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TAX POLICY, LUMP-SUM PENSION DISTRIBUTIONS, AND HOUSEHOLD SAVING
by
Angela E. Chang

Federal Reserve Bank of New York
Research Paper No. 9507

April 1995

This paper is being circulated for purposes of discussion and comment only.
The contents should be regarded as preliminary and not for citation or quotation without
permission of the author. The views expressed are those of the author and do not necessarily
reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.
Single copies are available on request to:

Public Information Department
Federal Reserve Bank of New York
New York, NY 10045

Abstrac t
As of May 1988, over 8 million workers had received their
pension benefits as lump-sum distribut ions (LSDs) when they changed jobs.
In 1986 Congress imposed a 10% tax penalty on the amount of LSDs not
rolled over into tax-defer red instrumen ts.

This paper examines the

effects of this tax penalty on the rollover decisions of LSD recipient s.
The penalty increases the probabili ty of rollover among higher-inc ome
recipient s; an increase of 1 percentag e point in the penalty is estimated
to increase the probabili ty of rollover by 1.1 percentag e point.

However,

the. penalty has not affected the rollover decisions of lower-inco me
recipient s, who are more likely to be liquidity- constrain ed.

I would like to thank Peter Diamond, Jonathan Gruber, James
Poterba, and participa nts at the Harvard-M IT Public Economics Seminar for
helpful comments. I would also like to thank.Dan iel Feenberg for
tabulatio ns from the U.S. Treasury Individua l Tax Model File (1984-89) .
Financial support from the National Science Foundatio n, Bradley
Foundatio n, and MIT World Economy Laborator y while at MIT is gratefull y
acknowled ged.

1.

Introduct ion
As of May 1988, over 8 million workers had received a total of $42

billion (1988 dollars) in pre-retire ment lump-sum distribut ions (LSDs) from
their pension plans when they changed jobs.

Most of these workers did not

roll over their LSDs into tax-defer red instrumen ts (e.g., IRAs) which are
close substitut es of pension plans.

Instead, they saved their LSDs in non

tax-defer red instrumen ts, such as savings accounts, or spent them (Fernande z

1992).
Congress is concerned about the low rollover rate, because the spending
of LSDs may reduce workers' accumulat ed retiremen t savings.

Also, the fact

that most LSD recipient s choose not to save their LSDs for retiremen t raises
the question of whether the recipient s ever intended to save their pension
money for retiremen t (Fernande z 1992).
pension plans as tax shelters.

Instead, they may have used the

To encourage the rollover of LSDs, Congress

introduce d in the Tax Reform Act of 1986 a 10% tax penalty on the amount of
LSDs not rolled over into tax-defer red instrumen ts, like the 10% penalty on
premature withdrawa ls from Individua l Retiremen t Accounts (Joint Committee on
Taxation 1987).
This paper examines the impact of the 10% tax penalty on workers'
decisions to roll over their LSDs. 1

Past studies of individua ls' use of LSDs

have not examined the impact of the tax penalty on rollovers (Andrews 1991,
Piacentin i 1990).

Estimates of the tax sensitivi ty of workers' rollover

decisions may provide insight into whether a penalty on consumpti on actually

1This paper does not examine the rollovers of lump-sum
distribut ions
received after age 59½, which are called normal or retiremen t distribut ions.
In 1990, pre-retire ment LSDs (i.e., received before the age 59½) accounted for
about 60% of all LSDs and 38% of the total amount of LSDs. Normal
distribut ions accounted for about 25% of all LSDs and 34% of the total amount
of LSDs in 1990 (Yakobosk i ·1994).

2

increase s saving.

This study may also contribu te to the empiric al literatu re

on individu als' saving decision .
The paper proceeds as follows.

Section 2 provides backgrou nd

informa tion about when workers receive LSDs and how the tax treatmen t differs
accordin g to the particu lar use of LSDs.

It also details changes in the tax

treatmen t of LSDs that occurred in 1986.

Section 3 describe s the May 1988

Current Populat ion Survey (CPS), which is the primary dataset.

Section 4

describe s the econome tric framewo rk, data limitati ons, and econome tric
issues.

The results are presente d in Section 5.

The results indicate that the

tax penalty signific antly increase s the probabi lity of rollover among higherincome recipien ts.

In contras t, the tax penalty does not signific antly affect

the rollove r decision s of lower-in come recipien ts.

Since lower-in come

recipien ts comprise the majority of LSD recipien ts, the tax penalty has raised
conside rably more tax revenue than Congress anticipa ted.
tax penalty raised over $1.9 billion in tax revenue; 2
$547 million (U.S. Joint Tax Committe e 1987). 3

During 1987-89 , the

Congress anticipa ted

Section 6 summari zes the main

findings and conclude s the paper with a discussi on of the policy implica tions
of the results.
2.

Backgrou nd

Workers can receive their pension benefit s as LSDs when they change jobs
2

This figure is an estimate from the U.S. Treasury Individu al Tax Model
dataset for 1984-89 and from the Interna l Revenue Service Individu al Income
Tax Returns for 1986-88.
3 The

revenue potenti al of the tax penalty may have motivate d a recent
change in the adminis tration of the tax penalty . As of January 1993, workers
who choose to receive their LSDs are subject to a 20% withhold ing tax [IRS
Taxpaye r Service s, Janssen (1992), Schultz (1992)]. This withhold ing tax was
included in the July 1992 bill that extended unemploy ment benefit s; it was
expected to pay for part of the cost of the extended unemploy ment benefit s.

3

under two circum stance s.

First, certai n pensio n plans give worke rs the option

to take their pensio n benef its as LSDs upon separa tion.

Worke rs in such plans

can exerci se the LSD option and thereb y receiv e LSDs when they
change jobs.
Define d contri bution (DG) pensio n plans typica lly give worke
rs the LSD option ;
where as, define d benef it (DB) pensio n plans typica lly do not. 4

DB plans

typica lly pay worke rs their pensio n benef its at retirem ent,
even to those who
leave the emplo yers before retirem ent.
Second , worke rs may receiv e LSDs as a result of unilat eral cashou
ts by
their emplo yers.

The Employ ee Retire ment Income Secur ity Act of 1974 (ERISA)

allowe d emplo yers to cash out employ ees with small accrue d benef
its
unilat erally .

In other words, emplo yers can give LSDs to .worke rs upon

separa tion regard less of whethe r the worke rs want to receiv e
them or not,
provid ed that the amount of accrue d benef its is less than the
legal maximum
unilat eral cashou t limit.

