The Optimal Early-Withdrawal Penalty on Tax-deferred

Saving Accounts∗

Anson T. Y. Ho†

Abstract

Tax-deferred savings accounts (TDA) are commonly used to encourage retirement

savings. While TDA have similar institutional settings in many countries, the penalty

rates on assets withdrawal before retirement differ significantly. Through an overlapping-

generations model calibrated to the U.S. economy, this paper shows that the optimal

early withdrawal penalty rate is 50.4%, which is substantially higher than the 10%

in the current regulation. Adopting the optimal penalty rate will obtain a welfare

gain equivalent to a 2.16% increase in per period consumption. A reform with income-

dependent early withdrawal penalty will improve welfare equivalent to a 2.90% increase

in per period consumption. Experiment results indicate that households facing negative

income shocks over withdraw TDA assets for consumption. Sensitivity test show that

the welfare gain from an income-dependent penalty is more robust to the assumption

on household’s time inconsistent preferences, and it provides four times more welfare

gain than a constant penalty rate if households are naıvete.

JEL classification: D14, D91, E21, H24

Keywords : Retirement, savings, tax-deferred savings accounts, hyperbolic discounting

∗I am grateful for comments from Dean Corbae, Kim P. Huynh, Jie Zhou, and participants at 2017

Asian Meeting of the Econometric Society. All errors are mine. I thank Johan Brannlund for his excellent

assistance with the Bank of Canada EDITH High Performance Cluster, where all the computations were

performed. The views expressed in this paper are mine. No responsibility for them should be attributed to

the Bank of Canada.†Bank of Canada, 234 Wellington Street, Ottawa, Ontario, K1A 0G9, Canada.

Email: ansonho@bankofcanada.ca.

1

1 Introduction

Tax-deferred saving accounts (hereafter TDA) are systematically used in many countries

to increase households’ preparedness for retirement. The most common types of TDA in

the U.S. are 401(k) and Individual Retirement Accounts (IRA).1 TDA provide significant

tax benefits to account holders for higher returns on savings – labor earnings contributed

to TDA are income-tax deductible and capital income within these accounts are untaxed.

Only when account holders withdraw assets from TDA, the whole amount taken out will be

taxed as ordinary income. However, savings in TDA also come with liquidity risk as early

withdrawal before before retirement age is subject to penalty payment in addition to the

income tax incurred. Thus, households’ use of TDA is a tradeoff between tax benefits and

assets liquidity, in addition to the intertemporal tradeoff on consumption. Although early

withdrawal penalty is a common regulation in place for TDA, Beshears, Choi, Hurwitz,

Laibson, and Madrian (2015) point out that TDA in the U.S. has one of the most liquid

arrangements.

Early withdrawals, also known as leakage, from TDA is an important consideration in

TDA institutional settings. Illiquidity, as a commitment to save for retirement, can also be a

risk. Using tax returns data, Amromin and Smith (2003) find that early withdrawals mainly

reflects consumption smoothing behavior by liquidity-constrained households, and Argento,

Bryant, and Sabelhaus (2015) show that early withdrawals increased during the great reces-

sion. Indeed, liquidity constraint also enables on “semi-liquid” TDA to serve as commitment

devices for retirement savings. Existing literature largely focuses on the theoretical context.

Amador, Werning, and Angeletos (2006) and Ambrus and Egorov (2013) theoretically an-

alyze the trade-off between commitment and flexibility. Beshears, Choi, Clayton, Harris,

Laibson, and Madrian (2015) explores the optimal penalty on early withdrawal in an ab-

stracted 3-period model. On the extensive margin, Diamond and Koszegi (2003) show that

households may use insufficient savings as a strategy to commit their future selves for later

retirement.

In a quantitative framework, Laibson (1997) argues that financial innovations lowered

saving rates in the U.S. as they increased the liquidity of savings. Laibson, Repetto, Tobac-

man, Hall, Gale, and Akerlof (1998) show that TDA is an effective commitment device for

household to save for retirement. Imrohoroglu, Imrohoroglu, and Joines (2003) point out

that the benefits of social security, as a mandatory defined-benefits retirement savings pro-

1Other less common types of TDA are 403(b) for nonprofit sector, 457 plan for public sector, and Keogh

accounts. They all have similar settings as 401(k).

2

gram for time-inconsistent household, is not substantial enough to overcome the distortions

created via payroll taxes. Love (2006) argues that the generosity of unemployment insur-

ance crowds out 401(k) contributions made by younger workers as they primarily save for

for precautionary reasons. Love and Phelan (2015) show that, with Epstein-Zen preferences,

the elasticity of inter-temporal substitution significantly increase the impact of hyperbolic

discounting on households’ wealth accumulation.

