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Stock market literacy, trust and participation
Adnan BallochyAnamaria NicolaeyDennis Philipy
August 2014
Abstract
This paper studies the importance of stock market literacy and trust for stock own-
ership decisions. We …nd that these two distinct channels simultaneously explain not
only the probability of participation, but, conditional on participation, also explain
the share of investment in stocks. Once we account for stock market literacy, socia-
bility is no longer signi…cant for participation; what matters is literacy rather than
sociability. Further, we observe that economic shocks and future expectations are key
behavioral characteristics that explain a household’s decision to invest in stocks. How-
ever, upon participation, a larger set of behavioral characteristics explains the level of
stock investment.
JEL Classi…cation: A13; D03; D12; G11
Keywords: Financial literacy, Trust, Sociability, Stock market participation, Partici-
pation cost
We wish to thank the editor, an anonymous referee, Joy Philip, and Simon Vicary for helpful suggestions
and comments.
yDurham University Business School, Mill Hill Lane, Durham DH1 3LB, UK; Emails:
a.g.balloch@durham.ac.uk, anamaria.nicolae@durham.ac.uk, dennis.philip@durham.ac.uk; Tel: +44 (0) 191
3345133; Fax: +44 (0) 191 3335201
1
1 Introduction
In explaining the stock market non-participation puzzle, there is a growing literature that
studies the behavioral and psychological factors acting as barriers to stock ownership. Re-
cent papers suggest that household participation in the stock market is driven by factors
such as optimism (Puri and Robinson, 2007), trust in …nancial markets (Guiso et al., 2008),
intelligence quotient (Grinblatt et al., 2011), genetics (Barnea et al., 2010), political orien-
tation (Kaustia and Torstila, 2011), the ability to understand investment (Graham et al.,
2009; Christelis et al., 2010), stock market return experience (Malmendier and Nagel, 2011),
educational attainment and …nancial sophistication (Christelis et al., 2011), …nancial literacy
(Cardak and Wilkins, 2009; Van Rooij et al., 2011), cognitive ability (Benjamin et al., 2013),
and sociability (Hong et al., 2004; Bönte and Filipiak, 2012).
Recently, Georgarakos and Pasini (2011) assess the joint importance of trust and so-
ciability on stock market participation. They show that trust and sociability a¤ect stock
ownership through distinct channels, where mistrust lowers the expected return on invest-
ment, making stock market participation unattractive, and sociability serves to reduce the
…xed cost of participation through cheaper information sharing. However, Bönte and Fil-
ipiak (2012) report that households’investment decisions are not strongly a¤ected by their
social interaction once the households are aware of shares, bonds and mutual funds. They
observe that although social interaction may not in‡uence investment in …nancial instru-
ments directly, word-of-mouth communication a¤ects individuals’awareness of the …nancial
instruments, thereby indirectly a¤ecting investment. Meanwhile, Van Rooij et al. (2011)
…nd that …nancial literacy plays a key role in understanding the non-participation puzzle.
They show that households with low …nancial literacy are signi…cantly less likely to invest in
stocks. However, the mechanism through which …nancial literacy in‡uences stock ownership
decisions is unclear.
In this paper, we propose a theoretical framework for stock market participation whereby
stock market literacy reduces the cost barriers, hence encouraging participation. Moreover,
1
we account for households’level of trust in the stock market, as advocated by Guiso et al.
(2008), and jointly consider the distinct role of stock market literacy and trust on households’
stock ownership decisions. Moreover, we empirically test whether sociability is capturing
the e¤ect of stock market literacy and hence whether it is literacy, rather than sociability,
that matters for understanding stock market participation. Georgarakos and Pasini (2011)
document that more sociable households reduce their participation costs through cheaper
information sharing, thereby increasing participation. We argue that sociability actually
proxies for households’stock market literacy, and hence introducing stock market literacy,
which is the aggregate product of stock market knowledge and awareness, should capture
the e¤ect of sociability on stock market participation. Moreover, we argue that the evidence
for the distinct roles of trust and sociability on stock ownership observed by Georgarakos
and Pasini (2011) can be explained by the unique and distinct e¤ects of trust and stock
market literacy on participation. As in Guiso et al. (2008), we de…ne trust as the …rm
reliance on the characteristics of the …nancial system such as sound management, quality
of investor protection, e¤ective regulation and supervision, etc. A household’s level of trust
in the stock market cannot necessarily be associated with their knowledge about the stock
market. Knowing about the market does not make the market trustworthy. Our empirical
…ndings support these conjectures.
To understand the distinct e¤ects of stock market literacy and trust on participation, we
adopt the standard two-asset portfolio model of Tobin (1958). In this theoretical framework,
we distinguish households according to their level of stock market literacy. We observe that
stock market literate households increase their expected return from participating in the
stock market by lowering their cost of participation, identi…ed as the income and substitution
e¤ect. Our framework is motivated by recent research showing that …nancial awareness
may lead to reduced pecuniary and non-pecuniary portions of participation cost, thereby
encouraging stock market participation (see, for example, Campbell, 2006; Jappelli and
Padula, 2013; and Khorunzhina, 2013). When we consider households’levels of trust in the
2
stock market, the probability of being cheated by participating in the stock market reduces
their expected returns, further contributing to the substitution e¤ect. However, households
that trust the stock market have a lower threshold level for the proportion of stock market
investment below which participation is not worthwhile and hence participate more in the
stock market. Thus, the theoretical framework shows how the two distinct channels –stock
market literacy and trust –explain stock market participation, where stock market literacy
has an income as well as a substitution e¤ect, and trust has a substitution e¤ect on portfolio
allocation.
To test the framework empirically, we use data from the American Life Panel (ALP)
survey, which consists of over 340 diverse surveys and 6,000 representative samples of U.S.
consumers of age 18 and above. ALP surveys capture a rich set of information that is
of scienti…c and policy interest, such as expectations, opinions, …nancial participation and
circumstances, cognition and demographics. Hence it is possible for us to measure stock
market literacy, sociability and trust in the stock market, and also construct proxies for a
wide range of household behavioral characteristics.
This paper contributes to the existing literature in four major aspects. First, we reassess
the previously documented relations between sociability and stock market participation,
once households’stock market literacy has been taken into account. Second, we propose a
theoretical framework to understand the distinct e¤ects of stock market literacy and trust
on stock ownership. The testable implications of the model are supported by the data. In
particular, we show that stock market literacy and trust have distinct and signi…cant e¤ects
on the probability of participation as well as the proportion of households’wealth invested in
stocks. Third, unlike previous studies, which use general …nancial literacy questions to mea-
sure …nancial knowledge, we construct a stock-market-speci…c literacy index that is related
to the understanding of the stock market and measures households’knowledge of investing in
stocks directly or indirectly through mutual funds or investment accounts. Thus, we are able
to reduce the noise in capturing households’knowledge of the stock market and study its role
3
for stock ownership. Fourth, using the rich set of data on household behavioral characteris-
tics, we additionally examine the importance of various behavioral and psychological factors
for stock market participation. In particular, we test the role of economic shock, optimism,
time preference, future expectations, self-con…dence, sense of commitment and risk aversion
for households’decisions to invest in stocks. Hence, we are also able to distinguish the e¤ects
of stock market literacy and trust from other behavioral characteristics. For instance, by
modeling both trust and self-con…dence in the empirical analysis enables us to separate their
distinct e¤ects, although the two characteristics might often be understood synonymously.
Previous studies allude to the signi…cant role of behavioral characteristics on stock market
participation, but fail to test adequately for these e¤ects due to data constraints. Hence we
…ll a noticeable gap in the literature by considering a wide range of behavioral characteristics.
It is important to emphasize that the analyses performed simply explain the existence of a
relationship between the various household characteristics and stock market participation,
and do not give rise to causal inferences.
The empirical results show that stock market literacy remains a key characteristic for
stock market participation, even after allowing for sociability, trust and a large set of be-
havioral characteristics. Before considering households’stock market literacy, we obtain a
signi…cant relationship for sociability, but once stock market literacy is accounted for, we
observe that sociability can no longer explain stock market participation. Hence, we …nd
that sociability captures the association between stock market literacy and participation.
To further analyze this, in the additional analysis, we investigate the relation between stock
market literacy, sociability and participation by separately analyzing highly sociable house-
holds that have low stock market literacy, and low sociability households with high stock
market literacy. Interesting results emerge - we …nd no association between sociability and
participation even among highly sociable households that have low stock market literacy. By
contrast, we observe that stock market literacy remains highly signi…cant for stock owner-
ship among households with low sociability. This means that households with low sociability
4
invest in stocks if they are stock market literate. Hence, we con…rm that what matters is
stock market literacy, rather than sociability, for stock market participation.
The other important characteristic that explains the probability of participation is house-
holds’level of trust in the stock market. We …nd that trusting households are more likely
to invest in the stock market, and for a given level of trust, lack of stock market literacy
additionally acts as a barrier to stock market participation. For US households, we …nd that
changing stock market literacy by one standard deviation varies the probability of participa-
tion by around 11%, while the equivalent change for trust in the stock market is around 17%.
Further, we …nd that demographic characteristics, including age, education and income, and
behavioral variables, including economic shock and future expectations, signi…cantly explain
the heterogeneity in stock market participation.
