1. finance
2. investing
3. stocks

Why Do So Few Hold Stocks? : Theory and Evidence
En-Te Chen*
ABSTRACT
This study develops a life-cycle model where investors make investment
decisions in a realistic environment. Model results show that personal
illiquid projects (housing and children), fixed costs (once-off/per-period
participation costs plus variable/fixed transaction costs) and endogenous
risky human capital (with permanent, transitory and disastrous shocks)
together are able to address both the non-participation puzzle and the
age-effects puzzle. Empirical implications of the model are examined
using Heckman’s two-step method with the latest five Surveys of
Consumer Finance (SCF). Regression results show that liquidity,
informational cost and human capital are indeed the major determinants
of participation and asset allocation decisions at different stages of an
investor’s life.
* School of Economics and Finance, Queensland University of Technology. This
paper is based on my Ph.D thesis at the University of Melbourne. I am indebted to my
supervisors, Christine Brown, Vance Martin and Simon Wheatley. I would also like to
thank Steven Gray, George Tauchen and Wai-Man (Raymond) Liu for comments and
suggestions. I am responsible for any remaining errors.
A decade ago, Haliassos and Bertaut (1995) asked the question “Why do so few hold
stocks?”, and since then several theoretical and empirical studies have attempted to
address this question.1 Empirical results in Guiso, Haliassos and Jappelli (2002) show
that non-participation in the stock market is commonly observed in every country
studied. At the same time, they also find humped-shape age-effects for both
participation and portfolio share (proportion of wealth in equity). The first finding
leads to the non-participation puzzle, as theory suggests every investor should hold
risky assets. The second finding leads to the age-effects puzzle where younger
households have lower participation and a lower proportion of their wealth in stocks
when theory predicts otherwise.2
This study brings new insights into the understanding of aforementioned
puzzles through its three main components. First, we show that Gomes and
Michaelides (2005) (G&M) do not provide adequate explanation for two puzzles,
despite G&M appears to be the only study claiming success in explaining both
puzzles. After recognizing that there is no conclusive solution to these puzzles, the
second part of this study provides a unique theoretical model that is capable of
generating the observed investment behaviors. The last part of this study is an
empirical study that examines household investment behavior using the latest Survey
of Consumer Finance. Both the theoretical and the empirical part of this study are
unique because of their focus on the examination of how human capital, liquidity and
information costs impact investment decisions. The following discussion argues the
importance of these three aspects and the need to properly account for these aspects in
a portfolio choice study whether theoretical or empirical.
Other than modeling investor behavior that contradicts existing empirical
findings, recent theoretical models also deliver a counter-intuitive conclusion on
human capital; they suggest that human capital is riskless despite the fact that the
2
return of human capital (income) is risky.3 Since human capital accounts for most of
our wealth (Baxter and Jarmann, 1997), it is tempting to use risky human capital to
explain (at least partially) non-participation and low stock holdings amongst the
younger households. For example, in theory, risky human capital negatively affects
the demand of stocks due to (i) the “crowding out effect” and (ii) the hedging motive
when returns from human capital and stocks are positively correlated. In this study,
we attempt to consider human capital in a more realistic context. First, we allow for
heterogeneity in income generating capacity by allowing for two different levels of
education attainment. Households can choose to stay at high school level or take on
further study and obtain a college degree. We further argue that college graduates
have informational advantages and thus incur less informational costs when investing.
Another plausible explanation for the two puzzles is liquidity, because people
who struggle for food and clothing generally do not invest in stock. In the U.S., 17.5%
of the population have less than $500 in financial assets and 99.7% of them do not
have direct holding of stocks.4 Consistent with Faig and Shum (2002), we show that
liquidity factors play a significant role in determining investment decisions. Faig and
Shum (2002) show that households with personal illiquid projects such as housing
purchase save using safer assets. Arguably, the most important personal illiquid
project is to raise and educate children. The Survey of Consumer Finance (SCF)
statistics show that more people save for their children’s education than for housing
purchase. In this respect, we consider three personal illiquid projects in this study,
namely housing, children, and investment in the investor’s own human capital.
Another potential reason behind non-participation lies in the fixed costs of stock
investing. These costs can be tangible costs such as the cost of setting up brokerage
accounts, variable and fixed transaction cost, or intangible costs such as the costs of
obtaining and processing information. In this study, we incorporate both costs by way
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of once-off plus per-period participation costs, and variable plus fixed transaction
costs. Vissing-Jørgensen (2002) reports that individuals who participate in the past are
more likely to participate in the current period, which implies a once-off participation
cost in investing in stocks. Other evidence shows that equity holdings are affected by
distance (Coval and Moskowitz, 1999) and language (Grinblatt and Keloharju, 2001).
These studies support the use of information / participation costs.
In the presence of risky human capital, different liquidity circumstances and
fixed costs, a finite-life investor makes two continuous decisions (how much to invest
in stocks and bonds) and two discrete decisions (participating or not in human capital
and stock investments). Model results show that liquidity, human capital and fixed
costs together are capable of explaining the non-participation and the age-effects
puzzle. In addition, the empirical part of this study also shows that these three aspects
are significant determinants of investment decisions at different stage of investors’ life.
These empirical finds are not only consistent with our existing theory and intuition but
also supportive for the theoretical model developed.
The rest of the paper is organized as follows. Section I shows the empirical
evidence on participation and conditional share and also discusses whether Gomes
and Michaelides (2005) address the two puzzles adequately. Section II describes the
model and the choice of parameters. Section III discusses the model results in terms of
its ability in explaining the two puzzles while Section IV seeks empirical
understandings into these two puzzles. Section V concludes.
I.
Are These Puzzles Resolved?
Gomes and Michaelides (2005) is the only study so far claiming success in solving
both the non-participation puzzle and the age-effects puzzle. This section scrutinizes
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this claim.
A.
Gomes and Michaelides (2005) and the Age-effects Puzzle
Before we proceed, it is worth emphasizing that modeling the data from the SCF in
one year can be very different from modeling the data from the SCF in another year.
This is because participation rates and proportions of financial assets in stocks vary
dramatically across time. Therefore, any model that justifies non-participation based
on static factors may have difficulty explaining non-participation across time.
[*** Insert Figure 1A. here ***]
Figure 1A is taken from Figure 5A of Gomes and Michaelides (2005). The stock
market participation rate implied by their model matches the SCF data particularly
well for household age group that are less than 65 years old, and the implied rate is
higher than the observed for households age 65 or more. However, it applies only to
the 2001 SCF survey, which has a very different stock market participation rate from
earlier surveys. According to Poterba (2001), households are becoming more and
more willing to participate in the stock market due to the “rise of the equity culture”.
[*** Insert Figure 1B. here ***]
Figure 1B shows that there is a strong humped-shape age profile of participation rates
before age 75 in both years. This offers a direct contrast with Gomes and Michaelides
(2005) results in Figure 1A. The difference will be even more pronounced if we use a
narrower age band.
[*** Insert Figure 1C. here ***]
Figure 1C displays the Figure 1B.’s results using a finer partition for the age groups.
In direct contrast to the humped-shape profile, participation rates from G&M stay at
about 50% regardless of the age groupings.5 Thus, their results are consistent only
with the 2001 data using their specific age groups. Once we use a different age group
5
or survey year, it cannot account for the humped-shape age pattern adequately.
B.
Gomes and Michaelides (2005) and the Non-participation Puzzle
The next question is whether the G&M model can account for non-participation. One
might be skeptical about the validity of such a question given that 50% of households
in their model are non-participants (see Figure 1A). However, the result shown in
Figure 1A. combines two groups of investors: one group has 100% participation while
the other group has almost no participation. As indicated in their study,
non-participation
only
occurs
amongst
near-risk-neutral
investors
(RRA=1.07/1.1/1.2).
[*** Insert Figure 1D here ***]
Figure 1D is taken from Figure 4B of their study. In their model, the representative
investor has the Epstein-Zin utility function and saves for two reasons: precautionary
saving or savings due to the elasticity of intertemporal substitution (EIS).6
Figure 1D illustrates that investors with normal relative risk aversion (RRA=2
or 5) still exhibit full participation by the age of 30, which is similar to the results
found in other studies. Non-participation is exclusive to those investors with low RRA
(1.2). Figure 1A represents their model results based on equal weighting of two
groups of investors: moderate-risk-averse investors (RRA=5 and EIS=0.5) and the
near risk neutral investors (RRA=1.2 and EIS=0.2). Therefore, the participation
profile in Figure 1A is approximately the average between the top and the bottom
curves in Figure 1D.7 This “heterogeneity in risk aversion” leads to an average
participation rate of about 50%, which closely matches with the non-participation
rates observed in the 2001 SCF. However, one may criticize the use of such low risk
aversion settings (RRA = 1.2) when other studies consider RRA = 2 for the similar
group. 8 Another criticism is the excessive proportion (50%) of near-risk-neutral
6
investors in the economy.
Other than these two criticisms, the greatest concern lies in the reasons behind
non-participation amongst the near-risk-neutral investors. First, consider the
risk-neutral investor (RRA=1). By definition, risk-neutral investors have no
precautionary saving motives and never save for consumption smoothing. More
specifically, for investors with Epstein-Zin utility, risk-neutrality implies that investors
do not care about the future and hence have no savings. Thus, they will not hold any
stock or bond. Non-participation is merely the results of risk-neutrality since there is
no saving to invest.