This paper explores the optimal early withdrawal penalty mechanism for TDA through

an overlapping-generations model, in which households exhibit time inconsistent preferences.

In the model, households are subject to idiosyncratic shocks on labor earnings and unemploy-

ment. They have assess to TDA that mimics 401(k) in the U.S., with certain contribution

limit and an employer match provision. Early assets withdrawal from TDA is subject to

10% penalty. Households’ income, after deducting TDA contributions, are taxed through a

progressive tax system. Social security and unemployment benefits are also included in the

model.

Two types of early withdrawal reforms are considered in this paper. Within the current

TDA regulatory framework, raising the early withdrawal penalty to about 50% will result in

welfare gains equivalent to a 4% per-period consumption. Although imposing a higher early

withdrawal penalty raises households’ liquidity risks and motivates them to substitute TA

savings for TDA savings, it also allows them to build precautionary savings in TA such that

they are less prone to withdraw from TDA in case of adverse income shocks. An income-

dependent penalty scheme for early withdrawal will further improve welfare equivalent to

a 0.5% increase in per-period consumption. Our findings shed light on the importance

of households’ liquidity concerns in accumulating wealth in semi-illiquid TDA. This paper

shows that simple reforms to the TDA early withdrawal policy can results in significant

welfare gains. It relates to the long-standing debate on the adequacy of households’ savings

for retirement and their participation in TDA.

The rest of the paper is organized as follow: Section 3 describes the model used for our

analysis, Section 4 explains the model calibration strategy, Section 5 conducts experiments

on the optimal early withdrawal penalty, Section 6 reports the results with naivete quasi-

hyperbolic discounting households, and Section 7 concludes.

3

2 TDA and Early Withdrawal Penalty

In general, distributions from conventional IRAs and 401(k) prior to age 59.5 are known as

early withdrawals, which are subject to a 10% penalty in addition to the income tax incurred.

Penalty-free early withdrawal is only allowed under specific circumstances for: (1) first-time

home purchase, (2) qualified education expenses, (3) death or disability, (4) unreimbursed

medical expenses, or (5) health insurance if the account holder is unemployed. According

to Vanguard (2016), about 1.5% of the aggregate assets are leaked out from 401(k) per year

from 0.79% of account holders. The most significant factors contributing to the leakage are

in-service withdrawals and cashouts.

Loan provisions for TDA differ based on account types. Conventional IRAs do not offer

loans under IRS regulations. On the other hand, Vanguard (2016) reports that 78% of 401(k)

plans offer loan options in 2015, covering 89% of plan participants. If account holders leave

their current jobs, they are typically required to repay the entire outstanding balance of

their 401(k) loans within 60 days. Any amount not repaid is considered an early withdrawal.

Non-hardship loans against 401(k) must be repaid within 5 years if an account holder stays

with her employer. Statutory regulation limits 401(k) participants to borrow at most 50%

of their 401(k) balance or up to $50,000, whichever is less. Generally, loans on 401(k) is not

common among US households. In 2015, only about 2% of the aggregate plan assets are in

loans.

3 Model

The life-cycle model used for analyzing households’ consumption-savings decisions is specified

in this section. Key features of the model includes households time inconsistent preferences,

uninsurable idiosyncratic risks on labor efficiency and unemployment, savings in tax-deferred

savings accounts (TDA) and taxable accounts (TA), and a progressive income tax system.

3.1 Demographics and Preferences

There is a large number of households born every period and the population grows at a

constant rate of g. Households have stochastic lifetime, entering the economy at age 25 and

live at most up to age 95 (J = 71 periods). Their conditional survival probability from

period j to period j + 1 is denoted by sj . Let µj be the fraction of population at age j,

the relative size of age j and age j + 1 households is given by µj+1 =sj1+g

µj and the total

4

population is∑J

j=1 µj = 1.

Preferences over lifetime consumption for a household of age j∗ exhibit time inconsis-

tency via hyperbolic discounting.2 Adopted from Laibson (1997), household’s preferences is

represented by

Uj∗ =

j∗−1∑

j=1

δj−j∗

b u(cj) + u(cj∗) + βEj∗

J∑

j=j∗+1

δj−j∗

f

j−1∏

t=j∗

stu(cj), (1)

where δb is the backward-looking discounting factor, δf is the forward-looking discounting

factor, and β ≤ 1 controls for households’ patience. The per-period utility function is given

by u(cj) =c1−γj

1−γ, where γ is the coefficient of relative risk aversion.

