3.1 Model I: Financial literacy and asset returns

In Model I, the portfolio return is paid at the beginning of period 1 on wealth transferred from period 0 to 1. Denoting by ω the share of wealth invested in the risky asset, the gross portfolio return is:

$$R({\Phi _1},\alpha, \zeta, \omega ) = \left\{ {\matrix{ {{\theta _1}({\Phi _1},\alpha, \zeta, \omega )} & {{\rm with}\;{\rm probability}} & {\eta ({\Phi _1}),} \cr {{\theta _2}({\Phi _1},\alpha, \zeta, \omega )} & {{\rm with}\;{\rm probability}} & {1 - \eta ({\Phi _1}),} }} \right.$$

where θ ₁(Φ ₁ ,α,ζ,ω) = Φ ₁ ^α (1+ωζ) and θ ₂(Φ ₁ ,α,ζ,ω) = Φ ₁ ^α (1−ωζ), ζ > 0 and η′(·) > 0 and η″(·) < 0. The higher the parameter α, the stronger the effect of raising literacy on the portfolio return. If ω = 0, wealth is entirely invested in the riskless asset and the gross return is Φ ₁ ^α . If ω = 1, wealth is entirely invested in the risky asset and the gross return is Φ ₁ ^α (1+ζ) with probability η(Φ₁) and Φ ₁ ^α (1−ζ) with probability 1 − η(Φ₁). Therefore, the mean return of the risky asset is {ζ[2η(Φ ₁)−1] + 1}Φ ₁ ^α and the first two moments of the equity premium distribution are [2η(Φ ₁) − 1]Φ ₁ ^αζ and Φ ₁ ^{2 α}ζ, respectively. The Sharpe ratio is an increasing function of financial literacy since η′(·) > 0, an assumption that is motivated by the empirical literature on portfolio performance and financial sophistication surveyed in Section 2.Footnote ¹⁰

Appendix A.1 solves the model and shows that the share of wealth invested in the risky asset is:

(2) $$\omega = \displaystyle{{\eta {{({\Phi _1})}^\sigma}- \mathop {\left[ {1 - \eta ({\Phi _1})} \right]}\nolimits^\sigma}\over {\zeta \left\{ {\eta {{({\Phi _1})}^\sigma}+ \mathop {\left[ {1 - \eta ({\Phi _1})} \right]}\nolimits^\sigma}\right\}}}.$$

Equation (2) has an important implication for empirical work. In a cross-section of households reporting information on financial literacy (Φ₁) and the risky asset share (ω), equation (2) implies a positive association between the two variables. But clearly it cannot be concluded from this correlation that a higher stock of literacy leads to a higher risky asset share, because both variables are endogenous. In our model, equation (2) is therefore an equilibrium condition between the optimal risky asset share and the optimal stock of literacy, not a reduced form equation. Thus, it implies that any factor that leads to higher financial literacy will also raise investment in the risky asset.

As we show in Appendix A.1, the marginal return of financial literacy depends on the effect of literacy on the expected portfolio return as well as on the distribution of the asset return. Furthermore, Appendix B derives the fairly general conditions under which the marginal return of financial literacy is a decreasing function of Φ₁, leading to the following proposition.

Proposition 1

If the marginal return of financial literacy is a decreasing function of Φ ₁ , the optimal level of financial literacy is an increasing function of α, β, Φ₀, and y and a decreasing function of p and δ, i.e.:

$$\displaystyle{{\partial \Phi _1^ *}\over {\partial \alpha}} \gt 0,\quad \displaystyle{{\partial \Phi _1^ *}\over {\partial \beta}} \gt 0,\quad \displaystyle{{\partial \Phi _1^ *}\over {\partial {\Phi _0}}} \gt 0,\quad \displaystyle{{\partial \Phi _1^ *}\over {\partial y}} \gt 0,\quad \displaystyle{{\partial \Phi _1^ *}\over {\partial p}} \lt 0,\quad \displaystyle{{\partial \Phi _1^ *}\over {\partial \delta}}\lt 0.$$

Figure 1 plots the marginal cost (straight line) and the marginal return (curved line) of investing in financial literacy as a function of Φ₁. The curved line shifts up if α increases, that is, the optimal level of literacy increases with α. The curve shifts upwards also if β, Φ₀, y increase, and downwards if p or δ increase.

