National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
LOCK-IN
EFFECT
WITHIN A SIMPLE MODEL OF CORPORATE
STOCK TRADING**
DONALD W. KIEFER*
ABSTRACT
gains tax cuts in Congress
in 1990 is
widely expected.
This article presents an overview of a
The capital gains tax has important
efsimple simulation
model of the lock-in efficiency effects because it affects the rate
fect of the capital gains tax on trading corof return on investing in capital assets and
porate stock. The results of simulations
of the cost of switching
capital assets, reseveral policy changes are reported, the
ferred to as the "lock-in" effect. The repolicies include a 15 percent flat capital
sponses of investors to these effects also
gains tax rate, President Bush's 1989 caphave "feedback" effects on tax collections.
ital gains tax cut proposal, and taxation of
If the lock-in effect were large enough, a
accrued capital gains at death
higher capital gains tax rate could actually result in lower capital gains tax receipts because of the reduced level of gains
rrHE
tax on capital gains was increased
realizations. 2 Conversely, a capital gains
JL by the Tax Reform Act of 1986 by retax cut could actually raise tax revemoving the exclusion of 60 percent of the
nue.
gains on assets held longer than 6 months.
There have been numerous attempts to
Combined with the tax rate changes in the
measure the magnitude
of the lock-in efAct, this revision increased the maximum
fect of the capital gains tax using crossmarginal tax rate on capital gains from
section analysis,'
time-series
analysis,'
20 percent to 28 percent for the highest
analysis of Vooled time-series
and crossincome taxpayers (the rate is 33 percent
section data, and panel data.6 While these
for some upper-income
taxpayers).
studies have contributed
significantly
to
The capital gains tax increase is one of our knowledge
of the responsiveness
of
the most controversial
elements of the
capital gains realizations
to tax rate
1986 tax reform. In 1989 Congress serichanges, they also suffer from important
ously considered four proposals to reverse
limitations.
One limitation is that there
it.1 President
Bush proposed cutting the
are virtually no data on several impormaximum tax rate on long-term gains to tant variables-for
example, the amount
15 percent; he also proposed gradually
ofaccrued but unrealized capital gains or
lengthening
the holding period to qualify
the amount of accrued gains passing
for the favorable treatment to tbxee years.
through estates-and
only very limited
Congressman
Rostenkowski,
Chairman
Of data are available on the holding periods
the House Ways and Means Conunittee,
of capital assets.
proposed indexation of the basis of capital
A second limitation is that the econoassets along with a minimum basis rule
metric studies have been largely unable
for assets held at least five years. The
to investigate the time pattern of the capHouse of Representatives
passed a capital
ital gains realization
response. It is gengains tax cut that would have lasted two
erally agreed that the long-run response
years and would have been followed by
of realizations
to a tax rate change should
indexation.
A capital gains tax cut Prodiffer from the short-run
response beposal that would have provided lower tax
cause the realization
of capital gains derates for longer holding periods received
pends, in part, on the level of unrealized
51 votes in the Senate, but failed to reaccrued gains on currently-held
assets,
ceive the 60 votes required to break a filwhich will change gradually.
Since only
ibuster. Further consideration
of capital
annual data on capital gains realizations
however,
a time-series
*Congressional Research Service, LibrM ,f c,,n@ are available,
gress, Washington,
DC 20540.
regression on post-war data does not have
75
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
76
NATIONAL
TAX JOURNAL
sufficient degrees of freedom to explore
extended lags. 7
Furthermore,
the econometric models
have not been derived from models of capital gains realization behavior. The estimation models are generally rather ad hoc
and are presumed to represent reduced
forms of the actual capital gains realization process. Indeed, while there have been
attempts to model some aspects of this
process,' there is no known model which
attempts to trace the time pattern of.the
adjustment of capital gains realizations
to changes in tax rates.
These limitations
of the econometric
approach suggest the potential usefulness
of an attempt to model the capital gains
realization process. While such an effort
would necessarily
be somewhat conj*ectural and would have to be greatly simplified from the real world, it may provide
insights which the econometric approach
has not. It may also provide testable hypotheses for further econometric work.
This paper presents an overview of a
simple simulation model that has been
developed to represent the capital gains
realization process. The model focuses on
the trading of common stock, the largest
source of taxable capital gains.' To explore relationships within the model, the
results of simulations of several tax policy changes are reported.
Section I of the paper briefly summarizes the model. Section II discusses the
parameterization
of the model and reports the results of a base simulation.
Section III displays the results of using the
model to simulate the response of capital
gains realizations and tax receipts to a tax
rate cut. Section IV provides econometric
results based on model simulations and
compares the results to the study by the
Congressional Budget Office (1988). Section V summarizes results of a simulation
of the capital gains tax cut proposal put
forward by President Bush early in 1989.
Section VI examine the effects of taxing
capital gains at death, and the final section offers conclusions.
1. The Model
The simulation model contains three
principal elements: the representation
of
[Vol. XLIII
investors, a model of the investor decision
to hold or trade shares, and a system of
accounting for all the stocks in the market which traces the value of shares and
the accrual and realization of capital gains.
The Investors
The model includes 40 cohorts of investors, assumed to range in age from 30 to
69. All investors in the model die at the
end of their 69th year; life expectancy is
known and is factored into the trading decision. Investors in each cohort buy shares
and inherit shares from dying investors.
The portfolios of investors in the first cohort consist entirely of shares held only
one year. Portfolios of investors in the older
cohorts consist of shares acquired in each
previous year that have not yet been sold
(e.g., investors in the 20th cohort hold 20
different vintages of stocks).
The investors are all assumed to face
the same tax rates on capital gains.
The Trading
Decision
The model contains a representation
of
the investor decision to hold or trade
shares; trading here means selling a share
and buying another one. The selling of
shares to finance consumption, and the
decision regarding the amount of the
investor's portfolio used to finance consumption versus the amount left to heirs,
are not modeled.10
All investors are assumed to share a
common expectation regarding the best
rate of return available during the next
year on shares they do not currently own
(alternative investments). On the other
hand, investors are assumed to have varied expectations regarding the likely rates
of return on the stocks in their portfolios
during the next year. As investors receive
new information on companies in which
they have invested, their expected returns on these stocks can go up or down
and can be lugher or lower than when they
bought the stocks. To capture this effect,
the model divides each cohort of investors
into 20 "probability classes" for each vintage of stocks.
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
LOCK-IN
The expected rate of return during the
coming year on stocks in investor portfolios is assumed to be normally distributed with a specified standard deviation,
a." Given this standard deviation and the
mean of the distribution,
K (the determination of which is discussed below),
investors are arrayed into 20 classes, each
containing
5 percent of the probability
density of the distribution."
The rate of
return corresponding
to the midpoint of
the class (in terms of probability) is used
as the expected rate of return for the whole
class. For example, the expected rate of
return assigned to investors in the first
class is the rate below which 2.5 percent
of investors would expect the rate to lie,
given the parameters
of the normal distribution. The expected rate in the second
class is the rate below which 7.5 percent
of investors would expect the rate to lie,
and so forth. Expectations
with regard to
each stock in an investor's portfolio and
each year are assumed to be independently distributed.
To the extent that the expected rate of
return on a stock (both stocks in the
investor's
portfolio and alternative
investments)
during the coming year deviates from the average rate of return in the
market,
the model assumes that the
investor expects the rate to move gradually toward the average market rate.