3.2 Income Process

Households are endowed with 1 unit of time each period and supply it inelastically to work

from age 25 to 64 (R = 40 periods). They enter the economy with different education levels

and are subject to idiosyncratic labor efficiency shocks and unemployment shocks.

The level of labor efficiency for a household at age j with education level i is given by

ej = exp(εj + εj), (2)

where εj is an age-specific deterministic efficiency, and εj is an uninsurable idiosyncratic

shock. The labor efficiency shock is persistent and follows the AR(1) process

εj = ρεεj−1 + ξj, (3)

where ξj is i.i.d. random variables normally distributed with mean zero and variance σ2ε .

The employment status of a household at age j is denoted by ηj ∈ {0, 1}, where ηj = 0

and ηj = 1 indicates that the household is being unemployed and employed, respectively.

The probability of unemployment, Pη(j), is conditional on a household’s age j. Unemployed

household receive unemployment insurance benefits with replacement rate λue of their em-

ployed labor earnings. Households retire after R periods and receive social security benefits,

which is a constant fraction, λss, of last working period’s labor income from employment.

This specification simplifies the solution for the model, as it retains heterogeneity in retire-

ment income without keeping track of households’ entire income histories. Let w be the

2Alternatively, self-control issues can be modeled via a class of utility function specified by Gul and

Pesendorfer (2004), with which Kumru and Thanopoulos (2008) and Kumru and Thanopoulos (2011) study

the U.S. social security system.

5

effective wage rate, the labor earnings, yj, for an age-j household is calculated as

yj =

{[(1− ηj)λue + ηj ]wej if j ≤ R

λssweR if j > R. (4)

3.3 Tax-deferred Accounts and Taxable Accounts

All households have access to tax-deferred savings accounts (TDA) and taxable savings

accounts (TA). Households can contribute their pre-tax labor earnings to TDA in each

employed period of their working lives. Contributions to TDA is limited to fraction q of

their current income or q amount in dollars, whichever is lower. After retirement, households

cannot contribute to TDA, and there is a minimum required distribution after period R+6.3

The amount of assets in TDA at the beginning of period j is denoted by aDj . Let qj denote

household’s period j contributions to TDA, with qj < 0 implies that assets are withdrawn

from TDA. Thus,

qj ∈

[−aDj ,min(q, qwej)

]if j ≤ R and ηj = 1

[−aDj , 0

]if j ≥ R + 1 and j ≤ R + 6[

−aDj ,−1

J−j+1aDj

]if j > R + 6

(5)

where 1J−j+1

is the minimum withdrawal rate.

Employed households also receive employers’ match of their TDA contributions, which is

q fraction of employee’s contributions up to 6% of the employee’s labor income. Therefore,

the amount of employer’s match, denoted by qEj , is

qEj =

{min(q ∗ qj, q ∗ 0.06yj) if qj > 0 and ηj = 1

0 otherwise. (6)

Assets in both TDA and TA earn a constant rate of return r.4 The amount of assets in

TDA grows as

aDj+1 = (1 + r)aDj + qj + qEj . (7)

3According to the current regulations in the United States, individuals must begin to take withdrawals

by age 70 1

2.

4To keep the model tractable, households’ portfolio choice and asset location problems are abstract

from this model. There is a strand of literature studying the portfolio choice in the presence of TDA.

See Amromin (2003), Dammon, Spatt, and Zhang (2004), Garlappi and Huang (2006), Huang (2008), and

Gomes, Michaelides, and Polkovnichenko (2009), among others.

6

Let aTj be the assets in households’ TA at the beginning of period j. Both TDA and TA are

subject to zero borrowing constraints

aTj ≥ 0 and aDj ≥ 0 for all j. (8)

Assets of deceased households are treated as accidental bequest (TR) and distributed evenly

across all households as lump sum transfers.

TDA assets withdrawn prior to age 59.5 (model period j < R − 4) is subject to early

withdrawal penalty at rate τpen ∈ (0, 1), in addition to the ordinary income tax incurred.