For those near-risk-neutral investors, the story is quite similar. Note that they
set the EIS of the near-risk-neutral investors to 0.2 which also implies minimal saving
motives. When RRA=1.2/1.1/1.07 and EIS=0.2, investors will have zero or close to
zero savings depending on their income status. A small group of investors with
unusually high income (simultaneous large positive permanent and transitory income
shocks) will participate in the stock market and save using only stocks. Therefore,
non-participation amongst those near-risk-neutral investors is due to the lack of
savings.9
Therefore, in the G&M model, non-participation is a result of (i) when
near-risk-neutral investors do not have excess income; and (ii) when investors have no
savings. This particular way of achieving non-participation is not very helpful in
explaining the non-participation puzzle since these non-participants have no savings
to participate. They do not make the decision to not to participate, but instead, they
make the decision to not to save. Therefore, their model can only explain
non-participation for minority households without savings. It does not address the
fundamental question about why many savers choose to save only in safe assets
(Haliassos and Bertaut, 1995) despite the high equity premium (Mehra, 1985). Their
7
model is also in contrast with the sample from the latest five SCF, where most
households with positive financial assets choose not to participate in the stock market.
If the G&M study does not provide adequate explanation towards these two puzzles,
what are the alternative explanations? The next two sections attempt to address this
question using a model unique to this study while Section IV examines this question
empirically. Consistent with each other, both the theoretical model and the empirical
study show that human capital, liquidity and information costs (entry costs) are
detrimental in the investment decision making process.
II. The Model
A.
Investors
Investors in this model have finite life and live up to 100 years. Let t denote discrete
adult age corresponding to effective age minus 19. Let Pt A denote the probability an
investor is alive at time ( t + 1 ) conditional on being alive at time t . All investors
enter the model at age 20 ( t = 1 ) and exit the model by the age of 100 if not earlier.
Thus P0A = 1 and P81A = 0 .
A.1. Preferences
Investors’ preferences take the constant relative risk aversion (CRRA) form which is
time-separable and time-additive, given by
u (Ct ) =
Ct1−γ
,
1− γ
u(Ct ) = ln(Ct ),
γ ≠ 1, γ > 0 ,
(1)
when γ = 1 .
(2)
where Ct is consumption at time t and γ represents the (positive definite)
coefficient of relative risk aversion. Let X t denote current cash on hand. Investors
can also generate utility from leaving wealth behind ( X t +1 ) depending on the strength
8
of their bequest motive δ . The bequest function ζ (⋅) is given by
( X t +1 / δ )1−γ
ζ ( X t +1 ) = δ
.
1−γ
(3)
A.2. Human capital
Investors have endogenous human capital which varies depending on age and
education. The associated income process is similar to that used in recent literature.10
Assuming retirement is certain at 65 years of age ( t = 46 ). During the first 46 years of
working life, the investor’s income is give by
ln Yedu ,t = f (t , edu ) + ln(ηt ) + ln(ε1,t ) + ln(ε 2,t ) .
(4)
The last two components of the RHS of equation (4) are temporary shocks and the
first two components are the permanent components of income. f (t , edu ) is a
deterministic function of the investor’s age and education state ( edu ),11 ε 2,t is an
idiosyncratic disastrous shock similar to the one used in Heaton and Lucas (1997),12
ε1,t is an idiosyncratic shock distributed N (0, σ ε2 ) and ηt is given by
1
ηt = ηt −1 + ε 3,t ,
(5)
where ε 3,t is idiosyncratic and is distributed N (0, σ ε23 ) . After retirement ( t > 46 ) the
investor’s retirement income is riskless and is given by
ln Yedu ,t = ln(λ ) + f (46, edu ) + ln(η46 )
for t > 46 .
(6)
Equation (6) implies retirement income is a constant proportion ( λ ) of the permanent
labor income during the last working year.13
B.
Environment
This subsection describes the environment faced by investors from three different
9
aspects. We first describe investment opportunities and constraints, and their personal
illiquid projects. Other aspects are discussed in the third section.
B.1. Investment Opportunities and Constraints
There are three assets investors can invest in. They include two financial assets (bonds
and stocks) and one human capital asset. Holdings a riskless bond Bt generate a
constant return of ( R f − 1 ) while holding a stock St generates a risky return of
( Rts+1 − 1 ), which is distributed N ( µs , σ s2 ) . Following recent studies, investors face the
following constraints:14
Bt ≥ 0 ,
(7)
St ≥ 0 .
(8)
One can easily relax the borrowing constraint by allowing Bt to be greater than a
certain negative amount. However, when borrowings are allowed, Davis, Kubler and
Willen (2004) show that only those in debt and paying an interest rate equal to the
expected return of stocks do not participate. These non-participants have no savings
with which to participate and participation is irrational since paying off the debt gives
the same return as stocks but without risk. Thus, relaxing the borrowing constraint
could not account for non-participation and therefore is not included in this model.
B.2. Personal Illiquid Projects
There are three personal illiquid projects in this model, two of which are exogenously
given while the other one – the human capital investment project is endogenously
given. This model incorporates housing expenditures in the same way as Gomes and
Michaelides (2005). It also incorporates expenditures on children as most households
in SCF save primarily for children’s education. We denote het and cet as the
10
expenditures on housing and children, respectively.
B.3. Other Aspects
Personal illiquid projects and investments described in the preceding sections affect
the evolution of wealth (cash on hand). The next period cash on hand X is given by
X t +1 = Bt R f + St Rts+1 + (1 − het − cet )Yt +1 .
(9)
The above specification is the same as that in Gomes and Michaelides (2005), except
that investors now incur an additional expense on children, cet .
In addition to the above, we also allow for a positive correlation between
income shocks and stock return innovations. More specifically, we allow a correlation
between the permanent shock to income and the stock return innovation (Cocco,
Gomes and Maenhout (2005)). 15 Let ρ s , y denotes the correlation coefficient
between the two shocks.
C. Choices and Optimizations
We now focus on the choices investors have and the optimization problem they face.
C.1. Investor Choices
At time t , investors make two continuous choices, St and Bt , and two discrete
choices, Dentry and Dstudy . Dentry is a dummy variable set to one at time t if the
investor enters the stock market for the first time. Dstudy is another dummy variable
set to one at time t if the investor decides to take on a (two-years) study course.
These four choice variables are the control variables in the model. The investor must
allocates her current cash on hand ( X t ) between consumption, investment in human
11
capital and financial assets.16 This can be summarized by the following expression:
X t = Ct + Bt + St + K edu + Dstudy P5 ,
(10)
where P5 is the associated cost of study and K edu is the transaction costs similar to
Vissing-Jorgensen (2002), which is given by
K edu = Dentry P1 + D part P2 + Da _ part P3 + St P4
(11)
Equation (11) shows that transaction costs K edu comprises of four components. The
first two are participation costs (once-off entry cost and per-period participation cost)
while the other two are tangible transactions costs (fixed and variable). D part
represents the investor’s participation status. It equals one if the investor is already a
participant and zero otherwise. Da _ part is a dummy variable that equals to one if
St > 0 . P1 to P4 represent four different transaction costs: once-off, per-period
participation costs, fixed and variable transaction costs, respectively.17
C.2. The Investor’s Optimization Problem
Investors are rational utility maximizing agents who make decisions that maximizes
expected lifetime utility. The optimization problem can be described by the Bellman
equation below:
Vt ( zt ) = max {u (Ct ) + β E [ Pt AVt +1 ( zt +1 ) + (1 − Pt A )ζ ( X t +1 )} ,
St , Bt , Dstudy
(12)
where zt is the current state that includes current cash on hand ( X t ), education
status ( edu ), participation status ( D part ), states of income ( Yt ) and stock return ( Rts ).
Equation (12) implies that the investor maximizes her lifetime utility V by finding
the optimal trade off between the current consumption {u(Ct )} and the expected
utility derived from future consumption {V ( zt +1 )} and from bequest {ζ ( X t +1 )} .
12
D.
The Solution Method and Parameter Settings
D.1. The Solution Method
There is no analytical solution to this problem. Therefore, to solve the optimization
problem we employ the numerical techniques used in Gomes and Michaelides (2005).
Detailed solution method can be found in Appendix C. The main concepts are as
follows. One can derive the policy functions for four control variables ( St , Bt , Dstudy
and Dentry ) using backward induction based on the Bellman equation (12) subject to
(7) and (8). Since the current period value function ( Vt ) and the policy functions can
be found when Vt +1 is known, the solution can be found by backward induction. The
value function at time T + 1 is trivial and it is given by the bequest function,
ζ ( X T +1 ) . We then use the derived VT +1 to solve for VT using the Bellman equation.
The process continues by backward iterating until t = 1 . Note that we can facilitate
this exercise by exploiting the normalization technique in Deaton (1991). All
monetary variables are normalized by the permanent component of income ( Yt ) and
hence the resulting policy functions are scaled. We multiply the normalized policy
functions or variables by Yt to reinstate the originals.
D.2. Parameter Settings
All parameter values are set in line with other studies. Parameter values are taken
from Deaton (1991) or Carroll (1992) when applicable. Detail parameter settings are
provided in Table I. Note that once-off and per-period participation costs ( P1 , P2 ) are
halved for those who are educated ( edu = 1 ) due to their informational advantages.
f (t , edu ) is based on PSID estimates given in Cocco, Gomes and Maenhout
(2005). 18 Specifically, the educated investor’s income profile { f (t , edu = 1)} is
13
taken from the “college graduates” income profile estimate, while the less educated
{ f (t , edu = 4)} takes the “high school only” estimate in their study. P5 and cet are
calculated using the 2001 SCF and statistics from other studies. 19 The cost of
education ( P5 ) is set to 20% of the income and we assume that during the two-year
studies, students receive partial income equal to 30% of what they used to receive
before study.20 Lino (2002) reports costs of raising a child ranging from six to seven
thousand dollars before the child reaches the age of 18.21 For simplicity, child-related
expenses start when the investor is 28 years old ( t = 9 ) until the child finishes college,
and we assume every investor has one child. The child related expenses are
exogenous and inflexible. The method we adopt is similar to that used in other studies
to incorporate expenditures on housing. Indeed, the focus is on the effect of greater
liquidity needs due from the personal illiquid projects rather than on the decision to
have children or decision on housing purchase.