Note: The figure plots the marginal return (MR) and the marginal cost (p) of financial literacy against Φ₁. Φ₁ ^* is the optimal level of financial literacy investment at which the marginal return equals the marginal cost.

Figure 1. Marginal return and cost of investing in financial literacy.

From equation (2), the risky asset share ω is positively associated with Φ₁ ^*; therefore the optimal share of risky assets is an increasing function of Φ₀. In addition, since Φ₁ ^* is an increasing function of αβ, Φ₀, and y and a decreasing function of p and δ, one can show the following proposition.

Proposition 2

If the marginal return of financial literacy is a decreasing function of Φ ₁ , then the optimal share of risky assets is an increasing function of α, β, Φ₀, and y and a decreasing function of p and δ, i.e.:

$$\displaystyle{{\partial {\omega ^ *}}\over {\partial \alpha}}\gt 0,\quad \displaystyle{{\partial {\omega ^ *}}\over {\partial \beta}}\gt 0,\quad \displaystyle{{\partial {\omega ^ *}}\over {\partial {\Phi _0}}} \gt 0,\quad \displaystyle{{\partial {\omega ^ *}}\over {\partial y}} \gt 0,\quad \displaystyle{{\partial {\omega ^ *}}\over {\partial p}} \lt 0,\quad \displaystyle{{\partial {\omega ^ *}}\over {\partial \delta}}\lt 0.$$

In addition, ${\rm lim}_{\sigma \to \infty} {\omega ^{\ast}} = {\textstyle{1 \over \zeta}} \gt {\rm lim}_{\sigma \to 0}\,{\omega ^{\ast}} = 0.$

Proposition 2 has three implications. First, any factor leading to a high share of wealth invested in risky assets also increases financial literacy. For instance, patient individuals (high β) feature a relatively high share of risky assets as well as relatively high levels of financial literacy.Footnote ¹¹ For the same reason, any variable that affects literacy also affects the risky asset share. For instance, as we shall see below, the generosity of the social security system affects the risky asset share as well as financial literacy. Second, the initial stock of literacy, Φ₀, affects the risky asset share only through its effect on the current stock of literacy Φ₁ ^*. The third implication is that while in standard models with constant relative risk aversion (CRRA) the risky asset share does not depend on wealth, in this setup the share depends – through its effect on literacy – on households’ resources. Therefore, the model delivers a positive correlation between the risky asset share and wealth, even with a CRRA utility function, contrary to the standard portfolio model.

To study the effect of social security on financial literacy investment and portfolio choice, we modify the baseline model and assume that in period 0 consumers earn income y, and in period 1 they collect pension benefits denoted by b. Appendix A.1 solves the model and shows that Φ₁ ^* is a decreasing function of b and that a higher Φ₀ dampens the effect of b on Φ₁ ^*. To provide the intuition for these results, we plot in Figure 2 the relation between the optimal stock of financial literacy and the replacement rate (b/y). The relation between these two variables is negative because a more generous social security system reduces private wealth and the incentive to invest in financial literacy as well as the risky asset share. Figure 2 also shows that the effect of the replacement rate on optimal literacy depends on the initial value of literacy Φ₀: the higher Φ₀ the lower the effect of the replacement rate on Φ₁ ^*, an implication of the model that we will empirically evaluate.

Note: The figure plots the optimal level of financial literacy, Φ₁ ^*, against the replacement rate (b/y). The model's parameters are set as follows: α = 0.3, β = 0.99, δ = 0.3, σ = 0.5, y = 1, p = 0.1. The continuous line is obtained setting Φ₀ to 2, the dotted setting Φ₀ to 2.5.