The early withdrawal penalty is specified as

pen(qj , j)

{= τpen × qj if qj < 0and j < R − 4

= 0 otherwise(9)

3.4 Taxes

Household’s labor earnings is taxed through a piece-wise linear progressive income tax sys-

tem, T (·), with contributions to TDA being tax deductible and Γ amount of income tax

exemption in the U.S. tax code. Taxable income in period j, denoted by AGIj , is defined as

the sum of labor earnings, interest income in TA, and the assets withdrawn from TDA, net

of TDA contributions and income tax exemption, such that

AGIj = we(εij, εj) + raTj − qj − Γ. (10)

Marginal income tax rates are conditional on household’s taxable income above the tax

exemption. Let IC = {IC1, IC2, IC3, IC4} be the cutoff points of the tax brackets and

{τ1, τ2, τ3, τ4, τ5} denote the corresponding marginal tax rates. For household with taxable

income AGIj ∈ (IC3, IC4], income tax payment is

T (AGIj) = τ1 (IC2 − IC1) + τ2 (IC3 − IC2) + τ3 (AGIj − IC3) . (11)

Households also pay payroll taxes and unemployment insurance tax, denoted by τss and

τui respectively, for balancing the social security and the unemployment insurance budgets.

Households’ capital income is subject to capital income tax at rate τk, included in the model

to mimic the corporate profits tax, and consumption is also taxed at rate τc.

7

3.5 Household Problem

The budget constraint for a household at age j is

cj + aTj+1 + qj

= yj + [1 + (1− τk)r]aTj + TR

−T (AGIj)− (τss + τui) yj − τccj if j ≤ R

= yj + [1 + (1− τk)r]aTj + TR

−T (AGIj)− τccj if j > R

. (12)

Households’ state variables are the current employment status, labor efficiency, TA and

TDA assets. Let xj be the set of state variables for a household in period j, with xj =(ηj, εj, a

Tj , a

Dj

)∈ 1η×R×R×R. They make decisions on consumption (cj), TDA contribution

(qj), and next period TA assets (aTj+1) based on their states, such that cj = c(xj), qj = q(xj),

and aTj+1 = aT (xj). Households are assumed to be sophisticated, who fully aware of their

time inconsistent preferences. They assume that their future selves will also engage in quasi-

hyperbolic discounting, and they account for that in their decision making in the current

period.

The decision problem for an age-j household in recursive form is written as

V (j, xj) = maxcj ,qj ,a

Tj+1

{c1−γj

1− γ+ βδfsj+1Ej

[V (j + 1, xj+1)

]}, (13)

where

V (j + 1, xj+1) =c1−γj+1

1− γ+ δfsj+2Ej+1

[V (j + 2, xj+2)

], (14)

subject to income processes (2) to (4) and constraints (5) to (12), in addition to the non-

negativity constraint on consumption.

3.6 Firm Problem

Firms have access to a Cobb-Douglas production function that uses capital and labor to

produce output. Factor markets are competitive. In addition to paying wages for labor input,

firms also match a fraction of their employees’ contributions to TDA. The representative

firm’s profit maximization problem is written as

π = zKαN1−α − (r + δ)K − wN −Qe (15)

where z is the total factor productivity (TFP), K is the aggregate capital, N is the aggregate

effective labor, and Qe is the total amount of employer’s match of employees contribution to

8

TDA specified in equation (6). The employer’s match can also be expressed as qe percentage

of total wages such that

Qe = qewN. (16)

The firm’s profit maximizing levels of capital and effective labor are characterized by the

first-order conditions

r = αzkα−1 − δ (17)

(1 + qe)w = (1− α)zkα. (18)

3.7 Stationary Equilibrium

To describe the heterogeneity among households of age j is described by A probability

measure ϕj that defines the subset of households state space (X). Let the probability space

be (X,B(X), ϕ), where B(X) is the Borel σ-algebra on X . For a household of age j > 1,

the probability measure is given by the recursion

ϕj+1(B) =

∫

X

Pr(x, j, B)dϕj, (19)

where

Pr(x, j, B) =

{ ∑i P

ηij

∫Pr(ε′, ε)dε if (η′, ε′, aD(x, j), aT (x, j)) ∈ B

0 otherwise. (20)

A stationary equilibrium consists of factor prices {r, w, qe}, household decision rules

{c(x, j), q(x, j), aT (x, j)}, employer’s match q, tax payments Γj, accidental bequests TR,

social security benefits bss, unemployment insurance benefits bue, aggregate capital K, aggre-

gate efficient labor N , government consumption G, payroll tax τss, unemployment insurance

tax τui, consumption tax τc, income tax regime T (·), and distributions of households {ϕj}Tj=1

such that

1. c(x, j), q(x, j), aT (x, j) are the optimal decision rules on consumption, TDA contribu-

tion, and TA assets, respectively.