While some stocks might be expected to
earn higher or lower than market rates of
return for some period of time, these market inefficiencies
should also be expected
to diminish over time. The expected rate
of return on a stock t years after its purchase, rt, is determined
in the model as
follows:
rt = r. + rele d(l -t)
where:
(1)
rm = the expected average rate
of return
in the stock
market
r., = the expected excess rate
of return on the stock in
the first year it is held (rl
can be negative)
e =the
base e, (approximately equal to 2.71828)
EFFECT
77
d
the parameter
that determines
the rate at
which the expected rate
of return approaches the
market rate
Hence, with regard to a stock that is in
the investor's Portfolio, the rate of return
expected over the next year adjusts from
Year to year as new information is received. Whatever the expected rate during the next year, however, it is expected
to approach the market average rate over
the long term.
The investors in the model face an almost infinite variety of potential investment strategies,
ranging from holding
their current stocks until death to trading
their stocks for new ones in the current
Year and every year until death. Since the
alternative strategies involve holding different investments over different time periods, the only time period necessarily
shared by the strategies is the time until
death- Hence, the model assumes that each
investor selects the strategy for each stock
in his POrtfOliO that appears to be consistent with the goal of wealth maximization at the time of death.
The model does not evaluate all of the
potential strategies available to an investor, but does evaluate a large subset of
them.13 For strategies that involve trading the current stock for an alternative
investment, the model calculates teminal wealth resulting from holding the altemative stock until death; it also evaluates holding periods for the alternative
stock of one year, two years, etc., up to
one half of the investor's remaining life,
and, for each holding period, trading the
alternative
stock once twice, etc., up to
the maximum nurnberof trades possible
in the investor's remaining life. The value,
VT at the end of the investors
life yielded
by trading the current stock for an alternative stock which is to be held for t years
is determined in the model by the following equation:
VT @ P(l
tg@9)[Mat(I
' [Maf(l
tgd) + tgd]
where:
p
t,.)
+ tg.1'
(2)
the price of the stock
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
NATIONAL TAX JOURNAL
78
t,,
g
M,
t,,,
n
[Vol. XLHI
currently in the invesrent stock is held for h years and then
tor's portfolio that is to traded, the value at the end of the invesbe traded
toes life, Vh, is:
= the current capital gains
tax rate
th(l
- 9)]
= the portion of p that is Vh = PIM@h(l - th) + n[Maf
IMt(i
accrued capital gain
tg.) + tgl
(1 - td)
= a multiplierindicating
(4)
+ td]
the growth in the value
of the alternative stock
where: Mh a multiplier indicating
held for t years, deterthe growth in the value
mined in accord with
of the current stock
equation I
when held h years de= the expected
capital
termined in accord with
gains tax rate when the
equation 1
alternative stock is to be
th the expected capital
traded
gains tax rate when the
= the number of times alcurrent stock is to be
ternative stocks are to be
traded
turned over during the
investor's
remaining
lifetime
M.f = a multiplier indicating
the growth in the value
of the alternative stock
in the final holding period after the last trade,
determined
in accord
with equation 1
tgd = the
expected
capital
gains tax rate at the
time of death
For strategies that involve holding the
stock currently in the investor's portfolio
rather than trading, the model calculates
the terminal wealth resulting from holding the stock until death, VH, as follows:
The structures of equations 2 through
4 make clear one of the advantages of using a structural model rather than a reduced form model. In most reduced form
models, the tax rate enters the model in
linear, log linear, or quadratic form (see,
for example, the equations in section IV
below). The way in which the tax rate enters the trading decision in equations 2
through 4, however, is more complex.
Furthermore, not only the current tax rate,
but also expected future tax rates are important to the trading decision.
For each vintage of stocks held by each
probability class of each cohort of investors, the model identifies the trading
strategy and holding strategy expected to
maximize terminal wealth. A stock is
(3) traded if any trading strategy dominates
VH = PIM(@d(l - tgd) + tgd(I - 9)]
all of the holding strategies; otherwise it
where: Ald = a multiplier indicating
is retained. The trading strategies are
the growth in the value
reevaluated each year; a dominant stratof the current stock
egy one year does not necessarily carry
when held until death
over into the following year. All after-tax
determined
in accord
proceeds from stock sales are reinvested
with equation I
in shares of the alternative stock. 14
In its initial solution, the model allows
The model also evaluates holding the
current stock for one year, two years, etc., the overall turnover rate of stocks in the
up until the year before death; for each market to be set. Given the values of the
holding period the model considers each other parameters, the model solves iterof the trading strategies described in the atively for the value Of III the mean of the
paragraph preceding equation 2 once the distribution of expected rates of return on
current stock has been traded. If the curshares currently owned, such that in
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
LOCK-IN EFFECT
equilibrium shares will be traded at the
specified turnover rate." Once this value
of li is determined, it is held constant in
further model solutions exploring the effects of alternative settings of the policy
parameters.
The Stocks
For simplicity and to focus on the effects of tax changes rather than other effects, stock prices are assumed to grow at
a constant rate in the model rather than
var)nng substantially as actual stock prices
do." Also, dividends and losses are ignored. Investors are assumed to buy and
sell shares based solely on their expected
capital gains.
For each investor cohort, the model
traces the market value and the tax basis
of each vintage of stocks in the investment portfolio. Vintage 1 contains stocks
purchased and inherited at the beginning
of the current year, vintage 2 contains
stocks obtained at the beginning of the
previous year, and so on.
The investors in cohort 40 are assumed
to die at the end of each year. The shares
remaining in their portfolios are inherited by younger investors with a steppedup basis.
11. Parameterization
and Base
Simulation
The model does not have a sufficient
number of control parameters to exactly
match actual stock market data for any
specific year. Nonetheless, an attempt was
made to parameterize the model as closely
as possible to data for 1981, since this is
a year for which considerable data on capital gains are available from tax returns.
17
The initial turnover rate was set at 15
percent (for the tax rates in effect in 1981).
While this is closer to the average turnover rates in the market during the 1950s
and 1960s than in the early 1980s," most
of the increase in trading activity in the
last 15 years has been in institutional
trading, not trading by individual investors.19 For the simulations reported here,
79
the prices of common stocks in the market were assumed to increase at a rate of
7.0 percent per year, which is close to the
average growth rate of the S&P 500 stock
index from 1950 to the end of 1988. The
expected rate of return on alternative investments (in the first year of ownership)
was arbitrarily set equal to 8.0 percent.
The distributions
of new stock purchases and inheritances
of stocks across
the cohorts of investors were set so the resulting distribution of share ownership
across age cohorts would
approximate the
observed distribution .20 The rate at Which
expected rates of return are assumed to
approach the market rate (d in equation
1) was arbitrarily set at .075 for the simulations reported here.
Simulations were performed for several
values of (r to examine the results under
different assumed degrees of sensitivity.
The smaller the value of or, the more responsive are capital gains realizations to
tax rate changes within the model. With
a smaller value of u, the different expected rates of return on stocks in investors' portfolios are clustered more closely
together. Hence, a given tax rate cut, for
example, will cause more shares held by
investors to be traded rather than retained.
Selected data from simulations assuming a = 0.2 11,which seem to be the most
consistent with observed data, will be reported to illustrate the behavior of the
model. Line 1 of table 1 reports the data
for the base simulation of 1981 tax law
(the data in the other lines of the table
are discussed in the sections below). The
tax law is characterized in the simulations by four features: the holding period
requirement, the tax rate on short-term
gains, the tax rate on long-term gains, and
the tax rate on gains at death. For 1981
law, these amounts are assumed to be 1
year, 70 percent, 24 percent, and 0."
The turnover rate of 15 percent, shown
in line 1, column 1, of the table, was assumed in the base simulation. The value
of R, the mean of the distribution of the
expected rate of return during the next
year on stocks in investors' portfolios, required to achieve this turnover rate given
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
Table 1
Summary of Simulation
Policy
1.
2.
3.
4.
5.
6.