Figure 2. Optimal stock of financial literacy and replacement rate

3.2 Model II: Financial literacy and transaction costs

We now assume that acquiring financial literacy reduces the transaction cost of entering the stock market, rather than assuming that it raises the asset return (as in Model I). In particular, we assume that:

$$R = \left\{ {\matrix{ {1 + \omega \zeta}& {{\rm with}\;{\rm probability}} & {\eta,}\cr {1 - \omega \zeta}& {{\rm with}\;{\rm probability}} & {1 - \eta,}}} \right.$$

where η > 1/2. Moreover, we assume that if ω > 0, the consumer incurs a transaction cost equal to (Φ ₁ ^−γ/γ), with γ > 0.

Under these assumptions the intertemporal budget constraint is

$${c_0} + \displaystyle{{{c_1}} \over R} - p{\Phi _1} + p(1 - \delta ){\Phi _0} - \displaystyle{{\Phi _1^{ - \gamma}} \over \gamma} 1\left\{ {\omega \gt 0} \right\} = y,$$

where 1{·} is an indicator function and the other variables are defined as in Model I. Appendix A.1 shows that in Model II the share of wealth invested in risky assets does not depend on financial literacy, contrary to what happens in Model I. Furthermore, one can show that the utility gain from stockholding is a monotonically increasing function of Φ₀ since the utility of investing in the risky asset is an increasing function of Φ₀, while the utility of not investing in risky assets is not affected. The result is summarized in the following proposition:

Proposition 3 implies that (in a random utility setting) the probability of stock-market participation increases with Φ₀, an important difference with respect to Model I. From Proposition 3 one can also show that the optimal level of financial literacy is an increasing function of Φ₀ (see Appendix A.1 for details). Moreover, the following proposition holds.

Proposition 4 implies that if Φ₀ is small enough it may not be optimal to invest in the risky assets. Despite this fact, as noted by Lusardi and Mitchell (Reference Lusardi and Mitchell2014), it might still be socially optimal to raise financial knowledge early in life, for instance teaching financial education in schools, because raising Φ₀ allows consumers to attain higher returns on their portfolios. From an empirical point of view, a further implication of Proposition 4 is that in a cross-section of households Φ₁ and Φ₀ are positively correlated (Model I has the same implication).Footnote ¹²

As in Model I, we introduce a social security system assuming that consumers pay a contribution in period 0 and receive a pension b in period 1. The budget constraint is:

$${c_0} + \displaystyle{{{c_1}} \over R} - p{\Phi _1} + p(1 - \delta ){\Phi _0} - \displaystyle{{\Phi _1^{ - \gamma}} \over \gamma} 1\left\{ {\omega \gt 0} \right\} = y + \displaystyle{b \over R}.$$

Appendix A.1 shows that the first-order conditions of the model are unchanged, and that Propositions 3 and 4 still hold. In addition, one can show that, ${\bar \Phi _0}$ , the level of financial literacy that triggers participation to the stock market, is an increasing function of b. Moreover, stock-market participation and investment in financial literacy are negatively correlated with the generosity of the social security system as measured by the replacement rate.

3.3 Empirical implications

In our model, consumers choose how much to invest in financial literacy, how much to save, and how much to invest in risky assets. Therefore, the endogenous variables are financial literacy, wealth, and the share of risky assets, and each depends on the model's parameters and the initial endowments of resources and literacy. In a related paper, we highlight two important determinants of financial literacy and wealth accumulation (Jappelli and Padula, Reference Jappelli and Padula2013). First, improving mathematical skills early in life eventually will raise households’ financial literacy and wealth accumulation. Second, a generous social security system reduces the incentive to invest in financial literacy, leading also to lower financial literacy and wealth later in life.

The present paper focuses on wealth composition, and attempts also to distinguish between two channels through which financial literacy can affect portfolio choice. Model I focuses on the effect of literacy on the distribution of asset returns, and posits that higher (and safer) returns are associated with higher financial literacy. Model II assumes that higher financial literacy reduces the cost of stock-market participation. Both models predict a positive effect of literacy earlier in life (Φ₀), on the trajectory of financial literacy (Φ₁) but differ along important dimensions. Model I implies that in a heterogeneous population, where people are identical except for their initial stock of literacy: (a) everyone participates in the stock market, and (b) the share of risky assets is positively related to financial literacy. Model II implies that (a) participation depends on literacy but (b) the asset share, conditional on participation, does not. Therefore, to compare the validity of the two models we need to study the correlation between shares of risky assets, stockholding, and financial literacy. A positive correlation between literacy and asset shares, and no correlation between literacy and participation, would support Model I. Alternatively, a positive correlation between literacy and stockholding and no correlation between literacy and the share of risky assets would support Model II.