2. Factor prices are determined competitively according to (17) and (18).

3. Markets clear

(a) Capital market clears

(1 + g)K =

J∑

j=1

µj

∫

X

aD(x, j) + aT (x, j)dϕj

9

(b) Labor market clears

N =

R∑

j=1

µj

∫

X

[1− Pη(j)] ejdϕj

(c) Goods market clears

C =J∑

j=1

µj

∫

X

c(x, j)dϕj

Y = C + (g + δ)K +G

4. Social Security budget balance

J∑

j=R+1

µj

∫

X

λsswejdϕj =R∑

j=1

µj

∫

X

ηjτsswejdϕj

5. Unemployment Insurance budget balance

R∑

j=1

µj

∫

X

λuewejdϕj =

R∑

j=1

µj

∫

X

ηjτuiwejdϕj

6. Government maintain a balanced budget

G =

J∑

j=1

µj

∫

X

T (AGI(x, j)) + τkr(aT (x, j) + aD(x, j)

)+ τcc(x, j)dϕj

7. Accidental bequest is equal to transfers

TR =J∑

j=1

(1− sj)µj

∫

X

(1 + r)[aD(x, j) + aT (x, j)]dϕj

4 Calibration

The model is calibrated to the long-run U.S. economy. Nominal values are adjusted to 2000

US dollars using the Consumer Price Index. Parameter values are summarized in Table 1.

Each model period is equal to 1 year. Households enter the economy at age 25 and live at

most to 95 years old. Household’s age-dependent survival probabilities, {sj}Jj=1, are taken

from year 2000 life table of the National Center for Health Statistics. The population growth

rate (g) is 1.2%, matching the long-run growth from 1960 to 2010 in the U.S.

Production and preference parameters are taken from Imrohoroglu, Imrohoroglu, and

Joines (2003). The capital share of output (α) is 0.31 and the depreciation rate of capital

10

(δk) is 0.044. The total factor productivity (z) is set at 0.986, so that the average labor

income of high-school graduates at age 25 ($29,343.28) is normalized to 1. For preference

parameters,household’s impatience parameter (β) is 0.85. Discount factors δf and δb are set

at 1.013 such that the benchmark capital-output ratio is 2.52. The coefficient of relative risk

aversion (γ) is 2, which is commonly used in the macroeconomic literature.

The earnings processes and the probabilities of unemployment are taken from Love (2006,

2007), in which estimates are constructed using data from the Panel Study of Income Dy-

namics and the Current Population Survey, respectively. The probabilities of unemployment

is reproduced in Table 2. The fraction of households with college degree is 37.5%.

Regulations on TDA follow the Employee Retirement Income Security Act of 1974

(ERISA). The benchmark penalty rate on early TDA assets withdrawal, τpen, is 10%. The

contribution limit in year 2000 was $10,500 in dollars (q) or 25% of household’s labor earnings

(q).

Consumption tax rate is 5.5%. Capital income tax rate is 10.7%. Payroll tax rate

(τss) estimated as the average percentage of social security payment (OASDI) to the total

compensation to employees and the labor share of propriety income from 1987 to 2000.

Correspondingly, the social security replacement rate (λss) is set at 51.2% to maintain the

social security budget balanced. Similarly, the unemployment insurance benefits replacement

rate (λui) is 25% and the unemployment insurance tax (τui) is 1.2%.5 The US income tax

code in year 2000. Tax brackets and the marginal tax rates are described in Table 3. To be

consistent with the income process, households are assumed to take the standard deduction

and personal exemption of $7,200 for their income tax exemptions.

5 Optimal Early Withdrawal Penalty

The policy reforms on early withdrawal penalty are considered in this section. The straight-

forward reform entails changing the penalty rate to one that maximizes households’ welfare.

In a more complete reform, the constant penalty rate is replaced by a scheme that includes

a certain level of exemption based on households’ on labor earnings.

For these policy experiments, I evaluate the welfare impacts as a consumption supplement

in the benchmark economy, such that the welfare of a household in the benchmark economy

5In reality, households are entitled to 26 weeks of unemployment benefits at 50% of their employed labor

income. There is also a dollar limit on the benefits, which varies by state with a median of 500 per week.

Extended benefits are also available in the times of recession. Given the dollar limit, the model unemployment

benefits are more generous than that in the actual system.

11

equals to the welfare of a household into the reformed economy. The consumption supplement

is computed as a fixed percentage increase in consumption at each age. This approach is used

in Imrohoroglu, Imrohoroglu, and Joines (2003), and Caliendo and Findley (2015) further

show that consumption-saving plan formulated by an unborn household Pareto dominates

the actual allocation from the view of all future selves. To illustrate the relative importance

of welfare gain from the optimal penalty reforms, results are compared with the impacts of

removing TDA from the economy.