The curren t maximum unilat eral cashou t limit is

$3,500 (Ferna ndez 1992).
Worke rs can alloca te their LSDs in three ways: (1) leave the
money with
the firms they are leavin g for future withdr awal, (2) receiv
e checks for the
amoun t of the LSDs and save or spend as they please , or (3)
arrang e to have
the money rolled over into their new emplo yers' DG pensio n plans. 5

Taxes may

affect indivi duals' choice s among these option s.
The tax treatm ent of LSDs has change d over the years.

Prior to 1987,

indivi duals paid income taxes on the amoun t of LSDs that they
did not invest
in tax-de ferred instru ments such as Indivi dual Retire ment Accou
nts (IRAs) ,
About 10% of DB plans and betwee n 80-90% of DG plans give worke
rs the
option of taking LSDs upon separa tion (Ferna ndez 1992).
4

5Few

pensio n plans offer worke rs the option of transf erring money
from
former emplo yers' pensio n plans.

4

insurance annuities, or their new employers' pension plans.
LSDs in such instruments is called rollovers.

Investment of

Not investing LSDs in tax-

deferred instruments will be referred to as non-rollovers.
The Tax Reform Act of 1986 (TRA) changed the tax price of non-rollovers
in two ways.

First, it changed the structure of federal personal income

taxes, generally lowering the marginal tax rates 6 and reducing the number of
tax brackets.

Second, it imposed a 10% penalty in addition to income taxes on

the amount of LSDs not rolled over within 60 days of receipt (Joint Committee
on Taxation 1987).
Certain workers are exempt from the 10% penalty on non-rollovers of
LSDs.

For example, workers who receive LSDs because they are totally or

permanently disabled are not subject to the penalty.

Workers who receive LSDs

due to medical expenses which are deductible are also not subject to the
penalty.

For the purposes of this paper, the exception of interest is that

workers who receive LSDs during or after the year they turn 55 years of age
are not subject to the 10% penalty (Joint Committee on Taxation 1987).

Thus,

the penalty raised the tax price of non-rollovers for only younger recipients
(under the age of 55).
The following discussion will focus on married recipients filing joint
returns.

Single recipients experienced similar changes in the tax price of

non-rollovers.

Figure 1 illustrates the marginal tax price of non-rollovers

for married recipients before and after TRA and across age groups (younger and
older than 55),. Figure 1 shows that in general older recipients faced a lower

6

For example, in 1986 the top marginal tax rate for married taxpayers
filing joint returns was 50%; in 1987, 38.5%; and in 1988, 33% (Coopers and
Lybrand 1986, Statistical Abstract of the United States 1982-90 editions).

5

margin al tax price of non-ro llover s in 1987 than in 1986.

For older

recipi ents, the change in the struct ure of the federa l income
tax rates was
the sole source of variat ion in the tax price of non-ro llover
s before and
after 1986, since they were not subjec t to the 10% penalt y.
Like older recipi ents, younge r recipi ents faced a margi nal
tax price of
non-ro llover s equal to the federa l income tax rates in 1986.

After 1986,

young er recipi ents were subjec t to the 10% penalt y, such that
their margin al
tax price of non-ro llover s equale d the federa l income tax rates
plus 10
percen tage points .

For most levels of taxabl e income , the net effect of lower

margin al tax rates and the 10% penalt y has been an increa se
in the margin al
tax price of non-ro llover s for younge r recipi ents (Figur e 1).

In fact, the

margin al tax price of non-ro llover s increa sed more for young
er recipi ents with
lower taxabl e income than for those at the high end of taxabl
e income .
3.

Data

The analys is in this paper is based prima rily on data from
the May 1988
Curren t Popula tion Survey (CPS), which includ es a supple ment
on employ ee
benef its.

The supple ment questi ons were asked of adults in one-h alf of
the

basic CPS sample who were employ ed for pay at the time of the
interv iew.

Out

of 109,19 2 adults in the basic CPS sample 27,701 worke rs answe
red the
supple ment questi ons.

Like the basic CPS data, the supple ment data provid e

weigh ts that allow adjust ing the sample to be repres entati ve
of the U.S.
popul ation.
The supple ment includ es a set of questi ons about the receip
t of LSDs
from pensio n plans on prior jobs.
about their most recent LSDs.

LSD recipi ents answe red questi ons only

They were asked to report the year they

receiv ed their most rece~ t LSDs and the amoun t.

6

About 8% of the supplement sample, or 2,162 workers, reported having
received at least one LSD from a prior job.

This translates into a weighted

figure of approximately 8.5 million workers who received LSDs.
a total of approximately $42 billion.

They received

This total is in 1988 dollars, as are

all dollar figures in subsequent tables.
The distribution of LSD recipiency is not uniform across age or family
income (Table 1).

Over half of the recipients were under the age of 35 when

they received their most recent LSDs.

About 45% of individuals who received

LSDs had a family income less than $30,000 in 1987.

Since younger and lower-

income workers are more likely to be liquidity-constrained, Table 1 suggests
that liquidity constraints may affect the rollover decisions of most LSD
recipients.

The last two columns of Table 1 indicate that the LSDs of younger
recipients were small.

Recipients under 35 comprised 61% of the recipients

yet received only 37% of the total amount of LSDs, a disproportionately low
percentage of the total amount.

Similarly, individuals with family income

less than $30,000 in 1987 received a disproportionately low fraction of the
total amount of LSDs.
The distribution of the size of LSDs also is not uniform across age or
family income (Table 2).

The average amount of LSDs rises with the age at the

time of receipt and with the recipients' 1987 family income.
average LSD was $5,989, the median was $2,451.

While the

This discrepancy between the

average and the median LSD is due to the fact that most LSDs were small; about
40% of the LSDs were less than $1,000.
The dataset contains yes/no responses to whether individuals allocated
any of their LSDs to various uses.

An overwhelming majority of recipients

7

(86.5%) did not roll over any of their LSDs into tax-deferred instruments
(Table 3).

In fact, approximately 41% of the recipients did not save any of

their LSDs. 7

Weighted by dollars, roughly three-fourths of the total amount

of LSDs were not allocated to tax-deferred instruments.•
Table 3 shows that about 16% of the recipients allocated at least some
of their LSDs toward investments such as starting or buying a business, buying
a house, 9 or paying educational expenses.