III. Model Results
A.
Matching Methods
An important issue overlooked by previous studies is the type of asset holdings
constitutes stock market participation. According to the theoretical model, it is the
holding of risky assets that require informational entry cost based on the investor’s
own investment decision. However, in the SCF data, there are numerous risky assets
some of which arguably involve no entry cost or no investment decision. For example,
people can inherit stocks or have stocks given to them as part of their salary package.
There are three main methods of obtaining stocks and they all involve different
information costs. These include stocks that are held directly by the investors, through
stock mutual funds, and through retirement accounts. Total stock holdings are called
“EQUITY” in SCF, which is also the variable other studies used, including Gomes
14
and Michaelides (2005). However, SCF does not ask any question about the
proportion of retirement accounts in stocks. Stock investment in retirement account is
approximated by an internal SCF algorithm. The greatest concern, however, is the
possibility that these investors never made a genuine stock market participation
decision. Using the SCF data, Mitchell (1988) shows that most investors do not know
the type of pension plans they have. For investors who do know their pension plan
and are also involved in a Defined Contribution Plan, Starr-McCluer and Sunden
(1999) show that about a half of these investors do not have the correct knowledge
about the investment option they chose. Therefore, we argue that the stock holding in
retirement accounts is distinctly different from directly-held stocks and inconsistent
with the definition of participation in the theoretical model. One can also argue that
investing in mutual funds requires a lower (if any) informational entry cost than that
in direct stock investment. Therefore, directly-held stock investments, mutual fund
investments and investments in stocks through retirement accounts have different
informational entry costs.
[*** Insert Table II here ***]
Table II reports empirical participation rates and proportions of financial assets in
stocks based on three different categories of stock investment mentioned earlier. The
first row refers to directly-held stocks investments. The second row refers to
directly-held stocks investments and stock investments via mutual funds. The third
row refers to “EQUITY” as defined in the SCF, which includes all stocks in the
second row plus the estimated value of stocks in the investors’ retirement accounts.
The left panel of Table II shows that participation rates can be as high as 51.9%
or as low as 16.9%, depending on how we define “participation” and which survey
year we use. Therefore, matching any particular participation rate from the table is
meaningless because a model that can only produces 51.9% participation rate cannot
15
explain the empirical participation rate if we use a different SCF year or definition of
participation. For a model to be successful in explaining non-participation, it should
be able to produce different participation rates as observed in Table II by varying the
informational participation costs. This is because the main difference between
columns and rows in Table II is the information cost.
The right panel of Table II reports the share of financial assets in stocks
conditional on having financial assets. The percentage of stocks in financial assets
ranges from 4.6% to 29.4% depending on which survey year we used and how we
define “participation”. Interestingly, there seems to be a time trend in the level of
participation and the percentage of stocks in financial assets, as both increases in
time.22 One plausible explanation is the gradual reduction in informational cost due to
more efficient access of information. Therefore, we also need to confirm whether the
decrease in the once-off participation cost and per-period participation cost in our
model can lead to higher participation rates and higher proportion of savings in stocks.
If that is the cases, our model is arguably consistent with the observed variation of
participation through time.
B.
Matching the Population Mean
[*** Insert Table III here ***]
Table III provides the model results across all ages and shows that a higher risk
aversion (γ) leads to a higher level of stock market participation and shares, except
when γ =8. When γ ≤ 5, the precautionary saving motives dominate the human
capital effects (“crowding-out” and “hedging” effect). When γ =8, the human capital
effects begins to dominate the precautionary savings effects.
Table III results show that participation rates and conditional shares are all
within the range observed in Table II when the entry cost is less than 2%. When the
16
entry cost exceeds 2%, we observe below 10% participation rates because the entry
cost is too high and unaffordable for most investors. Surprisingly, the model generates
a reasonable level of non-participation even when the entry cost is only 0.1%, which
is approximate to two hours of salary.23 This implies some potential investors who
have no knowledge of the stock market can be deterred from investing if the entry
requirement is to attend a two-hour stock market introductory free seminar. In contrast,
Gomes and Michaelides (2003, 2005) both produce full participation despite that low
equity premium (4%) and high entry cost (10% and 2.5% of income respectively).
Table III does not distinguish results according to the investor’s education level.
However, as one would expect that the more educated investor always has a higher
level of participation due to his informational advantage.24
The model is also consistent with the rise of the “equity culture” since a lower
entry cost leads to a higher level of stock market participation. This suggests that the
model may explain why the number of stock market participants increased in recent
years as the information cost declined.
C.
Matching the Life-cycle Profiles
C.1. Participation
[*** Insert Figure 3A here ***]
Figure 3A shows the age-effects of stock market participation for each risky asset
group. The humped-shape age pattern is more pronounced for “EQUITY” than the
other two. For “stocks + funds” which includes all risky assets with positive entry
costs, the level of participation increases with age until retirement and it decreases
after retirement.25
[*** Insert Figure 3B here ***]
Figure 3B shows the age-profile of stock market participation when γ =2 and when
17
the entry cost is 0.1%.26 The general trend is that the level of participation increases
until retirement then it decreases after retirement. More and more people join the
stock market as they are building up their wealth for retirement. Higher wealth makes
the stock market entry cost more affordable hence higher level of participation is
observed. After retirement, there is very little incentive to save since the precautionary
saving motive no longer exists due to constant retirement income. However, they may
still save for their heir depending on their willingness to bequeath. In our model, we
set the bequest coefficient ( δ ) to 1. Investors are not punished for leaving wealth
behind but they have no additional incentive to accumulate wealth for their heir. This
lack of additional bequest and precautionary saving imply that investors will run
down their savings and sell off their stocks. The model results are consistent with the
data in the sense that the level of stock market participation increases until retirement
and then decreases. However, the levels of stock market participation for the age
groups 50-60 and 70+ seem too low. There are three reasons behind this pattern. First,
for the age group 50-60, the participation rate drops because many of them are
liquidity constrained after paying their children’s college fees, which happened in
their early 50s. Some of them have to sell all of their stocks to finance consumption,
home loan and college fees. However, a more flexible scheme such as rescheduling
their children’s expenses and home loan repayments at the investor’s discretion can
ease this financial distress, and the sudden drop in participation should disappear.
Note that the empirical participation curve in Figure 3A shows a slight decrease for
age groups 35-39 and 45-49. Each might be related to, respectively, the start of taking
a home loan and sending their children to the college.
Another issue with our model results is the low stock market participation after
retirement and extremely low stock market participation for the age group beyond 75.
If we allow households to retire at any time between 55 and 75 (as people do in the
18
real world), we should see a high level of participation until 65 then gradually drops
as some others are still working and investing for retirement. Participation rates for
the age group 90+ can be increased by having higher bequest motive or by
introducing uncertainty during retirement. Despite these limitations, this model is the
first among relevant studies that shows humped-shape age pattern in stock market
participation.
C.2. Conditional Share
Cocco, Gomes and Maenhout (2005) and Gomes and Michaelides (2005) both show
that the conditional share of wealth invested in stocks decreases as the investor ages.
Both studies attribute this pattern to a decreasing proportion of wealth in riskless
human capital as the investor becomes older.
[*** Insert Figure 3C here ***]
Figure 3C shows the conditional share of financial wealth in stocks using the last five
SCF surveys (1989-2001). The top curve including all three types of stock holdings
which include stock holdings in retirement accounts. The bottom curve excludes
stocks holdings in retirement accounts. We argue the bottom curve is our chosen
benchmark because investments in retirement accounts are quite inflexible. Generally,
investment in retirement accounts only increases until the investor retires then
decreases after. This implies that investment in retirement accounts are bound to be
humped-shape as observed in Figure 3C.
Clearly, conditional share does not decrease as Cocco et al (2005) and Gomes
and Michaelides (2005) have suggested. In fact, according to Figure 3C, the
conditional share increases. This implies that households consider their human capital
as risky assets according to the argument provided in Cocco et al (2005). Since human
capital is an aggregate of the entire risky income streams, it is logical for investors to
19
consider human capitals as risky assets. In Section IV, we present empirical support of
this argument.
[*** Insert Figure 3D here ***]
Figure 3D shows the age profile in conditional share for the case when γ =2 and
entry cost=0.1%.27 As indicated in the figure, shares on average increases with age.
To the best of our knowledge, no existing studies have produced this result. Notice
that the pattern in Figure 3D does not seem to be consistent with Figure 3C. Again
this is because personal illiquid projects are identically and exogenously given to
every investor. For example, many households sell their shares to finance college fees
for their children in their 50s. However, if these personal illiquid projects are
endogenously determined by the investor, we will see a smoother upward trend
instead.
D.
Summary of Model Results
Section III results show that our model is capable of explaining the two puzzles. More
importantly, our model can generate non-participation for all types of investors
regardless of their backgrounds (education, age and risk aversion) and without relying
on extreme background risk assumptions or unusually high / low risk aversion setting.
Furthermore, we show that a reasonably low small entry cost is sufficient to generate
non-participation. Last but not least, for the first time, our model provides a
humped-shape age profile consistent with our observation.