5.1 Constant Rate

Simulation results, reported in the second column of Table 4, show that the optimal early

withdrawal penalty rate is 50.4%, which is substantially higher than the current rate of 10%.

The fraction of households who withdraw TDA assets before age 60 (j < 36) decreased from

30.3% to 5.5%, and the aggregate leakage of TDA assets due to early withdrawal decreases

from 3.26% to 0.43%. Households also contribute less to TDA due to the heightened liquidity

risk, and the aggregate TDA contribution decreases to 5.74% of labor earnings. The net effect

of imposing the optimal penalty rate is a 3.2% increase in net worth, with TDA assets reduce

by 5.5% and TA assets increase by 1.8 times. The weighted welfare gain from raising the

early withdrawal penalty is equivalent to 2.16% increase in per period consumption.

5.2 Income-dependent Penalty Rate

As TDA are semi-illiquid in the sense that withdrawals before retirement will incur penalties,

young and low-income households are generally more reluctant to contribute to TDA, due

to the liquidity risk they face with the lack of precautionary savings. I investigate a TDA

policy reform in which early withdrawal penalty is income dependent. This reform entails

an early withdrawal penalty and a penalty-free withdrawal limit conditional on households’

labor income. Specifically, the early withdrawal penalty (τpen) follows an exponential decay

structure such that

τpen = τ incpen ∗min{q − φp0 exp(−φ

p1inc), 0}, (21)

where φp0 is the maximum early withdrawal exemption provided that a household has no labor

earnings and φp1 governs the decrease in exemption level for each dollar of labor earnings.

TDA asset withdrawals above the final exemption levels will be taxed at rate τ incpen. The

optimal values for {τ incpen, φp0, φ

p1} are estimated within the model to maximize the welfare

gain from the policy reform.

12

Simulation results are reported in the last column of Table 4. The optimal φp0 and φ

p1

estimated from the model are -1.62 and -5.4, respectively. It implies that the maximum

amount of exemption is about $48,600 per year, and households lose $5.4 of exemption for

each dollar of labor earnings they receive, including benefits from unemployment insurance.

TDA assets withdrawn beyond the exemption level is taxed at a rate of 86%.

Since low-income households, mainly due to unemployment, can withdraw TDA assets

without penalty, the fraction of households withdrawing TDA assets before age 60 increases

to 33.2%. The aggregate percentage of TDA leakage is 0.49%, which is substantially lower

than the benchmark but sightly higher than the leakage with constant penalty rate. Due

to the very high penalty rate for early withdrawal beyond the allowance, the aggregate

TDA contribution rate further decreases to 5.68% of total labor income. Despite the lower

contribution and higher leakage rate, households’ average net worth increases more than that

with the constant penalty policy, showing a rise of 3.9% from the benchmark. Households’

TA assets increase by 3.09 time and their TDA assets reduce by 3.5%. The weighted welfare

gain from this policy reform is equivalent to a 2.9% increase in per period consumption.

6 Sensitivity

In this section, the robustness of the policy reforms is evaluated under different assumptions

on households’ time inconsistent preferences. Specifically, I assess the optimal policy on

TDA early withdrawals and its outcome under different views of their future-selves.

6.1 Naıvete Households

I explore the impacts of TDA early withdrawal penalty with an alternative assumption that

households are naıvete, who believe that their future selves will follow the optimal decision

rules that they formulate in the current period, despite repeated violations in the past.

Households’ perception of their future selves can have important implications on their use

of TDA. Since naıvete households expect their future selves to follow the decision rules that

they formulate in the current period, assets in TDA have higher growth potentials (i.e. less

leakage) and they have less incentives to make early withdrawals from TDA. On the other

hand, naıvete households do not expect their future selves to be nonresistant to temptations

and do not see the needs to commit to retirement savings by contributing to TDA, effectively

putting a liquidity barrier for future selves to consume savings prematurely.

13

Household’s dynamic programming problem in equation (13) is written as

V (j, xj) = maxcj ,qj

{c1−γj

1− γ+ βδfEj

[sj+1V (j + 1, xj+1) + (1− sj+1)

W1−γj+1

1− γ

]}, (22)

where

V (j + 1, xj+1) = max

{c1−γj+1

1− γ+ δfEj+1

[sj+2V (j + 2, xj+2) + (1− sj+2)

W1−γj+2

1− γ

]}, (23)

subject to income processes (2) to (??) and constraints (5) to (12), in addition to the non-

negativity constraint on consumption. The model with naıvete households is re-calibrated to

match the target capital-output ratio specified in Section 4. The calibrated discount factor

(δ) is 0.944 and total factor productivity (z) is 0.985. Experiments in Section 5 are repeated

and simulation results are reported in Table 5.