When we examine the characteristics that relate to households’share of wealth invested
in stocks, we …nd that stock market literate households invest a larger proportion of their
wealth in stocks. In addition, households trusting the stock market hold a higher portfolio
investment in risky assets, con…rming the …nding of Guiso et al. (2008). Sociability remains
insigni…cant and does not play a role in households’portfolio allocation decisions. Further,
we observe signi…cant positive associations for age, education, economic shock, future expec-
tations, self-con…dence and time preference, while income negatively explains the proportion
of investment in stocks. We see that some behavioral characteristics – self-con…dence and
time preference –that do not explain the probability of participation are now signi…cant.
This shows that there are di¤erent behavioral factors that explain a household’s decision to
participate in the stock market and, conditional on participation, their level of investment.
Our …ndings, while descriptive and not providing any causal explanations, will be of
interest to policy makers in their strategic endeavors to promote stock market participation.
For example, since stock market literacy and trust concurrently explain participation, this
relation should be taken into account while designing various …nancial literacy programs for
encouraging stock market participation. Also, our results show that social interaction and
5
peer-group e¤ects cannot explain stock ownership decisions per se; what matters is literacy
rather than peer e¤ects. Additionally, behavioral characteristics (economic shock, future
expectations, self-con…dence and time preference) are shown to explain the heterogeneity
observed in stock market participation.
The reminder of the paper is organized as follows: Section 2 presents the theoretical
model; Section 3 describes our data and variables; Section 4 reports the empirical analysis;
Section 5 provides results from the robustness analysis; and Section 6 concludes.
2 The Model
In this section, we propose a theoretical framework to understand the role of stock market
literacy and trust in households’decisions to invest in the stock market. For this purpose,
we adopt the standard two-asset portfolio model of Tobin (1958). In this setup, households
have the choice of investing in two …nancial assets: a risky asset, which yields the return rs,
considered here to be a stock with E[rs] = rsand standard deviation s>0, and a risk-free
asset, which yields the return rf(and rf<rs). We assume that the probability distribution
of the returns of the risky asset is normal. Therefore only the expected return and standard
deviation are relevant for a household iwho chooses the proportion wiof their initial wealth
Yito be invested in the risky asset in order to maximize the expected utility:
max
wi
EU [rfYi+wi(rsrf)Yi]:(1)
The household participates in the stock market if their expected utility from investing
their wealth in the stock market and in the risk-free asset is greater than (or equal to) the
utility from investing only in the risk-free asset U[rfYi]:Thus, the stock market participation
condition is:
EU [rfYi+wi(rsrf)Yi]U[rfYi]:(2)
6
Under the assumption of normality, we adopt the risk-return analysis to explore further
the e¤ects of stock market literacy and trust on the households’portfolio choice problem.
We use the standard deviation as a measure of the riskiness of the portfolio. In this setup,
the stock market participation condition is:
U[ER; ]U[rfYi;0];(3)
where ER is the expected return of the portfolio.
In Figure 1, ER is measured on the vertical axis and on the horizontal axis. In the
(ER; )space, we plot the investment opportunity locus for combinations of investment in
both the risk-free asset and the stock market expected return, ERs, and the investment
opportunity locus of investing only in the risk-free asset, Rf(when wi= 0). Following Tobin
(1958), ERs=rfYi+(rsrf)
s; knowing that =wiYis;and Rf=rfYi:Household ihas
preferences between expected return, ER, and risk, , represented by a …eld of indi¤erence
curves, and is indi¤erent between all pairs (ER; )on the indi¤erence curve Iplotted in
Figure 1. Ais the point at which the highest indi¤erence curve is tangent to the investment
opportunity locus, giving us the optimum proportion of wealth, wA
i, to be invested in the
stock market in order to maximize the expected return of the portfolio.
Further, in this model, we distinguish households according to their level of stock market
literacy. Our framework is motivated by several previous studies that document a relation
between …nancial literacy and stock market participation.1We propose that stock market
literacy increases participation by decreasing the participation cost. We de…ne the cost
function q, which reduces the disposable wealth to be invested between the two available
1Campbell (2006) shows that participating households, due to lack of …nancial literacy, may delegate the
decision making to professionals, resulting in higher fees paid and increased participation cost (aware of their
limited investment skills, some households withhold from investing in risky markets altogether). Further,
Khorunzhina (2013), using a dynamic model of stock market participation, argues that participation costs
are lower for more educated investors and shows that they further decrease with stock market participation
experience. The author …nds that …nancial education and counseling alleviate the burden on consumers’time
and e¤ort necessary for making …nancial decisions and reduce the objective cost of stock market participation.
Moreover, Van Rooij et al. (2011) establish a positive link between …nancial literacy and stock market
participation.
7
assets, as a function of household i’s stock market literacy level ki. Thus, q: [0; kmax]![0;1];
with q0(ki)<0, and kmax is the maximum level of stock market literacy household ican
attain and use for the purpose of stock market participation. q(ki)is decreasing in stock
market literacy. Capturing the e¤ect of stock market literacy, the expected return in the
participation condition given by Equation (3) becomes:2
rf(Yiq(ki)) + wi(rsrf)(Yiq(ki)):(4)
In Figure 2, in the (ER; )space, along with Rfand ERs,ERq(ki)
splots the new in-
vestment opportunity locus for combinations of investment in both the risk-free asset and
the stock market when the household iparticipates in the stock market and faces the cost
function, subject to their level of stock market literacy, q(ki). Here, the expected return in
the participation condition can be rewritten as ERq(ki)
s=rf(Yiq(ki)) + (rsrf)(Yiq(ki))
s,
where =wis. We see that the new investment opportunity locus ERq(ki)
sshifts downwards
and pivots clockwise relative to that of the baseline model, ERs, as both its intercept and
slope decrease. Further, the marginal expected return to risk-taking is lower in the model
with stock market literacy than in the baseline model, as @ ERq(ki)
s
@ <@ ERs
@ :This will cause a
reduction in the amount of risk taken by the household through stock market participation,
indicating that we have a “substitution e¤ect”between the two available assets. In addition,
the household will also encounter an “income e¤ect”, as their overall …nal wealth will be
lowered by the cost function.
Ton the budget constraint depicts the point below which the household is better o¤
investing only in the risk-free asset, while after Tthe household will have a higher expected
return from participating in the stock market. The cost function decreases the expected
return from participating in the stock market, making investing in the stock market less
attractive. The lower part of Figure 2 gives the minimum threshold proportion of investment
2This functional form of the expected return is in line with previous studies such as Vissing-Jorgensen
(2004), Guiso et al. (2008) and Georgarakos and Pasini (2011).
8
in the stock market necessary for stock market participation to occur, w
i(w
i>0) in this
model.
Another technology we introduce in this model is the households’level of trust. Recent
literature points out that less trusting households are less likely to participate in the stock
market.3Therefore, we incorporate the e¤ects of trust in our model along stock market
literacy, building a more realistic framework.4Here, independent of the probability distrib-
ution of the risky asset returns, we allow for the probability that a household’s investment
(in terms of both initial investment and returns) vanishes due to non-market sources of risk.
Suppose ai[0;1] is household i’s assessed probability of being cheated by the managers,
intermediaries or the …rm itself, and hence losing a proportion of their wealth invested in
stocks. This probability measures the degree of the household’s mistrust and serves as a
discount factor applied by the household to their return from investing in the stock mar-
ket.5Hence, household i’s expected return on the risky asset is now dependent not only on
the risk aversion incorporated in their utility function but also on their trust (or subjective
probability of being cheated) in the stock market, ai, where rs: [0;1] ![0; rfull
s]; r0
s(ai)<0
and rfull
sis the highest return attained for the highest level of trust in the stock market.
In the model with stock market literacy and trust, the expected return in the participation
condition in Equation (3) is now:
rf(Yiq(ki)) + wi(rs(ai)rf)(Yiq(ki)):(5)
In this case, we see that the expected return from investing in both the risk-free asset
and the stock market decreases even further for any ai2(0;1], as the already smaller
disposable wealth (due to the cost function) is distributed between the risk-free asset and
the stock market, which now has a discounted return (given by the household’s assessed
3See, for example, Guiso et al. (2008), Georgarakos and Pasini (2011), Pevzner et al. (2013) and Carlin
et al. (2009).
4We assume that the e¤ect of trust is independent of that of stock market literacy.
5We assume a partial equilibrium framework in the sense that the choice of one household does not a¤ect
the equilibrium level of ai:
9
level of trust in the stock market). In Figure 2, ERq(ki);ai
splots the investment opportunity
locus for combinations of investment in both the risk-free asset and the stock market when
household i, who participates in the stock market faces the cost function subject to their
level of stock market literacy, q(ki), and has a positive level of mistrust in the stock market,
where ERq(ki);ai
s=rf(Yiq(ki)) + (rs(ai)rf)(Yiq(ki))
s, and =wis:We assume rs(ai)> rf
for any ai2(0;1]. We observe that the new investment opportunity locus ERq(ki);ai
spivots
clockwise relative to ERq(ki)
s;as the slope of the schedule is now lower than in the case
when the household invests in stocks and has total trust in the stock market. In the model
with stock market literacy and lack of trust, the marginal rate of substitution between the
expected return and risk is lower than in the model with stock market literacy and total
trust, as ERq(ki);ai
s
@ <@ ERq(ki)
s
@ :We see here an additional “substitution e¤ect”, as the lack of
trust further reduces the marginal expected return from investing in the stock market.
T on the budget constraint depicts the point below which the household is better
o¤ investing only in the risk-free asset, while after T the household will have a higher
expected return from participating in the stock market. The lower part of Figure 2 shows
that the minimum threshold level of investment required to make participation worthwhile
has increased further to w
i, with w
i> w
i>0.