IV. Regression Analysis
This section focuses on examining household investment decisions using the last five
(1989-2001) Survey of Consumer Finance.28 Bertaut and Starr-McCluer (2002) also
have a similar regression analysis using the SCF (1989-1998). Nevertheless, we
20
would like to point out the distinct aspects of our empirical study. First, we provide
new insights to household investment decisions by introducing several new variables
related to liquidity, information costs and human capital. Second, as we focus on the
effects of these three sets of variables that also correspond to the three main aspects of
our theoretical model, this empirical study can provide direct and/or indirect support
for the theoretical model. Therefore and aim and focus of this study are quite different
from the Bertaut and Starr-McCluer (2002) study. Let us elaborate on these
differences below.
In our study, the dependent variable under investigation is the log of
investments. This is different from the Bertaut and Starr-McCluer (2002) study. Their
study uses the ratio of investments on financial assets as the dependent variables and
removes households with financial assets less than $500 who represent 17.5% of the
U.S. population. In our study, we include all households in our sample including these
households with low financial assets because one of the main aspects of interest is
liquidity constraint. This implies the need to use the level of investment not ratio since
8% of the US population has no financial asset and 17.5% with $500 or less in
financial assets.29 This difference in methodology together with new liquidity related
proxies arguably allows for better investigation into the effects of liquidity on
investment decisions.
In the theoretical model, the human capital aspect is equally important to the
liquidity aspect. Thus, we also have a set of human capital related variables to capture
both size and riskiness of the household’s human capital.30 Furthermore, we also
introduce new variables from the SCF that proxy for the level of information cost
faced by different households.31 As we focus on the impact of information cost, the
regression concentrates on the direct stock holdings because indirect holdings through
pension funds or mutual funds have little informational cost, if any.32 These new
21
liquidity, human capital and information cost aspects are deliberately included in this
study and most of the explanatory variables are new compared to the Bertaut and
Starr-McCluer (2002) study. Appendix E provides an annotated list of variables used
in our regression analysis. Appendix F presents a brief description of how we
construct the estimated size of human capital (HC).
A.
Unconditional Age Effects
[*** Insert Table IV here ***]
Table IV reports the Heckman two-step regression results. The Probit regression
models the investor’s participation decision while the OLS regression models the
investor’s investment (level) decision conditional on participation. The bottom three
rows report the estimated correlation between errors across the two equations ( ρ ),
goodness of fit (R2) and sample size. Following Bertaut and Starr-McCluer (2002),
SHOP_AROUND appears only in the participation regression on both economic and
statistical grounds. As discussed, the dependent variable is the log of the direct stock
holdings (LN_STOCKS).
Table IV suggests a humped-shape age profile for both the participation and the
investment decision. All variables are significant at the 1% level.
A.1. Age Effects and the Theoretical Model
It is imperative to understand that, in our theoretical model, age itself per se does not
influence investments. Younger households participate less in the stock market not
because of their age but because of the environment they faced while they are young.
The age profile generated by the model is the result of other factors that correlate with
age, namely human capital and liquidity factors. Thus we expect the humped-shape
age pattern to dissipate when human capital and liquidity regressors are included in
22
the regression.
According to the theoretical model, the crucial factors that should be controlled
for include informational costs, liquidity and human capital factors. To examine the
age-effects in a controlled environment, this study includes these three groups of
variable together with additional control variables. Instead of regressing all 30+
variables immediately, we will first discuss the age effects conditional on each group
separately. Examining these partial results is beneficial as it allows us to investigate
the impact of one particular type of variable on both age effects and investment
decisions. For instance, if by having age and additional human capital variables in the
regression can render humped-shape age patterns insignificant, then this suggests that
the age-effects puzzle can be explained by human capital factors.
In the following subsections we present partial regression results for each of the
four groups of variables. However in our discussion we preempt the results of the full
regression which are presented later in Table IX. The reader may need to refer to
Table IX, when reading the following results.
B.
Partial Regression Results
B.1. Fixed/Information Costs
[*** Insert Table V here ***]
Table V reports age effects and informational effects together. Results show that
education variables are significant in both panels. The more educated individual has
higher participation and a higher level of stock holdings. This is consistent with the
theoretical model results because the more educated individual enjoys higher income
and at the same time benefits from lower informational cost (both per-period
monitoring cost and once-off participation cost). This result remains in the full
23
regression (Table IX).
The other variable of interest is D_IND5 which is a dummy variable that
includes all households working in the financial sector. 33 Due to their superior
knowledge and better access to information, they have higher participation and higher
exposure to the stock market as shown in Table V. Again this result remains in the full
regression.
The humped-shape age patterns remain strong and significant. There is no
plausible reason for the age effects to dissipate here since older people do not
necessarily have higher education nor are they more likely to be in the financial sector.
Overall, Table V results show that information cost has significant impacts on
household investment decisions and the results here are consistent with the results
from the theoretical model.
B.2. Inertia and Other Variables
[*** Insert Table VI here ***]
Table VI reports the age effects with inertia and other effects together. Inertia
variables include race, sex and marital status that may affect one’s investment
decision indirectly through risk preferences, liquidity or other factors. These effects
involve complex issues that are beyond the scope of the theoretical model. They are
not the main focus of this study and are included mainly as control variables.
Results here show that males are more likely to participate and invest more.
This might be associated with different risk preference between males and females.
The results here show D_MARRIED has positive effects, but after controlling for
spouse employment, it is negative (Table IX). The last inertia factor is race. White and
non-Hispanic households have significant higher participation and investments. This
might be due to cultural differences or the fact that such households have
24
informational advantages.
D_TAKE_NO_RISK is a dummy variable equal to one when respondents
indicate that they are not willing to take any financial risk. The results indicate that
these households are less likely to participate and hold proportional less when
participated. The results remain the same in the full regression (Table IX). This is
consistent with the model results in Table III, which shows that the highly risk-averse
investors ( γ >8) have lower participation and portfolio share in stocks.
LN_STOCK_WORKFOR is the log of the amount of investment in a company
the respondent also works for. This variable can control for stock holdings that result
from the remuneration package, which is not the type of investment decision
considered in this study.34 This variable is positive and significant as expected.
The humped-shape age patterns remain strong and significant. This is again as
expected since the inertia variables and other variables included here have little
association with the age variables.
B.3. Liquidity
Liquidity plays an important role in the theoretical model. When facing greater
liquidity needs or/and lower wealth, investors act in a more risk adverse way to avoid
being liquidity constrained. If investors are liquidity constrained, they are said to be in
financial distress because they are trying to finance current consumption through
prohibited borrowings. Thus these investors will suffer from unsatisfactory current
(and possibly future) consumption. The theoretical model shows that those who are or
are close to being liquidity constrained restrain themselves from risky investments.
Possible reasons for the higher probability of being liquidity constrained include
higher liquidity needs, lower current cash on hand, higher income risk and lower
incomes.
25
[*** Insert Table VII here ***]
Table VII reports the age effects and liquidity or financial distress effects on
investment decisions. The only significant life cycle dummy is D_LIFECL4, which
indicates that the respondent is under 55, is not married and has children. These
respondents are in a more financially stressful environment than others and therefore
they invest less or are less likely to invest.
D_BUS_COLLATERAL indicates the respondent has personal assets pledged
as business collateral. This creates greater risks to personal assets and higher chances
of being liquidity constrained. Consequently, this group will avoid taking more risk
and investments. The results here are insignificant; however, they are significant with
the expected sign in the full regression model. LN_HOUSING_DEBT measures the
log of the housing debts. The higher is this debt the higher the liquidity needs, thus the
effects should be negative. However, the results can be distorted by mortgages of
investment properties that have little association with the inability of paying it
outright but more to do with tax incentives. Interestingly, the results here are positive
and significant while it is negative and significant in the full regression model.
D_EMPLOYED and D_SPOUSE_EMPLOYED show the respondent and the
spouse’s employment status respectively. The unemployed tend to have higher chance
of being liquidity constrained and thus employment dummies should have positive
effects. Intriguingly, the two dummies are both significant but with opposite signs in
the participation equation and both negative in the investment decision equation.
These results contradict our expectations. The reason for D_EMPLOYED to have the
unexpected sign is undetermined. Nevertheless, we should be reminded that the
respondent’s employment status is somehow captured by the size of income variable
(LN_NORMINC) and the life cycle dummies. D_SPOUSE_EMPLOYED is
significant and negative here and also in the full regression. This contradicts our
26
expectations since a second source of income helps with liquidity conditions. One
possible reason is as follows. More than 90 percent of the respondents are male and
the spouse’s employment status may indicate the female spouse’s influence over
financial decisions. As discussed, females tend to have lower participation and
investments, thus their influence may be negative in a joint income household.
D_TURN_DOWN indicates the respondent has high self-evaluated risk of
being turned down when applying for credit. These respondents are more likely to be
subject to financial distress. As a result, the coefficient on this variable should be
negative. This is indeed the case both here and in the full regression model. Note this
variable is not in the 1989 survey, hence we lose one year dummy in the regressions.
KIDS represents another important factor in the theoretical model. The theoretical
model shows that having children creates higher liquidity needs and hence lower
participation and lower investment levels. This conclusion is confirmed by the
regressions results.
LN_INHERITANCE is the log of the level of inheritance. The results show a
significant positive impact. The main purpose of including this variable is to capture
the level of stocks owned through inheritance and not through personal investment
decisions. Similar to the LN_STOCK_WORKFOR variable, it can capture investment
that is not self-initiated where no investment decisions involved. Note that higher
inheritance also means higher wealth which can lead to a lower chance of being
liquidity
constrained.
However,
this
effect
is
already
captured
by
the
LN_NETWORTH variable as inheritance is part of wealth.
LN_NETWORTH measures the log of total wealth. LN_NORMINC measures
the log of normal wage income. The regression results for both are significant and
positive. Higher wealth or income means less chance of being liquidity constrained,
thus more participation and investments. From the theoretical model, people with
27
higher level of current cash on hand do participate, and the more wealth they have the
more they invest. On the other hand, the effects of current income mainly come
indirectly through its effect on current cash on hand (wealth) in the model.