About 7% of the recipients

reported using some of their LSDs to pay expenses incurred during
unemployment.

Lastly, slightly over a quarter of the recipients used some of

their LSDs for uses not specified in the CPS questionnaire.
Table 3 also shows that the percentage of recipients who save at least
part of their LSDs in non tax-deferred instruments (e.g., savings accounts) is
substantially higher than the percentage who rolled over their LSDs.
Approximately 14% of the recipients invested at least some of their LSDs in
tax-deferred instruments; whereas, 24% invested at least some of their LSDs in
non tax-deferred instruments.

In terms of dollars, the percentage of the

7

I defined saving as allocating at least part of an LSD to financial
instruments or paying off debt.
8

The May 1988 CPS supplement does not provide the exact amount of LSDs
allocated to various uses. A range of the amount of rollovers was inferred
based on the number of uses reported. If a recipient reported more than one
use for the LSD, then he/she was assumed to have allocated a minimum of $1 and
a maximum of the entire amount to each reported use. Summing across these
minimum and maximum figures across recipients produces a range of the total
amount rolled over. The median value of the range of rollovers is $9.4
billion or about 22% of the total amount of LSDs.
9
Buying a house can be considered a form of saving for retirement, since
individuals can use the value of the house to obtain financial resources via
instruments such as home equity loans and reverse mortgages; however, Venti
and Wise (1989) show that the elderly are reluctant to reduce housing equity.
This suggests that financing consumption during retirement may not be the main
motivation for buying a house.

8
total amount allocat ed to non tax-def erred instrum ents is around 23%,
which is
about the same as the percent age allocat ed to tax-de ferred instrum ents.
4.

Econom etric Framework and Issues

4.1.

Econom etric Framework

The estima tion procedu re is based on the probit model.
compel led the use of a discret e depend ent variab le.

Data limitat ions

The ideal depend ent

variab le is the amount of the LSD rolled over into tax-de ferred instrum
ents,
such that the effect of the penalty on the amount rolled over can be
estimat ed.

The May 1988 CPS does not provide inform ation on the amount rolled

over but yes/no respons es to whethe r any of the LSD was allocat ed to
particu lar uses.

The datase t allows inferen ce about whethe r recipie nts rolled

over none, some, or all of their LSDs.
Within the contex t of the probit model, the observe d discret e choice
of
recipie nt i to roll over at least some of his/he r LSD is assumed to
be the
outcome of an unobse rvable proces s:

if

S-= [ 1
i
0 if

s/>O
s/~O

(1)

where Si denotes the observe d rollove r decisio n of the recipie nt; and
si", the
unobse rvable desired amount of LSD rollove r.

Si has been defined as equal to

1 if a recipie nts rolls over at least some of his/he r LSD and O otherw
ise. 10
Based on the probit model, the followi ng equatio n is estima ted:

si can also be defined as equal to 1 for recipie nts who roll over all
of their LSD and O otherw ise. The results using this measure of Si
are
simila r to those presen ted in the paper. I also estima ted ordered probit
equatio ns, where Si equals 2 for rollove r of the entire LSD, 1 for partia
l
rollove r, and O for no rollove r. The simila rity in the results is not
surpris ing, ·since 79% of recipie nts who rolled over any of their LSDs
actuall y
rolled over their entire LSDs.
10

9

(2)

wher e~(.) is the cumu lative distr ibuti on funct ion
for a stand ard norm al
distr ibuti on; and x 1 , a vecto r of obser vable char
acter istic s of the recip ient
and of the LSD.
The follo wing facto rs may influ ence the rollo ver
decis ion and have been
inclu ded in the vecto r x 1 : (1) the amount of the
LSD in 1988 dolla rs, (2) the
feder al income tax rates (MTRs), (3) the 10% tax
pena lty, 11 (4) age at the
time of recei pt of the LSD, (5) famil y incom e, (6)
years of schoo ling
comp leted , (7) gend er, and (8) mari tal statu s.
The means and stand ard
devia tions of the varia bles used in the prob it estim
ation are in Table 4.
I allow ed the MTRs and the tax pena lty to have separ
ate effec ts on the
prob abili ty of rollo ver, becau se their effec t on
rollo vers may diffe r
accor ding to the incom e of the recip ients . For
exam ple, Figur e 1 shows that
there are fewer tax brack ets at the highe r end of
taxab le income than at the
lower end. This impl ies that the 10% pena lty is
the major sourc e of varia tion
in the marg inal tax price of non- rollo vers for highe
r-inco me recip ients . This
is espe ciall y true for the recip ients in the top
tax brack et, for whom the 10%
pena lty is the only sourc e of varia tion in the marg
inal tax price of nonrollo vers. For lower -inco me recip ients , both the
MTRs and the pena lty
gene rate varia tions in the marg inal tax price of
non- rollo vers.
Chang es in the tax price of non- rollo vers impos ed
by the Tax Refor m Act
of 1986 (TRA) make poss ible the iden tific ation of
the effec t of MTRs on
rollo ver decis ions. Beca use the MTRs are a nonli
near funct ion of famil y
incom e, witho ut the 10% pena lty the effec t of MTRs
on rollo vers canno t be
1 1The

tax pena lty varia ble equa ls 0.1 for youn ger recip
ients after 1986
and O for all other recip ients .

10
identifi ed from the effect of family income on rollover s. 12
The impositi on of the tax penalty on younger recipien ts provides a
natural experim ent, whereby recipien ts with similar charact eristics faced
differen t tax prices dependin g on their age and whether they received their
LSDs before or after TRA.

The older recipien ts serve as the "control " group,

since they were not subject to the 10% penalty.

The younger recipien ts were

subject to the 10% penalty after 1986 and thus are the "treatme nt" group . 13
Differe nce-in-d ifferenc e probit equation s can be used to test whether the
penalty had any effect on the "treatme nt" group relative to the "control "
group.

Rollove rs should have increase d more among younger recipien ts than

among older recipien ts after 1986, all else being equal.
The sample for the probit equation s has been limited to workers who
received LSDs between 1984-88.

Not includin g years earlier than 1984 is an

attempt to control for aggrega te conditio ns.

Ideally, the sample would

include the two years before and two years after 1986, the year the Tax Reform
Act of 1986 was passed.

Given that the CPS was taken in May 1988, the sample

includes data for only about l½ years after the passage of TRA.
4.2.