1981
28%
15%
Bush
Tax
Tax
Turnover
Rate
(1)
Tax System
Flat Tax
Flat Tax
Proposal
at Death (28%)
at Death (12.5%)
.150
.197'
.308
.229
.324
.384
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
Result
Average
Holding
Period
(2)
Average
Market
Gains
(3)
Traded
Stock
Gains
(4)
3.24
2.24
2.27
2.81
2.45
2.34
.277
.290
.182
.217
.191
.141
.192
.135
.137
.164
.146
.141
E
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
LOCK-IN EFFECT
the values of the other parameters is .0839;
the expected rates in the highest and lowest probability classes of investors, given
iL and the assumed value of (y, are .1169
and .0510.
Column 2 in the table reports the average holding period on stocks sold in the
market. The average of 3.24 years is lower
than the actual average holding period of
5.3 years for stocks with capital gains sold
in 1981. The simulated pattern of sales by
holding period differs from the actual pattern in two respects. First, in the simulation there are substantially
fewer sales
of stocks held only one year. Second, there
are also fewer sales of stocks held for long
time periods. While actual data reveal
some stock sales after holding@ periods of
20 years, 25 years, and even 30 years, in
the simulation no stock held longer than
15 years is sold. There are reasonable explanations for both deviations from reality.
The difference regarding short-term
sales is probably due to the absence of
losses in the model. Real investors have
stocks with accrued losses. An optimal investment strategy usually involves realizing short-term losses. An investor with
short-term losses can realize short-term
gains (up to the amount of the losses) with
no tax consequence. Investors in the model
do not have this opportunity.
The lower sales of stocks held for long
periods in the model is probably due primarily to three factors. First, all stocks in
the model grow in value at a constant rate.
Thus, all stocks held for long periods have
sizeable accrued gains, and trading them
is costly. Real investors may have some
stocks held for long periods with small
gains or losses, so the tax cost of trading
them is small or negative. Second, the
model does not include sales of stock to
finance consumption. Some sales of longheld stock are, no doubt, to finance bigticket items such as childreres education
or to finance retirement consumption of
older investors. The third reason for lower
sales of long-held stocks is that all investors in the model know they will die at
age 70. Real investors may have much
longer life expectancies
(hopes) and
therefore factor in longer periods of time
81
for an alternative investment to recoup
the tax cost of trading. A variant of the
model allows specifying a longer life expectancy, and, as would be expected, this
results in a longer average holding period
for stocks.
The third and fourth columns in the table report accrued gains as a proportion
of total value for all stocks and for traded
stocks. In this simulation, accrued gains
equal 27.7 percent of the aggregate value
of all stocks, but only 19.2 percent of the
value of traded stocks, reflecting the tendency not to trade stocks with high accrued gains. Columns 5 and 6 report that
in the first simulation, realized gains each
year in equilibrium equal 2.87 percent of
the total value of all stocks in the market,
and the capital pins tax paid equals 0.70
percent of the total value of stocks. The
last two colunms report that the value of
net bequests equals 4.15 percent of the total value of stocks and the step-up in basis on bequested stocks equals 2.18 percent of the total value of all stocks (53
percent of the value of bequested stocks).
In equilibrium, the amount of realized
gains plus the basis step-up each year will
equal the growth in accrued gains multiplied by 1 minus accrued gains as a
fraction of total stock value. 22 Expressing
each amount as a fraction of total stock
value, growth in accrued gains in the
simulation equals 7 percent (the assumed
growth rate). Accrued gains are .277328
of total stock value; 1 minus this amount
is .722672. Muitiplication by the growth
rate yields .050587. This equals the sum
of realized gains (.028742) plus basis stepup (.021844). In this case basis step-up
amounts to 31 percent of annual accrued
gains, very close to the 30 percent level
estimated in U.S. Department
of the
Treasury (1985, p. 103).
If realizations increase permanently as
a result of a tax cut, then in equilibrium,
basis step-up will decrease and/or accrued gains as a fraction of total stock
value will decrease.
111. The Simulated Effects of a
Capital Gains Tax Cut
The principal advantage of a simulation model, of course, is that it can be used
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
[Vol. XLIII
NATIONAL TAX JOURNAL
82
to isolate and study phenomena that cannot be isolated in the real world. 'fhe model
presented here can be used, for example,
to study the effects of a capital gains tax
cut isolated from other influences on capital gains realizations (e.g., stock market
fluctuations) and from the effects of other
tax changes (during the last two decades,
the tax treatment of capital gains has been
changed, on average, every other year).
To this end, the model was used to examine the patterns of capital gains realizations and tax collections generated by
a tax cut from a flat 28 percent capital
gains tax to a flat 15 percent tax. Simulations were performed using five different values of a, ranging from 0.05 p to 0.4
@L,to explore different degrees of sensitivity. The capital gains realization response
is graphed in figure 1 and the tax revenue response is graphed in figure 2. The
graphs plot realizations and revenue as
fractions of the total value of stocks in the
market each year. The values plotted on
the vertical axis have been normalized so
Simulated
the level prior to the tax cut is set equal
to 1 (the tax cut occurs at year 0). The
last two digits of the variable names indicate the assumed value of or (as a multiple of ii). The plots for a = 0.2 IL are
shown by the dark solid line in each graph,
and the beginning and ending equilibrium values for this simulation are shown
in lines 2 and 3 in table 1.
The patterns in Figure 1 suggest that
the response to a capital gains tax cut in
the model seems to have three phases: the
first-year, when realizations jump sharply
upward; an intermediate
phase lasting
from 2 to 5 years, during which realizations decline; and a longer-term phase,
during which realizations rise gradually,
not reaching their new equilibrium level
until about 20 years after the tax cut. Each
of these effects is more pronounced for
lower values of a.
The patterns of tax revenues shown in
figure 2 mirror those of the realizations
in figure 1. For the smallest two values
of or, tax revenues increase in the first year
Capital Gains Realizations
2
............
After a Tax Cut
.. .. .......... .............
...... ................
1.6
------------------------------------........... I., ................................................
1.4
--------------------------I ...............
.....................
........ .........
Gains 05
1.2
Gains
10
Gains.20
-r777i
Gains 30
Gains 40
0.8
-6 . .
. *0 . . . .
@5
. . . * 2,0 . .
. . i5
Years
Figure
1
30
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 1]
LOCK-IN EFFECT
Simulated
Capital
Gains
83
Tax Revenue
... ..........
..........
----------
After
a Tax Cut
................ ...... ...
----------
---------------
0.9-
--------------------
---------------------
-------------------
07
... Tax.06
Tax 10
06
Tax.20
0.5
0.4-1-5
Ttx.30
Tax 40
. . . . . . . . . . . . . . . . . . .
5
10
15
20
. . 25. . . .
30
Years
Figure
2
of the tax cut because
of the large
jump
in realizations.
In all of the simulations,
revenues
are lower than prior to the tax
cut during the intermediate
phase and the
first several
years
of the longer-term
phase. For the smallest
value of cr, however, revenue
is higher in the long run
than prior to the tax cut.
Understanding
the dynamics
of the
patterns
shown in irigures 1 and 2 is aided
by the information
plotted in figure 3,
which traces several of the variables
in
the simulation
with a = 0.2 R. The immediate
effect of the tax cut is that more
alternative
investments
are attractive
relative
to existing
investments
because
the tax cost of trading has declined. Hence,
trading
increases.
The jump in trading
disproportionately
affects shares that have
been held for longer time periods because
these are the shares for which the tax cut
results in the biggest decrease
in trading
costs (because
they have the largest
accrued gains). In the simulation
with cr =
0.2 R, for example,
in the first year after
the tax cut, trading
of shares in vintage
2 (across all cohorts) increases
by 19 percent; trading of shares in vintage
10 more
than quadruples.
Thus, in figure 3, in the irirst year the
turnover
rate jumps upward and so does
the average
holding period for stocks sold
(the average
level of gains on the sold
stocks, "Traded
Gain," follows the pattem of the holding period). The first-year
jump in realizations
in figure I is attributable to both of these factors: higher sales
and higher realized
gains per sale.