Thus, in the complete model framework comprising the e¤ects of both stock market
literacy via participation cost, and trust via discounted return on investment in stocks, a
household ichooses wiin order to maximize their expected utility, conditional on their level
of stock market literacy, trust, initial wealth and the returns of the two assets in which they
can invest:
max
wi
ER [wijki; ai; Yi; rs; rf];where:
ER [wi] = 8
>
<
>
:
rf(Yiq(ki)) + wi(rs(ai)rf)(Yiq(ki));if wi>0
rfYi;if wi= 0:
(6)
10
This setup allows us to investigate the independent e¤ects of stock market literacy and
trust on stock market participation. We observe that the household’s level of stock market
literacy has a distinct e¤ect on the participation condition, over and above the e¤ect of
trust. Unlike the household’s level of stock market literacy, which a¤ects both the slope and
the intercept of the investment opportunity locus, trust only a¤ects the slope of this locus.
Hence, the slope is a¤ected by two distinct factors coming from stock market literacy and
trust.
2.1 Testable Implications
From the above participation condition, we observe that stock market literate households
have higher disposable wealth to invest in the stock market than their counterparts (as
their participation costs are smaller). For a given level of mistrust aiand initial wealth
Yi, the expected utility from investing in the available assets is monotonically increasing in
the disposable wealth Yiq(ki);and monotonically increasing in the level of stock market
literacy, ki.
In Figure 3, in the (ER; )space, along with Rfand ERs, we plot the investment
opportunity loci for a household with a high level of stock market literacy, k2, and a household
with low stock market literacy, k1, labeled as ERq(k2);ai
sand ERq(k1);ai
s, respectively. We see
that ERq(k2);ai
shas a steeper slope and the locus shifts upwards compared to ERq(k1);ai
s.
In other words, a more literate household will have a higher marginal rate of substitution
between the two available assets and a higher return given the lower participation cost, as
compared to that of a less literate household. Aand Bare the points at which the highest
indi¤erence curve is tangent to the two investment opportunity loci, giving us the optimum
proportion of wealth to be invested in the stock market wA
iand wb
i, respectively, in order
to maximize the expected return of portfolios. T1and T2on the budget constraints are the
cut-o¤ points below which the households are better o¤ investing only in the risk-free asset.
After these points, the households will have a higher expected return from participating
11
in the stock market. This gives us the minimum threshold proportion of stock investment
necessary for stock market participation to occur, wi1and wi2(wi1>0; wi2>0).
For identical degrees of risk aversion, given the positioning of the two loci for households
with levels of stock market literacy k1and k2, we have wB
i> wA
iand wi1> wi2:In Figure
3, we observe that on the segment [0,1], the interval (wi2; wB
i)is greater than the interval
(wi1; wA
i)showing that a more stock market literate household has a higher participation
interval compared to a less stock market literate household. Moreover, given that wB
i> wA
i,
conditional on participation, a high stock market literate household invests more in stocks.
Based on this model framework, the testable implications we draw are summarized as follows:
for a given level of mistrust aiand initial wealth Yi,
(i) a household with higher stock market literacy has a higher probability of stock market
participation;
(ii) conditional on participation, stock market literate households invest a higher proportion
of investment in stocks.
3 Data and Variables
Our data is sourced from various American Life Panel (ALP) surveys that gather information
from over 6,000 representative samples of US households.6ALP consists of a diverse set
of surveys (around 368 di¤erent surveys) that is of scienti…c and policy interest, covering
multiple aspects such as expectations, opinions, …nancial participation and circumstances,
cognition and demographics. Hence it is possible for us to measure stock market literacy,
6Other databases such as the DNB Household Survey (DHS) of Dutch households and the Survey of
Health, Ageing and Retirement in Europe (SHARE) database of multidisciplinary and cross-national house-
hold data do not contain adequate information on households’…nancial literacy and participation informa-
tion. For example, although DHS contains information on stock-holding status and …nancial literacy, the
number of households that actually possess stocks is very low. For instance, in the 2012 wave, only 218
households out of the 2155 responding households possess stocks. In addition, only 170 households shared
information on the amount of money invested in stocks. In the SHARE database, there is limited information
on …nancial literacy and households’investment in …nancial assets.
12
sociability and trust in the stock market, and construct proxies for a wide range of households’
behavioral characteristics. The interviews are conducted via an internet-based panel and take
advantage of its computerized nature, with visualization and interactive tools supporting
implementation. ALP allows for customized feedback to respondents as part of plausibility
checks of a given response. Further, the survey questions are also customized for clients who
have special requirements, thereby increasing the diversity of surveys. Chang and Krosnick
(2010) show that self-administered computer-based surveys facilitate optimal responding,
with higher concurrent validity, less survey satis…cing, and less social desirability response
bias than in the intercom mode, especially among households with limited cognitive skills.
Moreover, question orders and response choices have been randomly assigned in order to
avoid any response biases due to the order in which they appear.
We obtain information on whether households hold stocks or stock mutual funds from
the E¤ects of the Financial Crisis survey waves …elded between November 2008 and January
2011, with an average response rate of 79%. We do not consider stock holdings that are
part of an IRA, 401(k), Keogh or similar retirement accounts. In our sample, we …nd that
70% of the housholds participate in the stock market. Using the Cognition and Aging in the
USA survey (…elded between November 2008 and September 2009), we gather information on
households’share of wealth invested in the stock market, which is calculated as a proportion
of total …nancial assets invested in stocks. The total …nancial assets are made up of the value
of checking accounts, savings accounts, money market accounts, bond funds, balanced or life-
cycle funds, foreign investments, index funds, sector funds, other mutual funds, retirement
accounts, short-term assets, other stocks or funds not listed, educational savings accounts
and life insurance settlements. We observe that, on average, households in our sample invest
6.7% of their share of wealth in stocks.
13
3.1 Measuring Stock Market Literacy, Sociability and Trust in the
Stock Market
We develop an index for stock market literacy using questions from the Investing sub-module
developed by Hung et al. (2009) and part of the ALP Financial Literacy survey. This
survey is …elded between March 2009 and September 2009, with a response rate of 85.87%.
The Investing sub-module consists of Lusardi and Mitchell’s (2007) sophisticated …nancial
literacy items, as well as …ve additional items on investment markets and products. They
capture households’knowledge of investing directly in the stock market or indirectly using
mutual funds accounts. Hung et al. (2009) conduct a battery of tests to assess the construct
validity and …nd strong reliability and internal consistency, with a highest Cronbach’s alpha
as compared to other prominent …nancial literacy scales. Appendix A presents the questions
used to develop our stock market literacy index. Since the responses are a mix of nominal
and ordinal data, unlike previous studies that use linear principal component analysis, we use
categorical principal component analysis (CATPCA) to construct the stock market literacy
index. CATPCA is the non-linear equivalent of linear PCA and has been developed for
e¢ ciently handling categorical variables and nonlinear relationships.
Table 1 reports the CATPCA results for the stock market literacy index. The optimal
scaling level of all items is set to ordinal, and we use Kaiser’s criterion to determine the
number of signi…cant dimensions. We …nd that there are three signi…cant dimensions with
eigenvalues greater than one, explaining 52% of the variance of our data. We construct the
stock market literacy index as the weighted sum of the signi…cant dimensions, where the
weight is given by the eigenvalues. We scale the households’stock market literacy index
scores to lie between the range of zero and one. The summary statistics in Table 2 show
that our sample of households has an average stock market literacy score of 0.61. In Panel B
of Table 2, we report the sample characteristics of households with di¤erent levels of stock
market literacy. If we compare the stock ownership characteristics of household groups with
literacy scores in the upper and lower quartile, we observe that around 95% of the high stock
14
market literate households participate in stocks, while around 58% of the low stock market
literate households hold stocks. On average, high stock market literate households invest
12% of their …nancial wealth in stocks, which is about double the sample average (6.7%)
and low stock market literate households invest 4% of their wealth in the stock market.
We see that our high stock market literate group has an average education of roughly 13
years, is made up of largely male respondents (around 68%), with an average income double
that of the low stock market literate group, and has large average net wealth. The sample
characteristics suggest that, on average, wealthy households participate more in the stock
market and such households have the ability as well as the incentive to be more stock market
literate, as they participate more in the stocks.
For creating a measure for households’level of sociability, we utilize the broader de…nition
of sociability employed by Hong et al. (2004), and Georgarakos and Pasini (2011), among
others. In particular, households are considered sociable if they participate in formal training,
make donations of money or possessions totaling $500 or more, participate in volunteer
work, or spend time helping friends, neighbors, or relatives. According to Unger (1998),
sociability refers to the ease and urgency with which individuals pursue common goals,
which will otherwise be impossible or expensive to achieve if individuals operate in isolation.
Hence, households’involvement through cooperation in the organization of society is used
as a measure of sociability. We obtain information on these sociability characteristics from
various ALP surveys …elded between 2008 and 2013, with a minimum response rate of around
84%.7The sample characteristics for sociable (with sociability proxy equal to one) and non-
sociable (with sociability proxy equal to zero) households are reported in Panel C of Table
2. We observe that sociable households participate more in the stock market and hold a
greater proportion of their wealth in stocks than non-sociable households. In particular,
7More speci…cally, participation in formal training data is from the Financial Decision-making survey,
with a response rate of 97.74%; the charity donations data is from the Health and Retirement Study (Well
Being module 62), with a response rate of 83.94%; and we use the Health and Retirement Study (Well Being
module 66), which has a response rate of 97.81%, to obtain information on participation in volunteer work,
and time spent helping friends, neighbors or relatives.