Under the reform with a constant penalty rate and no withdrawal allowance (second

column), the optimal penalty rate is 32.3%, with which the fraction of households who

withdraw TDA assets early decreases to 21.7%. The average leakage of TDA assets reduces

to 1.7%. As TDA are more illiquid, the average contribution rate is lowered to 6.2%. The net

effect of the higher penalty rate is a 2.5% increase in households’ net worth, with households’

accumulating twice as much assets in the liquid TA. This reform is self-financing, and the

welfare gains from it is equivalent to 0.5% increase in per period consumption.

When an income-dependent withdrawal allowance is introduced (third column), the op-

timal penalty is 52.3% with an allowance of $54,720 (φP0 = −1.82). The allowance is reduced

by $2.56 for each dollar of household labor earnings (φP1 = −2.56). While this penalty sys-

tem increases the percentage of households withdrawing TDA assets early to 34.9%, the high

penalty charged on withdrawals beyond households’ penalty-free allowances also decreases

leakage of TDA assets to 1.8% on average. Overall, households’ net worth increase by 4.6%

as the withdrawal allowance reduces household’s liquidity risk. When compared to the case

without withdrawal allowance, households contribute more to TDA and save less in their

liquid TA, so that their assets in TDA and TA increase by 2.5% and 53.8% respectively.

The program is also self-financing, and the welfare gains are almost 4 times of that with-

out withdrawal allowance, because it does not penalize households who are most liquidity

constrained.

6.2 Comparison with Sophisticated Households

Experiment results indicate that the welfare gains from TDA penalty reforms for naıvete

households are smaller than that for sophisticated households, especially when a constant

14

penalty rate is considered. Since naıvete households believe their future selves will value

the growth potentials of TDA assets and resist the temptation of tapping into TDA for

consumption, the commitment value of TDA is lowered. As a result, raising the early

withdrawal penalty has a smaller effect on improving the value of TDA as commitment

devices while it also increases households’ liquidity risk. It is because the optimal penalty

for TDA early withdrawal are more lenient for naıvete households. Therefore, the optimal

penalty for TDA early withdrawal are more lenient for naıvete households, with lower penalty

rates and more generous penalty-free withdrawal allowance under the income-dependent

scheme.

The early withdrawal penalty, ex-post, becomes sub-optimally lenient for households’

current selves when they decide to use TDA assets for consumption smoothing in face of

negative shocks on labor earnings. As such, the penalty scheme becomes less effective in

preventing households who exhibits present bias from over-withdrawing their TDA assets

for current consumption.

7 Conclusion

This paper investigates the optimal early withdrawal penalty on TDA, through the lens of

an OLG model with households exhibiting time-inconsistent preferences. Policy experiments

indicate that the current penalty rate in the U.S. TDA system is sub-optimally low, inducing

households to become over reliant on their retirement savings to smooth their negative

labor earnings shocks. While raising early withdrawal penalty to the optimal level reduces

households’ desire to save in TDA, it also motivates households to accumulate precautionary

savings in TA and restrain themselves from prematurely consuming their TDA assets that

provide substantial tax benefits.

Reforming the early withdrawal penalty to an income-dependent penalty system provides

substantial welfare gains. Quantitatively, it increases the welfare gains from introducing the

TDA system by 30%. The welfare impacts are robust to the assumptions on households’

perceptions of their time-inconsistent preferences (sophisticated vs. naıvete), and they are

consistent with the multiself Pareto criterion in the sense that households at every vintage

point find that income-dependent penalty system welfare improving. This reform is easy to

implement and it is self-financing, as it stimulates aggregate economic activities such that

the government raise extra tax revenues from capital income tax and consumption tax to

compensate the loss of that from TDA early withdrawals. On the other hand, the impacts

15

of raising early withdrawal penalty within the current regulatory framework are sensitive to

assumptions on whether households are sophisticated or naıvete. It implies that the optimal

penalty rate hinges on households’ behavioral expectation of their future selves.

Findings in this paper highlights the importance of understanding TDA early withdrawal

penalty as a two-edged sword on promoting households’ retirement security and heightening

their liquidity risks. TDA reforms considered also contribute to policy concerns on reducing

households’ vulnerability to adverse labor earnings shocks.