Data Limitati ons

The advantag e of using the May 1988 CPS dataset is that it provides
detailed informa tion about pre-reti rement LSDs for a represe ntative sample.
From the CPS, workers who were subject to the 10% tax penalty can be
accurate ly identifi ed.

However , the CPS does present several data limitati ons

for the computin g the federal income tax rates.
12 Feenberg
13 For

(1992).

The most severe limitati on is

(1987) gives a clear discussi on of this identifi cation issue.

a discussi on of differen ce-in-di fference estimati on, see: Gruber

11
·the availabil ity of family income only for 1987.
To estimate the recipient s' family income and their federal marginal tax
rates (hencefor th, MTRs) at the time of receipt of the LSDs, I assumed that
real family income at the time of receipt was highly correlate d with family
income in 1987.

This assumptio n will be too strong if most workers receive

their LSDs as a result of being laid off and experienc e large unexpecte d drops
in income in the year they received their LSDs.
Tabulatio ns from the CPS data suggest that only about 10% of workers who
received LSDs as a result of layoffs in 1987. 14

Furthermo re, only 7% of

recipient s used their LSDs to pay expenses while unemploye d (Table 3).

These

tabulatio ns suggest that most workers do not experienc e large unexpecte d drops
in their income when they receive their LSDs.
Other considera tions pertain to the validity of the assumptio n.

First,

MTRs apply to brackets of income; therefore , the MTRs computed from the true
income in the year of LSD receipt may not differ much from the MTRs computed
from income in 1987.

Second, the analysis is limited to the period 1984-1988 .

Thus, the differenc e in time between the time of LSD receipt and 1987 is at
most three years.

These considera tions suggest that the assumptio n may not be

too unreasona ble.

The second data limitatio n is the availabil ity of the 1987 family income
in brackets.

To compute MTRs, I assumed the recipient s had 1987 family income

equal to the median value of the income brackets.

In other words, if a

14 This figure is based on
workers who received their LSDs in 1987 or
1988. For this group of workers, the May 1988 CPS provides enough informati on
to infer whether they received their LSDs as a result of quits or layoffs.
Results from probit equations estimated for this group indicate that whether a
worker was laid off in 1987 did not have a significa nt effect on the rollover
decision.

12
recipient reported having a family income in 1987 between $30,000-3 4,999,
he/she was assumed to have had family income equal to $32,500 in 1987.
Other assumptio ns were required to compute MTRs.

First, the marital

status of the recipient s as reported in 1987 was assumed to be the same in the
year they received the LSDs.
joint returns.

Second, married recipient s were assumed to file

Third, recipient s were assumed to take the standard deduction s

and not to itemize deduction s.

Lastly, single recipient s were assumed to take

one personal exemption ; and married recipient s, two personal exemption s.

The

number of dependent exemption s was based on the assumptio n that the number of
children in the year of LSD receipt was the same as the number of children
reported in the May 1988 CPS. 15
4.3.

Self-Sele ction Bias

Using the CPS data to estimate the effect of the tax penalty on the
rollover of LSDs raises the issue of self-sele ction bias.

A self-sele ction

bias may be present, because the sample consists of only workers who received
LSDs and does not include all workers who had the LSD option.

The total

effect of the tax penalty on rollovers consists of two componen ts: (1) the
effect on the decision to exercise the LSD option and (2) the effect on the
decision to roll over an LSD that has been received.
With a sample of LSD recipient s, the second effect is estimated without
taking into account the first effect; this will produce a self-sele ction bias.
Because individua l-level data are not available with which to separate workers
with and without the LSD option (i.e., belong to pension plans that allow

15Results

from probit equations with and without personal and dependent
exemption s are not substanti vely different .

13
LSDs) , 16 econom etric "correc tions" for self-se lection bias (e.g., Heckma
n's
two- step proced ure) cannot be utilize d. 17
Althoug h I cannot correc t for the self-se lection bias, the directi on
of
the self-se lection bias makes the estima ted effect of taxes in Section
5 more
plausib le.

If the tax penalty induced many workers to leave their pension

money with their former employ ers, then the estimat ed effect of the
tax
penalty on the rollove r decisio ns of worker s who chose to receive LSDs
will be
lower than the true effect for all worker s who had the LSD option.

In other

words, since leaving the money with the employ ers is equiva lent to
rollove rs,
my sample underr epresen ts the number of rollove rs due to the penalty
.

Thus,

if a self-se lection bias is presen t, then the estima ted effects of the
MTRs
and the tax penalty in Section 5 are lower bounds on their true effects
for
ali' workers eligibl e for LSDs.
5.

Results

5.1

Aggreg ate Eviden ce

Aggreg ate data indicat e that the 10% tax penalty has not increas ed
rollove rs to the extent that Congre ss expecte d.
revenue than Congre ss anticip ated.

Hence, it has raised more tax

Congre ss anticip ated raising $547 million

in revenue from the tax penalty during 1987-8 9.

The next table shows that the

16A

Gallup survey conduc ted during Februa ry-June 1991 provide s the only
availab le figures on the number. of worker s who left their pension money
with
their former employ ers. It indica tes that only 17% of individ uals between
the
ages 18 and 54 who had the LSD option chose not to exercis e the option.
The
sample consist ed of 327 individ uals. David Wray at the Profit Sharing
Coun~i l
kindly provide d the survey results .
17 For

a descrip tion of Heckma n's two-ste p proced ure, see Chapte rs 8 and 9
in Maddal a (1983).

14
tax penalty actuall y raised over $1.9 billion in revenue during 1987-89 8
.1
Tax Revenu e from the Tax Penalty
Year

Number Paid Penalty
(thousa nd)

Collec ted Revenue
(millio n)

Anticip ated Revenu e
(millio n)

1987

876

$364

$97

1988

1,524

711

209

1989

1,653

833

241

Source:

IRS U.S. Treasu ry Individ ual Tax Model File and SOI publica tions
(numbe r paid penalty , collect ed revenu e); U.S. Joint Tax
Commit tee, p. 719 (antici pated revenue )

The number of recipie nts who paid the 10% LSD penalty and the collect
ed
revenue from the penalty are estima ted from the U.S. Treasu ry Individ
ual Tax
Model and SOI public ations.

The IRS aggreg ates figures for the 10% penalty on

premat ure IRA withdra wals with those for the 10% penalty on non-ro llover
of
LSDs.

