is much flatter than the risk
aversion one and, even for a discount factor of 0.90, more than half of the workers are not
saving adequately.
Finally, an alternative way to look at our results is to ask what level of risk aversion
(discount factor) would make each worker appear adequately prepared, i.e. have a CEQR
equal to 1. Panel A (B) of Fig. 2 shows the cross-sectional distribution of risk aversion
(discount factor) parameters we obtain by conducting this exercise on 10,000 randomly
drawn accounts. While both distributions look very sensible, the analysis below shows that
the risk aversion and discount factor parameters consistent with all workers saving enough
have in most cases the opposite relationship with the worker demographics and allocation
decisions than the ones predicted by theory and the empirical literature.
Panel A shows that the distribution of relative risk aversion we obtain from the exercise
above has a mean of 4.17, a median of 4.12, and displays substantial heterogeneity. For a
small number of workers there is no value of the risk aversion parameter that make their
CEQR equal to one, but overall this distribution is consistent not only with those assumed in
the portfolio choice literature, but also with the findings from surveys, lab, and field studies
both in the U.S. and in developing countries. For comparison, Paravisini, Rappoport, and
Ravina (2016) find a mean RRA of 2.85, a median of 1.62, and significant heterogeneity,
when estimating the risk aversion of actual investors on a peer-to-peer lending platform.
Choi et al. (2007) find an implied risk aversion of 1.8 in their study of rainfall in Vietnam.
Holt and Laury (2002, 2005) estimate relative risk aversion below 1 when presenting lab
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participants with a series of lotteries designed to elicit their risk attitudes.36 Panel B shows
that the discount factor distribution is more tilted toward impatience and under-weighting
of the future than the findings in the literature. The average discount factor is 0.93 and the
median is 0.94, with values ranging from 0.87 at the 10th percentile to 0.996 at the 90th.37
In Panel D of Table 9 we examine how the values of risk aversion and discount factors
derived above relate to the workers’ demographic characteristics and asset allocation decisions. Columns (1) to (3) show that our implied risk aversion measure is either unrelated
or negatively related to age, counter to the vast empirical evidence finding that the elderly
are more risk averse than the young (Harrison et. al., 2007, among others). Our measure
of implied risk aversion is also positively related to account value, income, and the equity
share, counter to other evidence and to theory. Columns (4) to (6) show that the discount
factor implied by our results is unrelated to age, contrary to the findings in Green, Fry,
and Myerson (1994) and the subsequent literature. It is however positively related to the
account value, salary and the equity share, as we would expect. In Columns (7) to (12) we
confirm that these results are not due to a peculiarity of our dataset, as the equity share
and the account value are indeed related to these demographics and have highly statistically
significant coefficients of the expected sign. The equity share decreases with age, is higher
for workers with larger account values and higher salaries, and it is positively related to contribution rates and negatively related to tenure. Similarly, the size of the retirement account
is positively related to age, the equity share, salary, contribution rates, and tenure.
Most importantly, in Column (1) of Panel E, we show the strongly positive and extremely
large relationship between risk aversion and simulated age-65 wealth: to make our results
consistent with retirement preparedness, a $10,000 higher retirement-age wealth requires
the worker’s risk aversion to be 2.74 higher. In the following three columns we control for
the same demographics as in Column (1) to (3) of Panel D, and find that the coefficients
have the same sign and similar or larger magnitude. In Column (4) we show that the
relationship between simulated age-65 wealth and the discount factor is also strongly positive
36

They also show that risk aversion estimates increase with the stakes, which partially explains their lower
estimates.
37
See Angeletos et al. (2001), Shapiro (2005), Ashraf, Karlan, and Yin (2006) for estimates based on
consumption, savings, asset allocation, and voluntary adoption of forced savings technologies.

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and extremely large: a $10,000 increase in wealth is associated to a 0.9 higher discount factor,
which corresponds to a 1.5 standard deviation increase. In the next three columns we control
for the same demographics as in Column (4) to (6) of Panel D and find similar results.
While a vast literature in both psychology and economics has established risk aversion
is context-dependent and not necessarily consistent across domains (Weber and Milliman
(1997), Barseghyan et al. (2011)), the numerous studies of its relationships with demographics and asset allocations have yielded quite consistent findings (Harrison et. al. (2007),
Dohmen et al. (2011)). The fact that the risk aversion and discount factor parameters that
can explain our results have in most cases the opposite relationship with the worker demographics than the one overwhelmingly predicted by the literature, and specifically the fact
that the poor, or those who get a bad draw, are predicted to be very risk loving and yet
don’t have portfolio allocations reflecting these preferences cast doubt that the derived risk
aversion and discount factor parameters are a realistic depiction of workers’ preferences.
6.2.3

Lower average returns

In this Section we explore the sensitivity of our results to the possibility that future returns
on risky assets might be lower than in the past. Specifically, we repeat our simulations under
a more conservative scenario in which the expected returns on both stocks and bonds are 1
percentage point lower going forward.38
Table 10 reports the CRRRs and CEQRs under this scenario, and includes below each
entry the difference relative to the baseline case. The results show that those most affected
by lower future returns are the well-off, as a larger fraction of their wealth is in financial
assets, rather than housing or Social Security claims. Workers at the 75th percentile of the
distribution have a 30% probability of having a CRRR lower than 1, and thus being forced to
lower their standards of living during retirement. The losses diminish as we move down the
distribution. The CRRR of the median worker is 8% lower for the median simulation, and
the CRRRs of those at the 10th and 25th percentiles are only modestly affected. The CEQRs
fall by an amount between 4 and 2 percentage points, implying a retirement consumption
38

Horneff, Maurer and Mitchell (2018) study the impact of low future returns on 401(k) wealth accumulation in the context of a life-cycle model.

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between 2 and 4 ppt lower every year.
6.2.4

Catching up on contributions when account balances are low

While our analysis takes into account that after age 50 the cap on employee contributions
increases, so that workers who have not saved enough can contribute more if they want to,
we have not yet examined which type of worker does so, and what happens when we allow
the contribution rate to depend directly on the account balance accumulated up to that
point.
Fig. 3 shows the average contribution rate by age bracket and account decile. It shows
that account balances and contribution rates are positively correlated, and that older workers
tend to have higher contribution rates, but more so if they have high account balances and,
most likely, high salary. The slope of the relationship between contribution rates and account
balances is lower for workers in the 60-65 age bracket though, indicating that for workers
close to retirement, the differences in contribution rates between wealthier and poorer workers
while substantial are not as large as for the younger cohorts.
The last two columns of Panel A of Table 2 report the results of including the lagged
account balance in the contribution rate regressions. Column (9) shows that the main determinant of future contribution rates is the worker’s past contribution rate and that the
coefficient is stable compared to the specification we have used in our baseline simulations
(Column (5)). In addition, over the relevant values of the age parameter, the cubic polynomial in age has the same concave shape as the quadratic age function in Column (5).
Besides salary, tenure, and the lagged account balance, the regression also includes various
interaction terms of the lagged account balance, age, and the lagged contribution rate. The
coefficients point to a positive relationship between the account balance and future contribution rates. This is true for all workers, even those close to retirement.39 Column (10) shows
that these coefficients are robust to the inclusion of firm fixed effects in the regressions. Table
39

If we compare a 55 year old worker with the average contribution rate, salary, tenure, and account
balance of his cohort with a 55 year old with the same characteristics but in the 10th percentile of account
balances, a $10,000 higher account balance would translate in a 4.89 ppts higher contribution rate for the
worker with the higher balance, and a substantial, although smaller, 3.69 ppts higher contribution rate for
the worker with the lower one.

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11 hows that the CEQR s do not change by much, and if anything they are a few ppts lower
than the baseline. Similarly, most of the CRRRs stay the same, except for the workers at
the 75th and 90th percentiles for whom this specification results in CRRRs between 2 and
6 ppts lower. It is worth noting that this more complex specification generates a lower R2
than the one in Column (5) we picked for the baseline analysis.

7

Cross-sectional heterogeneity

In this section we regress the median wealth accumulated at retirement, the median CRRR,
and the CEQR on the initial characteristics of the workers in our sample. The objective is
to study how the outcomes and our measures of retirement preparedness relate to the initial
heterogeneity in our sample.

7.1

Regression Analysis

Panel A of Table 12 reports the coefficients from cross-sectional regressions of the median
wealth accumulated by age 65 on worker’s characteristics, while Panel B reports the coefficients from similar regressions of the median CRRR and the CEQR.
Column (1) of Panel A shows that median wealth at age 65 is a convex function of age at
the starting point of the simulations, and a concave function of salary. All else equal, a worker
who is 41 years old today and earns the median salary in our sample, $54,522, can expect to
have accumulated $584,270 at retirement, 3.2 times the wealth of a worker of the same age
who earns the 10th percentile of salary, $21,925, and slightly more than half the wealth of
a worker with the same age who earns the 90th percentile of salary, $96,794. These effects
are qualitatively robust when we control for account balance, contribution rates, tenure at
the firm, and the percent invested in equity. Column (4) of Panel A shows the importance
of the initial contribution rates and fraction invested in equity in explaining the variation in
age-65 wealth. A one percentage point higher contribution rate is associated to a $30,580
higher age-65 retirement wealth, while a ten percentage point higher equity allocation is
associated to a $7,120 higher retirement wealth, on average. Adding these account features

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to the regressions increases the R2 substantially, from 58.6% to 78.1%.
Column (5) of Panel A shows the coefficients from including plan and firm characteristics in the regressions. We find that, all else equal, workers employed at companies with
more generous employer contributions, companies that are older, privately held, invest more,
and have higher net income, tend to have more wealth by the time they reach retirement.
Workers employed at companies that all else equal are larger in terms of assets and number
of employees tend to have lower wealth, on average. Adding firm and plan characteristics
increases the R2 from 78.1% to 83.4%. Column (6) shows that the coefficients are robust
to including company fixed effects instead of controlling for the available firm-level characteristics. Finally, Column (7) shows that the coefficients on the state-level financial literacy
scores and the zip code-level education dummies have the expected sign, and are statistically
significant at the 5% or 10% level, although adding them doesn’t increase the R2 .40
We next turn our attention to the regressions of the median CRRR and the CEQR
reported in Panel B of Table 12.41 The coefficients show that the consumption replacement
ratios are a convex function of age, and that, unlike for retirement wealth, initial salary is
not statistically significant once we add regressors to the analysis. Column (4) shows the
important role of contribution rates in determining retirement adequacy. A one percentage
point higher contribution rate is associated to a 2.67 ppt increase in the median CRRR,
corresponding to a consumption level 2.67 ppt higher in all retirement years. The size of
the account and the equity share have the expected positive and statistically significant
coefficients, although their economic magnitudes is smaller: a $10,000 increase in account
balance corresponds to a 69 basis points increase in CRRR, while a 10 ppt increase in the
equity share corresponds, all else equal, to a 58 bps increase in CRRR. Similar to the findings
40
When we estimate the evolution equations for our simulations, we include the features and level of employer contributions among the explanatory variables, but exclude some of the firm and local characteristics
such as employer size and profitability, financial literacy, and education measures for the sake of tractability
and because of their small additional contribution to the explanatory power of the regressions. We include
them in the analysis here, as they are part of the retirement preparedness discussion and therefore it is
interesting to see how they are related to the simulation outcomes. The results in this Section confirm that
these variables are significantly related to retirement wealth and preparedness at age 65, but that including them in the regressions doesn’t significantly increase the R2 once all the other variables are taken into
account.
41
To save space we only report the coefficients of specifications (1), (4), (5), and (7). The full table is
available upon request.