In our empirical study, we verify some other important implications of the two models. In particular, we focus on the role of social security for the incentives to accumulate financial literacy, exploiting cross-country variation in replacement rates. We include in our regressions the replacement rate and its interaction with Φ₀, and test three empirical predictions: (a) financial literacy is a decreasing function of the replacement rate; (b) stock-market participation is negatively related to the replacement rate; and (c) a higher Φ₀ attenuates the effect of the replacement rate on Φ₁, stockholding, and the share of risky assets.

To make our tests operational, we estimate the linear projections of financial literacy, the share of risky assets, and stock-market participation, on the initial level of literacy and the social security replacement rate; the projections can be seen as linear approximations of the reduced form equations of the model. To account for the role of other potential effects on stockholding and the share of risky assets, we control for other exogenous variables, which are held constant in the theoretical model. Denoting households by i, countries by c, and survey year by t, we estimate the following regression:

(3) $${y_{i,c,t}} = {d_c} + {\xi _1}{\Phi _{i,0}} + {\xi _2}{\Phi _{i,0}} \times {\rho _{ic}} + {\xi _3}{\rho _{ic}} + {\xi _4}{x_{it}} + {\varepsilon _{it}};$$

where d _c is a country effect, ρ _ic the replacement rate, x _i,t a vector of additional variables affecting portfolio choice, ε _i,t an error term, and y _i,c,t either the current stock of financial literacy (Φ _i,t ), stock-market participation or the share of wealth invested in risky assets (ω _i,t ).

Suppose first that y _i,c,t is financial literacy. Both Models I and II imply a positive correlation between Φ _i,t and Φ _i,0, i.e., ξ ₁ > 0; see Propositions 1 and 3. Furthermore, in both models a higher replacement rate reduces Φ _i,t as well as the effect of Φ _i,0 on Φ _i,t , implying ξ ₂ < 0 and ξ ₃ < 0. If y _i,c,t is the decision to invest in stock, Model I predicts that everyone should invest in stocks, so that ξ ₁ = ξ ₂ = ξ ₃ = 0, while in Model II ξ ₁ > 0, ξ ₂ < 0, and ξ ₃ <  0. If y _i,c,t denotes the share of risky assets, then Model I predicts ξ ₁ > 0, ξ ₂ < 0 and ξ ₃ < 0, since the share of risky assets is an increasing function of financial literacy and a decreasing function of the replacement rate. Instead, in Model II ξ ₁ = ξ ₂ = ξ ₃ = 0, because conditional on stock-market participation, the share of risky assets does not depend on financial literacy.

The list of the x-variables is potentially large, but three variables are prominent in our specification. A first important variable is age which, in principle, may affect both portfolio decisions and financial literacy accumulation. The relation between age and financial literacy is likely to be negative in the 50+ sample since cognitive abilities tend to decline with age. However, our data do not allow us to distinguish between age and cohort effects, and therefore identification of a pure age effect is impossible in our empirical estimates. Previous studies report that the relation between age and the decision to invest in risky assets tends to be negative for the elderly, while there is a weaker relation for the share invested in risky assets. However, once more, cohort effects might cloud the identification of age effects. A second important element is that financial literacy and wealth are likely to be correlated with education, and therefore it is important to control explicitly for this variable. Third, households’ resources (real estate, financial wealth, and income) are likely to affect the incentives to acquire financial literacy, stock-market participation, and the share of risky assets. As we explain in the next section, we estimate the model using cross-country microeconomic data with information on wealth composition, current financial literacy, and financial literacy early in the life-cycle.