Stock investments can also impact on wealth levels. From the SCF, one can
observe that the majority of the wealthy households’ assets are in stocks. However the
direction of causality can not be determined from the results. That is whether it is
because they are wealthy that they invest in stocks or they invest in stocks then they
become wealthy. Unreported theoretical model results show that most wealthy
households invest early and most of their wealth comes from stock investments. This
suggests that the direction of causality is more likely to be both ways.
The humped-shape age patterns no long exist after controlling for liquidity
factors. This demonstrates that liquidity factors are important in explaining why
young people do not participate or invest less. Intuitively, most young people are
faced with low wealth coupled with higher liquidity needs (home loans and children
related expenses), and thus cannot afford to take on further risk and invest in equity.
This is also an outcome from the theoretical model where young investors avoid
stocks because they are closer to being liquidity constrained.
B.4. Human Capital
Human capital represents an important aspect of this study. It affects investment
decisions through its riskiness and size. Higher human capital risk or size can both
lead to lower investments and participation.
[*** Insert Table VIII here ***]
Table VIII reports age effects with human capital effects together. R_HC measures the
proportion of total wealth in human capital. This variable should have a negative
impact on investment decisions. Table VIII confirms our expectation. In fact R_HC is
28
not only the most significant explanatory variable here but also in the full regression
(Table IX). D_ACTIVE_BUS indicates the respondent is actively managing her own
business. This means the nature of the respondent’s human capital is different. One
would expect that the entrepreneurial component of their human capital is more risky
and has higher return. Heaton and Lucas (2000a) show those households have
significantly lower equity investments. Conversely, Table VIII shows significant
positive impacts because wealth is not controlled for in the regression. Full regression
results show that it is negative and significant as we expected.
D_DISABLE_INSURANCE and D_INCOME_CERTAIN both results in lower
human capital risks. Thus both of them should have a positive effect on investment
decisions. The results are generally supportive, except that D_INCOME_CERTAIN is
negative (but not significant) in the investment decision equation.
The humped-shape age patterns are still significant in the participation
regression. Nevertheless, the significance level has changed from the 1 percent to the
10 percent level. Furthermore, the sizes of the age impacts have reduced significantly
when compared to the results in Table IV. In the participation equation, the coefficient
on AGE has dropped from 0.09 to 0.01. In the investment decision panel, we see the
humped-shape age patterns have already dissipated. There are two reasons for this
significant reduction or dissipation in age effects and both of them are related to the
focus variable R_HC. First, R_HC has a highly significant impact on investment
decisions (Table VIII). Second, R_HC has a strong associate with age variables
through the relationship between age and human capital.
In Table VIII, R_HC has the highest t-statistic of -35.87. In terms of coefficient
size, it also has more impact than the other variables. The intuition behind this result
is simple. Human capital is an endowed non-tradable risky asset. When its returns are
positively correlated with equity returns, one can partially hedge this human capital
29
risk by selling equities. Thus the higher is the level of human capital; the higher is this
hedging motive and the lower is equity holdings. Even if the two risks are not
correlated, a higher level of endowed human capital risk can still have a “crowding
out” effect on other risky assets (Viceira, 2001). If one has the majority of wealth in a
risky asset that cannot be traded, she will certainly reduce her holdings in other risky
assets.35
R_HC takes the majority of the explanatory power away from AGE because
young people have higher levels of human capital and thus hold less or no equity at all.
As they grow older, the endowed risky human capital depletes and leaves more space
for other risky assets. If the correlation between returns from human capital and
stocks is positive, lower human capital will at the same time reduce the hedging
motive. Thus the investor will be more willing to invest in stocks. Therefore stock
investments can increase with age due to human capital effects. After retirement,
investors start to consume away their lifetime savings, so stock investments tend to
decrease.
The partial results from Tables V to Table VIII suggests the two groups of
variables that can potentially explain the age-effects puzzle are liquidity and human
capital variables, which also encapsulate the two key features of the theoretical model
developed.
C.
Full Regression Results
Table IX reports the full regression results using the “step-down” method to eliminate
insignificant variables.
[*** Insert Table IX here ***]
Most of the results here are consistent with the partial results discussed in previous
sections. Again, R_HC is the most significant explanatory variable with the highest
30
impact on both investment decisions. The only one contradictory to our expectation is
the coefficient on D_EMPLOYED. We can find no plausible explanation for this
result other than to argue that it is possibly due to the explanatory power of
D_EMPLOYED being reduced by LN_NORMINC and life cycle dummies. However,
this still does not explain why it is negative and significant in the investment
regression. Nevertheless, the overall results are supportive of the theoretical model
and consistent with intuition.
D.
Summary of Results
The above regression results demonstrate that non-participation and level of exposure
to the stock market are related to liquidity, human capital and informational factors.
Furthermore, the age-effects puzzle can be explained by liquidity or/and human
capital factors. Interestingly, Table IX results show that the marginal effect of age is
that younger households participate and invest more, which is consistent with results
from Bodie, Merton and Samuelson (1992), where they argue that young people can
afford to have more exposure to stocks because of their greater labour supply
flexibility.
V. Conclusion
This paper presents a life-cycle model with realistically calibrated investment
environment – heterogeneous human capital and education attainment, personal
illiquid projects including housing and children, and comprehensive investment costs
including fixed and variable transaction costs and once-off and per-period
participation costs. This model is able to generate observed participation rates even
when the entry cost is as little as 0.1% of annual income, without relying on assuming
a low equity premium, extreme assumptions about background risk or extreme values
31
for the investor’s risk aversion. Furthermore, for the first time, the model is able to
generate a humped-shape age pattern widely observed across countries. This study
also empirically examines the impacts of these three factors (human capital,
information and liquidity) found detrimental in the theoretical model using formal
regression analysis. Regression results provide strong supports for the theoretical
model.
Despite its success in tackling the two puzzles, the model still has several
limitations that make the model assumptions and results deviate from reality. First, the
model fails to properly account for investments in durable goods like housings.
Housing expense is only exogenously given to all investors. Second, the model
incorporates child-related expenses (including college fees) in an unrealistic manner.
In the model, investors always have one child at the same age, and send their child to
college at the same time. Third, the model has a simple retirement arrangement as
investors all retire at the same age and receive risk free income after retirement.
It is possible to extend our model by endogenizing the housing decision and
allow households to have a different number of children at different age at their own
will. Alternative retirement arrangement can also be considered if we allow for the
timing decision on retirement. However, these are computational costly decisions to
incorporate, as the ability to make each of these decisions at each point in time will
each add one dimension to the model.
32
Appendix A: List of Notations
B
bond holding
C
consumption
ce
children related expense
edu
equals to 1: educated 2: second year 3: first year student 4: less educated
Da _ part
dummy variable, set to one if St >0.
Dentry
dummy variable, set to one when entering the stock market for first time.
D part
dummy variable, set to one when the investor has paid the entry cost.
Dstudy
dummy variable, set to one for year the investor decides to study
he
housing expenditure
K
transaction costs.
Pt A
probability of being alive at time t+1 conditional on being alive at time t
P1
stock market entry cost.
P2
per-period participation cost.
P3
fixed transaction cost.
P4
variable transaction cost.
P5
fees for further education.
Rf
gross riskfree return
Rts
gross stock return between time t-1 to time t
S
stock
t
time index t ∈ {0,1,2,..., T }, T ≤ ∞
u
time separable and additive utility function
V
value function
33
X
cash on hand
Y
labour income
Y
conditional mean of labour income/permanent component of income
zt
current state
α
discount factor applied to P1 when experienced in the other risky asset.
β
discount factor
δ
measure the strength of the bequest motive
γ
coefficient of relative risk aversion
λ
replacement ratio.
ηt
the random walk component of income
ε1,t
transitory income shock
ε 2,t
disasterous income shock
ε 3,t
permanent income shock on ηt
ρ s, y
coefficient of correlation between ε 3 and stock innovations
ζ
bequest function
34
Appendix B: The Four Education Statuses
Linking Education States
Educated
(edu=1)
Educated
(edu=1)
Second Year Student
(edu=2)
Second Year Student
(edu=2)
First Year Student
(edu=3)
First Year Student
(edu=3)
Decide to Study
Less Educated
(edu=4)
Decide NOT
to Study
Now
Appendix C:
Less Educated
(edu=4)
Next Period
Numerical Solution Method
The solution method involves backward induction based on the Bellman equation. All
monetary variables are normalized by the permanent component (conditional mean)
35
of labor income ( Yt ). Thus, the transition equation, Bellman equation and resulting
policy functions are all rewritten in terms of these normalized variables. Following
Deaton (1991), normalized variables are in lower case (for instance, xt = X t / Yt ).
At time ( T + 1 ), policy functions are known and the value function is the same
as the bequest function {s( zT +1 ) = b( zT +1 ) = Dstudy ( zT +1 ) = 0; V ( xT +1 ) = ζ ( xT +1 )} . At
time T , one can find the policy functions and also the value function ( VT ) using the
Bellman equation and the value function just obtained ( VT +1 ). This procedure is then
iterated backwards until time ( t = 1 ).