15
we see that around 73% (42%) of (non-)sociable households hold stocks and on average,
(non-)sociable households invest around 6.8% (4.8%) of their wealth in stocks. The average
demographic characteristics (age, education, gender) between the two groups are similar;
however we observe that sociable households have a larger average income and net wealth
than non-sociable households.
To measure households’trust in stock markets, we use the Trust in Financial Institutions
sub-module under the Department of Labor (DOL) Pilot survey. This survey is …elded
from June 2011 until August 2011, with a response rate of 85.04%. We incorporate three
questions about households’ level of trust in the stock market, trust in stockbrokers and
trust in investment advisers. The choices of responses range from 1 (I do not trust at all) to
5 (I trust completely). We take the average of the responses to the aforementioned questions
and scale them between zero and one, where zero corresponds to households who have the
lowest trust in the stock market and one corresponds to those with the highest level of trust
in the stock market. While previous studies such as Guiso et al. (2008) use trust in bank
o¢ cials and …nancial advisers as a proxy for personalized trust in the stock market, our
measure is more speci…c to households’trust relating to stock market investment decisions.
The summary statistics in Table 2 show that our sample of households has an average trust
score of 33%. From the correlations reported in Table 3, we observe that our key variables
–stock market literacy, sociability and trust measures –are not highly correlated with each
other, with trust being correlated only 19% with stock market literacy.
3.2 Measuring Demographic and Behavioral Characteristics
We consider the key demographic characteristics related to stock ownership decisions in
the literature, including age, education, employed (indicator for being an employee), male
dummy, income and net wealth. For example, Guiso et al. (2008) …nd that age is negatively
related to stock ownership and investment in stocks, while employment is positively related
to participation in the risky assets. They further report that males and investors with
16
a college education have a higher proportion of investment in stocks, while employment
increases the share of investment in risky assets. Likewise, Guiso et al. (2008), Hong et al.
(2004), Georgarakos and Pasini (2011) and Van Rooij et al. (2011) report the importance of
education for stock market participation; Haliassos and Bertaut (1995) and Van Rooij et al.
(2011) …nd a signi…cant role of gender, observing that stock market participation is much
lower among women than men; Haliassos and Jappelli (2002), Campbell (2006) and Van
Rooij et al. (2011) show that stock market participation increases strongly with income and
wealth; and Vissing-Jorgensen (2004) reports that non-…nancial income is positively related
to both the stock ownership and share of investment in stocks.
We obtain the demographic characteristic variables – age, education, employed, and
gender –from the ALP household information. Our selected sample of respondents is aged
between 18 and 93. As can be seen from Table 2, the average age of our respondents is around
51 and the average number of years in education is around 12, with about 42% males and
62% of respondents in employment. Utilizing information from the E¤ects of the Financial
Crisis survey, we calculate households’total income as the sum of respondents’and their
partners’monthly income from work and other sources. We take the average of their income
during 17 months starting from October 2009, to deal with abnormal income in any month.
The summary statistics in Table 2 show that, on average, households in our sample have a
monthly income of around $7000 (with sample median of $5150). In order to measure net
wealth, we use the HRS Q Income and Assets section survey that is …elded between June
2009 and August 2013 and has a response rate of 97.74%. We calculate net wealth as the
total value of all assets (excluding equity wealth) minus total household debt.
We include a large set of behavioral characteristic variables, including economic shock,
optimism, time preference, future expectations, self-con…dence, sense of commitment and
risk aversion. We utilize information from a wide range of ALP surveys to construct proxies
for these behavioral characteristics. Exact wordings of the survey questions utilized, choices
of responses and the construction of the variables are provided in Appendix B. The summary
17
statistics from Table 2 show that households in our sample on average are largely optimists
but at the same time risk averse, with low expectations of the future. Further, we observe
that the households on average are moderately self-con…dent and committed. From Table
3, we …nd that overall the behavioral characteristics are not strongly correlated with each
other, with positive correlations noted between optimism and self-con…dence, and negative
correlations noted between future expectations and risk aversion.
4 Empirical Analysis
4.1 Who Participates in Stock Markets?
In this section, we investigate the importance of stock market literacy, sociability, trust and
other household characteristics for stock market participation. We estimate the following
binary choice model for the participation condition in Equation (3):
P ROB _S T OCKi=SLi+SOi+T Ri+ +j[Xji] + "i
and "iN(0;1);(7)
where the response variable is probability of stock market participation. We include the key
explanatory variables –stock market literacy (SL), sociability (SO) and trust (T R) –and
a large set of household characteristic variables, Xj, outlined in Section 3.2.
The …rst set of results are reported in Table 4. We report the fully standardized coef-
…cients, allowing us to measure accurately the association of variables among the various
probit models.8We …nd that stock market literacy, sociability and trust are strongly signif-
8When including di¤erent predictor variables in the various probit model speci…cations, the scaling of
the response variable changes and therefore the changes in estimated coe¢ cients might not entirely be
due to the suppressor e¤ect (see Winship and Mare, 1984; Williams, 2009; Mood, 2010; among others).
Standardizing only the response variable does not adequately …x the scaling issue and hence we perform
a full standardization (that is, standardization of both response and explanatory variables). In this way,
the changes to a reported coe¢ cient estimates in the various nested model speci…cations can be accurately
associated with the suppression e¤ect rather than the scaling e¤ect (see Long and Freese, 2006 for details).
18
icant when considered independently. Moreover, the e¤ect of sociability remains signi…cant
contemporaneously with trust. This is in line with Hong et al. (2004), Guiso et al. (2008)
and Georgarakos and Pasini (2011), who …nd that trust and sociability play distinct roles
for stock market participation. However, when we introduce stock market literacy, the re-
lationship between sociability and participation vanishes; and what matters is stock market
literacy, along with trust, which is also strongly signi…cant. This …nding is also consistent
with those documented by Hilgerth et al. (2003), Cardak and Wilkins (2009), Christelis et
al. (2010) and Van Rooij et al. (2011), showing that more …nancially literate people are more
likely to invest in the stock market. Our results indicate that sociability actually proxies
for …nancial awareness and stock market literacy, which a¤ects stock market participation.9
In terms of demographic characteristics, we …nd that age, education, employment, income
and net wealth are important indicators of stock ownership, with income having the highest
explanatory power (around 53%) for households’probability of participation.
Next, we examine the importance of household behavioral characteristics for explaining
the probability of participation. We add a rich set of behavioral and psychological measures
to the model speci…cation used in Table 4, including economic shock, future expectations,
optimism, risk aversion, self-con…dence, sense of commitment and time preference. In doing
so, we are also able to distinguish the distinct roles of stock market literacy and trust from
other household behavioral characteristics that can explain the probability of participation.
Table 5 reports the test results. We …nd that the introduction of behavioral and psychological
characteristics in the model speci…cations does not alter the previous results from Table 4.
In particular, we …nd that stock market literacy and trust remain the signi…cant indicators,
along with age, education, employed, and income, even after the introduction of behavioral
and psychological characteristics. Changing stock market literacy by one standard deviation
varies the probability of participation by around 11%, while the equivalent change for trust
9Since a large proportion (93%) of our selected sample is considered sociable, we carry out robustness
checks to ensure that the low variability of the sociability measure is not in‡uencing the results. In particular,
we rerun the analysis on various household groups based on the number of sociable activities participated in
and our …ndings are fully upheld.
19
in the stock market is around 17%. As before, sociability does not signi…cantly explain stock
ownership, once we account for stock market literacy. With regard to the behavioral charac-
teristics, we observe that past economic shock is positive and strongly signi…cant for stock
market participation. This result may be driven by the fact that during periods of economic
downturn and large drops in the stock market, households holding stocks experience a higher
exposure to these shocks. We further …nd that future expectations is positive and strongly
signi…cant, showing that people who want to leave more inheritance have a higher probability
of stock market participation. Risk aversion remains negative and signi…cant at the 5% level,
before considering the e¤ect of households’trust in the stock market. In addition, we …nd
some marginal signi…cance for time preference, but its relation with participation vanishes as
we include stock market literacy. We note here that since these analyses are descriptive, the
results reveal associations between behavioral characteristics and households’probability of
participation, and no causal e¤ects can be established from these results.
4.2 Analysis of Households’Share of Investment in Stocks
Conditional on participation, in our model framework stock market literacy reduces the cost
barriers and increases the disposable wealth that can be invested between the risky and risk-
free assets. Further, trusting households invest a larger share of their wealth in stocks (Guiso
et al., 2008). In this section, we empirically investigate the characteristics that explain the
households’share of investment in stocks. We estimate the following ordinary least squares
regression:
INV _P ROPi=+SLi+SOi+T Ri+j[Xji] + "i;(8)
where the response variable is investment proportion in stocks, which is measured as total
investment in stocks as a percentage of total …nancial assets (see data section for details).10
10 We also consider wealth invested in stocks as a percentage of total assets. In this case, we calculate the
total assets of households as the sum of total …nancial assets and total value of farm equity livestock and
equipment, non-farm partnerships, and all other assets (such as trusts, limited partnerships, hedge funds,
commodities, timber or mineral rights, valuable art, jewelry, metals, coins and collectables). We do not
20
All explanatory variables are as in Equation (7).