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on median retirement wealth, workers with longer tenures at the firm end up with lower
CRRRs: a 5 year higher tenure corresponds to a 4.87 ppts lower CRRR. Column (5) of Panel
B shows that a more generous employer match, proxied by a higher tier one match rate, is
associated with higher retirement consumption: each 1 ppt higher employer match generates
a 29.5 bps higher annual retirement consumption.42 The same column shows that, all else
equal, workers employed at firms that are private, older, and have higher capital expenditures
and net income tend to have higher CRRRs on average. On the contrary, workers at larger
firms and firms with more employees have on average lower CRRRs. Finally, Column (7)
shows that workers living in areas with higher financial literacy and with a higher fraction of
college educated people tend to have higher CRRRs. The results are similar for the CEQR,
except that salary is significant, while the equity portfolio share is not.

7.2

Worker Profiles

In this section we further illustrate the retirement preparedness outcomes by looking at how
workers with different initial profiles fare in our simulations. Panel A shows the outcomes by
age bracket, while Panel B shows the outcome for workers with the median characteristics
of their age bracket.
The last three rows of Panel A show that for workers ranking at the 50th percentile
and higher in the outcome distribution, the median CRRR and the CEQR are a U-shaped
function of age. By contrast, the CRRRs fall from 1.08 to 0.83 for the worker at the 25th
percentile of the distribution, and from 0.96 to 0.67 for the one at the 10th. The Panel also
shows that, as a result of this pattern, the dispersion in outcomes increases significantly with
age: the difference in CRRRs (CEQRs) between the 10th and 90th percentiles increases from
0.67 (0.41) for the younger cohort to 1.01 (0.61) for the oldest one. This increase in dispersion
is primarily driven by the left tail of the distribution: more than 85% of those in the 20 to 35
years old age bracket have a median CRRR higher than one, while only about 50% of those
in the older groups have this level of retirement preparedness. This finding is particularly
42

Regressions available upon request indicate that the results are robust to more complex specifications of
the employer matching contribution schemes, and that the effect of higher fees is negative but not statistically
significant.

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concerning since older workers have less time to adjust their wealth accumulation paths. One
possible reason for these findings is that younger cohorts are enrolled in plans with more
generous matching contributions: their employers match, on average, 66.24% of the worker’s
contributions up to a cap, compared to an average of 57.22%for the older cohorts.43
In Panel B of Table 13 we take the coefficients from Panels A and B of Table 12 and
use them to compute the expected age-65 wealth, median CRRR, and CEQR for selected
worker profiles progressively controlling for more worker characteristics. The first three
columns illustrate the results for a worker who is about 41 years old, the median age in our
sample, Columns (4) to (6) report the results for a 26 year old, the 10th percentile of age in
our sample, and Columns (7) to (9) for a 57 year old, the 90th percentile.
In the first section of the Panel, we report fitted values for these three worker profiles
based on the coefficients in Column (1) of Panels A and B of Table 12, i.e. controlling for
their age and salary, but no other characteristics. The first three columns show that a 41
years old worker would have accumulated an estimated $508,770 at retirement age if, on the
last day we observe her in the sample, she had the median income in her age group (40-42
years old), $48,323, instead of the median for the general population. This is 2.5 times the
wealth she would accumulate if at the start of the simulations she earned a salary at the
10th percentile of the distribution for her age group, $23,492, and 44% of the wealth she
would have accumulated if she earned the 90th percentile for her age, $103,316. Columns
(7) to (9) show that the variance in median age-65 wealth is slightly higher for the 57 years
old. By contrast, Column (4) to (6) show that the variance in wealth i s much smaller for
younger workers: a 26 year old is predicted to have median wealth at retirement equal to
$524,520 if today she earns the median salary in her age group, $34,292. This is only 1.56
times the wealth she would accumulate if she earned the 10th percentile salary, i.e. $19,195,
and 58% of the wealth if she earned the 90th percentile salary, $65,625.
The second section of Panel B shows that controlling for account balance, contribution
rates, tenure at the firm, and fraction of the portfolio invested in equity at the start of
the simulations accentuates the variance across salary levels for the younger worker, and
decreases it for the middle and older ones. The predicted wealth at retirement for a 26 year
43

The subsequent tiers and caps of the employer contribution rules are also better for the younger cohort.

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old earning the median salary is now 1.61 times the wealth she would have if her salary was
at the 10th percentile for people her age, and 53% of the wealth she would have if she earned
the 90th percentile salary. By contrast, the ratio of the median to 10th percentile worker
drops to 2.1 for the 41 year old and to 2.3 for the 57 years old, and the ratios of the median
to 90th percentile worker are now 44% and 39%, respectively. The values for the 57 and
the 26 year old workers illustrate how those in the 10th and 90th percentiles in these age
groups are on different trajectories in the labor market. A 57 year old at the 10th percentile
of salary has typically been at his current firm for only 3.4 years, has a very small account
balance, $3,057, low contribution rates for his age, 4.3%, and has only 60% of his portfolio
invested in equities. By contrast, a 57 year old worker at the 90th percentile of her ageadjusted salary distribution has typically been at her current firm for more than 16 years,
has a very large account balance, $171,567 on average, takes advantage of the additional
contributions allowed after age 50 and contributes a large fraction of her salary, 16.1%, and
on average invests 64% of her retirement portfolio in stocks. By contrast, relative to her
counterpart at the 90th percentile, a 26 years old earning the 10th percentile salary for her
age has been at her current company longer (2.33 vs. 1.94 years), contributes a smaller
fraction of his salary (2.29% vs. 6.68%), and allocates a significant lower fraction of her
account to equities (59% vs. 78%). These profiles illustrate the interplay of labor market
trajectories, saving behavior, and investment choices in determining variation in wealth levels
at retirement.
The results in the third section of Panel B, based on the coefficients in Column (5)
of Table 12, indicate that workers sort into companies that exacerbate the cross sectional
variance in retirement wealth highlighted above, and that this is especially the case for
younger ones. Once we take company features into account, the ratios for a 26 years old
become 2.44 and 47%. This spread is significantly larger than those calculated based on
just age and salary (1.56 times and 58%) or age, salary, and account-level variables (1.61
times and 53%). The Panel shows that the spread also increases for the 41 and 57 year old
workers, albeit to a lesser extent. As one might expect, wealth heterogeneity is even larger
if we consider other values of the account- and plan-level variables, instead of the mean for
the specific age and corresponding salary intervals. For example, a 41 year old worker with
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salary, account balance, contribution rates, and equity allocations at the 10th percentile of
her age group, would have retirement wealth of $116,390, while a 41 year old worker with
salary, account balance, contribution rates, and equity allocations at the 90th percentile of
her age group, would have retirement wealth of $1.4 million.
Finally, the patterns for the median CRRRs ’s sake By contrast, the variation in CEQR
across workers with different initial salaries is much smaller, especially when we only use
initial age and salary to predict retirement preparedness. Panel B shows that the crosssectional variation increases when we use other worker and plan characteristics to compute
the fitted values, and that the workers with of median age are the ones with overall a lower
degree of preparedness as measured by the CEQR, while the older workers are the ones
displaying the biggest amount of variation within their age group.

8

Counter-factual experiments

In this Section we perform a series of counterfactual experiments in an attempt to quantify,
within our framwork, the impact of alternative policy interventions aimed at improving
retirement savings adequacy.
A limitation of our approach is that the results are subject to the Lucas critique, since
we are not using a structural model with optimizing agents for the pre-retirement period,
and assume instead that the stochastic processes for contributions and portfolio allocations
remain unchanged following the policy change. In addition, in our counterfactual experiHW
FW
)
ments we will keep non-retirement financial wealth and housing wealth (W65
+ θW65

constant at the level estimated in the baseline scenario. In reality, when forced to increase
their contributions to DC accounts, some workers might respond by saving less in their
non-retirement accounts. For these reasons, we view our results as a best-case scenario for
these policies. It is worth noting that the empirical evidence overwhelmingly shows that
individuals often respond very passively to changes in the features of their 401(k) plan, both
in terms of contribution rates and investment decisions (e.g. Choi, Laibson and Madrian
(2009), Choi, Laibson, Madrian and Metrick (2003, 2004), Madrian and Shea (2001), and
Chetty et al. (2014)).
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The policies we consider are removing penalty-free withdrawals upon reaching age 59 1/2,
except in case of hardship and unemployment; imposing a minimum contribution rate for
all workers; increasing all workers’ contribution rate by a fixed percentage; and automatic
rollovers following a job switch.

8.1

Removing penalty-free age 59 1/2 withdrawals

Munnell and Webb (2015) show that individuals withdraw significant amounts from their
retirement accounts before age 65. Restricting such withdrawals could therefore potentially
decrease the large shortfalls in wealth accumulation that we have documented.
We evaluate the effect of removing the ability to withdraw funds from age 59 1/2 onwards
without a justification, while still allowing those due to hardship and unemployment at
any age. Table 14 shows that this measure would have the largest impact on the wealth
accumulation of workers in the bottom half of the distribution, causing increases in retirement
wealth between 15% and 21%. The reason is that both the probability of a withdrawal and
the percentage of the account being withdrawn decrease with wealth (see Section 3.2). Yet,
the increases in CRRRs and CEQRs are higher for workers who were already better-off in
the baseline scenario, since the fraction of retirement consumption financed by DC wealth,
as opposed to Social Security benefits, is increasing in total wealth. The results in Table 14
show that preventing individuals from withdrawing funds from their DC accounts without
justification after age 59 1/2 can increase annual retirement consumption levels by 5% for
poorer workers to 9% for wealthier ones. Yet, despite these substantial improvements, about
2/3 of the workers would still end up with a CEQR below 1, and close to 25% of them would
still have a median CRRR below 1, due to the low CRRRs and CEQRs in our baseline
results.

8.2

Minimum contribution rate

In this Section we explore the effect of a mandatory minimum contribution rate of either
2.5% or 5%. While this kind of measures might be more effective for workers who are not
saving in a 401(k) altogether, we explore them here to see if they could also help increase
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the saving rates of the workers who already have a 401(k) but are saving very little.
For comparison’s sake, the average contribution rate in our sample is 6.3%, the median is
5.2%, and the 25th percentile is 2.2%. Table 15 shows that imposing a minimum contribution
rate of 2.5% (Panel A), or even 5% (Panel B), has negligible effects on the retirement savings
of the workers in our sample. The average increases in CRRRs never exceed 2% and, as
discussed above, such increases might be lower or inexistent if we allowed for crowding out
of non-retirement wealth.
Panel C reports the results across age groups for the case of a 5% minimum contribution
rate, and shows that, while the improvements are negligible for the overall sample, workers
younger than 35 experience increases in median CRRRs of about 4%. The reason is that the
young have the lowest contribution rates in the sample, due to their lower income at this
stage of their life cycle.44 In addition, most of their savings are precautionary and should not
be invested in an illiquid retirement account. Carroll (1997), Gourinchas and Parker (2002),
and Gomes, Michaelides and Polkovnichenko (2009) indeed show that the optimal retirement
saving rate of the young can be much lower than 5%. Forcing them to contribute more may
be suboptimal and could lead several of them to opt out of the pension plan altogether.
Thus, in Table 16 we explore the possibility of setting the following age-dependent minimum
contribution rate:
kmin = 4.5% + (age − 21) ∗ 0.25%

(38)

where the minimum contribution age averages 10% between ages 21 to 65, but starts at a low
level of 4.5% and increases gradually to 15.5% just before retirement, when the worker can
presumably afford to save more. An average contribution rate of 10% is certainly substantial,
since the average contribution rate in our sample is 6.3%, and might not be feasible for the
older workers with low income. Yet, given the magnitude of the under-savings problem we
have documented, this is the change needed to get significant improvements. Panel A of Table
16 shows that those in the left tail of the distribution would experience increases in their
median CRRR of about 5 ppts, and increases in their CEQR of 3 ppts. More importantly,
Panel B shows that the gains would be similar for all age groups within a given decile.
44

In our sample, 58% of workers younger than 35 have contribution rates below 5%, while only 43% of
older workers do.