Note, one should be cautious when performing the above iteration regarding the
state space of the value functions. In this case, the value function has six dimensions
since there are six state variables, z = {t , D part , edu, Rts , Yt , X t } . To find Vt ( zt ) , one
must obtain Vt +1 ( zt ) from the appropriate space within each of the six dimension. To
elaborate on this point, let us focus on the edu dimension for an example. Appendix
B shows how each education state evolves. If the investor has not yet taken up any
study, solving for Vt ( zt , edut = 4) requires Vt +1 ( zt +1 , edut +1 = 4) if she decides not to
study ( Dstudy = 0 ) or Vt +1 ( zt +1 , edut +1 = 3) if she decides to study ( Dstudy = 1 )
The numerical optimization is achieved by grid search which avoids finding
local optima. Equal-space grids are created for continuous monetary variables
including xt , st and bt . The expectation function in the Bellman equation is
replaced by matrix multiplication using Gaussian quadrature methods from Tauchen
and Hussey (1991). The upper bound of xt is chosen to be non-binding in all
periods.
We use at least 100 grids for cash on hand ( x ). However, Vt +1 ( zt +1, xt +1 ) still
requires interpolation when the next period cash on hand ( xt +1 ) resides between the
36
grid points. This study applies the cubic spline interpolation on the next period value
functions ( Vt +1 ). This method is also chosen by other studies due to its advantage of
being continuously differentiable.
Appendix D: The Survey of Consumer Finance
This study draws on the Survey of Consumer Finances (SCF) as the data source for
empirical analyses. SCF is arguably the most comprehensive survey for household
financial decisions in the United States. In recent years, the SCF sample has consisted
of about 3,000 households randomly drawn from a standard representative sample,
supplemented by about 1500 households drawn from a special high wealth sample
based on tax records. In order to convert the sample into a sample representative of
the US population, each observation is assigned a sample weight which indicates how
many households this observation represents. Sample weights allow users to provide
descriptive analysis representative of the population as a whole. This is the “Dual
frame” sample design that provides adequate representation of both broadly-held
items, like homes and vehicles, and other items, like stocks and bonds, held
disproportionately by the wealthy.
The SCF is conducted by the Board of Governors of the Federal Reserve System
every three years since 1983. The SCF data set is comprehensive, altogether there are
about 2,700 main variables in the data set, of which about 500 variables are from
questions about dollar amounts. Some of the financial behaviors measured by the
survey are relatively rare—for example, the respondent’s degree of risk aversion. This
study uses the latest five waves of SCF which includes the 1989, 1992, 1995, 1998,
2001 surveys. All dollar amounts are in 2001 dollars and all descriptive statistics
incorporate the sample weights.
37
Appendix E: List of Regression Variables
Variable Name
Definition
Dependent Variables
LN_STOCKS*
direct investment in stocks
LN_FOREIGN_STOCKS*
direct foreign stocks holding
R_STOCKS_FIN*
ratio of STOCKS to financial assets
R_EQUITY_FIN
ratio of EQUITY to financial assets
Independent Variables
AGE
age of the respondent
AGE2
age squared divided by 1000
D_1989
1989 SCF
D_1992
1992 SCF
D_1995
1995 SCF
D_1998
1998 SCF
D_2001*
2001 SCF
D_ACTIVE_BUS*
actively managing own business
D_BUS_COLLATERAL*
use personal asset as business collateral
D_DISABLE_INSURANCE* have disable insurance
D_EDU1
no high school or diploma
D_EDU2
high school or diploma
D_EDU3
some college
D_EDU4
college degree
D_EMPLOYED*
employed
D_INCOME_CERTAIN*
income is certain for the next few years
D_IND5*
working in industry group 5 including banking and finance
D_LIFECL1*
under 55 + not married + no children
D_LIFECL2*
under 55 + married + no children
D_LIFECL3*
under 55 + married + children
D_LIFECL4*
under 55 + not married + children
D_LIFECL5*
55 or older and working
D_LIFECL6*
55 or older and not working
38
D_MALE
male
D_MARRIED
married or living with partner
D_SPOUSE_EMPLOYED*
spouse employed
D_TAKE_NO_RISK
take no risk at all
D_TURN_DOWN*
high self-evaluated risk of being turn down from applying credit
D_WHITE
white and non-Hispanic
EQUITY
all holdings of stocks, including STOCKS, STOCKFUNDS etc
INV_MILLS
the Inverse Mills ratio
KIDS*
number of dependent children
LN_HOUSING_DEBT*
housing debt
LN_INHERITANCE*
inheritance
LN_NETWORTH
total assets less total debt as defined in the public SCF
LN_NORMINC
normal income
LN_STOCKS_WORKFOR* holdings of stocks in a company that the respondent also work for
ratio of human capital to total wealth (NETWORTH+HC)
R_HC*
1-10 scale of the degree of shopping for investment/saving
SHOP_AROUND
1 = least shopping
All monetary variables has prefix of “Ln_” to indicate that they are in nature logs. Prefix “D_”
indicates the variable is a dummy variable and “R_” is for ratio variables.
* New variables compared to Bertaut and Starr-McCluer (2002)
Appendix F: Constructing Human Capital
Human capital is the investor’s expected total non-financial incomes in present terms.
Thus, if we can estimate an investor’s expected income at different age, we can
estimate the value of her human capital with appropriate discounting.
Estimated incomes are generated using the approach similar Moskowitz and
Vissing-Jorgensen (2002) by regressing the log of hourly wage on age, age squared,
dummies for education attainment, work industries, marital status, sex, race and active
managerial role in own business. The following table reports the earning regression
39
results.
Table: The Earning Regression
Coeff.
S.E.
AGE
0.059**
0.00
AGE2
-0.444**
0.03
D_EDU1
-0.851**
0.01
D_EDU2
-0.509
**
0.01
D_EDU3
-0.364**
0.01
D_IND1
0.414
**
0.05
D_IND2
1.043**
0.05
D_IND3
1.137**
0.05
D_IND4
0.956
**
0.05
D_IND5
1.169**
0.05
D_IND6
1.061
**
0.05
D_IND7
1.006**
0.05
D_MALE
0.285**
0.01
D_MARRIED
0.474
**
0.01
D_WHITE
0.135**
0.01
**
0.01
0.162
D_ACTIVE_BUS
R2
0.314
**
Significant at 1 percent level. * Significant at 5 percent level
+
Significant at 10 percent level.
All regressors are significant at the one percent level including the dummy for active
management in one’s own business. Heaton and Lucas (2000a) found that
entrepreneurs tend to hold less proportion of their assets in stocks. The
D_ACTIVE_BUS variable is included to account for possible size difference between
entrepreneurial and ordinary human capital.
Estimated earnings at different age until retirement are discounted and
aggregated to form the estimated human capital. The discount rate is 6%. However,
40
conclusions remain the same for values ranging from 2% to 10%. Six percent is
chosen because it is close to but still lower than the expected equity return of 8% used
in the model. In other word, human capital is risky but less risky than equities.
Everyone is assumed to work full time until 65 years of age. The estimated total
human capital is about 60 percent of the total wealth (including both human capital
and non-human capital wealth). This is consistent with the estimation obtained by
Baxter and Jermann (1997).
References
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vary with age?, Working Paper. Columbia University
Baxter, Marianne, and Urban J. Jermann, 1997, The international diversification
puzzle is worse than you think, The American Economic Review 87,
170-180.
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united states, in Luigi Guiso, Michael Haliassos, and Tullio Jappelli, eds.:
Household Portfolios (MIT Press, Cambridge, MA).
Bodie, Zvi, Robert C. Merton, and William F. Samuelson, 1992, Labor supply
flexibility and portfolio choice in a life cycle model, Journal of Economic
Dynamics and Control 16, 427-449.
Campbell, John Y., Joao F. Cocco, Francisco J. Gomes, and Pascala J. Maenhout,
2001, Investing retirement wealth: A life-cycle model, in John Y. Campbell,
and Martin S. Feldstein, eds.: Risk Aspects of Investment-Based Social
Security Reform (University of Chicago Press).
Campbell, John Y., and Luis M. Viceira, 2001. Strategic Asset Allocation: Portfolio
Choice for Long-Term Investors (Oxford University Press, New York).
Carroll, Christopher, 1992, The Buffer-Stock Theory of Saving: Some
Macroeconomic Evidence., Brookings Papers on Economic Activity 2,
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Cocco, Joao F., Francisco J. Gomes, and Pascala J. Maenhout, 2005,
Consumption and portfolio choice over the life-cycle, Review of Financial
Studies 18, 491-533.
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Coval, Joshua D., and Tobias J. Moskowitz, 1999, Home bias at home: local
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demand for equity over the life cycle, Working paper. University of
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1221-1248.
Faig, Miquel, and Pauline Shum, 2002, Portfolio choice in the presence of
personal illiquid projects, Journal of Finance 57, 303-328.
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household portfolios, in Luigi Guiso, Michael Haliassos, and Tullio
Jappelli, eds.: Household Portfolios (MIT Press, Cambridge, MA).
Gomes, Francisco, and Alexander Michaelides, 2003, Portfolio choice with
internal habit formation: A life-cycle model with uninsurable labor
income risk., Review of Economic Dynamics 6, 729-766.
Gomes, Francisco, and Alexander Michaelides, 2005, Optimal life cycle asset
allocation: understanding the empirical evidence, Journal of Finance 60,
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culture influence stockholdings and trades, Journal of Finance 56,
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Portfolios (MIT Press, Cambridge, MA).
Haliassos, Michael, and Carol C. Bertaut, 1995, Why do so few hold stocks?, The
Economic Journal 105, 1110-1129.
Haliassos, Michael, and Alexander Michaelides, 2003, Portfolio choice and
liquidity constraints, International Economic Review 44, 143-177.
Heaton, John, C., and Debra J. Lucas, 2000b, Portfolio choice in the presence of
background risk, The Economic Journal 110, 1-26.
Heaton, John C., and Debrorah J. Lucas, 2000a, Portfolio choice and asset prices:
the importance of entrepreneurial risk, Journal of Finance 55, 1163-1198.