The test results are reported in Table 6. We …nd that stock market literacy is consistently
positive and highly signi…cant in all model speci…cations considered. This shows that stock
market literate households are not only more likely to participate in stocks, but conditional
on participation, they also invest a larger share of their wealth in stocks. In addition, we
…nd that trust in the stock market, which is also highly signi…cant, positively a¤ects the
share of investment in stocks. Our results corroborate those of Guiso et al. (2008), who
…nd that trusting households have a higher portfolio share invested in stocks, conditional
on participation. Further, accounting for households’trust in the stock market does not
change the relationship or the signi…cance of stock market literacy. Changing stock market
literacy or trust in the stock market by one standard deviation increases the share of stocks
in a household’s portfolio by 0.087 standard deviation. Sociability remains insigni…cant in
all model speci…cations and does not explain households’portfolio allocation decisions.
In terms of household demographics, we observe that age, education, and income have
a signi…cant association with the proportion of wealth invested in stocks. In addition, we
see that a large set of behavioral characteristics exhibit signi…cance. In particular, be-
havioral characteristics including economic shock, future expectations, self-con…dence and
time preference signi…cantly explain the heterogeneity in the share of wealth invested in the
stock market, with past economic shock having the highest explanatory power of around
11% (and highly signi…cant). Notice that several of the behavioral characteristics such as
self-con…dence and time preference, which did not explain the probability of households’
participation in stocks, now signi…cantly explain the share of wealth invested in the stock
market. Although a causal relationship cannot be established from the analysis, our results
show that there are distinct behavioral characteristics that are associated with a household’s
decision to participate in the stock market and, conditional on participation, a household’s
decision on how much to invest in stocks.
report the results for investment in stocks as a percentage of total assets, as they are qualitatively identical
to those reported in Table 6 (available upon request).
21
5 Additional Analysis
5.1 The E¤ect of Sociability on Stock Market Participation
The results thus far provide a consistent picture that stock market literate households and
households that trust the stock market are more likely to participate in the stock market.
These two characteristics concurrently explain participation. Moreover, the results indicate
that sociability does not explain participation per se, but rather mirrors stock market literacy.
To further analyze this, we separately investigate what explains stock market participation
among high sociability and low sociability households. We use our proxy for sociability
that de…nes households to be sociable if they participate in formal training, make donations
of money or possessions totaling $500 or more, participate in volunteer work, or spend
time helping friends, neighbors, or relatives. Using this proxy, we de…ne high sociability
households as those that participate in two or more sociable activities and low sociability
households as those that participate in at most one sociable activity.
The test results for the two groups are reported in Table 7. Interestingly, we …nd that
stock market literacy is strongly signi…cant for both high sociability and low sociability
households. Moreover, although sociability is signi…cant for both groups initially, it becomes
insigni…cant once stock market literacy is considered. Also, we observe that trust in the
stock market is highly signi…cant only for high sociable household groups. The results of this
table con…rm that no matter how sociable a household is, stock market literacy signi…cantly
explains their probability of owning stocks. Further, for high sociable household groups,
trust has signi…cant explanatory power for participation.
In order to further understand the role of sociability, we segregate high and low socia-
bility groups further into high and low stock market literacy groups. Households with the
stock market literacy index score above (below) the median are considered high (low) stock
market literate. Here we are interested in investigating whether high sociability increases
the probability of participation for those households who have low stock market literacy and
22
whether high stock market literacy increases the probability of participation for households
with low sociability. Table 8 reports the results for these two household groups. We …nd
that sociability is insigni…cant for high sociable but low stock market literate households.
As expected, stock market literacy is insigni…cant for this household group and as in the
previous table, trust remains strongly signi…cant. For the low sociable but high stock mar-
ket literate household groups, stock market literacy remains a signi…cant determinant of
participation. These results con…rm that sociability does not play an important role for par-
ticipation, while stock market literacy remains a signi…cant determinant of stock ownership
even among households with low sociability. Hence, we do not …nd supportive evidence of
participation explained by social interactions with cheaper information sharing, and peer-
group e¤ects; however participation can be explained by households’level of stock market
literacy.
5.2 An Alternative Measure of Sociability
In this section, we test the association between sociability and stock ownership using house-
holds’participation in national elections as an alternative de…nition for sociability. Previous
studies such as Rogers et al. (2012) argue that participation in elections is a volunteering act
for society and fundamentally a social behavior. Hence, sociable households will take active
part in setting up the organization of their community and exercise their voting rights. Their
research …nds that, for voting behavior, personal means of contact such as face-to-face can-
vassing are more motivating than less personal ones such as telephone calls. In this scenario,
less sociable households will be di¢ cult to reach and therefore less likely to participate in
the electoral process.
Our alternative measure of sociability takes the value of one if the households voted in the
recent national elections, and zero otherwise. We obtain the information from the ALP Post
Election survey, …elded between November 2008 and September 2009, with a response rate of
91.21%. The results with this new measure are reported in Table 9. In Panel A, we examine
23
the households’ probability of participation. We observe that our alternative sociability
proxy is positive and remains signi…cant in the presence of trust. However, corroborating
our previous …ndings, when we introduce stock market literacy in the model speci…cations,
the signi…cant association of sociability on stock market participation vanishes, while stock
market literacy remains signi…cant, along with trust. Hence, it is stock market literacy
rather than sociability that matters for households’probability of participation. In Panel B,
we investigate the households’share of investment in stocks. Using the alternative measure
of sociability, we obtain similar results to those reported in Section 4.2, with sociability
negative and insigni…cant in all speci…cations. Hence we conclude that stock market literacy
and trust are the key indicators of households’stock ownership decisions.
6 Conclusion
In this paper, we set up a theoretical framework and empirically assess the distinct channels
of stock market literacy and trust that simultaneously explain households’stock ownership
decisions. Additionally, we investigate whether the previously documented evidence for
sociability is in fact capturing the role of stock market literacy and hence whether it is
literacy, rather than sociability, that matters for understanding stock market participation.
We construct a stock-market-speci…c literacy measure and investigate the factors that explain
households’decisions to participate in the stock market and their wealth allocation in the
stock market. Moreover, using a rich set of behavioral characteristic variables, including
past economic shocks, future expectations, optimism, risk aversion, self-con…dence, sense of
commitment, and time preference, we explain the heterogeneity observed in stock market
participation.
The results indicate that stock market literate and trusting households are more likely
to participate in stocks and invest a higher proportion of their wealth in the stock market.
These two independent household characteristics concurrently remain signi…cant even after
24
accounting for several other important behavioral variables. Although one cannot place
any causal interpretation on the results, we observe that changing stock market literacy by
one standard deviation varies the probability of participation by 11%, while the equivalent
change for trust in the stock market is around 17%.
Further, we …nd no association between sociability and participation, once we account for
stock market literacy. In the additional analysis, we …nd that sociability is insigni…cant even
among highly sociable households, if they have low stock market literacy, while conversely,
we see a signi…cant relation between stock market literacy and participation even among low
sociable households. These results indicate that households with low sociability invest in
stocks if they are stock market literate; and hence participation is explained by households’
level of stock market literacy rather than their level of sociability.
Further, we observe that a large set of household behavioral characteristics play an im-
portant role for households’investment decision making. We …nd that past economic shocks
and future expectations explain households’probability of participation and, conditional on
participation, several other behavioral characteristics such as self-con…dence and time prefer-
ence, along with past economic shocks and future expectations, explain households’portfolio
choice decision of how much to invest in stocks. Our …ndings aid the strategic endeavors of
policy makers in promoting stock market participation.
25
Appendices
Appendix A: Stock Market Literacy Questionnaire
S. No. Question Options
1 Which of the following statements describe the main function of the stock market? a. The stock market helps to predict stock earnings
b. The stock market results in an increase in the price of stocks
c. The stock market brings people who want to buy stocks together with
those who want to sell stocks
d. I don’t know
2 [Stocks/Bonds/Cap] are normally riskier than [Stocks/Bonds/Cap] a. True
b. False
c. I don’t know
3 Considering a long time period (for example 10 or 20 years), which asset normally gives a. Savings accounts
the highest return? b. Bonds
c. Stocks
d. I don’t know
4 Normally, which asset displays the highest ‡uctuations over time? a. Savings accounts
b. Bonds
c. Stocks
d. I don’t know
5 When an investor spreads his money among di¤erent assets, does the risk of losing money: a. Increase
b. Decrease
c. Stay the same
d. I don’t know
6 What happens if you buy a company’s stock? a. You own a part of the company
b. You have lent money to the company
c. You are liable for the company’s debts
d. The company will return your original investment to you with interest
e. I don’t know
f. You have lent money to the company
g. You are liable for the company’s debts
h. You can vote on shareholder resolutions
i. I don’t know
7 A stock mutual fund combines the money of many investors to buy a variety of stocks. a. True
b. False
c. I don’t know
8 If you were to invest 1000 in a stock mutual fund, it would be possible to have less than a. True
1000 when you withdraw your money. b. False
c. I don’t know
9 Which of the following statements is correct? a. Once one invests in a mutual fund, one cannot withdraw the money
in the …rst year
b. Mutual funds can invest in several assets, for example invest in both
stocks and bonds
c. Mutual funds pay a guaranteed rate of return which depends on their
past performance
d. None of the above
e. I don’t know
10 Buying a [Single/Mutual] usually provides a safer return than a company stock? a. True
b. False
c. I don’t know
11 It is hard to …nd mutual funds that have annual fees of less than one percent of assets. a. True
b. False
c. I don’t know
12 Mutual funds pay a guaranteed rate of return. a. True
b. False
c. I don’t know
d. False
e. It depends on the type of 401(k) plan
f. I don’t know
26
Appendix B: Exact Wordings of Survey Questions
B.1. Economic shock
Over the past months there have been reports about the nation’s …nancial problems
including large drops in the stock market and in the housing market and increased
rates of foreclosures and joblessness. As this …nancial crisis unfolds, more and more
people have been a¤ected in di¤erent ways. Have you (or your husband/wife/partner)
been a¤ected by these problems?