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8.3

Increase in contributions rates for all workers

In this section we study the impact of an increase in every worker’s contribution rate by
either 2 or 5 percentage points, regardless of their current saving rate. Again, our goal is to
evaluate the additional savings effort required to address the shortfalls that emerged from
our baseline results, rather than being prescriptive.
The results reported in Table 17 are promising. A 2 ppts increase in contribution rates
improves yearly retirement consumption levels by 2% to 9% (Panel A). A 5 ppts increase
raises the standard of living at retirement by between 4% to 20% (Panel B).45 It is worth
noting that a 5 ppt increase in retirement contributions represents a quite significant savings
effort. Also, the improvements are highest for those who are already better off, as these
workers tend to have higher salaries and end up saving larger amounts as the result of this
policy. Compared to the baseline results in Table 7, the percentage of workers not saving
enough for retirement, i.e. with a CEQR less than 1, falls from 3/4 to about 2/3. While
this is quite a significant improvement, these figures are still worrisome and highlight the
magnitude of the current under-saving problem.
Panel C shows the results across age groups for an increase in contribution rates of 2
ppt. The largest effect is for younger workers who would have more time to benefit from
the increased saving rate. Their CRRR would be between 9% to 15% higher. Those in 35
to 49 age group would increase annual retirement consumption by about 4% to 5%, while
those currently in the 50 to 64 age bracket would enjoy a more modest boost between 1 and
3 ppts, as they have less years left before retirement.

8.4

Automatic rollover following a job switch

One of the recently proposed policy measures to decrease leakages and improve retirement
savings is to make the plans portable so that they are automatically transferred to the new
employer in case of a job separation. In this Section we estimate the potential effect of such
policy by completely removing the possibility of withdrawals following a job switch.
45

Notice that our simulations take into account IRS limits on total employee annual contributions and age
50 catch-up additional contributions.

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Table 18 shows that both the CRRR and CEQR increase across the worker distribution,
and, within each worker, across the outcome distribution. The size of the consumption
increase ranges between 1 and 7 ppts and is significantly larger for workers who are already
better off. While effective, this policy alone, in the context of our model and assumptions,
would not address the retirement savings crisis. Additional changes related to increasing
savings for everyone, but especially for the poorer workers, or a combination of various
policy measures are necessary to address the shortfall.

9

Conclusions

Are Americans adequately prepared for retirement? In this paper we have explored retirement
savings adequacy of a large and representative sample of U.S. workers saving in their company
401(k) by simulating their wealth accumulation forward till age 65 and examining if, after
considering longevity, medical, and investment risks, it is sufficient to maintain their standard
of living in retirement. We find that, based on their current account balances, income, saving,
and investment patterns, on the probabilities of withdrawing funds following unemployment,
job switches, hardship, and reaching age 59 1/2, about 3/4 of the workers in our sample are
not saving enough for retirement. Several factors contribute to the dispersion in outcomes
across individuals. The most significant ones are the heterogeneity in the generosity of
employer contributions, individual saving rates, and asset allocations.
Our results are robust to various alternative calibrations. Only if we assume both low
risk aversion and very high discount rates, do we conclude that the median worker is saving
enough.Yet, the risk aversion and discount factor parameters that can explain our results
have in most cases the opposite relationship with the worker demographics and allocation
decisions than the ones predicted by theory and the empirical literature.
While the picture of retirement preparedness emerging from our analysis is somber, there
are various reasons to believe it is an understatement of the paucity of retirement savings.
Data from the Bureau of Labor Statistics indicate that only 65% of private sector workers
have access to a retirement plan, and only 48% participate in them. Furthermore, we have
not included in our analysis risks such as potential reductions in social security benefits, or
55

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increases in medical costs. On the other hand, we don’t study an increasingly small fraction
of workers with access to a defined benefit plan, which might, if its promises are fulfilled,
provide better retirement adequacy.
Finally, the analysis we have conducted here is in many ways exploratory, and many
open questions remain. We have only analyzed a few policies aimed at increasing retirement
savings, while others, such as postponing retirement, mandatory automatic enrollment for
all workers, and financial education could also be beneficial. In future work we also plan to
explore a wider range of preference parameters and return environments, to allow for more
asset classes, and for the possibility that some workers end up in firms with no retirement
plan and fail to make up the lack of savings on their own.

56

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Appendix: Results with different assumptions regarding new pension plan following a job loss
As discussed in Section 3, we consider three different scenarios regarding the worker’s
new pension plan following a job loss:
- The new DC plan is identical to the current one
- The new DC plan is randomly drawn from our sample of workers within the same
(initial) income decile.
- The new DC plan is randomly drawn from our full sample.
Table A1 shows that the baseline results are quantitatively almost identical across all
three scenarios. Panel A reports the results when the new DC plan is randomly drawn from
our sample of workers within the same income decile, and Panel B reports the results for a
random plan. The CEQs are all exactly identical to the baseline ones reporter in Table 8
in the paper up to the 2 decimal points. The vast majority of CRRRs are almost identical,
and the few differences are in the order of 0.01.

57

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Figure 1
Percentage of Workers with CEQR less than 1 for Different Combinations of the Preference Parameters
Panel A shows the percentage of workers with CEQR less than 1 for different values of the coefficient of relative risk
aversion, keeping the discount factor constant at the baseline value of 0.95. The results are obtained by interpolating
the CEQRs for the coefficients of risk aversion of 2, 5 and 8 using a second-order polynomial. Panel B shows the
percentage of workers with CEQR less than 1 for different values of the discount factor, keeping the coefficient of
relative risk aversion kept constant at the baseline value of 5. The results for the [0.925-0975] range are obtained by
interpolating the CEQRs for the discount factors of 0.925, 0.95 and 0.975, using a second-order polynomial. The
results outside of this range are obtained by extrapolating from the same polynomial.
Panel A – Relative risk aversion

Panel B – Discount factor

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Figure 2
Implied Preference Parameters Required for Retirement Adequacy
Panel A shows the distribution of relative risk aversion coefficients that would make each worker adequately prepared
for retirement, i.e. have a CEQR equal to 1. The discount factor is set to the baseline value of 0.95. For 2.08% of the
workers we found no value of risk aversion that would make them adequately prepared. Panel B shows the distribution
of discount factors coefficients that would make each worker adequately prepared for retirement. The risk aversion
coefficient is set to the baseline value of 5.

0

200

# of Workers
400
600

800

1000

Panel A – Relative risk aversion

0

2

4
6
Relative Risk Aversion

8

10

0

200

# of Workers
400
600

800

1000

Panel B – Discount factor

.4

.6

.8
Discount Factor

1

1.2

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Figure 3
Contribution Rates by Age Bracket and Account Decile
This graph shows the average contribution rate by age bracket and account value deciles in the estimation sample.

0.14

0.12

0.1

0.08

0.06

0.04

0.02
20-24

25-29

30-34

35-39

40-44

45-49

50-55

55-59

60-65

Account balance Dec1

Account balance Dec2

Account balance Dec3

Account balance Dec4

Account balance Dec5

Account balance Dec6

Account balance Dec7

Account balance Dec8

Account balance Dec9

Account balance Dec10

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Table 1
Summary Statistics
Panel A reports the mean, median, standard deviation, 5th, 25th, 75th and 95th percentiles and number of observations for our estimation sample, while Panel C reports the same
statistics for the baseline sample, comprising workers at firms that offer one or more defined contribution plans, but no defined benefit plans. Both samples comprise the last sample
observation for all workers with valid tenure data, who earn at least the minimum wage salary, and whose individual characteristics are not missing. Panels B and D report the
summary statistics for the firms who offer both DC and DB plans and the ones that offer only DC plans, respectively. All variables are defined in the Appendix.
Panel A – Estimation sample – Worker Characteristics
Mean

Std Dev

5th Percentile

25th Percentile

Median

75th Percentile

95th Percentile

Obs.

Age

42.442

11.293

24.000

33.000

43.000

51.000

60.000

1,557,604

Salary

56,738

48,004

14,315

31,063

46,538

71,688

125,043

1,557,604

Tenure at the firm

9.852

9.467

0.077

2.137

6.912

14.984

29.545

1,557,604

Contribution Rate

6.93%

6.79%

0.00%

2.31%

5.56%

10.02%

19.56%

1,557,604

Account Balance

56,593

109,837

160

2,145

14,562

63,429

251,749

1,557,604

% invested in Bonds

19.36

19.31

0.00

4.00

13.00

30.00

57.00

1,557,604

% invested in Equity

67.00

31.17

0.00

49.00

78.00

90.00

100.00

1,557,604

Bond fees

0.26

0.18

0.03

0.12

0.24

0.44

0.52

1,557,604

Equity fees

0.33

0.23

0.05

0.18

0.27

0.48

0.76

1,557,604

Median House Value (Zillow)

256,413

203,818

79,300

131,200

190,700

312,900

631,100

1,557,604

Panel B – Estimation sample – Firm Characteristics
Estimation Sample - Worker level

Estimation Sample - Firm level

Mean

Std. Dev.

Median

Obs.

Mean

Std. Dev.

Median

Obs.

Private Dummy

38.80%

48.70%

0.00%

1,557,604

56.33%

49.76%

100.00%

158

Firm Age (years)

74.14

47.93

63.00

1,495,308

73.67

45.00

74.00

146

# of Employees

102,346

101,338

57,000

1,347,103

26,729

61,801

6,948

147

Total Assets (USD mil)

215033.91

525064.00

26413.40

1,147,715

65964.98

289504.71

8036.88

92

Leverage (%)

23.50

13.32

24.91

1,058,194

30.06

21.58

28.21

78

Sales/Assets (%)

88.73

55.07

93.39

1,099,139

98.15

76.18

84.00

89

Profitability (%)

3.43

4.70

4.33

1,147,715

3.52

8.69

3.00

92

Investment Intensity (%)

4.70

4.01

3.36

1,058,194

4.47

3.49

3.73

78

Total Plan Assets (USD mil)

548.10

669.88

385.00

1,058,194

173.522

383.257

56.495

78

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Panel C – Baseline sample – Worker Characteristics
Mean

Std Dev

5th Percentile

25th Percentile

Median

75th Percentile

95th Percentile

Obs.