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Table 1: Summary of Calibrated Parameter Values

Parameter Description Value Target / Data Source

Demographics

J Lifespan 71 Age 25 to 95

R Number of working periods 40 Work until age 64

{sj}Jj=1 Survival probability Life table in year 2000

g Population growth 0.012 Avg. population growth 1960-2010

Preferences

γ Relative risk aversion 2 Imrohoroglu, Imrohoroglu, and Joines (2003)

β Impatience 0.850 Imrohoroglu, Imrohoroglu, and Joines (2003)

δf Discount factor 1.013 Capital-output ratio is 2.52

Income

{fj} Age earnings profile Love (2006, 2007)

ρCOLǫ Persistence of income shock 0.887 Love (2006, 2007)

σCOLε Std. dev. of income shock 0.253 Love (2006, 2007)

ρHSε Persistence of income shock 0.780 Love (2006, 2007)

σHSε Std. dev. of income shock 0.239 Love (2006, 2007)

λ Social security replacement rate 0.512 Social Security budget balance

b Unemployment benefits 0.250

TDA Savings

τpen Early withdrawal penalty rate 10% ERISA of 1974

q Contribution limit (% of income) 0.25 ERISA of 1974

q Contribution limit in dollars 0.358 Contribution limit of $10,500

q Employer’s match 50%

Production

z Total factor productivity 0.986 Avg. age-1 labor income of HS = 1

α Capital share of output 0.310 Imrohoroglu, Imrohoroglu, and Joines (2003)

δk Depreciation rate 0.044 Imrohoroglu, Imrohoroglu, and Joines (2003)

Tax

τc Consumption tax 5.5%

τk Capital income tax 10.7% Estimated from OMB data

τss Payroll tax rate 9.8% Estimated from OMB data

τui Unemployment insurance tax 1.0%

17

Table 2: Probability of household unemployment risk

Age High school graduate College graduate

25-34 0.052 0.035

35-44 0.043 0.030

45-54 0.039 0.028

55-64 0.039 0.027

Note: Age and education dependent probably of unemployment is taken from Love (2006).

Table 3: Income Tax Scheme

Labor income Dollars Model unit Marginal tax rate

(0, I1] ($0− $26, 250] (0.0− 0.895] τ1 = 0.15

(I1, I2] ($26, 250− $6, 3550] (0.895− 2.166] τ2 = 0.28

(I2, I3] ($63, 550− $132, 600] (2.166− 4.519] τ3 = 0.31

(I3, I4] ($132, 600− $288, 350] (4.519− 9.827] τ4 = 0.36

> I4 > $288, 350 > 9.827 τ5 = 0.396

Note: The average labor income of high school graduate in age 1 ($29,343.28) is normalized

to 1 in the model. Households in the model is assumed to take standard deduction of $4,400

and personal exemption of $2,800, totaling $7,200.

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Table 4: Estimated optimal early withdrawal penalty (sophisticated households)

Benchmark Constant penalty Income-dependent

Penalty rate 0.100 0.504 0.860

% households with early withdrawal 30.32% 5.51% 33.20%

Avg % of TDA contribution 8.20% 5.74% 5.68%

Avg % of TDA leakage -3.26% -0.43% -0.49%

Net worth 1.000 1.032 1.039

TDA 1.000 0.945 0.965

TA 1.000 2.764 4.090

r 0.071 0.068 0.068

w 1.000 1.015 1.016

τadj · -0.003 0.000

Weighted welfare gain · 2.16% 2.90%

Note: Experiment results are based on the assumption that households are sophisticated

towards their time-inconsistent preferences. For income-dependent early withdrawal penalty,

the optimal penalty-free early withdrawal parameters are φP0 = −1.622 and φP

1 = −5.398.

19

Table 5: Estimated optimal early withdrawal penalty (naıvete households)

Benchmark Constant penalty Income-dependent

Penalty rate 0.100 0.323 0.523

% households with early withdrawal 32.55% 21.69% 34.92%

Avg % of TDA contribution 8.69% 6.18% 7.80%

Avg % of TDA leakage -3.36% -1.68% -1.81%

Net worth 1.000 1.025 1.046

TDA 1.000 0.982 1.025

TA 1.000 2.048 1.538

r 0.071 0.069 0.067

w 1.000 1.008 1.016

τadj · -0.009 -0.003

Weighted welfare gain · 0.51% 2.01%

Note: Experiment results are based on the assumption that households are naıvete towards

their time-inconsistent preferences. Model parameters are re-calibrated to match the capital-

output ratio. Re-calibrated values for the discount factor (δ) and the total factor productivity

(z) are 0.944 and 0.985, respectively. For income-dependent early withdrawal penalty, the

optimal penalty-free early withdrawal parameters are φP0 = −1.824 and φP

1 = −2.556.

20

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