[ ] No [ ] Yes, a little [ ] Yes, a lot
The above question is taken from E¤ects of the Financial Crisis survey, measuring
households’exposure to economic shock. We take the average of the responses over
the 22 months between 2009 and 2012 as a proxy for economic shock (and scale them
between zero and one). By using the average over multiple periods, we not only
capture the intensity of the economic shock but also incorporate the frequency of the
households’exposure to economic shock. A household facing the greatest number of
economic shocks with the highest impact will have the highest economic shock score.
B.2. Future expectations
What are the chances that you (and your husband/wife/partner) will leave an inher-
itance totaling $10,000 or more? Include properties and other valuable items as well
in your total estimate. Remember, 0% means absolutely no chance, and 100% means
you are absolutely certain.
For this question, the respondents provide a percentage number between 0 and 100.
The question is further repeated twice with an increased inheritance amount of $100,000
and $500,000 respectively. The questions are obtained from the HRS P Expectations
and N Healthcare sections survey. This survey is …elded from September 2009 until
August 2013 and has a response rate of 98.52%. Our proxy for future expectations is
27
based on the inheritance-weighted average of the responses on the three questions (and
scaled between zero and one).
B.3. Optimism
i. If something can go wrong for me it will.
ii. I’m always optimistic about my future.
iii. In uncertain times, I usually expect the best.
iv. Overall, I expect more good things to happen to me than bad.
[ ] I strongly disagree, [ ] I somewhat disagree, [ ] I slightly disagree, [ ] I slightly agree,
[ ] I somewhat agree, [ ] I strongly agree
Questions i to iv are taken from the Optimism sub-module of the Health Expectations
survey, which is …elded from July 2010 to May 2011, with a response rate of 89.49%.
The households’score on optimism is the average of the responses to these four ques-
tions and numerated such that a score of zero corresponds to the households who are
least optimistic and one corresponds to the households who are most optimistic.
B.4. Risk aversion
Suppose that you unexpectedly inherited 1 million dollars. You have the chance to take
a risky but possibly rewarding investment option that has a 50-50 chance of doubling
the money to 2 million dollars in a month, and a 50-50 chance of reducing the money
by one third, to 667,000 dollars in a month. Would you choose to invest in the risky
asset?
[ ] Yes [ ] No
Following Barsky et al. (1997) and Hung et al. (2009), we use the above question from
the Risk and Time Preference sub-module of the Department of Labor (DOL) Pilot
survey, …elded between June 2011 and August 2011 with a response rate of 85.04%, to
create the households’risk aversion proxy. If the respondent chooses the …xed income
28
over the lottery option, the above question is repeated with a reduced level of potential
loss in income by one-…fth and one-tenth, until the respondent switches from the …xed
option to the lottery option. However, if the respondent chooses the lottery option in
the …rst question, the questions are repeated with an increased level of potential loss
in income by half and three-quarters, until the respondent switches from the lottery to
the …xed amount option. If the proportion of potential loss that a household is willing
to forgo is de…ned as 1then is the risk aversion measure of the household and it
is calculated at the point where the household decides to switch from the …xed income
to lottery options (or vice versa). Hence, our risk aversion variable takes the value
of zero for households that are total risk-takers, while takes the value of one for fully
risk-averse households.
B.5. Self-con…dence
I hardly ever expect things to go my way.
[ ] I strongly disagree [ ] I somewhat disagree [ ] I slightly disagree [ ] I slightly
agree
[ ] I somewhat agree [ ] I strongly agree
The Optimism sub-module of the Health Expectations survey contains the aforemen-
tioned question that we use to create a proxy for households’self-con…dence. We scale
the responses between zero and one where zero corresponds to the households who
strongly agree and one corresponds to the households who strongly disagree with the
above statement.
B.6. Sense of commitment
i. How closely do you follow the suggestions of your doctor? Please indicate which of
the below.
[ ] I closely follow the suggestions [ ] I loosely follow the suggestions [ ] I rarely follow
29
the suggestions [ ] I would like to follow the suggestions but I don’t manage to do so
ii. Are you currently smoking cigarettes?
[ ] Yes [ ] No
iii. Do you go to a doctor to have a routine examination at least twice a year?
[ ] Yes [ ] No
iv. How many servings of alcohol do you have on a typical day? (One serving is a can
of beer, a glass of wine or a shot of liquor.)
[ ] None [ ] 1 [ ] 2 [ ] 3 or more
v. How many times per week do you do some sort of moderate activity (like walking
or raking the leaves) for at least 30 minutes?
[ ] None [ ] 1 [ ] 2 [ ] 3 or more
vi. All in all, how many hours per week do you do some sort of moderate activity?
[ ] 0 [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 or more
vii. On average, how many servings of fruits and vegetables do you eat in a day?
[ ] 0 [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 or more
viii. And how many servings of cereal …ber or whole grain (wheat bread, whole grain
pasta, brown rice, oatmeal, whole grain breakfast cereal, bran or popcorn) do you eat
in a typical day? A serving is one slice of bread, 1 ounce of breakfast cereal or 1
2cup of
cooked cereal, pasta or rice. How many servings of re…ned grains (white bread, white
rice, white pasta, white potatoes or low …ber cereals like crispy rice and corn ‡akes)
do you eat in a typical day? A serving is one slice of bread, 1 ounce of breakfast cereal
or 1
2cup of cooked cereal, pasta or rice.
[ ] 0 [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 or more
The eight questions above are part of the Health Behaviors/Risk Factors sub-module
of the Health Expectations survey that we use to create a proxy for households’sense
30
of commitment. All above questions re‡ect how responsibly households treat them-
selves. Households with a sense of commitment will also treat their own lives with
responsibility/commitment. We take the average of the responses on these questions
and scale them between zero and one to establish a proxy for sense of commitment.
B.7. Time preference
Imagine you just won a lottery prize and have to choose now between one of two options
for receiving your payment. Which would you choose?
[ ] $1000 today [ ] $1,250 a year from today
The question is further repeated two times with di¤erent amounts o¤ered in one year’s
time: $1,650 and $1,100. These questions measuring time preference of the households
is taken from the Risk and Time Preference sub-module of Department of Labor (DOL)
survey. If the households choose to receive money today then they prefer present as
compared to the future. Our proxy for time preference is the average of the responses
on the three questions (and scaled between zero and one).
31
References
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35
Figure 1: This …gure plots a household’s investment opportunity loci in the (ER; )space
for combinations of investment in both the risk-free asset and stocks, labeled ERs, and only
in the risk-free asset, labeled Rf. The lower part of the …gure depicts the optimal proportion
of wealth invested in the stock market, wA
i, on the [0;1] segment.
36
Figure 2: This …gure plots a household’s investment opportunity loci in the (ER; )space for
combinations of investment in both the risk-free asset and the stock market in the baseline
model (labeled ERs), in the model with stock market literacy (labeled ERq(ki)
s), and in
the model with stock market literacy and lack of trust (labeled ERq(ki);ai
s). Rflabels the
opportunity locus of investing only in the risk-free asset. On the [0;1] segment in the lower
part of the …gure, w
iand w
iare the the minimum threshold proportions of stock investment
necessary for stock market participation to occur.
37
Figure 3: This …gure plots investment opportunity loci in the (ER; )space for combinations
of investment in both the risk-free asset and the stock market in the baseline model, labeled
as ERs, and in the model with stock market literacy and trust, with stock market literacy
levels, k1and k2, labeled as ERq(k1);ai
sand ERq(k2);ai
s, respectively. k2indicates a higher level
of stock market literacy than k1.Rflabels the opportunity locus of investing only in the
risk-free asset. On the [0;1] segment in the lower part of the …gure, wA
iand wB
iare the
optimal proportions of wealth invested in the stock market corresponding to households’
stock market literacy levels, k1and k2, respectively. wi1and wi2are the minimum threshold
proportions of stock investment necessary for stock market participation to occur.
38
Table 1: Categorical principal component analy-
sis results for stock market literacy index. This
table reports the eigenvalues and the proportion of the
variance explained by the dimensions. The total num-
ber of dimensions is 12, which is the number of items
in our questionnaire. Optimal scaling level of all the
variables is set as ordinal.
Dimension Eigenvalues Percentage of variance
1 4.138 34.481
2 1.092 9.104
3 1.004 8.365
4 0.883 7.36
5 0.82 6.832
6 0.74 6.165
7 0.67 5.582
8 0.644 5.365
9 0.563 4.696
10 0.522 4.349
11 0.492 4.098
12 0.432 3.602
39
Table 2: Summary statistics. This table reports the summary statistics of our sample. The description and construction of all the variables is detailed in Section
3. The data have been obtained from the American Life Panel (ALP) surveys. Panel A reports the summary statistics (mean, standard deviation, minimum and
maximum values) of the variables, the selected sample size (N), and the ALP survey labels. N refers to our selected sample of households that have responded to
the survey question(s) used for the variable construction as well as responded to the survey question on whether they own stocks or not. Panel B reports sample
characteristics for households with di¤erent levels of stock market literacy and Panel C reports sample characteristics for households that are sociable (with sociability
proxy equal to one) and non-sociable (with sociability proxy equal to zero). In both Panels B and C, we report the averages, with number of samples provided in
parentheses.