The intermediate
phase of the response
to the tax cut could be said to result from
a "vintage
effect." The pattern
of realizations during this phase is dominated
by a
decline in the average
gain realized per
share traded,
as shown in figure 3; this
decline results from the shift of shares in
the market
toward the lower vintages.
Beginning
the second year after the tax
cut, a higher
number
of later-vintage
stocks have been sold the previous
year
and reappear
as vintage-1
stocks. In any
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
NATIONAL
84
Simulated
TAX JOURNAL
[Vol. XLIII
Market Responses After a Tax Cut
.. ........ . ...... ........ .. ... .. . .. ... ... ....... ... ..
Turnover
14
Holding Period
Traded Cain
1.2
--- Basis Step-up
Mark!L.@@
0.8
...............
------------------------------------...............
.......................
0.6
0.4
-5. . . . . 0. . . . . 5. . . . . 10. .
15
20
25
30
Years
Figure
3
given year, a higher proportion of lowvintage stocks is sold (because of smaller
gains), so as the distribution of shares
shifts toward the lower vintages, the
turnover rate continues to increase, as
shown in figure 3. The average holding
period of sold stocks decreases, however,
also because of the higher concentration
of low-vintage stocks among those traded.
As the average holding period decreases,
so does the average level of capital gain
per trade. The lower average gain per
trade results in a decrease in realizations
during the intermediate phase of the response to the tax cut (see figure 1), despite the continuing rise in turnover.
The longer-term phase of the response
to the tax cut could be said to result from
a "cohort effect." The pattern of realizations during this phase is reflected by the
decrease in the step-up in the basis of
stocks held by dying investors and the decrease in the average level of accrued gain
on shares in the market, both of which are
shown in figure 3. These two changes result primarily from the year-by-year
movement up through the investor cohorts of stock portfolios that have been
traded largely under the new lower tax
rate.
The declining step-up in basis of shares
held by dying investors results from two
changes. First, older investors in the cohorts just prior to the last one trade
slightly more shares as a result of the
lower tax rate. This effect is limited, however, because these investors are largely
locked into their investments even at low
tax rates. Investors in the 39th cohort, for
example, trade just 0.03 percent of their
shares the year before the tax cut; the first
year after the tax cut they trade 1.9 percent. The comparable figures for the 35th
cohort are 7.0 percent and 14.1 percent.
The second change that results in the
declining step-up in basis of shares of dying
investors is that, under the lower tax rate,
aging investors have portfolios with reduced levels of accrued gains because the
portfolios have been traded more actively
during the investors'younger
years. This,
of course, is an effect that can occur only
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
LOCK-IN EFFECT
over a lengthy time period, as stock portfolios that have been traded under the
lower tax rate move up through the cohorts. The lower accrued gains in portfolios of older investors not only directly reduce basis step-up, but also further
increase turnover of older investors' portfolios because the tax cost of trading is
decreased. In the 35th cohort, for example, accrued gain as a fraction of the total
portfolio decreases from 38.4 percent in
the year of the tax cut to 21.6 percent
twenty years later because of the more
active trading by the investors in that cohort (as they moved from cohort 16 to cohort 35) during the twenty years under
the lower tax rate. As a result, their turnover rate increases from 14.1 percent immediately after the tax cut to 24.2 percent twenty years later.
The diminished amount of accrued gain
in the portfolio of each cohort, of course,
reduces the total amount of accrued gain
in the market. Realizations continue to
increase until a new equilibrium is established at a higher level of realizations and
at lower levels of basis step-up and average accrued gains in the market.
The data reported in lines 2 and 3 of
table I provide a more detailed impression of the beginning and ending equilibria for the simulation in which (r = 0.2 @L.
The turnover rate increases by 56 percent
in this simulation. Despite the higher
turnover rate, the average holding period
of traded stocks (and the average gain on
traded stocks) increases slightly. The
higher concentration of stocks in the lower
vintages and the higher turnover rate
disproportionately
affecting the upper
vintages both increase the overall market
turnover rate, but almost exactly offset
each other in influencing the average
holding period of traded stocks. The average accrued gain on shares in the market declines by 37 percent because of the
higher concentration of shares in the lower
vintages.
Realized gains are 58 percent higher in
the new equilibrium than prior to the tax
cut. For this reason, equilibrium tax revenues drop by only 15 percent in this simulation instead of the 46 percent revenues
would drop in the absence of any market
85
response to the tax cut. The amount of basis step-up on shares passing through estates decreases by 35 percent.
As stated in the introduction,
the
econometric research on the subject has
been largely unable to investigate the time
pattern of the response of capital gains
realizations to a change in the tax rate.
Most of the econometric models assume
explicitly or implicitly that the response
is immediate or that it occurs within two
years. Indeed, some of the policy analysis
also seems to assume an immediate response .21 If the model developed here captures the essential aspects of the actual
market adjustment, however, the adjustment is far more complex and extends over
a very lengthy time period. The implications of these findings for the econometric
research are explored in the next section.
IV. Econometric
Results
One test of plausibility of the model is
to see whether it can simulate the results
of time-series econometric studies. For this
purpose, the 1988 study by the Congressional Budget Office (CBO) was chosen.
The basic equation estimated by CBO had
the following form:
log (LTG) = C + bi log (Bi) +
+ b,, log
where:
(Bn)
+ bn+IMTR
(5)
LTG = Net long-term capital
gains
C = A constant
Bi =A non-tax independent variable
MTR = The weighted average
marginal tax rate on
capital gains
The non-tax independent variables used
by CBO were the price level, the real value
of corporate equity held by individuals,
real GNP, and the change in real GNP.
The tax rate used by CBO was the
weighted average marginal tax rate on
capital gains reported on individual income tax returns. The equation was estimated for the period 1954-1985, and the
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
NATIONAL
86
TAX JOURNAL
estimated value of b,,,, was -0.0310 (MTR
is stated as a percent rather than a decimal value).
The model was used to simulate capital
gains over a similar historical period and
a regression equation was fit to the resulting data. Since the model was calibrated to the statutory tax rate, the max
imum marginal tax rates on capital gains,
as reported by CBO for 1954-1988,'
were
used in the model simulation over a 35year period (assuming cr = 0.2 @L).Then
the following re ession was run on the
simulated data:'
F
[Vol. XLIII
- 2.9611 + 1.0107
(-5.3)
(21.0)
- log (value) - 0.03061MTR
(-31.4)
+ 0.00290MTR(-1)
(2.98)
log (gains)
where:
(7)
MTR(-l) = The maximum
marginal tax rate
lagged one year
W = 0.9997
RHO = 0.939
In this regression the coefficient of the
lagged tax rate is significant. On the other
log (gains)
2.6032 + 0.9843
hand, the t statistic of the coefficient is
(-9.6)
(40.4)
substantially smaller than the t statistics
of the other coefficients. The t statistics
log (value) - 0.02977MTR
(6) and R2s for these regressions are much
(-28.7)
larger than normally observed because the
data are artificial; there is no "noise" in
where: gains = Simulated
realized
this system. It is not difficult to believe
gains in the model
value= The total value of that in a "noisy" real world setting which
yielded more normal values for the t stastocks in the model
tistics of the other coefficients, the influMTR The maximum marginal tax rate on cap- ence of the lagged tax rate term could be
obscured and its coefficient would not be
ital gains
significant.