4.1 Financial literacy

SHARE includes four questions referring to simple financial decisions, which allow us to construct a measure of financial literacy. The first question is aimed at understanding whether respondents know how to compute a percentage. The second and third questions ask respondents to compute the price of a good offered at a 50% discount, and the price of a second-hand car that sells at two-thirds of its cost when new. The fourth question is about understanding interest rate compounding in a saving account, and is commonly considered a good proxy for financial literacy; see Lusardi and Mitchell (Reference Lusardi and Mitchell2008), Lusardi et al. (Reference Lusardi, Mitchell and Curto2010), Hastings et al. (Reference Hastings, Madrian and Skimmyhorn2013), and Lusardi and Mitchell (Reference Lusardi and Mitchell2014).

The first three questions reflect the ability to apply a minimal level of mathematical literacy, and the fourth is a question typically included in almost all financial literacy assessment studies.Footnote ¹⁵ Following Dewey and Prince (Reference Dewey, Prince, Börsch-Supan, Brugiavini, Jürges, Mackenbach, Siegrist and Weber2005), we combine the responses to the four questions into a summary indicator of the current stock of literacy Φ _it . Details on the wording of the questions and the construction of the indicator are given in Appendix C and discussed further in Christelis et al. (Reference Christelis, Jappelli and Padula2010).

Our approach recognizes that a certain level of mathematical competence is a necessary condition for financial skills; in fact, any financial literacy assessment invariably includes questions that require some amount of mathematical literacy. For instance, a minimum level of mathematical literacy is required to compute a percentage, to understand the meaning of interest compounding and uncertainty, and to evaluate asset returns. Therefore, in our empirical application, we are confident that our SHARE indicator of financial literacy is closely correlated to a broader concept of financial literacy, such as that provided by the OECD which defines financial literacy as: ‘Knowledge and understanding of financial concepts, and the skills, motivation and confidence to apply such knowledge and understanding in order to make effective decisions across a range of financial contexts, to improve the financial well-being of individuals and society, and to enable participation in economic life.’

In the model in Section 3, Φ _i0 is the financial literacy endowment before entering the labor market. SHARE retrospective data (SHARELIFE) provide a plausible measure of this endowment. Survey participants report their mathematical ability at age 10 in response to the question: ‘How did you perform in Maths compared to other children in your class? Did you perform much better, better, about the same, worse or much worse than the average?’Footnote ¹⁶ Although mathematical skills do not span exactly the same domain as financial literacy, ongoing research shows that there is a close correlation between the two concepts. Indeed, preliminary results from the most recent PISA survey show that financial literacy among the young is strongly correlated with mathematical literacy, and these financially sophisticated respondents are also likely to be relatively skilled in terms of mathematical competence.Footnote ¹⁷

The indicator of current financial literacy (Φ _it ) ranges from 1 to 5, with a sample mean of 3.43 for Wave 1 and 3.48 for Wave 2 (Table 1). In both waves, the indicator exhibits considerable sample variability, with a coefficient of variation of 0.32. Our measure of initial literacy (Φ _i0) also ranges from 1 to 5, with similar means and coefficients of variation. Our measures of Φ _it and Φ _i0 are imperfect proxies for financial literacy, and can therefore be seen as error-ridden measures of financial literacy. To the extent that both variables are affected by measurement error, the sample correlation between Φ _it and Φ _i0 (0.28) actually underestimates the true correlation.

4.2 Replacement rate

The old-age pension replacement rate measures how effectively a pension system provides a retirement income to replace earnings. We adopt the OECD definition of gross replacement rates (OECD, 2009), i.e., individual gross pension entitlement divided by gross pre-retirement earnings, taking account of both public and private mandatory pension schemes. Pension benefits are expressed as a share of individual lifetime average earnings (re-valued in line with economy-wide earnings growth). Under the baseline assumptions, workers earn the same percentage of economy-wide average earnings throughout their careers. The OECD reports gross replacement rates for all countries in our sample at average earnings and at 0.5 and 1.5 times average earnings levels. These replacement rates are generally lower for higher levels of income, and are imputed to our sample using the earnings distribution. Although the replacement rate varies across countries and individuals, it exhibits little variability in our data. Considering that we introduce country dummies, there are only three different values of the replacement rate in each country. For this reason, the coefficient of the replacement rate is likely to be imprecisely estimated.