Heaton, John, and Debra Lucas, 1997, Market frictions, savings behavior, and
portfolio choice., Macroeconomic Dynamics 1, 76-101.
Heckman, James J., 1979, Sample selection bias as a specification error,
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U.S. Department of Agriculture, Center for Nutrition Policy and Promotion.
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Mehra, Rajnish, and Edward C. Prescott, 1985, The equity premium: A puzzle,
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Labor Economics 6, 21-39.
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Entrepreneurial Investment: A Private Equity Premium Puzzle?,
American Economic Review 92, 745-778.
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patterns, 1989-1998, Working paper. Hoover Institution
Rubin, Donald B., 1987. Multiple Imputation for Nonresponse in Surveys (John
Wiley and Sons, New York).
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Vissing-Jorgensen, Annette, 2002, Towards an explanation of household portfolio
choice heterogeneity: Nonfinancial income and participation cost
structures, Working paper. University of Chicago
Figures
43
Figure 1A. Stock market participation rates implied by the Gomes and
Michaelides (2005) model. Source: Figure 5A of Gomes and Michaelides
(2005)
70%
60%
50%
40%
30%
20%
10%
0%
Age < 35
Age: 35-44
Age: 45-54
Age: 55-64
Age: 65-74
Age >= 75
Age Groups
1989
2001
Figure 1B. Stock market participation rate from the 1989 and 2001 samples
of the SCF.
70%
60%
50%
40%
30%
20%
10%
0%
[20: 24]
[25: 29]
[30: 34]
[35: 39]
[40: 44]
[45: 49]
[50: 54]
[55: 59]
[60: 64]
[65: 69]
[70: 74]
[75: 95]
Age Groups
2001
1989
Figure 1C. Stock market participation rate from the 1989 and 2001 samples
of the SCF.
44
Figure 1D. Stock market participation rate for different values of the
coefficient of RRA taken from Figure 4B of Gomes and Michaelides (2005).
70%
60%
50%
40%
30%
20%
10%
0%
[20: 24]
[25: 29]
[30: 34]
[35: 39]
[40: 44]
[45: 49]
[50: 54]
[55: 59]
[60: 64]
[65: 69]
[70: 74]
[75: 95]
Age Groups
STOCKS
EQUITY
Stocks+funds
Figure 3A. Stock market participation rate from the 2001 sample of the
SCF for different types of holdings.
45
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
[20: 24]
[25: 29]
[30: 34]
[35: 39]
[40: 44]
[45: 49]
[50: 54]
[55: 59]
[60: 64]
[65: 69]
[70: 74]
[ 75+ ]
Age Groups
Figure 3B. Stock market participation rate for the case when RRA=2 and
entry cost=0.1%.
30.0%
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
[20: 24]
[25: 29]
[30: 34]
[35: 39]
[40: 44]
[45: 49]
[50: 54]
[55: 59]
[60: 64]
[65: 69]
[70: 74]
Age Groups
Stock+Funds
Equity
Figure 3C. Proportion of financial assets in stocks from the 1989, 1992, 1995,
1998 and 2001 samples of the SCF.
46
[75: 95]
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
[20: 24] [25: 29] [30: 34] [35: 39] [40: 44] [45: 49] [50: 54] [55: 59] [60: 64] [65: 69] [70: 74] [ 75+ ]
Age Groups
Figure 3D. Share of Wealth invested in stocks when RRA=2 and entry cost
is 0.1%
Tables
Table I
Parameter Settings
Parameter
Value
p1
0.1 ~ 5%
p2
0.2 p1
p3
0.1 %
P4
0.1%
p5
0.2
Rf
1.02
Rts
N (1.08,0.0324)
β
0.9
47
γ
2, 3, 5, 8
δ
1
λ
0.9
σε
0.08
3
σε
0.1
ρ s, y
0.2
ε 2,t
⎧0.5 | prob(0.65%)
=⎨
⎩ 1 | prob(0.9935)
1
Note: Yt ,edu =2 = Yt −1,edu =3 = 0.3Yt −2,edu =4 and p1,edu =1 = 0.5 p1, edu =4
Table II
Average Stock Market Participation Rate and Average Share of Wealth in Stocks
for different Survey Years and Different Definitions of Participation
Source: Author’s tabulation using the 1989 and 2001 samples of Survey of Consumer finance (detail in
Appendix D). First row “Stocks” refers to directly-held stocks. Second row “Stocks&Funds” refers to
directly-held stocks and stocks indirectly held through mutual funds. Third row “Equity” includes all
forms of stock holdings (SCF variable name EQUITY), including stock investments in retirement
accounts.
Participation
Conditional Share
1989
2001
1989
2001
Stocks
16.9%
21.3%
4.6%
5.8%
Stocks&Funds
20.5%
30.5%
6.4%
11.3%
Equity
31.8%
51.9%
11.7%
29.4%
48
Table III
Model Results for Average Stock Market Participation Rate and Average Share
of Wealth in Stocks for Different Values of Both the Entry Cost ( p1 ) and the
Coefficient of Risk Aversion ( γ )
All statistics are age-weighted using 2001 SCF age density
Average Participation Rate
p1 = 0.1%
p1 = 0.5% p1 = 1% p1 = 2% p1 = 5%
Gama = 2
33.9%
32.4%
22.4%
2.9%
0.0%
Gama = 3
37.7%
36.2%
30.8%
13.6%
0.6%
Gama = 5
50.4%
49.1%
48.2%
44.1%
32.2%
Gama = 8
45.0%
41.6%
36.1%
29.2%
19.3%
Average Proportion of Savings in Stock
p1 = 0.1%
p1 = 0.5% p1 = 1% p1 = 2% p1 = 5%
Gama = 2
53.7%
50.5%
36.8%
16.3%
5.6%
Gama = 3
52.1%
49.8%
43.5%
25.1%
10.0%
Gama = 5
54.5%
52.8%
51.5%
47.4%
36.3%
Gama = 8
37.0%
34.1%
30.3%
25.8%
19.4%
Table IV
Unconditional Age Effects on Participation and Investment Decisions
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Probit
Intercept
-3.28**
49
0.10
Coeff.
S.E.
OLS
-2.19
1.52
AGE
0.09**
0.00
0.34** 0.04
AGE2
-0.65**
0.03
-2.29** 0.28
D_1992
-0.03
0.03
0.40** 0.11
D_1995
-0.04
0.03
0.35** 0.11
D_1998
0.06+
0.03
1.11** 0.11
D_2001
0.10**
0.03
1.23** 0.11
SHOP_AROUND
0.04**
0.00
1.54** 0.48
Inverse Mills Ratio
Estimate of ρ
R
0.47
2
Sample Size
0.17
100,475
31,567
Table V
Effects of Informational Cost on Participation and Investment Decisions
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Probit
Coeff.
S.E.
OLS
-2.26**
0.11
AGE
0.06**
0.00
0.31**
0.03
AGE2
-0.38**
0.04
-1.85**
0.24
D_EDU1
-1.52**
0.04
-4.79**
0.76
D_EDU2
-0.92**
0.03
-3.13**
0.44
D_EDU3
-0.54**
0.03
-1.85**
0.26
D_IND5
0.38**
0.03
1.52**
0.17
Intercept
50
-2.00
1.60
D_1992
-0.10**
0.03
0.22*
0.11
D_1995
-0.13**
0.03
0.17
0.12
D_1998
-0.04
0.03
0.92**
0.11
D_2001
-0.01
0.03
0.98**
0.10
2.33**
0.66
SHOP_AROUND
0.03**
0.00
Inverse Mills Ratio
Estimate of ρ
0.64
R2
0.25
Sample Size
100,475
31,567
Table VI
Effects of Inertia and others Factors on Participation and Investment Decisions
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Probit
Coeff.
S.E.
OLS
-3.09**
0.11
-8.04**
2.29
AGE
0.06**
0.00
0.33**
0.04
AGE2
-0.33**
0.04
-1.92**
0.24
D_MALE
0.29**
0.04
1.48**
0.21
D_MARRIED
0.25**
0.03
0.79**
0.16
-1.00**
0.03
-4.02**
0.57
Intercept
D_TAKE_NO_RISK
51
D_WHITE
0.55**
0.03
LN_STOCK_WORKFOR
2.20**
0.34
0.08**
0.01
D_1992
-0.02
0.04
0.43**
0.11
D_1995
-0.12**
0.03
0.12
0.12
D_1998
-0.03
0.03
0.90**
0.11
D_2001
0.01
0.03
1.00**
0.10
SHOP_AROUND
0.02**
0.00
3.34**
0.76
Inverse Mills Ratio
Estimate of ρ
0.74
R2
0.25
Sample Size
100,475
31,567
Table VII
Effects of Liquidity on Participation and Investment Decisions
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Coeff.
Probit
S.E.