.9997
This single test of the ability of the
RHO 0.871
model to simulate the time series relat statistics are shown in parentheses
tionships observed in the econometric
In the model there are no influences on studies, therefore, does not reject the model
the realization of capital gains other than
as being unreasonable.
the dynamics of the market and the tax
The CBO study also examined alterrate. Hence, the log of the total value of native equation forms for the relationship
stocks serves as the only non-tax inde- between the tax rate and capital gains
pendent variable in the regression. The revenue by performing
time-reries
coefficient of MTR is of the same order of regressions using different forms for the
magnitude and, in fact, is quite close to tax rate variable in equation 5. The simthe CBO estimate based on actual data.
ulation model can be used to explore the
CBO also did a regression which in- fit of different equation forms directly.
cluded a lagged tax rate variable to test
Figure 4 plots the relationship between
for a time pattern in the response to the revenue and the tax rate for rates rangtax rate change. In this regression, the ing from 0 to 50 percent. The values for
coefficient of the lagged tax rate variable
revenue at the various tax rates have been
was not significant, and the values of the normalized by setting the revenue at a tax
other coefficients did not change much.
rate of 20 percent equal to 1.
Because the graphs in the previous secThe heavy line in the graph plots simtion clearly show a time pattern in the ulated equilibrium tax revenue in the
capital gains response in the model, a model at the various tax rates in simuregression including a lagged tax rate was lations assuming u = 0.2 @L.The model is
also run on the simulated data. The re- clearly consistent with the notion of a
sults were as follows:
revenue maximizing marginal tax rate;
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 1]
LOCK-IN EFFECT
Revenue-Tax
Rate
87
Relationship
1.4
1.2
I
zs
Q@
0.8
Equklibrium
0.6
Revenue
lanear
Estimate
--- After-Tax
Rate Estimate
Quadratic
Estimate
0.4
0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.6
Tax Rate
Figure
4
in this case the revenue
maximizing
rate
is 24 percent (the graph plots values only
at increments
of 5 percentage
points).
The other lines in the graph plot the relationship
between
tax rates and revenue
estimated
using
three different
regression equations
applied to the simulated
data for the period 1954-1988.
The three
lines are nearly coincident.
The dotted line
is the relationship
between
tax revenue
and the tax rate estimated
in equation
6
above, in which the tax rate variable
enters the equation linearly.
CBO explored two other equation
forms
that are consistent
with a revenue
maximizing marginal
tax rate. In the first
form, the log of 100 minus the tax rate
(expressed
as a percentage)
was entered
as the tax rate variable
in the regression.
A similar regression
was performed
on the
simulated
data;16 the dashed line in the
graph plots the revenue-tax
rate relationship from this estimated
equation.
CBO also explored a quadratic
relationship between the tax rate and revenue.
The
dot-dashed
line in the graph plots the revenue-tax
rate relationship
based on a
quadratic
equation
fit to the simulated
data."
Figure
4 shows that the regression
equations
have a rather curious property.
The marginal
tax rate on capital gains
over the period 1954 to 1988 used in the
simulation
ranged from 20 percent to 35
percent.
The figure
reveals
that the
regression
equations
fit the actual tax raterevenue relationship
almost perfectly for
tax rates ranging from 0 to 20 percent. For
rates
above 20 percent,
however,
the
equations
increasingly
overestimate
revenues. Hence, the regression
equations
fit
the equilibrium
relationship
outside of the
sample range (merely a coincidence)
and
do not fit within the sample range! The
three regression
equations
imply revenue
maximizing
marginal
tax rates between
31.6 percent and 33.6 percent,
whereas the
actual
equilibrium
revenue
maximizing
rate is 24 percent.
The pattern
of capital gains tax rates
over the sample period and the time pattem of the revenue
response
to a change
in the tax rate explain this anomaly. The
maximum
tax rate on capital gains was
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
88
NATIONAL
TAX JOURNAL
stable at 25 percent until 1968. Beginning that year, the rate increased each
year, reaching 35 percent in 1972. The rate
remained at that level until it was reduced to 28 percent in 1978; it was further decreased to 20 percent in 1982, where
it remained until being increased to 28
percent in 1987.
The revenue response to a capital gains
tax rate increase in the model is the mirror image of the pattern shown in figure
2; revenues first rise above the equilibrium level and then slowly approach the
new equilibrium.
Hence, as the tax rate
rises, then falls, then rises again in the
simulation, the revenue response is greater
than in the long-run relationship.
The observed data, therefore, reflect the intermediate phase of the revenue response to
the tax rate change, but not the longerterm response. The intermediate
phase
may be the most relevant for making revenue estimates
for tax legislation,
since
the forecast period is usually 5 years and
the tax rate is likely to be changed again
before the long-run relationship
is attained anyway. Nonetheless,
if the tax
rate-revenue
relationship
in the model
accurately
reflects reality, then regressions based on the observed time-series
data may overestimate
the long-run revenue responsiveness
to a tax rate change
(that is, they may underestimate
the longrun responsiveness
of realizations
to a tax
rate change).
While the implications
of the response
pattern of capital gains realizations
and
revenue to a tax rate change are most obvious for time-series
estimation, there are
also potentially important implications for
cross-section
studies.
The premise of cross-section
analysis is
that the relationships
between the variables that are observed in the cross-seetion sample are the long-run relationships that would be observed in response
to changes in the independent
variables.
This presumption
is not justified, however, if the cross-section
sample is taken
at a time when the relationships
are not
at their long-run equilibrium levels. If the
relationship
between two variables takes
a long time to adjust to a change in the
independent
variable, then the results of
[Vol. XLHI
a cross-section
study of the relationship
can be affected by when the cross-section
sample is taken. This is particularly
true
if the change in the independent
variable
has not affected all observations
in the
same way. Most of the cross-section
studies of the effect of a change in the tax rate
on capital gains realizations
have used
sample data from years closely following
changes in the capital gains tax rate. 21
These observations
suggest that the results of both the time-series and the crosssection studies of the response of capital
gains realizations to tax rate changes may
have been strongly influenced by shortterm or intermediate-term
effects and may
not reflect long-run relationships.
V. The Bush Capital
proposal
Gains Tax
As stated in the introduction,
four capital gains tax cut proposals were considered by Congress in 1989. These proposals were among the most controversial
items considered by Congress during the
year, and further debate on capital gains
taxation is expected in 1990. None of the
specific proposals, however, seemed to have
achieved a dominant position by the time
Congress adjourned its 1989 session. This
section illustrates
use of the model in policy analysis by simulating
effects of the
first proposal placed before Congress in
1989, the one advanced by President Bush
in his fiscal year 1990 budget proposals.
For purposes of the simulation,
the essential features of the proposal are that it
would reduce the maximum tax rate on
capital gains to 15 percent on qualifying
assets held for the required holding period. Corporate stock would be among the
qualifying
assets. The required holding
period initially would be one year; it would
increase to two years on January
1, 1993,
and to three years on January 1, 1995.
Among the claims made by the Administration for the proposal is that it would
prckinote long-term, rather than short-term,
investment.
Additionally,
the Administration claimed that the tax cut would so
substantially
reduce lock-in that tax revenue actually would increase rather than
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
LOCK-IN EFFECT
No. 11
decline. These effects can be studied witlun
the model.
The simulated effects of the proposal are
shown in figure 5. The proposal is assumed to go into effect at time zero. The
two-year holding period requirement goes
into effect in year 4, and the three-year
requirement becomes effective in year 6.
Two different simulations
were performed. In the first, taxpayers are assumed to react to tax rate changes as they
occur without any anticipation. The results for this simulation are shown with
the solid line for the path of realized gains
and the dashed line for the path of revenues.
In the second simulation, taxpayers are
assumed to take into account the expected tax rate one year hence in making
their investment decisions (investors are
not assumed to be able to anticipate implementation of the tax cut before it is enacted, however). Any legislated tax rate
changes more than one year in the future
are assumed to be fully discounted. The
results for this simulation are shown by
89
the two dotted lines that eventually become coincident with the solid and dashed
lines. The movements of pins and revenues in this simulation are somewhat
greater than without anticipation, particularly during the phase in of the longer
holding periods, but the patterns do not
differ substantially.