Age

41.11

10.88

25.00

32.00

41.00

50.00

59.00

350,859

Salary

56,465

39,437

21,127

32,746

46,071

70,990

118,598

350,859

Tenure at the firm

7.87

8.27

0.19

1.76

4.92

10.97

26.21

350,859

Contribution Rate

6.33%

6.27%

0.00%

2.19%

5.20%

8.74%

18.69%

350,859

Account Balance

42,974

94,336

241

1,435

8,342

39,900

205,702

350,859

% invested in Bonds

25.54

20.99

0.00

9.00

20.00

46.00

63.00

350,859

% invested in Equity

62.44

30.55

0.00

44.00

70.00

89.00

99.00

350,859

Bond fees

0.25

0.17

0.08

0.09

0.21

0.40

0.51

350,859

Equity fees
Median House Value
(Zillow)

0.33

0.20

0.06

0.19

0.28

0.39

0.73

350,859

321,837

240,536

88,700

156,000

245,600

430,700

748,800

350,859

Panel D – Baseline sample – Firm Characteristics
Baseline Sample - Worker level

Baseline Sample - Firm level

Mean

Std. Dev.

Median

Obs.

Mean

Std. Dev.

Median

Obs.

Private Dummy

44.65%

49.71%

0.00%

350,859

62.79%

48.91%

100.00%

43

Firm Age (years)

60

25

66

342,178

59

42

46

40

# of Employees

64,089

56,040

37,700

244,479

13,674

30,864

3,300

40

Total Assets (USD mil)

72426

63357

52019

217,081

18923

37714

2842

21

Leverage (%)

23.72

9.70

24.91

197,382

29.67

25.47

27.18

18

Sales/Assets (%)

71.12

47.99

58.83

217,081

98.98

69.49

81.88

21

Profitability (%)

4.68

3.40

4.83

217,081

5.64

6.08

5.65

21

Investment Intensity (%)

3.54

2.52

3.36

197,382

4.16

3.70

3.52

18

Total Plan Assets (USD mil)

$

193,982

75.97

136.92

13.90

17

226

$

170

$

136

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Table 2
Estimates of the Evolution Path of Contribution Rates and Asset Allocations
The regressions in this table estimate the evolution equation of workers’ contribution rates (Panel A) and allocations to equity and bonds (Panel B) as a function of workers’ and
account characteristics. The even-numbered Columns control for firm fixed effects. All variables are defined in the Appendix. The errors are clustered at the firm level. The superscript
*** denotes significance at the 1% level, ** at the 5% level and * at the 10% level. Panel C presents summary statistics of the various components of the employer contribution.
Panel A – Worker Contribution Rate Evolution Equations
(1)
Contr. Rate

(2)
Contr. Rate

(3)
Contr. Rate

(4)
Contr. Rate

(5)
Contr. Rate

(6)
Contr. Rate

(7)
Contr. Rate

(8)
Contr. Rate

(9)
Contr. Rate

(10)
Contr. Rate

0.837***
[110.5]
0.000596***
[5.298]

0.468***
[7.711]
9.09e-05
[0.541]

0.425***
[7.560]
-5.51e-05
[-0.382]

0.882***
[13.83]
-0.00167***
[-3.967]

0.811***
[12.96]
-0.00174***
[-4.481]

-5.12e-06***
[-4.061]

-4.35e-07
[-0.263]

1.03e-06
[0.731]

4.10e-05***
[4.948]

4.09e-05***
[5.310]
-2.97e-07***
[-6.036]
-2.44e-08***
[-5.577]
-0.000142***
[-6.753]
-0.0128***
[-2.858]

Lag Contr. Rate
Age

0.00104**
[2.121]

0.000722**
[2.549]

-0.000259
[-0.675]

-0.000240
[-0.715]

0.851***
[100.5]
0.000692***
[5.795]

Age2

-1.70e-06
[-0.288]

1.47e-06
[0.376]

1.40e-05***
[3.204]

1.33e-05***
[3.220]

-6.28e-06***
[-4.773]

Age3
3.92e-07***
[2.741]

3.75e-07***
[2.961]

Lag Contr. Rate*Age

0.0158***
[6.080]

0.0168***
[6.858]

-3.06e-07***
[-5.896]
-2.48e-08***
[-5.080]
-8.70e-05***
[-3.103]
-0.0154***
[-3.249]

Lag Contr. Rate*Age2

-0.000154***
[-5.256]

-0.00016***
[-5.761]

0.000481***
[4.836]

0.000446***
[4.866]

-3.91e-06***
[-5.788]

-3.75e-06***
[-6.102]

Annual Salary
Tenure

1.46e-07***
[6.450]

1.08e-07***
[5.305]

1.53e-07***
[5.381]
0.000478***
[4.555]

1.02e-07***
[4.873]
0.000457***
[6.187]

8.15e-08
[1.327]

5.48e-08
[1.363]

Lag Contr. Rate*Age3
Lag Cont.
Rate*Salary

Age*Salary

-2.44e-06**
[-2.549]
-2.75e-09
[-1.131]

-1.63e-09
[-0.953]

Lag Contr.
Rate*Age*Salary
Age2*Salary
Lag Contr.
Rate*Age2*Salary

0
[1.079]

0
[0.750]

-1.38e-08***
[-2.663]

-2.75e-06**
[-2.144]
-1.31e08***
[-2.799]

8.00e-08**
[2.353]

9.20e-08**
[2.076]

1.20e-10**
[2.565]

1.13e-10***
[2.646]

-6.00e-10*
[-1.866]

-7.56e-10*
[-1.907]

Electronic copy available at: https://ssrn.com/abstract=3294422

Account Balance

2.44e-06***
[7.761]

2.47e-06***
[7.321]

-1.05e-05***
[-5.315]
-1.25e-07***
[-7.458]

-1.04e-05***
[-4.873]
-1.25e-07***
[-7.142]

Age2*Acct Bal.

2.13e-09***
[7.209]

2.12e-09***
[6.970]

Age3*Acct Bal.

-0***
[-6.995]

-0***
[-6.800]

6.01e-07***
[5.839]

5.93e-07***
[5.281]

-1.10e-08***
[-6.083]

-1.08e-08***
[-5.485]
6.42e-11***
[5.558]
0.0344***
[5.931]
7,099,244
0.699
Yes
Yes

Lag Contr. Rate*Acct
Bal.
Age*Acct Bal.

Lag Contr.
Rate*Age*Acct Bal.
Lag Contr.
Rate*Age2*Acct Bal.
Lag Contr.
Rate*Age3*Acct Bal.

Observations
R2
Firm Fixed Effects

0.0149
[1.364]
12,838,416
0.036
No

0.0247***
[4.355]
12,838,416
0.102
Yes

0.0383***
[4.692]
9,159,667
0.054
No

0.0421***
[6.296]
9,159,667
0.102
Yes

-0.00960***
[-3.679]
9,958,921
0.701
No

-0.00669***
[-2.809]
9,958,921
0.705
Yes

0.00459
[1.055]
9,958,921
0.702
No

0.00897**
[2.447]
9,958,921
0.706
Yes

6.56e-11***
[6.147]
0.0311***
[4.989]
7,099,244
0.695
No

Firm Clustered SE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Constant

Electronic copy available at: https://ssrn.com/abstract=3294422

Panel B – Asset Allocation Evolution Equations

Lagged Equity Share

(1)
Equity Share
0.916***
[88.17]

(2)
Equity Share
0.911***
[85.07]

Lagged Bond Share

(3)
Bond Share

(4)
Bond Share

0.905***
[202.3]
0.0134
[1.251]

Age

-0.0410
[-1.222]

-0.0102
[-0.649]

0.914***
[161.4]
0.0347**
[2.428]

Age2

-0.000528
[-0.999]
4.92e-06
[1.040]

-0.000860***
[-2.818]
6.57e-06***
[3.360]

0.000147
[0.867]
-4.09e-06**
[-2.291]

0.000414***
[3.081]
-3.36e-06**
[-2.452]

Salary2

-0
[-1.068]

-0***
[-3.026]

0**
[2.416]

0***
[2.889]

Age2*Salary

-1.08e-09
[-0.804]

-1.38e-09**
[-2.064]

1.20e-09**
[2.100]

8.60e-10*
[1.891]

Age2*Salary2

Observations
R2
Firm Fixed Effects

0
[1.034]
8.188***
[8.362]
9,958,921
0.857
No

0***
[2.655]
7.811***
[8.671]
9,958,921
0.858
Yes

-0***
[-2.615]
0.172
[0.542]
9,958,921
0.855
No

-0***
[-2.833]
0.749***
[3.582]
9,958,921
0.856
Yes

Firm Clustered SE

Yes

Yes

Yes

Yes

Salary

Constant

Electronic copy available at: https://ssrn.com/abstract=3294422

Panel C - Employer Contribution Rules
This Panel presents summary statistics for the parameters characterizing the employer contribution schemes in our sample. ke0i denotes the employer basic contribution, i.e. the
contribution independent from the employee’s own contributions, expressed as a fraction of the worker’s salary, while the other parameters capture the matching portion of the
employer contribution (Kimatch), which is specified as

Mean

Std.
Dev.

Estimation Sample
25th
75th
Median
pctile
pctile

Employer basic contribution - % of
employee comp

1.83

3.80

0.00

0.00

Employer matching contribution - first
tier (% of employee contribution)

72.08

56.71

50.00

Employer matching contribution - cap to
1st tier (%)

3.82

6.80

Employer matching contribution - 2nd
tier (% of employee contribution)

16.19

Employer matching contribution - cap to
2nd tier (%)

Baseline Sample
25th
75th
Median
pctile
pctile

Obs.

Mean

Std.
Dev.

2.00

1,557,604

1.57

2.23

0.00

0.00

5.00

350,859

60.00

100.00

1,557,604

62.77

45.22

0.00

100.00

100.00

350,859

1.00

4.00

6.00

1,557,604

3.20

2.57

0.00

4.50

6.00

350,859

27.46

0.00

0.00

25.00

1,557,604

7.934

18.48

0.00

0.00

0.00

350,859

1.35

2.06

0.00

0.00

3.00

1,557,604

0.69

1.70

0.00

0.00

0.00

350,859

Employer matching contribution - 3rd
tier (% of employee contribution)

0.57

5.35

0.00

0.00

0.00

1,557,604

0.00

0.00

0.00

0.00

0.00

350,859

Employer matching contribution - cap to
3rd tier (%)

0.06

0.53

0.00

0.00

0.00

1,557,604

0.00

0.00

0.00

0.00

0.00

350,859

Electronic copy available at: https://ssrn.com/abstract=3294422

Obs.