To estima te the figures for the 10% LSD penalty , I assumed that for

1987-89 the number of taxpay ers who paid the 10% IRA penalty and the
revenue
from the IRA penalty were the same as in 1986. 19
Tabula tions from the May 1988 CPS also sugges t that the impact of the
penalty on the overal l group of LSD recipie nts has been small.

The followi ng

18Figures from the May 1988 CPS are similar
to those in the table. Based
on the CPS data, about 926,000 LSD recipie nts paid an estima ted $360
million
in tax penalty in 1987. Figures for 1988 cannot be tabulat ed from the
CPS,
since it does not cover the entire year of 1988.
19How this assump tion biases the figures for
the 10% LSD penalty is
ambigu ous. If the upward trend in the revenue from the IRA penalty
during
1984-86 continu ed during 1987-89 or if more taxpay ers made prematu re
IRA
withdra wals in 1987-89 to make advanta ge of the lower tax rates, then
my
estima tes of the 1987-89 revenue from the LSD penalty are too high.
On the
other hand, IRA partici pation decline d dramat ically after 1986 (Engen
et al.
1994), such that the number of premat ure IRA withdra wals may have decline
d
after 1986·. This would sugges t my estima tes of the revenue from the
LSD
penalty are too low.

15
table shows that rollover s have increase d over time; thus, the increase in
rollove rs after 1986 may be due to a time trend or changes in the aggrega te
conditio ns of the U.S. economy and not necessa rily due to the tax penalty .
Rollove r by Year of Receipt
Year

Percenta ge of Recipien ts

Before 1980

Percenta ge of Amount

4.0%

7.6%

1980-84

14.9

29.0

1985-86

17.5

23.8

1987-88

20.6

30.7

Source: May 1988 CPS
A cross tabulati on by year of receipt and age group is more meaning ful,
since only younger recipien ts (under 55) became subject to the tax penalty
after 1986.

The table below shows that rollover s increase d among younger

recipien ts after 1986 but remained fairly steady among older recipien ts.
Rollove r by Year of Receipt and Age Group
Year

Percenta ge of Younger
Recipie nts

Before 1980

3.6%

Percenta ge of Older
Recipie nts
27.0%

1980-84

13.3

44. 7

1985-86

15.9

28.0

1987-88

20.3

27.4

Source: May 1988 CPS
The increase in rollove rs among younger recipien ts after 1986 but not
among older recipien ts suggests that the tax penalty imposed on younger
recipien ts may have increase d rollove rs.

Since there has been an upward trend

in rollove rs among younger recipien ts througho ut the 1980s, the increase in

16
.rollo vers after 1986 canno t be attrib uted solely to the tax
penalt y.

A time

trend or change s in the demog raphic chara cteris tics of the
recipi ents may
explai n the increa se in rollov ers.
5.2

Probi t Resul ts

A natura l extens ion of the cross tabula tions above is the differ
ence- indiffer ence probit equati ons that includ e demog raphic variab
les but not the tax
variab les.

They provid e insigh t into whethe r differ ent trends for rollov
ers

are observ ed for young er and older recipi ents, withou t relyin
g on tax
variab les which may be noisy (e.g., MTRs as compu ted from the
CPS).

Result s

from probi t equati ons that includ e the tax variab les are presen
ted later in
this sectio n.
The depend ent variab le in the differ ence-i n-diff erence equati
ons equals
1 for recipi ents who rolled over at least some of their LSDs
and O for
recipi ents who did not roll over any of their LSDs.

The indepe ndent variab les

of intere st are as follow s:

• LESS55: 0 for recipi ents 55 or older, 1 for recipi ents under
55;
• POST86: 0 for LSD receip t before 1986, 1 for after 1986; and
• (LESS55)*(POST86): an intera ction term of the two variab les.
The differ ence- in-dif ferenc e probit equati ons take the follow
ing form:

PI(S1 =1)=

~[p 0 +P 1 (LESS55)+P 2 (POST86)+P 3 (LESS 55)*(P OST86 )+y 1z

1]

(3)
where z; is a vector of demog raphic variab les and the real amount
of the LSD.
The hypoth esis that the tax change s affect ed only younge r recipi
ents
after 1986 transl ates into a test that the coeffi cient P >0.
3

This test is

based on the assum ption that there are no unobse rvable variab
les that

17
increase d rollover s among younger recipien ts but not among older recipien ts
(i.e., age-spe cific time trends).
The estimate d coeffici ents for the interact ion term (LESS55)*(POST86)
are positive but not statisti cally signific ant (Table 5).

The P-values for

the one-side d test (Ho: P3-0, H1 : p 3>0) reflect the statisti cal insignif icance
of the coeffici ent Pa-

The P-values are 0.20 for both equation s; the null

hypothe sis cannot be rejected at the convent ional 5% level.
A measure similar to a tax elastici ty can be computed from the
differen ce-in-d ifferenc e probit results as follows:

(4)
where M denotes the change in the predicte d probabi lity of rollover between
1984-86 and 1987-88; and ~t, the change in the margina l tax price of nonrollove rs.

The supersc ripts denote the age groups: Y for younger recipien ts

and O for older recipien ts.
Several assumpt ions were made to compute the predicte d probab ilities for
the "average " younger and older recipien ts.
married males with 14 years of schoolin g.

The recipien ts were assumed to be
For younger recipien ts, the real

amount of LSD was assumed to equal $6,000; and for older recipien ts, $16,000 .
The real amount of LSD and the persona l charact eristics were chosen to
resemble the means for the two age groups.
Based on these predicte d probabi lities, the estimate d "tax elastici ty"
is 0.8 percenta ge point.

In other words, a 1 percenta ge point increase in the

margina l tax price of non-roll overs for younger recipien ts relative to older
recipien ts raises the probabi lity of rollove r by 0.8 percenta ge point more
among younger recipien ts relative to older recipien ts, control ling for

18
demogra phic variable s.

This estimate of the "tax elastici ty" is similar to

those from the probit equation s with the tax penalty variable , which are
presente d below.
The estimate s from the probit equation s that include the tax variabl es
are in Table 6.

The depende nt variable in these equation s equals 1 for

recipien ts who rolled over at least part of their LSDs into tax-defe rred
instrume nts and O for recipien ts who did not roll over any of their LSDs.
Table 6 shows that MTRs do not signific antly affect the probabi lity of
rollover .
income.

One explana tion may be the high correlat ion between MTRs and family
Multico llineari ty would also explain why MTRs are signific ant in

probit equation s that do not include family income.
In contras t, the coeffici ent for the tax penalty fs statisti cally
signific ant and positive .