The effects of the lengthened holding
period requirements are visible in the
patterns of gains realizations and revenues. In years 4 and 6, when the longer
required holding periods become effective, gains and revenues decline because
of lower turnover of the vintage of stocks
that has been made short-term for the first
time .2' The following year gains and revenues pick up again as the deferred sales
occur and the stocks have higher accrued
gains because of the 1-year delay in their
turnover.
Aside from the more sawtoothed intermediate
phase, the overall
pattern of adjustment is similar to those
shown in figures 1 and 2.
Data for the market equilibrium under
the Bush proposal are shown in line 4 of
Simulated Effects of Bush Capital Gains Tax
Proposal on Realizations and Revenue
2
1.6
1.4
1.2
----------------------------------------------08
- Realized
Gains
0.6
Tax Revenue
0.4
0.2
--5
. . . . .
0
. . .
5
. . .
.
;o
. . . .
15
. . . .
20
25
30
Year
Figure
5
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
90
NATIONAL TAX JOURNAL
table 1. The simulated data (compared to
line 2, the 28 percent flat tax) are consistent with the claim that the proposal would
promote longer-tenn investment while at
the same time reducing lock-in, since the
average holding period increases from 2.24
years to 2.81 years while the turnover rate
increases from 19.7 percent to 22.9 percent. Given the parameters used for this
simulation, however, the results suggest
that the proposal would yield somewhat
lower long-run tax revenues. Long-run
revenues decline from 0.75 percent of the
total value of stocks to 0.72 percent, a decline of only 4 percent in the face of a 46
percent decline in the tax rate. The revenue decline is substantially less than that
resulting from the flat 15 percent tax rate
shown in line 3 of table 1; this difference
is due to the three-year holding period that
results in higher realizations per trade
under the Bush proposal.
VI. Taxation of Gains at Death
An alternative approach to reducing the
lock-in effect is to tax capital gains at
death. While the advantage of deferral
would remain, the very strong lock-in effect on older investors resulting from the
prospect of a zero tax rate on gains passing through their estates would be eliminated.
Two simulations were performed to explore the effects of taxing gains at death.
In the first, the 28 percent flat tax rate
assumed to apply to realized capital gains
in the simulation reported in line 2 of table 1 was also assumed to apply to unrealized gains on assets held at death. The
results of this simulation are reported in
line 5 of table 1. Taxation of gains at death
results in a substantial increase in trading, raising the turnover rate from 19.7
percent (in line 2) to 32.4 percent (in line
5). Despite the higher trading activity, the
average holding period for traded shares
rises slightly from 2.24 years to 2.45 years.
This is because the biggest effect of taxing gains at death is on sales of shares
with large gains (that is, shares that have
been held for a long time) owned by older
investors. Tax payments more than double in this simulation, reflecting the 77
[Vol. XLIII
percent increase in realizations plus the
taxation of gains at death that previously
escaped tax. The unrealized gain on shares
passing through estates in this simulation is only about 41 percent of such gain
in the second simulation, reflecting the
lower vintages of stocks in the portfolios
of dying investors resulting from more active trading later in investors' lives. Net
bequests also decrease because of the tax
payment on unrealized gains at death.
The second simulation exploring the effects of taxing gains at death was an attempt to find the tax rate that, when applied to both realized gains and unrealized
gains on assets held at death, would raise
the same tax revenue as the flat 28 percent tax rate in simulation 2 in table 1.
A tax rate of 12.5 percent (very nearly)
achieved this equality. This simulation is
reported in line 6 of the table.
In this simulation, the turnover rate has
nearly doubled compared to the flat 28percent tax rate simulation. By design, tax
collections remain the same. All of the
other results are similar to those for simulation 5, except that lock-in is reduced
even more because of the lower tax rate.
VII. Conclusion
This paper has developed a simple model
of the lock-in effect of the capital gains
tax on trading corporate stock. 'fhe model
includes 40 cohorts of investors who trade
or hold shares each year attempting to
maximize end-of-life wealth. The investors are assumed to have common expectations regarding the rate of return available on shares they do not currently own.
The expected rate of return on stocks in
investors' portfolios is assumed to be normally distributed with a specified standard deviation that determines the sensitivity of the model to changes in tax
rates.
The model is intended to supplement the
knowledge derived from the econometric
analyses that have so far dominated research into the effects of the capital gains
tax. The model simulations include variables for which there are little or no real
world data, for example, the amount of
accrued but unrealized capital gains and
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
LOCK-IN EFFECT
the amount of accrued gains passing
through estates. The model enables examination of the time pattern of capital
gains realizations in response to a tax
change. The econometric studies have
largely been unable to investigate this
time pattern because of limitations in the
available data. Furthermore, the model is
a simplified attempt to model the capital
gains realization process rather than rely
on an ad hoc, reduced form representation. Equations 2, 3, and 4 in the text,
which are the basis of the trading behavior in the model, show that the tax rate
enters the realization decision in a more
complex way than has been incorporated
in the reduced form econometric models.
Model simulations presented in the paper provide several insights. The response of capital gains realizations to a
tax cut in the model has three distinct
phases: the first-year, when capital gains
realizations jump sharply upward; an intermediate phase lasting from 2 to 5 years,
during which realizations decline; and a
longer-term phase, during which realizations rise gradually, not reaching their new
equilibrium level until about 20 years after the tax cut.
The initial jump in trading disproportionately affects shares that have been
held for longer time periods because these
are the shares for which the tax cut decreases trading costs the most. The decreasing realizations during the intermediate phase result from the shorter
average holding periods of traded shares
during this phase. The increase in realizations during the longer-term phase results partially li7om somewhat more active trading by older investors due to the
lower tax rate on gains. Most of the
change, however, results from more active trading by younger investors; as they
become older investors with the passage
of years, they take with them portfolios
with lower levels of accrued gains because they have been traded more actively due to the lower tax rate. The lower
accrued gains in portfolios of older investors directly reduce basis step-up and also
further increase turnover of older investors@ portfolios because the tax cost of
trading is decreased.
91
The simulation results make it clear
that one should not expect a fixed relationship between market turnover rates
and the average holding period of traded
shares or the amount of accrued gain on
traded shares, as has been assumed in
some earlier modelling efforts such as
Bailey (1969). A tax cut, for example, will
increase the turnover rate but will also
more than proportionately
increase the
trading of long-held shares because these
are the ones for which the tax cut reduces
trading costs the most. Indeed, in several
of the tax cut simulations, the turnover
rate increased and so did the average
holding period of traded shares.
Econometric results based on a model
simulation of capital gains realizations
over the period 1954-1988 parallel reasonably closely the results obtained by the
Congressional Budget Office (1988). The
analysis suggests that the intermediate
phase of the capital gains response to a
tax rate change drives the econometric
results (at least over this period of frequent tax rate changes). This further suggests that regressions based on the observed time-series data may overestimate
the long-run revenue responsiveness to a
tax rate change (that is, they may underestimate the long-run responsiveness
of
capital gains realizations to a tax rate
change). The time pattern of the capital
gains response to a tax rate change in the
model also implies that most of the crosssection econometric studies may not have
measured the long-run relationship between the tax rate and capital gains realizations.
A simulation of the capital gains tax cut
proposed by President Bush in 1989 produced results that are consistent with the
claim that the proposal would promote
longer-terin investment while at the same
time reducing lock-in (a claim that, in the
absence of a model like the one reported
here, might seem self-contradictory).
The
simulation results suggest, however, that
the proposal would yield somewhat lower
long-run tax revenues.