OLS
Intercept
-4.64**
0.15
-19.22**
0.99
AGE
-0.01*
0.00
-0.02
0.01
AGE2
0.09*
0.04
D_BUS_COLLATERAL
0.02
0.04
52
0.36**
-0.12
0.11
0.08
D_EMPLOYED
0.13+
0.07
-0.54**
0.20
0.41+
0.24
D_LIFECL1
-0.14
0.09
D_LIFECL2
-0.17+
0.09
-0.12
0.23
D_LIFECL3
-0.17+
0.09
-0.11
0.23
D_LIFECL4
-0.28**
0.10
-0.66*
0.29
D_LIFECL5
-0.16+
0.08
0.14
0.23
D_SPOUSE_EMPLOYED
-0.10**
0.03
-0.69**
0.06
D_TURN_DOWN
-0.25**
0.04
-1.57**
0.15
LN_HOUSING_DEBT
0.01**
0.00
0.01**
0.01
LN_INHERITANCE
0.03**
0.00
0.12**
0.01
LN_NETWORTH
0.11**
0.01
0.76**
0.03
LN_NORMINC
0.25**
0.01
1.27**
0.05
KIDS
-0.05**
0.02
-0.18**
0.04
D_1992
-0.03
0.04
0.27**
0.09
D_1995
-0.08*
0.04
0.07
0.09
D_1998
0.05
0.04
0.97**
0.08
D_2001
0.06
0.03
0.91**
0.08
SHOP_AROUND
0.03**
0.00
4.96**
0.23
Inverse Mills Ratio
Estimate of ρ
0.85
R2
0.57
Sample Size
100,475
53
31,567
Table VIII
Effects of Human Capital on Participation and Investment Decisions
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Probit
Coeff.
S.E.
OLS
Intercept
0.17
0.16
14.39** 0.58
AGE
0.01+
0.01
-0.03+
0.02
AGE2
-0.29**
0.05
-0.11
0.18
R_HC
-2.12**
0.06
-7.76** 0.59
D_ACTIVE_BUS
0.28**
0.03
0.46** 0.10
D_DISABLE_INSURANCE
0.37**
0.03
0.43** 0.12
D_INCOME_CERTAIN
0.14**
0.03
D_1998
0.12**
0.03
0.61** 0.09
D_2001
0.15**
0.03
0.60** 0.09
SHOP_AROUND
0.05**
0.01
-0.05
0.83*
Inverse Mills Ratio
Estimate of ρ
0.36
R2
0.46
65,230
Sample Size
54
0.09
0.41
20,709
Table IX
Full Regression Results
This table reports the Heckman two-stage regression results based on the 1989, 1992, 1995, 1998 and
2001 Survey of Consumer Finance. The Probit regression models the household’s participation decision
while the OLS regression models the household’s investment decisions (amount of stocks to invest).
The dependent variable is the log of the value of stocks (LN_STOCKS). Appendix E provides a list of
definitions for all independent variables. ** indicates significant at 1 percent level. * Indicates significant
at 5 percent level. + Indicates significant at 10 percent level.
Coeff.
S.E.
Probit
Coeff.
S.E.
OLS
Intercept
-1.83**
0.19
AGE
-0.02**
0.00
-0.09**
0.01
AGE2
0.11*
0.05
0.72**
0.13
R_HC
-1.09**
0.06
-5.14**
0.27
D_ACTIVE_BUS
-0.12**
0.03
-0.25**
0.08
D_EDU1
-0.70**
0.05
-2.37**
0.23
D_EDU2
-0.45**
0.03
-1.45**
0.11
D_EDU3
-0.24**
0.03
-0.70**
0.10
D_IND5
0.17**
0.03
0.37**
0.07
D_LIFECL2
0.07+
0.04
0.46*
0.18
D_MALE
0.18**
0.04
0.50**
0.13
D_TAKE_NO_RISK
-0.57**
0.03
-1.83**
0.14
D_TURN_DOWN
-0.09+
0.05
-0.93**
0.15
D_WHITE
0.24**
0.04
0.64**
0.12
LN_INHERITANCE
0.02**
0.00
0.04**
0.01
LN_NETWORTH
0.05**
0.01
0.29**
0.02
LN_NORMINC
0.14**
0.01
0.72**
0.02
55
D_1998
0.07*
0.03
0.56**
0.08
D_2001
0.07*
0.03
0.42**
0.07
D_DISABLE_INSURANCE
0.13**
0.03
SHOP_AROUND
0.02**
0.01
D_BUS_COLLATERAL
-0.17+
0.10
D_EMPLOYED
-0.29+
0.17
D_INCOME_CERTAIN
-0.13*
0.07
D_LIFECL1
0.31+
0.18
D_LIFECL3
0.41*
0.17
D_LIFECL5
0.40*
0.17
D_MARRIED
-0.39**
0.13
D_SPOUSE_EMPLOYED
-0.33**
0.07
LN_HOUSING_DEBT
-0.02**
0.01
LN_STOCK_WORKFOR
0.09**
0.01
Inverse Mills Ratio
3.07**
0.23
Estimate of ρ
0.86
R2
0.63
84,760
Sample Size
20,709
Endnotes
1
See, for instance, Vissing-Jorgensen (2002) and Bertaut and Starr-McCluer (2002) for U.S. empirical
studies; Heaton and Lucas (1997, 2000b), Viceira (2001) and Haliassos and Michaelides (2003) for
infinite-horizon theoretical models; Campbell, et al. (2001), Cocco, Gomes and Maenhout (2005),
Davis, Kubler and Willen (2004) and Gomes and Michaelides (2003, 2005) for finite-horizon
56
theoretical models.
2
Bodie, Merton and Samuelson (1992) argue that everyone should hold risky assets and young
investors should invest more due to greater labour flexibility. Similar predictions can be found in
Gollier (2002) and Cocco, Gomes and Maenhout (2005).
3
Similar statements can be found in most recent studies. See, for instance, Heaton and Lucas (2000b),
Campbell and Viceira (2001), Gomes and Michaelides (2003) and Viceira (2001).
4
These statistics are calculated using the latest five SCF (1989-2001).
5
This will become obvious after we discuss the reasons for this 50% participation.
6
Investors are willing to sacrifice current consumption because E ( Rt − 1) > 1 / β in their model.
7
The participation curve for RRA=5 and EIS=0.5 is higher than the top curve in Figure 1D.
8
The usual range considered is between 2 to 8. See for example, Heaton and Lucas (2000b)
9
Although the asset allocation and wealth accumulation behaviors of the near-risk-neutral investors
s
are omitted from their study (see their Figure 4C and 4A), one can still deduce a similar conclusion
from Footnote 25 and Figure 4A of their study. Due the space limitation, we do not provide the whole
proof but it will be available upon request.
10
The specification is similar to Gomes and Michaelides (2005). In addition, we allow for disastrous
income shocks as in Heaton and Lucas (1997) and income dependence on the investor’s education
attainment.
11
See Appendix B for a description of the four edu statuses.
12
In this study, the income is reduced by 50% in the disastrous state. This is in contrast to the estimates
of Carroll (1992), which shows that the average income is reduced by 90%. This is because we take
into account all source of income including welfare in order to be consistent with the definition of
calibrated income profiles.
13
Same arrangement can be found in Gomes and Michaelides (2005) and other studies. Ideally, we
should allow for an average of the last few working years’ labor income (say 3 to 5 years). However, it
will undesirably create significant burden to the model as the state space expands.
14
See, for example, Deaton (1991), Heaton and Lucas (1997, 2000b) and Gomes and Michaelides
(2005).
15
One can also allow for correlation between the transitory income shock and stock innovations.
However, it is shown to have little effect (Heaton and Lucas, 1997; Gomes and Michaelides, 2005). It
is therefore no included.
16
Note the total cost of investing in stocks involves the value she invested plus the associated
transaction costs.
17
Note all upper-case monetary variables including P1 to P5 should have t and edu subscripts
due to their dependence on Yedu ,t . We omit them for notation conveniences. For example, the once-off
participation (entry) cost is a constant proportion of the investor’s permanent income, P1 = p1Yedu ,t .
18
We would like to thank Francisco Gomes for his permission to use their estimates.
57
19
Costs of college are from CollegeBoard (2003), child expenditures are from Lino (2002).
20
30% partial income is used because it is sensible to assume people take on part-time jobs or seek
other sources of additional income.
21
Estimates are based on the Consumer Expenditure Survey excluding housing cost.
22
1992, 1995 and 1998 surveys results can be found in Bertaut and Starr-McCluer (2002).
23
Recall that the entry cost is expressed as a percentage of the income. Normally people work 48
weeks in a year and 40 hours each week. Thus 0.1% of the income is about two hours wage.
24
Results are available upon request.
25
Ameriks and Zeldes (2001) point out that one cannot separate the cohort effects from the age effects
using cross-sectional surveys like the SCF. Despite this, they show that participation increases with age
until mid-50s for both effects. Then it decreases (age effects) or stays the same (cohort effects).
Therefore, regardless of which effects are in place, our model is able to explain why young households
have significantly lower participation.
26
Figures with other risk aversions or entry costs smaller than 2% give similar conclusions and are
available upon request.
27
Again, figures with other risk aversions or entry costs smaller than 2% give similar conclusions and
are available upon request.
28
Appendix D provides a brief description of the SCF. Each survey comprises of five implicates due to
the use of multiple imputation. Heckman model is applied to each implicate, and results from each
implicate are aggregated using the Repeated Imputation Inference technique. See Heckman (1979) for
the statistical treatment of selection bias and Rubin (1987) for statistical treatment of generating
statistics under multiple imputation.
29
To continue controlling for the wealth effect, we allow wealth to be an additional regressor.
30
We create a new variable for the size of human capital. See Appendix F for more detail.
31
For example, we argue that households working in the finance and banking industry face less
information costs and hence have lower once-off participation cost (entry cost) and per-period
participation cost (cost of keeping up with the market and monitoring investments).
32
Note using their dependent variable gives the same conclusion that human capital, liquidity and
informational factors all have significant impact on investment decisions. Results are available upon
request.
33
It includes all banking and finance professions but together with other professions like repair man.
34
Note that this variable is excluded from the participation equation because everyone has stock
holdings in their own company must already be participants in the stock market.
35
Assuming risky assets are not negatively correlated with the non-tradable asset.
(1999) Grinblatt and Keloharju (2001) Mehra and Prescott (1985) Heaton and Lucas (1997)
58
Coval and Moskowitz