This indicate s that younger recipien ts who are

subject to the tax penalty are more likely to roll over their LSDs.

Table 7

shows that the estimate d margina l effect of the tax penalty on the probabi lity
of rollover is 0.6 percenta ge point.

In other words, increasi ng the tax

penalty by 1 percenta ge point would raise the probabi lity of rollover by 0.6
percenta ge point.
This implies a rough approxim ation that the impositi on of the tax
penalty (i.e., an increase in the penalty from Oto 10%) raised the
probabi lity of rollove r by 6 percenta ge points. 20

This is not a negligib le

effect, since the probabi lity of rollover among younger recipien ts prior to
the impositi on of the tax penalty was only about 16%.
The probabi lity of rollover also increase s with the real amount of LSD,

20 This

is a rough approxim ation, because the effect of the tax penalty
appears to be nonline ar; its effect diminish es as the tax penalty increase s.

19
·age, and family income (Table 6). 21

These findings challenge the predictions

of the standard Life-Cycle Hypothesis.

The standard Life-Cycle Hypothesis

predicts that taxes, the real amount of LSDs, and the age at the time of
receipt should have little effect on the probability of rollover, so long as
the receipt of an LSD is basically a change in the timing of income receipt.
On the other hand, the findings are consistent with an extended version
of the Life-Cycle Hypothesis, in which consumption decisions are made under
uncertainty about future income.

Given uncertainty about future income,

workers may prefer to keep some liquid assets.

Since tax-deferred instruments

such as IRAs are less liquid than non-tax deferred instruments, 22 as
uncertainty increases workers may prefer non tax-deferred instruments.

In

particular, if job separations increase uncertainty about future income, then
workers may prefer not to roll over their LSDs until they are more certain of
their future prospects.
Within this framework, if workers desire a fixed amount of liquid assets
as protection against unexpected drops in income, then they would be more
likely to roll over larger LSDs; they would roll over the portion of the LSDs
that exceeds the desired amount of liquid assets.

If younger workers and

lower-income workers face more uncertainty about their future income or are

less likely to have accumulated the desired amount of liquid assets, then the
probability of rollover would increase with age and family income.
The results are also consistent with two other models of saving

21

In the probit equations, the base age group is 35-44 and the base
income group is $30,000-39,999.
22 Engen

et al. (1994) analyze how individuals may not view tax-deferred
and non tax-deferred instruments as close substitutes and may want to invest
in both.

20

behavior.

The first is the model of saving under liquidity constrain ts.

Liquidity constrain ts are especiall y relevant within the context of preretiremen t LSDs, since most recipient s are younger and lower-inco me workers
(Table l) who are more likely to be liquidity -constrai ned.

Liquidity

constrain ts may thus explain the increase in the probabili ty of rollover with
the age and family income.
Liquidity constrain ts may also explain the positive relations hip between
LSD size and the probabili ty of rollovers .

Larger LSDs are more likely to

exceed the desired level of consumpti on of liquidity -constrai ned recipient s;
liquidity -constrai ned recipient s would roll over the amount of the LSDs that
exceeds what is necessary to attain the desired level of consumpti on.
The second is the behaviora l model of saving that emphasize s
individua ls' categoriz ing bundles of money into three different "mental
accounts" : (1) current income, (2) assets, and (3) future income. 23

The

model assumes that individua ls have the lowest marginal propensit y to save
bundles of money that they have categoriz ed as current income, and the highest
marginal propensit y to save money categoriz ed as future income.
This behaviora l model provides an explanati on for the positive effect of
the amount of LSD and age on the probabili ty of rollover.

Recipient s are more

likely to classify larger LSDs as assets or future income than as current
income; this would explain why larger LSDs are more likely to be rolled over.
Similarly , older recipient s may be more concerned about retiremen t income and
more likely to classify LSDs as assets or future income than younger
recipient s.

23 For

The behaviora l model, however, does not provide a good

a detailed discussio n of behaviora l models of saving behavior, see:
Shefrin and Thaler (1988) and Thaler (1991).

21
explanation for the positive relationship between family income and the
probability of rollover.
To explore further the differential effect of the tax penalty by family
income, I estimated separate probit equations for lower-income and higherincome recipients.

Lower-income recipients are defined as those with less

than $40,000 in family income in 1987.

Higher-income recipients are defined

as those with 1987 family income greater than $30,000.
Table 7 presents the estimated marginal effect of the tax penalty for
the two income groups.

The marginal effect of the tax penalty is larger for

higher-income recipients than for lower-income recipients.

An increase of 1

percentage point in the tax penalty raises the probability of rollover among
the higher-income group by 1.1 percentage point.

In contrast, the marginal

effect for the lower-income group is 0.4 percentage point.

This contrast is

noteworthy, since the tax penalty raised the marginal tax price of nonrollovers more for lower-income recipients than for higher-income recipients.
The results cast doubt on the idea of including one tax price variable
that equals the sum of MTRs and the tax penalty.

The results show that the

MTRs do not have a statistically effect on the probability of rollover.

In

contrast, the coefficient for the tax penalty is significantly positive.
Nonetheless, I have done likelihood ratio tests to determine if the
coefficients on the MTRs and the tax penalty are equal (i.e., the MTRs and the
tax penalty can be summed into one variable).
The results from the likelihood ratio tests indicate that for the whole
group of LSD recipients and for the lower-income group, the null hypothesis
that the coefficients are equal cannot be rejected at the conventional 5%
level.

Since most LSD recipients are in the lower-income group, it is not

22
.surpris ing that the results from the likeliho od ratio tests for the whole
group and for the lower-in come group lead to the same conclusi on.

On the

other hand, the null hypothe sis is rejected at the 1% level for the higherincome group.

The MTRs and the tax penalty cannot be summed for the higher-

income group.
The results from the likeliho od ratio tests are consiste nt with the
discussi on in Section 4.1.

The 10% penalty is the major source of variatio n

in the margina l tax price of non-roll overs for higher-i ncome recipien ts.

In

contras t, for lower-in come recipien ts, both the MTRs and the penalty generate
variatio ns in the margina l tax price of non-roll overs.