Simulations of a policy of taxing capital
gains at death imply that this approach
could substantially
reduce the lock-in effect. With the current capital gains tax
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
NATIONAL TAX JOURNAL
92
rate, the policy would also raise ad(litional
revenue.
Alternatively,
the tax rate
could be reduced to a revenue-neutral
level
and an even greater
decrease
in lock-in
could be achieved.
The development
in the paper points to
several further
avenues
of research
that
might prove fruitful. The first is to learn
more about investor
behavior
in trading
stock. While there are competing
models
in the finance literature
regarding
how
investors
should
behave,
there
seems to
be very little solid information
about how
investors
actually
do behave.
We have
little knowledge
regarding
investor
motivation in stock trading and formation
of
the expectations
on which trading
decisions are based. Such information
would
permit making models such as the one developed in this paper more representative
of the actual stock trading
process.
There are also several
potential
enhandements
to the model that would make
it more representative
and permit
stud y ing a wider range of issues. The decision
of how much of an investor's
portfolio to
use to finance consumption
versus leaving as a bequest,
as well as stock sales to
finance
the consumption,
could be included in the model. Uncertainty
could be
incorporated
into the model, both with regard to expected rates of return and expected life. Dividends
could be included to
focus on shifts between
"growth"
stocks
and "income" stocks as the capital gains
tax rate changes.
Losses could be incorporated in the model to study the effects
of the loss offset rules. Finally, the model
could be embedded
within a more general
model of the flow of funds between alternative investment
markets
to study the
effects of the capital gains tax on realizations and tax revenue
across different
types of investments.
ENDNOTES
**The views in this paper are those of the author
and do not necessarily represent the position of the
Congressional Research Service or the Library of
Congress.
The author wishes to gratefully acknowledge helpfW comments from Gerald Auten, Jane Gravelle, John
Greenlees, Andrew Lyon, Peter merrill, Larry ozarme,
[Vol. XLIII
and Eric Toder on earlier versions of the model. Comments from two anonymous referees were also helpful
ill@repaxing
For
th! final draft of the paper.
summaries and analyses of the first three of
these proposals see Kiefer (1989a) and Kiefer (1989b).
21n fact, Lindsey (1987) argues that the higher capital gains tax rate in the Tax Reform Act will have
this effect.
'See: Feldstein and Yitzhaki (1978), Feldstein,
Slemrod, and Yitzhaki (1980), Minafik (1984), and U.S.
Department of the Treasury (1985).
'In addition to U.S. Department of the Treasury
(1985), see: Lindsey (1986), U.S. Congressional Budget Ofrice (1988), Darby, Gillingham, and Greenlees
(1988), and Jones (1989).
'See: Lindsey (1986), and Gillingham, Greenlees,
and Zieschang (1989).
6See: Auten and Clotfelter (1982), and Auten, Burin7', and Randolph (1989).
For a further discussion of this problem, see: U.S.
Congressional Budget Office (1988), p. 102-103.
8See: Sprinkel and West (1962), Holt and Shelton
(1962), Bailey (1969), and Stiglitz (1983).
9In 1981, for example, gains oD corporate stock constituted 28 percent of total capital gains reported on
individual income tax returns and 35 percent of the
total ignoring gains on personal residences, most of
which is not taxable. See: Clark and Paris (1985-86).
'oMe model is not nemmnly lumted to those stocks
intended to be bequeathed, however. Some investors
y fi,.ce
consumption late in life by borrowing
against the value of appreciated capital assets, or by
borrowing against or selling other assets, to avoid
paying the capital gains tax before death. Furthermore, in the real world, because of uncertainty of the
date of death, some investors no doubt die with stocks
in their portfolios that, had they lived longer, would
have been used to finance consuraption. In terms of
investment strategy, the only distinction bet-een these
stocks and those intended to be bequeathed is the date
on hich their value is to be ma2dmized. Since this
date is beyond the date of death, the representation
in the model closely approximates the trading decision for these shares. (A variation of the model allows
the expected date of death for investors to be set up
to 10 years beyond the actual date of death, resulting
in shares being traded somewhat later in the investors' lives.)
"The distribution of expected rates of return on
portfiolio stocks can be viewed alternatively
as a representation of differences among investors in inclination to trade the shares for whatever reason. The
reasons could be differences in assessment of risk, different tax positions of investors, more or less aggressive trading behavior, etc.
12
While the expected rate of return is assumed to
be distributed normally among investors, each investor is assumed to have deternumsuc expectations. That
is, investors in the model do not take uncertainty into
account in calculating expected returns from alternative investment strategies.
"The model does not incorporate trading strategies
that depend on use of options or futures, that may, in
"perfecv' capital markets, enable investors to avoid
the capital gains tax. For analyses of such strategies
see: Constantinides,
and Scholes (1980), Constantinides (1983), and Stiglitz (1983). Such stmtegies do not,
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
No. 11
91:
LOCK-IN EFFECT
in fact. seem to be used very heavily; see: Poterba
(1986)
"In aggregate terms, of course, the sum of stock
purchases must equal the sum of stock sales. Hence,
in addition to shares purchased fi-om reinvested funds,
new share purchases equal in value to the aggregate
amount of capital gains taxes paid are assumed each
year.
"Equilibrium is defined as a setting in which all
values expressed as fractions of the total value of stocks
in the market remain constant from one year to the
next.
16N%le this assumption greatly simplifies the model,
it does suppress some behavior. In the real world, the
tax system creates an incentive to sell stocks with the
smallest gains among those that have been held for
a given period. In the model, however, all stocks held
for the same period have the same capital gain.
There is a somewhat uncomfortable inconsistency
between the assumption that the prices of all shares
in the market grow at the same constant rate and the
assumed trading behavior, which is based on the belief on the part of investors that they can select superior stocks. But this inconsistency seems to mirror
reality. There seems to be ample anecdotal evidence
that substantial numbers of investors trade and select stocks on the basis of expected superior performance. While one might speculate about how investors maintain faith in the ability to select superior
stocks in the face of performance that, for most investors, over the long term approximates the averagethey might, for example, take disproportionate
satisfaction in the stocks that perform well (or the periods during which their portfolios perform well) and
discount the poor performance of other stocks (or periods)-this
quandary will not be addressed further
here.
"See: Clark and Paris (1985-1986)
"See: New York Stock Exchange, Fact Book 1988,
p. 73.
"See: Henderson (1989), especially Appendix D,
"Data on Transactions Volume."
'The distribution achieved in the model places
somewhat too much share ownership in the oldest cohorts. The actual distribution of share ownership by
age bracket and the distribution within the model are
as follows:
Mean Value
of Shares
Owned
Ratio to
First Age
Bracket
Age Bracket
Less than 35
years
$ 8,934
1.00
35 to 44 years
16,376
1.83
45 to 54 years
21,830
2.44
4.98
55 to 64 years
44,526
65 years and
4.73
over
42,265
Data for mean value of shares owned from:
Bureau of the Census (1986), table 3, p. 14.
Ratio
Within
Model
1.00
1.87
2.43
4.98
5.37
U.S.
"The tax rate used in the model is the maximum
rate on capital ganis in the lughest tax bracket, where
gains am heavily concentrated. The maximum tax rate
on long-term gains was reduced from 28 percent to 20
percent for gains realized after June 20, 1981 in the
Tax Equity and Fiscal Responsibility Act of 1981; the
rate used here is the average of the two rates,
22Let ut@l be aggregate unrealized accrued gains at
a fractioii of total stock value in year t + 1. Then:
-@i -
ut - (r + b)Vt + 9vt
where:
Vt+ 1
Ut = the aggregate amount of unrealize(
gains at time t (measured before re
alizations and basis step-up)
r = realized gains as a fraction of tota
stock value
b = basis step-up as a fraction of tota
stock value
g = the rate of growth of stock prices
Vt = total stock value at time t
In equilibrium, ut@l = ut = u, so Ut = uVt. Substi
tuting these terras into the equation and simplitrini
yields: r + b = g(l - u).