Table 3
Estimation of Leakage Parameters
This table presents the calculations underlying the estimation of the parameters for the leakage events. Panel A covers unemployment and voluntary job changes. Column (1) and (2)
are based on Table 2 in Munnell and Webb (2015) and Vanguard’s How America Saves for year 2013. Columns (5) and (6) are based on Engelhardt (2003), who estimates that in
case of unemployment, the probability of cashing out is 46.7 % higher than for voluntary job switches. All other calculations are based on our data. Panel B covers withdrawals from
age 59 1/2 onwards. The salary decile thresholds in Panel B are $17,381, $24,954, $30,640, $36,036, $42,404, $50,567, $60,201, $ 73,763, and $93,540.
Panel A – Withdrawals due to unemployment and voluntary job changes
(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Age

% of workers
cashing out
upon job
separation

% of
available $
in account
that is
cashed out

Prob. of
unemployme
nt

Prob. of
job switch
or
retirement

% of workers
cashing out upon
unemployment

% of workers
cashing out upon
job separation
different than
unemployment

Total assets available to
these age categories
(from our dataset)

Total #
of
workers

Average
account value

20s
30s
40s
50s
60s
70s

35%
32%
32%
24%
19%
26%

15%
11%
10%
7%
4%
6%

5.94%
4.80%
4.36%
4.35%
4.79%
6.02%

10.55%
8.28%
7.24%
7.08%
7.82%
10.29%

43.84%
39.97%
39.83%
29.82%
23.61%
32.45%

30.03%
27.38%
27.28%
20.42%
16.17%
22.22%

$
$
$
$
$
$

3,290,000,000
18,800,000,000
46,700,000,000
75,100,000,000
29,800,000,000
2,520,000,000

397,908
681,738
787,604
729,114
261,404
21,727

$
$
$
$
$
$

8,268
27,577
59,294
103,002
114,000
115,985

All Ages

28.80%

7%

4.73%

7.98%

35.90%

24.59%

$

176,210,000,000

2,879,495

$

61,195

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

Age

# of
workers
becoming
unemployed

# of workers
switching
jobs

Total asset available to
those who left

Amount of total
asset withdrawn
by those who left

# of workers
withdrawing
upon
unemployment

# of workers
withdrawing
upon job
switch

Average
amount
withdrawn

Fraction of
own
account
withdrawn

20s
30s
40s
50s
60s
70s

23,621
32,752
34,331
31,710
12,516
1,309

41,993
56,469
57,021
51,611
20,442
2,235

$
$
$
$
$
$

542,514,420
2,460,416,160
5,416,597,570
8,582,180,170
3,757,270,420
411,013,512

$
$
$
$
$
$

81,377,163
270,645,778
541,659,757
600,752,612
150,290,817
24,660,811

10,356
13,091
13,675
9,456
2,956
425

12,609
15,460
15,557
10,541
3,306
497

$
$
$
$
$
$

3,544
9,479
18,529
30,042
24,000
26,766

42.86%
34.38%
31.25%
29.17%
21.05%
23.08%

All Ages

136,239

229,740

$

22,395,991,443

$ 1,567,719,401

48,910

56,492

$

14,874

24.31%

Electronic copy available at: https://ssrn.com/abstract=3294422

Panel B – Withdrawals from age 59 ½ onwards

Salary threshold

Average account
value

# of workers

Cumulative #
of workers

Total account value in
that salary decile

Fraction
withdrawn by
salary decile

Probability of
withdrawing by
salary decile

<= $17,381

$

28,201.39

28,317

28,317

$

798,578,761

46.51%

17.70%

$17,382 - $24,954

$

28,554.39

28,310

56,627

$

808,374,781

45.93%

17.70%

$24,955 - $30640

$

46,779.13

29,029

85,656

$

1,357,951,365

28.04%

13.00%

$30,641 - $36,036

$

60,647.59

27,598

113,254

$

1,673,752,189

21.63%

13.00%

$36,037 - $42,404

$

71,740.23

28,312

141,566

$

2,031,109,392

18.28%

9.49%

$42,405 - $50,567

$

95,148.48

28,422

169,988

$

2,704,310,099

13.78%

9.49%

$50,568 - $60,201

$ 121,029.00

28,211

198,199

$

3,414,349,119

10.84%

4.75%

$60,202 - $73,763

$ 155,783.50

28,307

226,506

$

4,409,763,535

8.42%

4.75%

$73,764 - $93,540

$ 210,436.00

28,318

254,824

$

5,959,126,648

6.23%

2.50%

>= $93,541

$ 322,656.10

28,307

283,131

$

9,133,426,223

4.06%

2.50%

Overall

$ 114,097.58

11.49%

9.49%

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 4
Estimation of Outside Wealth
This Table reports the summary statistics (Panel A) and the regression coefficients (Panel B) used in the estimation of outside wealth for each individual in our sample. The estimation
is based the 2010 Wave of the Health and Retirement Study (HRS) comprising the married individuals between the age 62 of and 67. The summary statistics in the last column of
Panel A are from our 401(k) sample.
Panel A – Summary statistics – Health and Retirement Study, married couples between 62 and 67 years old
Total account value
in our sample at the
end of 2010 for
workers of age
>=62 & <=67

Account value
at last
employer

Account value
at last
employer,
if >0

Total
retirement
wealth

Total
retirement
wealth, if >0

Mean

120,843.81

121,373.83

103,066.58

125,992.75

121,011.50

Std. Dev

223,700.48

224,047.13

311,246.68

216,389.62

197,142.90

10th pctile

3,000.00

3,000.00

0.00

6,000.00

707.65

25th pctile

12,000.00

12,000.00

0.00

19,000.00

11,086.34

Median

45,117.50

46,000.00

5,000.00

51,000.00

52,639.49

75th pctile

138,100.00

139,500.00

100,000.00

148,000.00

156,789.10

90th pctile

300,000.00

300,000.00

300,000.00

300,000.00

316,010.70

2,748.00

2,736.00

22,035.00

9,219.00

49,891.00

Obs.

Panel B – Regression analysis

DC account balance

(1)

(2)

(3)

(4)

Total outside
wealth

Total outside
wealth

Total outside
wealth

Total outside
wealth

0.960***

0.963***

0.464***

0.464***

[8.079]

[8.074]

[3.502]

[3.485]

2.042***

2.042***

[6.507]

[6.475]

Salary
Constant

1,288

41.71

-63,253*

-63,297*

[0.0361]

[0.00116]

[-1.859]

[-1.853]

Observations

206

205

206

205

Adjusted R2

0.239

0.239

0.367

0.367

No

Yes

No

Yes

Conditional on DC account balance> 0

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 5
Estimation of Housing Equity
This Table reports the summary statistics (Panel A) and the regression coefficients (Panel B) used in the estimation of housing equity for each individual in our sample. The estimation
is based the 2010 Wave of the Health and Retirement Study (HRS) comprising the married individuals between the age 62 of and 67. The summary statistics in the 4th row of Panel
A is from our Zillow and based on the zip code where the workers in our sample live.
Panel A – Summary statistics
Mean

Std Dev

10th pctile

25th pctile

Median

75th pctile

90th pctile

Obs.

Value of 1st Residence in the HRS

227,542

249,981

50,000

95,000

170,000

275,000

450,000

2,322

Value of Other Real Estate in the HRS

38,107

171,393

0

0

0

0

89,000

2,322

Total Value of Real Estate in the HRS

265,649

331,396

50,000

100,000

177,000

300,000

550,000

2,322

Median House Value in the Zip code in our
sample (from Zillow)

260,598

191,756

100,400

138,000

198,100

325,200

493,500

42,875

LTV 1st Residence

27.42%

43.26%

0.00%

0.00%

5.73%

46.81%

78.19%

2,294

LTV for all Real Estate

26.60%

42.55%

0.00%

0.00%

6.50%

44.23%

76.00%

2,294

Panel B – Regression analysis

Homeowner

(3)
LTV 1st Residence

(4)
LTV for all Real Estate

2.16e-06***

1.23e-06***

-1.63e-08

-1.74e-08

[5.586]

[3.176]

[-1.147]

[-1.185]

-3.04e-07

-1.52e-06

3.79e-07*

3.55e-07*

[-0.186]

[-1.446]

[1.854]

[1.647]

1.215***

1.540***

0.267***

0.259***

[23.03]

[18.19]

[25.44]

[19.78]

Observations

1,894

1,271

1,739

1,216

Adjusted R2

0.0548

0.0352

0.001

0.002

No

Yes

NA

NA

Total Retirement Wealth
Salary
Constant

Conditional on Total Retirement Wealth>0

(1)

(2)

Homeowner

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 6
Estimation of Working-Age Consumption
This Table reports the regression coefficients used in the estimation of working age consumption for each individual in our sample. The
estimates are based on the 2006-2011 Waves of the Consumer Expenditure Survey (CEX) and comprise all respondents between the
age 20 and 65. Total expenditure is defined as the sum of food and alcohol, tobacco, apparel and services, entertainment, personal care,
housing and shelter, health, reading and education, transportation, and miscellaneous. We calculate adult equivalents for each household
based on Deaton and Zaidi (2002) and convert household-level expenditures into individual-level ones. To avoid the effect of outliers
and unusual circumstances, we limit the regressions to households in the interquartile range of the ratio of total expenditure over salary.
(1)
Total
expenditure
52.45***
[3.575]
0.504***
[96.83]

Respondent Age
Salary

(2)
Total
expenditure
52.19***
[3.559]
0.504***
[96.95]

Salary2

(3)
Total
expenditure
49.69***
[3.392]
0.549***
[41.83]

(4)
Total
expenditure

-2.61e-07***
[-3.725]

-2.76e-07***
[-3.944]
-1,369**
[-2.451]
-763.0
[-1.405]
120.2
[0.220]
501.5
[0.696]

Age 30-39
Age 40-49
Age 50-59
Age 60-65

0.553***
[42.18]

Salary*Age 20-29
Salary2*Age 20-29

Salary2*Age 30-39

-7.03e-07***
[-3.968]
0.501***
[19.37]

Salary*Age 40-49
Salary2*Age 40-49

1.39e-08
[0.100]
0.539***
[21.06]

Salary*Age 50-59
Salary2*Age 50-59

-1.67e-07
[-1.266]
0.540***
[11.69]

Salary*Age 60-65
Salary2*Age 60-65

Years Fixed Effects
Observations
R2

-12,437***
[-8.046]
-9,173***
[-6.152]
-9,500***
[-6.317]
-9,187***
[-4.427]
0.261***
[6.311]
8.42e-07***
[3.315]
0.605***
[20.18]

Salary*Age 30-39

Constant

(5)
Total
expenditure

2,321***
[3.393]
N
2,253
0.810

2,654***
[3.482]
Y
2,253
0.811

1,162
[1.551]
N
2,253
0.811

3,686***
[6.257]
N
2,253
0.812

Electronic copy available at: https://ssrn.com/abstract=3294422

-1.76e-07
[-0.794]
13,593***
[11.40]
N
2,253
0.787

Table 7
Baseline Results
This table shows the results from our baseline simulations. The rows refer to workers ranking at different percentiles in the worker population, and display, for each individual, the
CRRRs (Columns (1) to (5)), the CEQR (Column (7)), and the total wealth accumulation at age 65 excluding Social Security benefits (WT65) (Columns (8) to (12)) for the 10th to
the 50th percentiles across her 10,000 simulations. Column (6) presents the average CRRR across the 10,000 simulations. Total wealth at age 65 is reported in ,000 and expressed
in 2010 constant dollar terms.