Thus, the effect of

the tax penalty differs from the effect of the MTRs more among the higherincome group than among the lower-in come group.
The presenc e of a self-sel ection bias, as discusse d in Section 4.3,
would imply that the estimate s in Tables 6 and 7 underes timate the true effect
of the tax penalty on the entire group of workers who had the LSD option.
While more precise estimate s may be possible in the future with better data,
the policy interes t in the rollove r decision s of LSD recipien ts warrant s the
present endeavo r to estimate the effect of the tax penalty.
6.

Conclus ion
Congres s has often attempte d to raise persona l saving with tax penaltie s

on consump tion.

They imposed a 10% tax penalty on early withdraw als from IRAs

since 1982, when IRAs became availab le to all workers (Ozanne 1992).

In 1986,

Congres s imposed a 10% tax penalty on the amount of lump-sum distribu tions
(LSDs) not rolled over into tax-defe rred instrume nts.
This paper presents the first estimate s of the effect of the 10% tax
penalty and federal income taxes on individu als' use of LSDs.

Aggrega te data

23
show that rollover s increase d after the tax penalty went into effect but not
to the degree expected by Congres s.

Consequ ently, the penalty has raised more

tax revenue than Congress anticipa ted.
An analysis of individu al-level data from the May 1988 CPS indicate s
that the tax penalty signific antly increase s the probabi lity of rollove r among
higher-i ncome recipien ts (i.e., recipien ts with income above $30,000 ).

A 1

percenta ge point increase in the tax penalty produces a 1.1 percenta ge point
increase in the probabi lity of rollover among higher-i ncome recipien ts.

In

contras t, the tax penalty does not signific antly affect the rollove r decision s
of lower-in come recipien ts.

One explana tion for the differen tial impact of the tax penalty by income
is that the lower-in come recipien ts are more likely to be liquidit yconstrai ned; therefor e, their rollover decision s are less sensitiv e to tax

concern s.

The importan ce of liquidit y constra ints in the rollove r decision s

of LSD recipien ts cannot be examined with the currentl y availab le datasets .
Once adequate data become availab le, an examina tion of the importan ce of
liquidit y constra ints in the rollove r decision may provide importa nt insights
into the tax sensitiv ity of rollove rs.
As the trend continue s toward defined contribu tion pension plans, more
workers will receive LSDs.

Most of the recipien ts are young, lower-in come

workers who use their LSDs to finance current consump tion.

Thus, for most

recipien ts, the receipt of LSDs is associat ed with a reductio n in their
accumul ated retireme nt savings.

The combina tion of increasi ng prevalen ce of

LSDs, the spending of most LSDs, and the insignif icant effect of the tax
penalty on the rollove r decision s of lower-in come recipien ts suggests that the
non-rol lover of LSDs will continue to be a policy concern in the near future.

24

Figure 1.

(I)
(.)

·c:
a.

Marginal Tax Price of Non-Rollovers:
Younger and Older Married Recipients

0.6

X

~
<ti

0.5
1987: Younger

C:

·e
<ti

~

0.4

1986
1987: Older

0.3
0.2
0.1
0.0 ..._____ ___,___________._...._ ...._.... .,_......_..... ,_ __.__
0
20 40
60 80 100 120 140 160 180 200
Taxable Income
(Thousands)

Sourc e:

Coope rs & Lybra nd (1986 )[p.2, 166], ACIR (1986 )[p.22 ],
ACIR (1987 )[p.20 ].

25

Table 1.

Distrib ution of Recipie ncy of Lump-Sum Distrib utions

Charac teristic s
Total
Age at time of receip t:
Under 35
35-44
45-54
55+
1987 Family Income:
Less than $10,000
$10,000 -19,999
$20,000 -29,999
$30,000 -39,999
$40,000 -49,999
$50,000 -74,999
$75,000 +

Recipie nt-Wei ghted
thousan ds
percen tage

Dollar- Weight ed
billion s percen tage

8,478

100%

$42.0

100%

5,201
2,042
850
385

61.4

37.4

24.1
10.0
4.5

15.7
15.3
6.5
4.5

344
1,610
1,710
2,042
1,002
682
818

4.2
19.6
20.8
24.9
12.2
8.3
10.0

1.8
6.6
6.6
9.9
4.9
3.8
7.6

36.4
15.5
10.7

4.3
15.7
15. 7
23.6
11.7
9.0
18.l

All figures have been compute d using weight s provide d in the May 1988
CPS supplem ent. The sample consis ts of 2,162 worker s who reporte d receivi
ng
at least one pre-ret iremen t lump-sum distrib ution from a prior job.

26

Table 2.

Characteristics

Distribution of Size of Lump-Sum Distributions

Average

Amount of Lump-Sum Distribution
$1$1,000 $3,000 $5,000 $10,000
999
-2,999 -4,999 -9,999 -19,999

$20,000+

Age at time of
receipt:
Under 35
35-44
45-54
55+

$3,673
8,546
9,789
15,449

46.4%
29.6
35.3
30.6

25.4%
19.1
16.1
14.1

10.7%
11. 7
11.4
10.5

10.4%
17.0
18.8
13.3

5.2%
13.5
8.8
12.9

1. 9%
9.1
9.5
18.6

1987 Family Income:
Less than $10,000
$10,000-19,999
$20,000-29,999
$30,000-39,999
$40,000-49,999
$50,000-74,999
$75,000+

$6,543
4,836
4,751
5,534
6,059
6,786
11,739

45.0%
44.5
43.5
38.5
37.8
32.9
32.2

21. 7%
22.9
24.9
24.9
19.5
19.6
19.0

8.2%
12.7
9.3
12.2
9.5
16.5
8.5

10.2%
8.5
12.4
12.9
17.3
18.0
16.7

8.7%
2.4
6.5
7.8
12.2
6.2
8.8

6.2%
4.0
3.5
3.9
3.7

$5,989·
2,451b

40.5%
2.2

22.4%
8.3

11.0%
8.6

13.0%
10.9

7.9%

Recipient-Weighted
Dollar-Weighted

•Mean amount of lump-sum distributions received
bMedian amount of lump-sum distributions received

21. 7

6.9
14.8

5.2%
40.6

27

Table 3.