23See: Ross (1989)
24The mainrnurn marginal tax rates are reported ii
U.S. Congressional Budget Office (1988), table 7, p
36. The rates including the ordinary and aiternativ(
tax were used. The 1985 Treasury study used similai
tax rates; it used the marginal tax rate on capital gam
on tax returns with adjusted gross income equal tA
$200,000 or more (in 1982 dollars).
'Me Cochrane-Orcutt procedure was used in all o
the regressions to correct for serial correlation.
'In terms of statistical properties, CBO found thi
equation form to be virtually indistinguishable
fron
equation 6 in the text. The regression on the simu
lated data yielded similar results, as follows:
log (gains) = -12.6447 + 0.9805 Iog (value)
(49.9)
(-32.4)
+ 2.16348 log (100 - MTR)
(28.1)
R2 = .9996
RHO -- 0.834
"CBO found the quadratic equation form to be un
satisfactory; while the overall statistical propertie
remained about the same, the coefficients of the ta)
rate term and the squared tax rate term were not Big
nificant. When a similar regression was performed ox
the simulated data, the squared tax rate term was no
significant; the tax rate term was significant, but ha(
a far lower t statistic than the coefficients in the othe
regressions. The result was as follows:
log (gains)
2.6155 + 0.9842 log (value)
(-9.0)
(39.9)
- 0.028729MTR - 0.0000195MTW
(-3.53)
(-0.13)
le = .9997
RHO = 0.869
'See, for example: Feldstein, Slemrod, and Yit
zhaki (1980), Auten and Clotfelter (1982), Minaril
(1984), and U.S. Department of the Treasury (1985)
'Me actual reaction to the longer holding perioc
requirements
would also include increased realize
National Tax Journal, Vol. 43, no. 1,
(March, 1990), pp. 75-94
94
NATIONAL
TAX JOURNAL
tions the year before the longer period became effective. Under the Bush proposal, for example, gains on
a stock bought on October 1, 1991, would be long-term
if the stock were sold between October 1, 1992, and
December 31, 1992. If the stock were sold between
January 1, 1993, and October 1, 1993, however, the
gains would again be regarded as short-term. This recharacterization
of gains would provide an incentive
for investors with stocks that recently qualified for
long-term treatment to realize the gains before the
longer holding period went into effect. This aspect of
the reaction to the longer holding periods is not captured in the model because, in effect, trading occurs
in the model only once each year at the end of the
year.
REFERENCES
Auten, Gerald E., Leonard E. Burman, and William
C. Randolph, "Estimation and Interpretation
of
Capital Gains Realization Behavior: Evidence From
Panel Data," OTA Paper 67, Ofrice of Tax Analysis,
U.S. Department of the Treasury, May 1989, 28 p.
Auten, Gerald E. and Charles T. Clotfelter, "Permanent Versus Transitory Tax Effects and the Realization of Capital Gains," Quarterly Journal of Economics, November 1982, p. 613-631.
Bailey, Martin J., "Capital Gains and Income Taxation" [in] Harberger, Arnold C. and Martin J Bailey [ed.sl, The Taxation of Income From Capd@al,The
Brookings histitution, Washington, D.C, 1969, p.
11-49.
Clark, Bobby and David Paris, "Sales of Capital Assets, 1981 and 1982," SOI Bulletin, Department of
the Treasury, Winter 1985-86, p. 65-89.
Constantinides, George M., "Capital Market Equilibrium With Personal Tax," Econometrica, May 1983,
p. 611-636.
Constantinides,
George M. and Myron S. Scholes,
"Optimal Liquidation of Assets in the Presence of
Personal Taxes: hnphcations for Asset Pnmng" The
Journal of Finance, May 1980, p. 439-452.
Cook, Eric W. and John F. OHare, "Issues Relating
to the Taxation of Capital Gains," National Tax
Journal, September 1987, p. 473-488.
Darby, Michael, Robert Gillingham, and John S.
Greenlees, "The Direct Revenue Effects of Capital
Gains Taxation: A Reconsideration of the Time-Series Evidence," Research Paper No. 8801, Office of
the Assistant Secretary for Economic Policy, U.S.
Department of the Treasury, May 24, 1988, 9 p.
Feldstein, Martin, Joel Stemrod, and Shlomo Yitzhaki, "The Effects of Taxation on the Selling of
Corporate Stock and the Realization of Capital
Gains," Quarterly Journal of Economics, June 1980,
p. 777-791.
Feldstein, Martin, and Shlomo Yitzhaki, "The Effects
of the Capital Gains Tax on the Selling and Switching of Common Stock," Journal of Public Economics, February 1978, p. 17-36.
[Vol, XLIII
Gravelle, Jane G., A Proposal for Raising Revenue by
Reducing Capital Gains Taxes,? Congressional Research Service, U.S. Library of Congress, June 30,
1987, 10 p.
Gillingham, Robert, John S. Greenlees, and Kimberly
D. Zieschang, "New Estimates of Capital Gains Realization Behavior: Evidence From Pooled CrossSection Data," OTA Paper 66, Office of Tax Analysis, U.S. Department of the Treasury, May 1989,
31 p.
Henderson, Yolanda K., "Capital Gains Rates and
Revenues," New England Economic Review, Federal Reserve Bank of Boston, Jan./Feb. 1989, p. 320.
Holt, Charles C. and John P. Shelton, -The L-ock-In
Effect of the Capital Gains Tax," National Tax
Journal, December 1962, p. 337-352.
Jones, Jonathan D., "An Analysis of Aggregate Time
Series Capital Gains Equations," OTA Paper 65,
Office of Tax Analysis, U.S. Department of the
Treasury, May 1989, 20 p.
Kiefer, Donald W., The Bush Capital Gains Tax Proposal, Congressional
Research Service, U.S. Library of Congress, June 2, 1989a, 28 p.
Kiefer, Donald W., Capital Gains: the Rostenkowski
and JenkinsIPlippolArcher
Tax Cut Proposals,
Congressional
Research Service, U.S. Library of
Congress, August 15, 1989b, 18 p.
Lindsey, Lawrence B., "Capital Gains: Rates, Realizations, and Revenues," NBER Working Paper Series, No. 1893, April 1986, 43 p.
Lindsey, Lawrence B., "Capital Gains Taxes Under
the Tax Reform Act of 1986: Revenue Estimates
Under Various Assumptions," National Tax Journal, September 1987, p. 489-504.
Minarik, Joseph J., "The Effects of Taxation on the
Selling of Corporate Stock and the Realization of
Capital Gains-. Comment," Quarterly Journal of
Economics, February 1984, p. 91-110.
Poterba, James M., "How Burdensome Are Capital
Gains Taxes?," NBER Working Paper Series, No.
1871, March 1986, 33 p.
Ross, Dennis E., Acting Assistant Secretary (Tax Policy), Department of Treasury, Statement Before the
Committee on Finance, United States Senate, March
14,1989.
Sprinkel, Beryl W. and Kenneth West, "Effects of
Capital Gains Taxes on Investment Decisions,"
Journal of Business, April 1962, p. 122-134.
Stiglitz, Joseph E., "Some Aspects of the Taxation of
Capital Gains," Journal of Public Economics, July
1983, p. 257-294.
U.S. Bureau of the Census, Current Population Reports, Series P-70, No. 7, Household Wealth and
Asset Ownership: 1984, 1986.
U.S. Congressional Budget Office, How Capital Gains
Tax Rates Affect Revenues: The Historical Evidence, March 1988, 106 p.
U.S. Department of the Treasury, Report to Congress
on the Capital Gains Tax Reductions of 1978, September 1985, 199 p.