Panel A: Summary statistics
Variable Mean Stdev Minimum Maximum N ALP survey labels
Stock market literacy 0.612 0.248 0 1 1707 Financial Literacy
Sociability 0.929 0.257 0 1 2649 Financial Decision-making; and HRS surveys (Well Being 62, 66)
Trust in stock market 0.330 0.195 0 1 2090 Department of Labor (DOL) Pilot
Age 50.931 15.071 18 93 2711 Demographics and survey selection
Education 11.561 2.115 1 16 2711 Demographics and survey selection
Employed 0.621 0.485 0 1 2711 Demographics and survey selection
Male 0.422 0.494 0 1 2710 Demographics and survey selection
Income ($000s) 7.066 8.682 0 145.469 2477 E¤ects of the Financial Crisis
Net wealth ($000s) 293.727 1248.477 -954 38000 2545 HRS Q Income and Assets section
Economic shock 0.458 0.261 0 1 2675 E¤ects of the Financial Crisis
Future expectations 0.263 0.290 0 1 2480 HRS P Expectations and N Healthcare sections
Optimism 0.728 0.182 0 1 2355 Health Expectations
Risk aversion 0.822 0.181 0.25 1 2098 Department of Labor (DOL) Pilot
Self-con…dence 0.605 0.225 0 1 2355 Health Expectations
Sense of commitment 0.531 0.135 0.095 1 2355 Health Expectations
Time preference 0.326 0.318 0 1 2093 Department of Labor (DOL) Pilot
Panel B: Sample characteristics according to stock market literacy levels
Stock market literacy Age Education Male Income ($000s) Net wealth ($000s) Stock ownership Share of investment in stocks
>75th percentile 57.789 12.774 0.679 10.164 760.142 0.949 0.120
(336) (336) (336) (318) (328) (336) (323)
25th to 75th percentile 55.203 11.957 0.438 7.871 358.640 0.820 0.074
(950) (950) (950) (912) (928) (950) (866)
<25th percentile 49.295 10.829 0.271 5.284 87.880 0.575 0.040
(351) (421) (421) (382) (410) (421) (351)
Panel C: Sample characteristics for social and non-social households
Sociability Age Education Male Income ($000s) Net wealth ($000s) Stock ownership Share of investment in stocks
Social 51.219 11.651 0.418 7.240 309.669 0.727 0.068
(2460) (2460) (2460) (2315) (2385) (2461) (1873)
Non-social 47.319 10.282 0.410 4.232 56.094 0.420 0.048
(188) (188) (188) (147) (160) (188) (116)
40
Table 3: Correlations matrix. This table reports the Spearman’s rank correlations for all the variables in our sample. The description and construction of all the variables is
detailed in Section 3.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 Stock Ownership 1
2 Share of investment in stocks 0.378 1
3 Stock market literacy 0.316 0.388 1
4 Sociability 0.120 0.052 0.114 1
5 Trust in stock market 0.258 0.208 0.190 0.121 1
6 Age 0.079 0.197 0.219 0.061 0.022 1
7 Education 0.276 0.195 0.319 0.130 0.118 -0.025 1
8 Employed 0.079 -0.043 -0.054 0.044 0.023 -0.483 0.123 1
9 Male 0.113 0.134 0.314 0.026 0.033 0.099 0.071 0.024 1
10 Income 0.355 0.169 0.255 0.121 0.168 -0.080 0.318 0.215 0.093 1
11 Net wealth 0.326 0.386 0.418 0.112 0.226 0.360 0.218 -0.198 0.108 0.311 1
12 Economic shock 0.196 0.164 0.191 0.038 0.010 0.012 0.114 0.034 0.015 0.086 0.118 1
12 Future expectations 0.304 0.270 0.356 0.137 0.216 0.081 0.255 -0.036 0.112 0.392 0.533 0.074 1
14 Optimism 0.097 0.127 0.170 0.141 0.128 0.144 0.097 -0.068 0.029 0.118 0.149 -0.031 0.178 1
15 Risk aversion -0.124 -0.087 -0.176 -0.056 -0.189 0.191 -0.127 -0.124 -0.156 -0.177 -0.051 -0.048 -0.108 -0.018 1
16 Self-con…dence 0.119 0.157 0.200 0.140 0.120 0.211 0.124 -0.074 0.023 0.140 0.181 0.027 0.158 0.642 -0.025 1
17 Sense of commitment -0.000 0.023 0.032 0.042 0.001 0.191 0.050 -0.190 -0.051 -0.051 0.074 -0.063 0.049 0.108 0.038 0.082 1
18 Time preference 0.136 0.197 0.337 0.047 0.121 0.065 0.186 0.004 0.202 0.169 0.298 0.064 0.171 0.061 -0.150 0.080 0.026 1
41
Table 4: Analysis of stock market participation. This table reports the fully standardized probit regression
estimates of Long and Freeze (2006). The robust standard errors are reported in parentheses. The dependent
variable is a dummy variable equal to one for households owning stocks and zero otherwise. The explanatory
variables are stock market literacy, sociability, trust in stock market and demographic variables. ***, ** and *
denote signi…cance at 1, 5 and 10 percent respectively.
(1) (2) (3) (4) (5) (6) (7) (8)
Stock market literacy 0.472*** 0.150*** 0.150*** 0.138*** 0.138***
(0.031) (0.025) (0.025) (0.029) (0.029)
Sociability 0.066*** 0.052** 0.01 -0.002
(0.022) (0.025) (0.019) (0.022)
Trust in stock market 0.221*** 0.219*** 0.156*** 0.156***
(0.027) (0.027) (0.027) (0.028)
Age 0.092*** 0.245*** 0.236*** 0.231*** 0.091*** 0.082*** 0.082***
(0.024) (0.025) (0.028) (0.028) (0.024) (0.028) (0.028)
Education 0.135*** 0.274*** 0.265*** 0.259*** 0.133*** 0.146*** 0.146***
(0.025) (0.028) (0.03) (0.03) (0.026) (0.029) (0.029)
Employed 0.056** 0.087*** 0.096*** 0.093*** 0.056** 0.066** 0.066**
(0.026) (0.026) (0.029) (0.029) (0.026) (0.03) (0.03)
Male 0.005 0.051** 0.038 0.037 0.006 0.012 0.012
(0.024) (0.024) (0.026) (0.026) (0.024) (0.029) (0.029)
Income 0.543*** 0.423*** 0.376*** 0.373*** 0.542*** 0.528*** 0.529***
(0.108) (0.119) (0.138) (0.137) (0.108) (0.114) (0.114)
Net wealth 0.43** 0.093 0.073 0.071 0.429** 0.361* 0.361*
(0.186) (0.071) (0.059) (0.059) (0.186) (0.186) (0.185)
Pseudo R-Squared 0.133 0.269 0.193 0.228 0.230 0.270 0.293 0.293
Observations 1707 1595 2410 2019 2019 1595 1351 1351
42
Table 5: Behavioral characteristics explaining stock market participation. This
table reports the fully standardized probit regression estimates of Long and Freeze (2006).
The robust standard errors are reported in the parentheses. The dependent variable is
a dummy variable equaling one for households owning stocks and zero otherwise. The
explanatory variables are stock market literacy, sociability, trust in stock market, demo-
graphic and behavioral variables. ***, ** and * denote signi…cance at 1, 5 and 10 percent
respectively.
(1) (2) (3) (4) (5) (6)
Stock market literacy 0.138*** 0.138*** 0.113*** 0.113***
(0.03) (0.03) (0.031) (0.031)
Sociability 0.046* -0.001 -0.007
(0.024) (0.025) (0.024)
Trust in stock market 0.203*** 0.165*** 0.166***
(0.026) (0.029) (0.029)
Age 0.109*** 0.232*** 0.109*** 0.226*** 0.107*** 0.108***
(0.031) (0.028) (0.031) (0.028) (0.031) (0.031)
Education 0.156*** 0.243*** 0.156*** 0.216*** 0.143*** 0.144***
(0.031) (0.029) (0.031) (0.029) (0.031) (0.031)
Employed 0.081** 0.113*** 0.081** 0.102*** 0.068** 0.068**
(0.032) (0.029) (0.032) (0.029) (0.032) (0.032)
Male 0.008 0.021 0.008 0.02 0.017 0.017
(0.03) (0.026) (0.03) (0.026) (0.03) (0.03)
Income 0.476*** 0.321*** 0.476*** 0.3*** 0.486*** 0.487***
(0.12) (0.115) (0.12) (0.115) (0.112) (0.112)
Net wealth 0.287 0.043 0.287 0.039 0.259 0.26
(0.215) (0.047) (0.215) (0.045) (0.194) (0.194)
Economic shock 0.126*** 0.149*** 0.126*** 0.156*** 0.137*** 0.137***
(0.032) (0.027) (0.032) (0.027) (0.031) (0.031)
Future expectations 0.105** 0.178*** 0.105** 0.163*** 0.091** 0.092**
(0.05) (0.04) (0.05) (0.039) (0.047) (0.047)
Optimism 0.037 -0.007 0.038 -0.01 0.03 0.031
(0.036) (0.031) (0.036) (0.031) (0.036) (0.035)
Risk aversion -0.062** -0.059** -0.062** -0.034 -0.038 -0.038
(0.028) (0.027) (0.028) (0.027) (0.028) (0.028)
Self-con…dence -0.004 0.039 -0.004 0.028 -0.008 -0.007
(0.035) (0.031) (0.036) (0.031) (0.035) (0.035)
Sense of commitment -0.015 0.003 -0.015 0.019 -0.011 -0.011
(0.028) (0.025) (0.028) (0.025) (0.028) (0.028)
Time preference 0.012 0.065** 0.012 0.047* -0.002 -0.002
(0.03) (0.026) (0.03) (0.026) (0.029) (0.03)
Pseudo R-Squared 0.301 0.243 0.301 0.266 0.326 0.326
Observations 1332 1993 1332 1989 1331 1331
43
Table 6: Analysis of households’share of investment in stocks. This table reports the standardized
beta estimates obtained from ordinary least square regressions. The dependent variable is investment
in stocks as a percentage of total …nancial assets. The explanatory variables are stock market literacy,
sociability, trust in stock market, demographic and behavioral variables. ***, ** and * denote signi…cance
at 1, 5 and 10 percent respectively.