10th Percentile
25th Percentile
50th Percentile
75th Percentile

(1)
10%
0.54
0.60
0.69
0.80

(2)
20%
0.61
0.69
0.80
0.94

CRRR
(3)
30%
0.68
0.76
0.90
1.06

90th Percentile

0.92

1.08

1.24

(4)
40%
0.73
0.84
1.00
1.2

(5)
50%
0.78
0.91
1.11
1.35

(6)
Mean
0.83
1.02
1.28
1.6

1.4

1.59

1.95

0.68
0.76
0.86
0.99

(8)
10%
117
152
234
419

(9)
20%
132
180
287
526

WT65
(10)
30%
148
208
339
625

1.14

668

848

1017

CEQR
(7)

(11)
40%
164
238
394
730

(12)
50%
182
270
456
850

1199

1412

Table 8
Results with Bequest Motive and with No Housing Wealth Availability
Panel A reports the results from assuming a target bequest of 10% of age-65 wealth, and that only savings in excess of this amount can be used to finance retirement consumption.
Panel B reports the results from assuming that all housing equity is left unused (θ=0). Columns (1) through (5), and (7) through (11), show different percentiles of the distribution of
CRRRs across realizations for the same individual, from the 10th lowest percentile to the median. Columns (6) and (12) report the CEQR from the two experiments. The rows
represent percentiles of the distribution across individuals. The amounts in italics under each item are the differences from the baseline results.
Panel A: Bequest Motive
CRRR

10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

10%
0.51
-0.03

20%
0.58
-0.03

30%
0.63
-0.05

Panel B: No Housing Wealth
CEQR

40%
0.68
-0.05

50%
0.73
-0.05

0.64
-0.04

CRRR
10%
0.46
-0.08

20%
0.53
-0.08

30%
0.58
-0.10

CEQR
40%
0.63
-0.10

50%
0.68
-0.10

0.58
-0.10

0.57

0.65

0.72

0.79

0.86

0.72

0.49

0.58

0.65

0.71

0.79

0.63

-0.03

-0.04

-0.04

-0.05

-0.05

-0.04

-0.11

-0.11

-0.11

-0.13

-0.12

-0.13

0.65

0.75

0.84

0.94

1.04

0.81

0.54

0.65

0.75

0.85

0.96

0.68

-0.04

-0.05

-0.06

-0.06

-0.07

-0.05

-0.15

-0.15

-0.15

-0.15

-0.15

-0.18

0.75

0.88

0.99

1.11

1.25

0.93

0.63

0.78

0.91

1.05

1.20

0.76

-0.05

-0.06

-0.07

-0.09

-0.10

-0.06

-0.17

-0.16

-0.15

-0.15

-0.15

-0.23

0.86

1.01

1.15

1.30

1.47

1.07

0.75

0.93

1.09

1.25

1.45

0.87

-0.06

-0.07

-0.09

-0.10

-0.12

-0.07

-0.17

-0.15

-0.15

-0.15

-0.14

-0.27

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 9
Alternative Preference Parameters and/or Retirement Portfolio Allocations
This Table reports the results from repeating the baseline simulations for different combinations of risk aversion, discount factor, and the share of age-65 wealth invested in the risky
asset. Panel A (B) reports the CEQR (CRRR) of the median worker for the baseline retirement portfolio risky share of 50%, and values of risk aversion of 8, 5, and 2, respectively.
Panel C reports the CEQR of the median worker for the baseline risk aversion coefficient of 5, and risky shares in the retirement portfolio of 0%, 50%, and 100%, respectively. The
rows report results for values of the discount factor of 0.97, 0.95, and 0.925, respectively.
Panel A: different values of g (aR = 0.5)

Panel B: different values of g (aR = 0.5)

CEQR

Median CRRR

Panel C: different values of aR (g = 5)
CEQR

g=8

g=5

g=2

g=8

g=5

g=2

a =0%

a =50%

aR=100%

b=0.975

0.59

0.78

1.27

0.82

1.01

1.36

0.75

0.78

0.72

b=0.95

0.61

0.86

1.46

0.86

1.11

1.55

0.82

0.86

0.8

b=0.925

0.65

0.92

1.64

0.91

1.2

1.75

0.89

0.92

0.86

R

R

Panel D – Implied parameters and worker demographics and asset allocation decisions

Age

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

RRA

RRA

RRA

Discount
factor

Discount
factor

Equity share

Account
value

Account
value

Account
value

-0.00532***

-0.00248

4.13e-05

-6.99e-06

Equity
share
0.0944***

Equity
share

0.000714

Discount
factor
0.000157*

-0.376***

-0.463***

3,295***

3,371***

493.3***

[0.438]

[-3.106]

[-1.318]

[0.459]

[-1.653]

[-0.0667]

[-2.989]

[-11.69]

[-13.54]

[34.09]

[36.12]

[5.921]

1.83e-06***

1.33e06***

5.51e08***

3.61e-08***

8.56e05***

3.36e-05***

[10.91]

[5.893]

[6.426]

[3.185]

[27.13]

[8.156]

Account
value
Equity share

Salary
Contribution
rate
Tenure

Constant
Observations
2

R

0.00310***

0.000141***

801.2***

196.7***

[5.688]
2.03e06***

[4.658]

[27.13]

[8.156]

7.88e-08***

0.000167***

1.279***

[3.661]

[2.763]

[16.83]

[61.56]

-0.127

-0.00616

67.83***

272,185***

[-0.619]

[-0.548]

[18.33]

[31.36]

-0.00426*

-0.000193

0.0538

4,241***

[-1.767]

[-1.478]

[1.214]

[43.12]
114,569***

3.974***

4.128***

3.793***

0.929***

0.934***

0.918***

61.24***

68.40***

59.30***

-83,624***

132,691***

[51.38]

[52.80]

[42.56]

[217.4]

[215.8]

[182.8]

[40.83]

[46.48]

[38.87]

[-18.22]

[-27.73]

[-30.23]

9,959

9,959

9,959

5,773

5,773

5,773

10,000

10,000

10,000

10,000

10,000

10,000

-0.000

0.012

0.017

-0.000

0.007

0.013

0.001

0.069

0.119

0.104

0.165

0.506

Electronic copy available at: https://ssrn.com/abstract=3294422

Panel E – Implied parameters and age-65 simulated wealth

Median age65 simulated
wealth

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

RRA

RRA

RRA

RRA

Discount
factor

Discount
factor

Discount
factor

Discount
factor

0.274***

0.276***

0.157***

0.0307

0.00993***

0.00995***

0.00691***

0.00250

[6.972]

[10.33]
Age

[10.34]

[4.690]

[0.518]

[6.958]

[3.807]

[0.821]

-0.00105

-0.00434**

-0.00242

-1.20e-05

-0.000102

-1.15e-06

[-0.645]

[-2.520]

[-1.285]

[-0.134]

[-1.066]

[-0.0110]

1.23e06***

1.27e-06***

2.96e08***

3.13e-08**

[5.820]

[5.120]

[2.724]

[2.460]

Account
value

Equity share
Salary
Contribution
rate
Tenure

0.00306***

0.000137***

[5.556]

[4.482]

1.73e-06**

5.67e-08

[2.183]

[1.449]

-0.201

-0.0122

[-0.804]

[-0.907]

-0.00363

-0.000140

[-1.341]
Constant
Observations
2

R

[-0.953]

3.788***

3.835***

3.998***

3.789***

0.922***

0.923***

0.928***

0.918***

[143.4]

[49.10]

[48.26]

[42.33]

[623.7]

[212.7]

[200.0]

[181.4]

9,959

9,959

9,959

9,959

5,773

5,773

5,773

5,773

0.011

0.010

0.014

0.017

0.008

0.008

0.009

0.013

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 10
Lower Expected Returns
This Table reports the results from repeating our baseline analysis assuming 1 ppt lower future expected returns. Columns (1) to (3) report the results for different percentiles of the
distribution of the CRRR across realizations for the same worker. Columns (5) to (7) report the same statistics but for wealth accumulation at age 65 (WT65), while column (4) reports
the certainty equivalent ratio. The rows represent different percentiles of the workers distribution. Below each entry we report the difference relative to the baseline case.
CRRR
10%
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

30%

WT65

CEQR
50%

10%

30%

50%

0.53

0.65

0.75

0.66

115

143

173

-0.02

-0.03

-0.03

-0.02

-2%

-3%

-5%

0.59

0.74

0.88

0.74

147

197

250

-0.01

-0.03

-0.04

-0.02

-3%

-5%

-7%

0.66

0.85

1.04

0.83

223

311

408

-0.02

-0.05

-0.08

-0.03

-5%

-8%

-11%

0.76

0.99

1.24

0.95

38

557

746

-0.04

-0.08

-0.11

-0.04

-9%

-11%

-12%

0.89

1.15

1.44

1.1

604

897

1227

-0.04

-0.09

-0.15

-0.04

-10%

-12%

-13%

Table 11
Contribution Rate Evolution Equation depending on Past Account Values
This Table reports the results from repeating our baseline analysis using as an input the contribution rates evolution equations estimated in Column (9) of Panel A of Table 2. Columns
(1) to (5) report the results for different percentiles of the distribution of the CRRR across realizations for the same worker. Column (6) reports the CEQR. The rows represent
different percentiles of the workers distribution. Below each entry we report the difference relative to the baseline case.
CRRR
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

CEQR

10%
0.54

20%
0.61

30%
0.67

40%
0.72

50%
0.77

0.67

0.00

0.00

-0.01

-0.01

-0.01

-0.01

0.60

0.68

0.76

0.83

0.91

0.75

0.00

-0.01

0.00

-0.01

0.00

-0.01

0.67

0.78

0.88

0.98

1.09

0.85

-0.02

-0.02

-0.02

-0.02

-0.02

-0.01

0.78

0.91

1.03

1.16

1.30

0.97

-0.02

-0.03

-0.03

-0.04

-0.05

-0.02

0.90

1.05

1.19

1.35

1.53

1.12

-0.02

-0.03

-0.05

-0.05

-0.06

-0.02

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 12
Cross-Sectional Heterogeneity
This Table reports the coefficients from cross-sectional regressions of age-65 simulated wealth (WT65), the median CRRR, and the CEQR on the initial characteristics of the workers,
plans, and firms in our sample. The errors are clustered at the firm level. The superscript *** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level.
Panel A - Age-65 Wealth (WT65) Regressions
(1)
Median

(2)
WT65

Median

(3)
WT65

Median

(4)
WT65

Median

(5)
WT65

Median

(6)
WT65

Median

(7)
WT65

Median WT65

Age

-39.22***
[-8.820]

-32.83***
[-6.700]

-29.34***
[-7.101]

-23.64***
[-5.009]

-17.04***
[-6.015]

-19.50***
[-3.734]

-15.66***
[-5.463]

Age squared

0.400***
[8.766]

0.289***
[5.568]

0.226***
[4.456]

0.210***
[3.875]

0.142***
[4.715]

0.170***
[2.824]

0.127***
[4.268]

Salary

0.0128***
[14.78]

0.0114***
[12.40]

0.0108***
[12.73]

0.0104***
[12.64]

0.0115***
[10.53]

0.0100***
[11.26]

0.0112***
[10.97]

-6.25e-09***
[-4.843]

-5.60e-09***
[-4.661]

-5.14e-09***
[-4.986]

-4.98e-09***
[-4.827]

-1.05e-08***
[-6.988]

-4.73e-09***
[-4.718]

-1.03e-08***
[-6.988]

0.00130***
[5.276]

0.000682***
[3.397]

0.00129***
[5.713]

0.00145***
[4.547]

0.00131***
[8.149]

0.00143***
[4.441]

3,203***
[11.64]

3,058***
[11.56]

3,233***
[15.69]