Uses

Uses of Lump-Sum Distribut ions

Recipient -Weighted
thousands
percentag e

Tax-defer red instrumen ts:
Retiremen t programs

1,142

Insurance annuities
Savings accounts

198
1,478

Other financial instrumen ts

944

532

13 .5%

Dollar-We ighted
billions
percentag e

11.1
2.3
17.4
6.3

$9.4
7.7
1. 7
5.1
4.5

22.3%
18.4
4.1
12.0
10.6

2.5
4.8
1.4
4.9
1.6

5.9
11.5
3.4
11. 7
3.7

1.8
7.7

4.3
18.4

Start or buy a business
Buy a house
Buy a car
Pay off debt
Pay education al expenses
Pay expenses during

233
756
310
1,843
355

2.7
8.9
3.7
21. 7
4.2

unemploym ent
Other

552
2,250

6.5
26.5

All figures have been computed using weights provided in the May 1988 CPS
supplemen t. The sample consists of 2,162 workers who reported having received
at least one pre-retire ment lump-sum distribut ion from a prior job.
The May 1988 CPS supplemen t does not provide the exact amount of lump-sum
distribut ions allocated to various uses; therefore , only a range of the amount
allocated to each use can be inferred. If a recipient reported more than one
use, then he/she was assumed to have allocated a minimum of $1 and a maximum of
the entire amount of the lump-sum distribut ion to each reported use. Summing
across these minimum and maximum figures across recipient s yields a range of
total amount allocated to each use. The figures in the fourth and fifth columns
are the median values of these ranges.

28
Table 4. Means: By Age Group and Time Period

Variables

Younger Recipient s

Older Recipient s

1984-86

1987-88

1984-86

1987-88

% rolled over any of lump-sum

16.0
[36.7]

19.2
[39.5]

35.7
(48.5]

%

12.8
(33.4]

15.6
[ 36. 3 J

28.6
[45.7]

27.3
[ 45. 6 J
13.6
[35.1]

5,916
[10,301]

5,792
[11,542]

16,373
[20,669]

11,785
[11,910]

0.30
[0.10]

0.34
[0.09]

0.29
[0.12]

0.27
[0.10]

34.8
(8.3]

34.5
[7.9]

59.2
[ 3. 3 J

60.1
(4.4]

35,396
[20,350]

30,609
[17,649]

28,748
[18,176]

31,350
[20,507]

14.2
[ 2. 4 J

14.2
[2.3]

13.2
[3 .2J

13.4
(3.1]

distribut ion (LSD)
rolled over all of LSD

Amount of LSD in 1988 dollars
Marginal tax price of non-rollo vers
Age at time of LSD receipt
Family income in 1987
Years of schooling completed
%

female

46.9

47.0

(SO.OJ

[SO.OJ

23.8
[43.1]

45.5
(51.0]

% married

79.2
[40.6]

67.3
(47.0]

88.1
[32.8]

68.2
(47.7]

% owned home in 1987

73.1
(44.4]

66.2
(47.4]

90.5
(29.7]

81. 8
[39.5]

17.6
(38.1]

19.7
(39.9]

35.7
(48.5]

27.3
[45.6]

501

385

42

22

%

contribut ed to IRA in 1987

Number of observati ons

The figures above are unweighte d. The standard deviation s are listed in
brackets. The marginal tax price of non-rollo vers incorpora tes the 10% penalty
that was imposed on younger recipient s after 1986. The sample consists of 950
workers who received pre-retire ment lump-sum distributi ons between 1984-88.

29

Table 5.

Differen ce-in-D ifferenc e Probit Results

Explana tory Variable s
Real amount of LSD

If less than 55 years of age: LESS55
If received LSD after 1986: POST86
(Ps)(LESS55)*(POST86)

Years of schoolin g

Coeffic ients
1. 7x10- 5 ••
1. 6x10- 5••
(4. Oxl0- 6 )

(4.0xl0- 6 )

-0.46**

-0.53''*

(0.24)

(0.24)

-0.18

-0.17

(0.38)

(0.38)

0.34

0.33

(0.40)

(0.40)

---

0. 05**
(0.02)

If female

-- -

0.02
(0.10)

If married

- --

0.04
(0.12)

Constan t

•

-0. 67**

-1.37**

(0.23)

(0.39)

-Log likeliho od

391.45

388.51

Test: Ps>O
[p values]

0.34

0.33

(0.20]

[o. 20 J

Statisti cally signific ant at the 10% level

** Statist ically signific ant at the 5% level

The depende nt variable is binary and represen ts whether a recipie nt rolled
over any of his/her lump-sum distribu tion (LSD) into tax-defe rred instrum ents.
Standard errors are in parenth eses. The sample size is 855.

30
Table 6.

Probit Results

Exnlanato""'' Variables
Real amount of LSD
Federal income tax rates (MTRs)
Tax penalty

Age when received LSD: Under 35
45-54
55+

Family income in 1987: Less than $10,000
$10,000-19,999
$20,000-29,999
$40,000-49,999
$50,000-74,999
$75,000+

Years of schooling
If female
If married
Constant
- Loo: likelihood

I

Coefficients
9. 5x10-s•
(4. 9xl0- 6 )
0. 77
(0.89)
2.34*
(1. 25)

I

-0. 23*
(0.12)
0. 34••
(0.16)
0. 51 ••
(0.22)
-0.14
(0.32)
-0. 37••
(0.17)
-0.11
(0.15)
0.05
(0.19)
0.03
(0.24)
0.20
(0.22)
0.03
(0.02)
0.02
(0 .11)
-0.04
(0.14)
-1. 60··
/0.49)
373.48

• Statistically significant at the 10% level
•• Statistically significant at the 5% level
The dependent variable denotes whether a recipient rolled over any of
his/her LSD. Standard errors are in parentheses. The sample size is 855.

31

Table 7.

Marginal Effect of.the Tax Penalty on Non-Rollovers:
By Income Group

Sample
Full Sam12le:
coefficient for tax penalty

ll(prob)/ll(p)

Estimates

2. 34*
(1. 25)
0.6%

Lower Income: a

coefficient for tax penalty

fl (prob)/ /l(p)

1. 74
(1. 67)
0.4%

Higher Income:•
coefficient for tax penalty

1.1%

fl(prob)/ll(p)

•
••
a

3. 74••
(1.61)

Statistically significant at the 10% level
Statistically significant at the 5% level
The base family income bracket is $30,000-39,999.
Recipients in this bracket are in both income groups.
~

This table summarizes estimates from three probit equations. The
standard errors are in parentheses. The MTRs in these probits are the federal
income tax rates. The probit equations also include the following variables:
real amount of LSD, family income brackets, marital status, years of schooling
completed, gender, and age brackets. The estimates for ll(prob)/ll(p) represent
the change in the probability of rollover per 1 percentage point change tax
penalty.