(1) (2) (3) (4) (5) (6) (7)
Stock market literacy 0.210*** 0.095*** 0.097*** 0.085*** 0.087***
(0.014) (0.019) (0.019) (0.019) (0.019)
Sociability -0.026 -0.044 -0.050
(0.019) (0.027) (0.027)
Trust in stock market 0.082*** 0.083*** 0.086***
(0.018) (0.023) (0.023)
Age 0.159*** 0.190*** 0.162*** 0.183*** 0.156*** 0.160***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Education 0.058* 0.096*** 0.062** 0.085*** 0.055* 0.059**
(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)
Employed -0.013 -0.021 -0.010 -0.027 -0.017 -0.013
(0.009) (0.007) (0.009) (0.007) (0.009) (0.009)
Male 0.021 0.035 0.020 0.034 0.025 0.025
(0.008) (0.007) (0.008) (0.007) (0.008) (0.008)
Income -0.091*** -0.077*** -0.091*** -0.079*** -0.091*** -0.091***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Net wealth 0.062 0.053 0.062 0.050 0.058 0.058
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Economic shock 0.103*** 0.131*** 0.104*** 0.131*** 0.106*** 0.107***
(0.017) (0.014) 0.017) (0.014) (0.017) (0.017)
Future expectations 0.085** 0.098*** 0.087** 0.084*** 0.076** 0.078**
(0.017) (0.014) 0.017) (0.014) (0.017) (0.017)
Optimism -0.047 -0.028 -0.043 -0.036 -0.053 -0.049
(0.03) (0.024) 0.029) (0.024) (0.029) (0.029)
Risk aversion -0.011 -0.012 -0.012 -0.000 -0.000 -0.001
(0.023) (0.017) 0.023) (0.017) (0.022) (0.022)
Self-con…dence 0.075** 0.073** 0.077** 0.067** 0.073** 0.076**
(0.023) (0.018) 0.023) (0.018) (0.023) (0.023)
Sense of commitment 0.015 0.001 0.017 0.004 0.017 0.019
(0.032) (0.026) 0.032) (0.026) (0.031) (0.031)
Time preference 0.080*** 0.110*** 0.079*** 0.106*** 0.076** 0.075**
(0.014) (0.011) 0.014) (0.011) (0.014) (0.014)
Adjusted R-squared 0.044 0.114 0.122 0.115 0.127 0.119 0.121
Observations 1542 1239 1577 1239 1575 1239 1239
44
Table 7: Stock market participation for high and low sociability households. This table reports the
fully standardized probit regression estimates of Long and Freeze (2006). Panel A reports regression estimates
for the high sociability households, while Panel B reports regression estimates for the low sociability households.
We de…ne high sociable households as those that participate in two or more social activities and low sociable
households as those that participate in at most one social activity. The robust standard errors are reported in
parentheses. The dependent variable is a dummy variable equal to one for households owning stocks and zero
otherwise. The explanatory variables are stock market literacy, sociability, trust in stock market and demographic
variables. ***, ** and * denote signi…cance at 1, 5 and 10 percent respectively.
(1) (2) (3) (4) (5) (6)
Panel A: High sociability households
Stock market literacy 0.422*** 0.405*** 0.117*** 0.092**
(0.036) (0.037) (0.036) (0.036)
Sociability 0.154*** 0.083* 0.010 0.002 0.01
(0.032) (0.044) (0.038) (0.033) (0.038)
Trust in stock market 0.202*** 0.185***
(0.031) (0.033)
Demographics and behavioral characteristics No No No Yes Yes Yes
Pseudo R-Squared 0.108 0.011 0.111 0.277 0.238 0.309
Observations 1345 1984 1347 1088 1565 1087
Panel B: Low sociability households
Stock market literacy 0.515*** 0.508*** 0.101*** 0.099***
(0.065) (0.065) (0.033) (0.035)
Sociability 0.140*** 0.056 -0.027 0.035 -0.028
(0.048) (0.062) (0.032) (0.048) (0.033)
Trust in stock market 0.165*** 0.036
(0.05) (0.034)
Demographics and behavioral characteristics No No No Yes Yes Yes
Pseudo R-Squared 0.146 0.009 0.147 0.432 0.298 0.436
Observations 358 691 358 244 424 244
45
Table 8: Stock market participation for households with various sociability and stock market literacy levels. This
table reports the fully standardized probit regression estimates of Long and Freeze (2006). Panel A reports regression estimates for
households with high sociability and low stock market literacy and Panel B reports regression estimates for households with low
sociability and high stock market literacy. We de…ne high sociable households as those that participate in two or more social activities
and low sociable households as those that participate in at most one social activity. Households with the stock market literacy
index score above (below) the median are considered high (low) stock market literate. The robust standard errors are reported
in parentheses. The dependent variable is a dummy variable equal to one for households owning stocks and zero otherwise. The
explanatory variables are stock market literacy, sociability, trust in the stock market and demographic variables. ***, ** and * denote
signi…cance at 1, 5 and 10 percent respectively.
(1) (2) (3) (4) (5) (6)
Panel A: Households with high sociability and low stock market literacy
Stock market literacy 0.212*** 0.202*** 0.056 0.037
(0.051) (0.051) (0.046) (0.045)
Sociability 0.103* 0.076 0.033 0.045 0.042
(0.054) (0.055) (0.049) (0.048) (0.049)
Trust in stock market 0.235*** 0.232***
(0.047) (0.047)
Demographics and behavioral characteristics No No No Yes Yes Yes
Pseudo R-squared 0.022 0.005 0.025 0.229 0.269 0.270
Observations 659 659 659 526 525 525
Panel B: Households with low sociability and high stock market literacy
Stock market literacy 0.415*** 0.411*** 0.107** 0.107**
(0.125) (0.123) (0.043) (0.043)
Sociability 0.076 0.05 0.022 0.017 0.022
(0.104) (0.094) (0.030) (0.032) (0.030)
Trust in stock market 0.014 0.001
(0.033) (0.035)
Demographics and behavioral characteristics No No No Yes Yes Yes
Pseudo R-squared 0.085 0.003 0.086 0.483 0.425 0.483
Observations 178 178 178 128 128 128
46
Table 9: Analysis of stock market participation with the alternative sociability measure.
This table reports in Panel A the fully standardized probit regression estimates of Long and Freeze
(2006), while Panel B reports the standardized beta estimates from ordinary least squares regressions.
The robust standard errors are reported in parentheses. The dependent variable in Panel A is a dummy
variable equal to one for households owning stocks and zero otherwise. In Panel B, the dependent
variable is investment in stocks as a percentage of total …nancial assets. The explanatory variable
sociability takes the value of one if the households have casted their votes in national elections, and
zero otherwise. The other explanatory variables are stock market literacy, trust in stock market,
and all demographic and behavioral variables previously considered. For readability, we only report
estimates for key explanatory variables. ***, ** and * denote signi…cance at 1, 5 and 10 percent
respectively.
(1) (2) (3) (4) (5) (6) (7)
Panel A: Results for stock market participation
Stock market literacy 0.138*** 0.134*** 0.113*** 0.11***
(0.03) (0.031) (0.031) (0.031)
Sociability 0.069*** 0.023 0.056** 0.008
(0.023) (0.024) (0.023) (0.023)
Trust in stock market 0.203*** 0.165*** 0.180*** 0.166***
(0.026) (0.029) (0.028) (0.029)
Pseudo R-Squared 0.301 0.286 0.323 0.266 0.326 0.310 0.323
Observations 1332 1688 1316 1989 1331 1684 1315
Panel B: Results for share of investment in stocks
Stock market literacy 0.095*** 0.096*** 0.085*** 0.086***
(0.019) (0.019) (0.019) (0.019)
Sociability -0.008 -0.013 -0.017 -0.021
(0.008) (0.010) (0.008) (0.0109
Trust in stock market 0.082*** 0.083*** 0.086*** 0.084***
(0.0183) (0.023) (0.019) (0.023)
Adjusted R-squared 0.124 0.130 0.123 0.135 0.130 0.136 0.129
Observations 1239 1552 1234 1575 1239 1550 1234
47