2,917***
[12.12]

3,212***
[16.00]

-15.12***
[-8.736]

-17.80***
[-5.464]

-14.98***
[-7.308]

-17.40***
[-5.076]

0.712**

0.725*

0.947***

0.731**

[2.086]

[2.110]

[3.637]

[2.229]

Salary squared
Account Balance
Contribution Rate
Tenure
Equity Share
% employer match, 1st tier

3.440***
[3.934]
166.6***
[3.575]

3.269***
[4.127]
153.3***
[3.531]

1.556**
[2.727]

1.797***
[3.379]

-0.00159***
[-5.072]

-0.00121***
[-4.934]

Capital Expenditure

0.0376***
[3.947]

0.0301***
[3.748]

Net Income

0.0228***
[3.962]

0.0180***
[3.214]

-0.000563**
[-2.349]

-0.000528**
[-2.264]

Privately held company
Firm Age
Total Assets

# of Employees
Financial Literacy at the state level

2.862**

Electronic copy available at: https://ssrn.com/abstract=3294422

[2.590]
% advanced degree in zip code

2.313***
[3.349]

% bachelor degree in zip code

1.665**
[2.441]

% high school degree in zip code

Observations
R2
Firm Fixed Effects

841.6***
[8.793]
350,859
0.586
No

802.1***
[7.994]
350,859
0.625
No

623.9***
[7.659]
350,859
0.745
No

501.0***
[4.648]
350,859
0.781
No

-102.5
[-0.930]
195,397
0.834
No

414.5***
[5.055]
350,859
0.815
Yes

-2.165**
[-2.715]
-121.9
[-1.126]
191,389
0.839
No

Firm Clustered SE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Constant

Panel B - Median Consumption Retirement Replacement Ratio and Consumption Equivalent Ratio Regressions

Age
Age squared
Salary
Salary squared
Account Balance
Contribution Rate
Tenure
Equity Share

% employer match, 1st tier

(1)

(4)

(5)

(7)

(1)

(4)

(5)

(7)

Median CRRR

Median CRRR

Median CRRR

Median CRRR

CEQR

CEQR

CEQR

CEQR

-0.0535***

-0.0428***

-0.0392***

-0.0383***

-0.0324***

-0.0241***

-0.0213***

-0.0197***

[-14.41]

[-16.82]

[-14.56]

[-14.45]

[-7.155]

[-7.242]

[-12.39]

[-15.04]

0.000564***

0.000429***

0.000391***

0.000382***

0.000373***

0.000263***

0.000240***

0.000223***

[13.88]

[15.59]

[15.46]

[16.30]

[7.248]

[7.411]

[10.83]

[13.19]

1.75e-06***

6.73E-08

1.13E-07

-2.32E-07

2.26e-07

-1.03e-06***

-1.19e-06***

-1.76e-06***

[6.477]

[0.318]

[0.270]

[-0.568]

[0.610]

[-3.020]

[-3.535]

[-5.168]

-0**

0

0

0

0

0***

0*

0***

[-2.059]

[0.0195]

[-0.957]

[-0.541]

[0.0214]

[3.573]

[1.979]

[3.084]

6.95e-07***

8.12e-07***

7.99e-07***

7.52e-07***

9.39e-07***

9.22e-07***

[4.640]

[4.036]

[3.871]

[8.127]

[8.075]

[7.399]

2.661***

2.828***

2.804***

1.522***

1.463***

1.420***

[15.98]

[13.77]

[13.74]

[28.74]

[16.98]

[16.27]

-0.00975***

-0.0109***

-0.0105***

-0.00682***

-0.00755***

-0.00697***

[-7.830]

[-4.529]

[-4.020]

[-10.12]

[-7.550]

[-5.323]

0.000583*

0.000753**

0.000743**

-0.000273

0.000169

0.000154

[1.853]

[2.699]

[2.723]

[-1.043]

[1.182]

[1.131]

0.00295***

0.00279***

0.00221***

0.00194***

Electronic copy available at: https://ssrn.com/abstract=3294422

Privately held company
Firm Age
Total Assets
Capital Expenditure
Net Income
# of Employees

[4.393]

[4.306]

[4.196]

[4.637]

0.130***

0.120***

0.0552*

0.0400*

[3.514]

[3.474]

[2.053]

[1.883]

0.00135***

0.00151***

0.000138

0.000433

[3.173]

[3.677]

[0.405]

[1.725]

-6.06e-07**

-3.21E-07

-1.57e-06***

-1.09e-06***

[-2.384]

[-1.528]

[-11.26]

[-13.93]

1.57e-05**

9.28e-06*

2.76e-05***

1.74e-05***

[2.638]

[1.885]

[6.558]

[6.371]

1.12e-05**

7.77e-06**

1.43e-05***

8.53e-06***

[2.806]

[2.177]

[4.627]

[3.533]

-5.01e-07***

-4.69e-07***

-1.60e-07

-1.19e-07

[-3.051]

[-2.933]

[-1.237]

[-1.074]

Financial Literacy

% advanced degree in zip code

0.00374***

0.00504***

[3.809]

[3.048]

-0.000391

2.59e-05

[-0.771]
% bachelor degree in zip code

[0.0689]

0.00242***
0.00380***
[3.488]

% high school degree in zip code

[6.617]

-0.00117
-0.00252***
[-1.451]

Constant

[-3.205]

2.011***

1.746***

1.280***

1.165***

1.535***

1.404***

1.094***

0.991***

[26.68]

[22.91]

[13.37]

[10.63]

[19.34]

[20.53]

[14.88]

[13.05]

350,859

350,859

195,397

191,389

350,859

350,859

195,397

191,389

0.139

0.616

0.716

0.73

0.047

0.371

0.546

0.622

Firm Fixed Effects

No

No

No

No

No

No

No

No

Firm Clustered SE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations
R2

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 13
Consumption Replacement Ratios and Certainty Equivalent Ratios Across Worker Types
Panel A reports the median CRRR and CEQR from the baseline simulations for different age groups. The rows represent different percentiles of the distribution across workers.
Panel B provides calculations of the simulated median age-65 wealth for workers with various profiles based on the coefficients in Panels A and B of Table 12. Column (1) of Panel
B report median age-65 wealth, CRRR and CEQR for a worker of median age, the median salary and at the average of the other covariates for that age bracket (40-42); Column (2)
of Panel B reports the same variables for a worker of median age, 10th percentile salary and at the average of the other covariates for that age bracket (40-42); Column (3) of Panel
B reports it for a worker of Worker of median age, 90th percentile salary and at the average of the other covariates for that age bracket (40-42). Column (4) to (6) report the same
information for a 26 years old worker, the 10th percentile of age, while Columns (7) to (9) illustrate those outcomes for a 57 years old worker, the 90th percentile of age.
Panel A – Consumption Replacement Ratios and Certainty Equivalent Ratios Across Age Groups
Median CRRR

Median CEQR

20-34

35-49

50-64

All

20-34

35-49

50-64

All

10th Percentile

0.96

0.76

0.67

0.78

0.75

0.67

0.63

0.68

25th Percentile

1.08

0.87

0.83

0.91

0.81

0.74

0.74

0.76

50th Percentile

1.25

1.03

1.03

1.11

0.89

0.83

0.88

0.86

75th Percentile

1.45

1.24

1.32

1.35

1.02

0.94

1.05

0.99

90th Percentile

1.63

1.47

1.68

1.59

1.16

1.07

1.24

1.14

Panel B – Median Age-65 Wealth (WT65), Consumption Replacement Ratios, and Certainty Equivalent Ratios for Selected Worker Profiles
(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

57
53,270.04
570.677

57
24,053.15
210.182

57
106,953.90
1205.237

2.715

0.473

0.831
1.059
0.91
1.007

0.967
0.911
0.92
0.987

3,057.19
4.30%
3.50
60
208.404
2.343
0.819

171,567.50
11.20%
16.11
64
1257.965
0.388
1.005

Based on Column (1) of Panels A and B
Age
Salary
Median WT65

41
48,323.29
508.773

Ratio of median worker
wealth to 10th and 90th
percentiles
Median CRRR
Ratio
CEQR
Ratio

0.843
0.84

41
23,492.63
201.542

41
103,315.80
1161.753

2.524

0.438

0.801
1.052
0.84
1.007

0.932
0.905
0.86
0.985

26
34,292.29
524.522

1.059
0.95

26
19,195.15
335.995

26
65,624.68
906.695

1.561

0.578

1.033
1.025
0.95
1.004

1.111
0.953
0.96
0.993

0.881
0.91

Based on Column (4) of Panels A and B
Account balance
Contribution rate
Tenure
Equity share (%)
Median WT65
Ratio
Median CRRR

10,556.54
5.20%
5.92
75
509.6
0.844

1,583.65
3.40%
2.73
79
243.344
2.094
0.82

46,269.95
6.80%
5.88
96
1151.517
0.443
0.928

2,528.79
3.40%
3.07
73
490.641
1.029

710.99
2.30%
2.33
59
303.497
1.617
0.997

5,328.66
6.70%
1.94
78
926.669
0.529
1.135

35,332.27
6.30%
11.12
60
488.363

Electronic copy available at: https://ssrn.com/abstract=3294422

0.822

Ratio
CEQR
Ratio

0.83

1.029
0.85
0.986

0.909
0.82
1.013

76.256
0.355
52.24
70,724.96
2,324.69
2,190.56
87,278
198.083
2.442
0.774
1.031
0.81
0.962

66.206
0.423
61.28
66,124.13
2,266.61
2,572.96
53,437
1165.343
0.415
0.904
0.883
0.78
0.993

0.93

1.032
0.94
0.993

0.906
0.96
0.972

0.86

1.004
0.89
0.969

0.818
0.95
0.908

73.198
0.459
53.73
74,186.58
2,626.36
2,264.08
79,552
183.523
2.532
0.784
0.989
0.85
0.942

59.464
0.45
79.36
56,960.20
2,821.84
1,745.77
35,827
1305.854
0.356
1.007
0.77
0.92
0.870

Based on Column (5) of Panels A and B
% Employer match
Privately held company
Firm age
Total assets (‘000)
Capital expenditure (‘000)
Net income (‘000)
# of employees
Median WT65
Ratio
Median CRRR
Ratio
CEQR
Ratio

65.261
0.428
58.61
76,082.28
2,692.65
2,463.47
68,730
483.731
0.798
0.78

66.237
0.43
56.74
78,956.64
2,800.56
2,991.85
71,062
438.831
0.97
0.87

55.546
0.522
56.17
70,118.51
2,467.32
2,035.90
101,228
179.687
2.442
0.889
1.092
0.84
1.035

47.717
0.531
69.95
56,320.14
3,048.22
2,759.39
34,760
934.913
0.469
1.093
0.888
0.90
0.962

55.97
0.492
68.50
59,235.30
2,485.75
1,835.90
51,027
464.68
0.775
0.80

Based on Column (7) of Panels A and B
Financial literacy

40.50

39.83

40.64

40.81

40.27

40.91

40.57

39.91

40.97

% with advanced degree
in the worker's zip code

12.52

9.43

17.71

11.18

9.55

15.24

11.62

10.70

15.45

% with bachelor degree or
more in the worker's zip
code

33.75

27.15

44.64

30.84

27.71

39.17

31.65

29.87

39.50

% with high school degree
or more in the worker's
zip code

87.59

84.66

91.30

85.17

83.69

86.78

87.76

86.23

90.05

489.001

196.688
2.486
0.775
1.039
0.81
0.973

1175.908
0.416
0.913
0.882
0.79
0.995

437.749

181.09
2.417
0.894
1.089
0.84
1.028

938.112
0.467
1.098
0.886
0.90
0.960

462.766

182.012
2.543
0.786
0.988
0.85
0.939

1305.089
0.355
1.006
0.772
0.91
0.878

Median WT65
Ratio
Median CRRR
CEQR
Ratio

0.805
0.78

0.973
0.87

Electronic copy available at: https://ssrn.com/abstract=3294422

0.777
0.80

Table 14
Removing age 59 ½ penalty-free withdrawals
This Table reports the results from repeating our baseline simulations disallowing penalty-free age 59 ½ early withdrawals. Columns (1) to (3) report the results for different
percentiles of the distribution of the CRRR across realizations for the same worker. Columns (5) to (7) report the same statistics but for wealth accumulation at age 65 (WT65), while
column (4) reports the certainty equivalent ratio. The rows represent different percentiles of the distribution across individuals. Below each entry we report differences relative to the
baseline case.
CRRR

10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

WT65

CEQR

10%

30%

50%

10%

30%

50%

0.59

0.71

0.83

0.73

136

179

216

0.04

0.04

0.05

0.05

16.00%

21.00%

19.00%

0.66

0.84

1

0.83

180

249

317

0.06

0.08

0.09

0.07

18.00%

20.00%

17.00%

0.75

0.99

1.21

0.93

274

390

510

0.06

0.09

0.10

0.07

17.00%

15.00%

12.00%

0.86

1.15

1.44

1.07

461

672

902

0.06

0.09

0.09

0.08

10.00%

8.00%

6.00%

0.99

1.31

1.69

1.23

706

1061

1463

0.06

0.08

0.10

0.09

6.00%

4.00%

4.00%

Table 15
Setting minimum contribution rates at 2.5% and 5%
Panel A (B) reports the results from requiring a minimum contribution rate of 2.5% (5%). Columns (1) through (3), and (5) through (7) present the results for different percentiles of
the distribution of CRRRs across realizations for the same individual. Columns (4) and (8) report the CEQR from the two experiments. Panel C reports the median CRRR and CEQR
for the minimum contribution rate of 5% for different age groups. The rows represent percentiles of the distribution across individuals. Below each entry we include differences from
the baseline case.
Panel A - 2.5% minimum
CRRR
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

Panel B: 5% minimum

CEQR

10%

30%

50%

0.55

0.68

0.78

0.01

0.00

0.00

0.6

0.76

0.00

0.00

0.69
0.00

CRRR

Panel C - 5% minimum, by age bracket

CEQR

10%

30%

50%

0.68

0.55

0.69

0.79

0.00

0.01

0.01

0.01

0.93

0.76

0.61

0.78

0.00

0.00

0.01

0.01

0.9

1.11

0.86

0.69

0.00

0.00

0.00

0.00

Median CRRR

CEQR

20-34

35-49

50-64

20-34

35-49

50-64

0.69

1

0.78

0.69

0.76

0.68

0.64

0.01

0.04

0.02

0.02

0.01

0.01

0.01

0.94

0.77

1.12

0.89

0.83

0.82

0.74

0.75

0.02

0.01

0.04

0.02

0.00

0.01

0.00

0.01

0.9

1.13

0.87

1.29

1.04

1.03

0.9

0.83

0.88

0.00

0.01

0.01

0.04

0.01

0.00

0.01

0.00

0.00

0.8

1.06

1.35

1

0.8

1.08

1.36

1

1.48

1.24

1.33

1.03

0.95

1.05

0.00

0.00

0.00

0.01

0.00

0.01

0.01

0.01

0.03

0.00

0.01

0.01

0.01

0.00

0.93

1.24

1.59

1.15

0.93

1.24

1.6

1.15

1.67

1.47

1.68

1.17

1.07

1.24

0.00

0.00

0.00

0.01

0.00

0.00

0.01

0.01

0.04

0.00

0.00

0.01

0.00

0.00

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 16
Age-dependent contribution rate
This Table reports the results from setting an age-dependent minimum contribution rate kmin = 4.5% + (age - 21) * 0.25%. Columns (1) to (3) report the results for different percentiles
of the distribution of the CRRR across realizations for the same worker. Columns (5) to (7) report the median CRRR by age bracket, while Columns (4) and (8)-(10) report the
certainty equivalent ratios. The rows represent different percentiles of the workers distribution. Below each entry we report the difference relative to the baseline case.
Panel A - All
CRRR
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

Panel B: 2 ppts increase in contribution rates, by age bracket
CEQR

Median CRRR
20-34

35-49

CEQR

10%

30%

50%

50-64

20-34

35-49

50-64

0.56

0.71

0.83

0.71

1.01

0.83

0.72

0.77

0.7

0.67

0.02

0.04

0.05

0.03

0.05

0.07

0.05

0.02

0.03

0.04

0.63

0.8

0.96

0.79

1.13

0.93

0.86

0.83

0.77

0.77

0.02

0.04

0.05

0.03

0.05

0.06

0.03

0.02

0.03

0.03

0.7

0.93

1.15

0.88

1.3

1.08

1.06

0.92

0.85

0.9

0.01

0.03

0.04

0.02

0.05

0.05

0.03

0.03

0.02

0.02

0.81

1.09

1.38

1.01

1.49

1.27

1.34

1.04

0.97

1.06

0.01

0.02

0.02

0.02

0.04

0.04

0.02

0.02

0.03

0.01

0.94

1.26

1.63

1.16

1.68

1.49

1.69

1.18

1.09

1.25

0.01

0.03

0.04

0.02

0.05

0.02

0.01

0.02

0.02

0.01

Table 17
Increasing the contribution rate for all workers by 2 or 5 percentage points
Panel A(B) reports the results the results from increasing each worker’s saving rate by 2(5) ppts. Columns (1)-(3) / (5)-(7) present results for different percentiles of the distribution
of the CRRR across realizations for the same worker, while Column (4) and (8) presents the certainty equivalent ratio. Panel C reports the results by age group for the case of a 2
ppts increase. The rows represent different percentiles of the distribution across individuals. Below each entry we report the differences relative to the baseline case.
Panel A - 2 ppts increase
10%
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

CRRR
30% 50%

Panel B - 5 ppts increase

CEQR
10%

CRRR
30% 50%

Panel C - 2 ppts increase by age bracket

CEQR
20-34

Median CRRR
35-49
50-64

20-34

CEQR
35-49

50-64

0.56

0.7

0.81

0.71

0.59

0.74

0.86

0.74

1.05

0.81

0.7

0.82

0.73

0.67

0.02

0.03

0.04

0.03

0.04

0.06

0.09

0.06

0.09

0.05

0.03

0.07

0.06

0.04

0.61

0.8

0.96

0.79

0.64

0.84

1.03

0.82

1.18

0.92

0.84

0.88

0.79

0.78

0.01

0.04

0.05

0.03

0.04

0.08

0.11

0.06

0.1

0.05

0.01

0.07

0.05

0.04

0.71

0.94

1.18

0.89

0.74

0.99

1.25

0.92

1.36

1.08

1.05

0.97

0.88

0.91

0.03

0.04

0.06

0.03

0.05

0.09

0.14

0.06

0.09

0.05

0.02

0.08

0.06

0.03

0.83

1.11

1.43

1.02

0.85

1.18

1.51

1.05

1.57

1.28

1.34

1.1

1

1.08

0.03

0.05

0.07

0.03

0.05

0.11

0.16

0.06

0.12

0.04

0.02

0.08

0.06

0.03

0.95

1.29

1.68

1.17

0.98

1.36

1.79

1.2

1.78

1.51

1.69

1.25

1.13

1.27

0.03

0.05

0.09

0.03

0.05

0.13

0.20

0.06

0.15

0.04

0.01

0.09

0.06

0.03

Electronic copy available at: https://ssrn.com/abstract=3294422

Table 18
Automatic rollover following a job switch
This Table reports the results from repeating our baseline simulations disallowing withdrawals following a job switch. Columns (1) to (3) report the results for different percentiles
of the distribution of the CRRR across realizations for the same worker. Columns (5) to (7) report the same statistics but for wealth accumulation at age 65 (WT65), while column (4)
reports the certainty equivalent ratio. The rows represent different percentiles of the workers distribution. Below each entry we report the difference relative to the baseline case.
CRRR
10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

WT65

CEQR

10%

30%

50%

10%

30%

50%

0.55

0.68

0.79

0.69

119

152

187

0.01

0.00

0.01

0.01

0.02

0.03

0.03

0.61

0.78

0.94

0.77

155

216

282

0.01

0.02

0.03

0.01

0.02

0.04

0.04

0.7

0.92

1.15

0.88

241

356

481

0.01

0.02

0.04

0.02

0.03

0.05

0.05

0.82

1.1

1.4

1.02

438

660

900

0.02

0.04

0.05

0.03

0.05

0.06

0.06

0.95

1.28

1.66

1.17

705

1078

1498

0.03

0.04

0.07

0.03

0.06

0.06

0.06

Electronic copy available at: https://ssrn.com/abstract=3294422

Table A1
Different assumptions regarding new employer’s 401(k) plan following a job loss
Panel A (B) reports the results from assuming that following a job loss the worker’s new DC plan is randomly drawn from those with workers within the same initial income decile
(the full sample). Columns (1) through (5) and (7) through (11) report the results for different percentiles of the distribution of the CRRR across realizations for the same worker,
while Columns (6) and (12) report the certainty equivalent ratio. The rows represent percentiles of the distribution across individuals.
Panel A: Random plan from same income decile
CRRR

10th Percentile
25th Percentile
50th Percentile
75th Percentile
90th Percentile

10%

20%

0.54
0.00

Panel B: Random plan from the full sample

CEQR

30%

40%

50%

0.62

0.67

0.73

0.78

0.01

-0.01

0.00

0.00

0.6

0.69

0.76

0.84

0.92

0.00

0.00

0.00

0.00

0.01

CRRR
10%

20%

0.68

0.54

0.62

0.00

0.00

0.01

0.76

0.6

0.69

0.00

0.00

0.00

30%

CEQR
40%

50%

0.67

0.72

0.78

0.68

-0.01

-0.01

0.00

0.00

0.76

0.84

0.92

0.76

0.00

0.00

0.01

0.00

0.68

0.79

0.89

1

1.11

0.86

0.68

0.79

0.89

1

1.11

0.86

-0.01

-0.01

-0.01

0.00

0.00

0.00

-0.01

-0.01

-0.01

0.00

0.00

0.00

0.8

0.93

1.06

1.19

1.34

0.99

0.8

0.93

1.06

1.19

1.34

0.99

0.00

-0.01

0.00

-0.01

-0.01

0.00

0.00

-0.01

0.00

-0.01

-0.01

0.00

0.92

1.08

1.23

1.39

1.57

1.14

0.91

1.08

1.23

1.39

1.57

1.14

0.00

0.00

-0.01

-0.01

-0.02

0.00

-0.01

0.00

-0.01

-0.01

-0.02

0.00

Electronic copy available at: https://ssrn.com/abstract=3294422