4.3 Stockholding and risky asset share

SHARE provides detailed information on financial and real assets. Financial assets include bank and other transaction accounts, government and corporate bonds, stocks, mutual funds, individual retirement accounts, contractual savings for housing, and life insurance policies. The questions on real assets refer to the value of the house of residence, other real estate, business wealth, and vehicles (see Christelis et al. Reference Christelis, Jappelli and Padula2010).

We adopt two definitions of stockholding: direct stockholding and total stockholding, defined as stocks held directly plus stocks held through mutual funds and investment accounts (assuming that whoever holds mutual funds and retirement accounts has some stocks in them).Footnote ¹⁸ Figure 3 reports participation in direct and total stockholding in the 11 countries in our sample. The prevalence of direct stockholding ranges from less than 6% in Greece and Italy, to 49% in Sweden. Total stockholding goes from about 10% in Austria, Spain, and Italy to 75% in Sweden.Footnote ¹⁹

Note: The country means are computed merging the Waves 1 and 2 of SHARE. Total stockholding is defined as direct ownership of stocks and ownership through mutual funds.

Figure 3. Stock-ownership, by country

Broadly speaking, stockholding increases, from Southern to Northern Europe, with a group of intermediate countries (France, Germany, Belgium, the Netherlands, and Switzerland). Sweden and Denmark have by far the highest direct and total stockholdings, whereas Austria, Spain, Greece and Italy are at the other end of the spectrum. The graph suggests that country effects are potentially quite important for explaining the stockholding decisions of European investors. Thus, our regression framework introduces country fixed effects in each of the specifications.

In contrast, Figure 4 shows that cross-country differences in conditional asset shares (excluding households with zero stockholding) are much less pronounced. The share of wealth held directly in stocks ranges from 20% in Denmark and Sweden, to 35% in Austria and Italy. Therefore, the relatively small number of stockholders in Italy and Greece invest in stocks more than the average European household. Northern countries feature intermediate values for the share of risky assets, with the notable exception of Sweden, where the share of wealth invested directly and indirectly in risky assets represents almost 40% of financial wealth.

Note: The country means are computed merging the Waves 1 and 2 of SHARE. Total stockholding is defined as direct ownership of stocks and ownership through mutual funds.

Figure 4. (colour online) Asset shares, by country

5.1 Financial literacy

Table 2 presents the OLS regressions for financial literacy, separately for Waves 1 and 2. Each regression also includes a full set of country dummies; for reasons of space, these coefficients are not reported here.Footnote ²⁰ In the baseline specification in column 1 we find that Φ _i0 is a strong predictor of Φ _it . The coefficient of Φ _i0 is large (0.27) and quite precisely estimated (the standard error is 0.02). This finding is consistent not only with our model's prediction but also with other evidence on the long-term impact of early-life conditions (see, for instance, Herd et al. Reference Herd, Holden and Su2012). The age coefficient is negative (−0.018), and shows that in this sample of older individuals, the stock of literacy falls by about 0.5% per year, suggesting that households incentives to invest in financial literacy decline with age, when wealth tends also to fall.

Table 2. Financial literacy

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

The coefficient of the female dummy is negative. Women have lower levels of financial literacy than men which are in line with the results from other studies (see Lusardi and Mitchell, Reference Lusardi and Mitchell2008). Our model also predicts a negative effect because women generally have less wealth than men, and therefore fewer incentives to invest in financial literacy. Education is strongly correlated with literacy (a coefficient of 0.41 for high-school and 0.59 for college graduates). The positive correlation is also consistent with our model, because higher human capital and lifetime income are associated with a higher stock of financial literacy. The negative signs of the coefficient of the dummy for singles and family size are likely to depend on the fact that these variables are negatively correlated with wealth. The coefficient of the interaction term between the replacement rate and Φ _i0 is negative, indicating that more generous social security systems attenuate the effect of Φ _i0 on later financial literacy, as predicted by Models I and II.

The coefficient of the replacement rate is negative as expected, although not precisely estimated. The coefficient of the interaction term (Φ _i0 × ρ _ic ) is negative and statistically different from zero at the 1% level. It implies that a 1% increase in the replacement rate reduces the effect of Φ _i0 on Φ _it by 0.17%. The effect of Φ _i0 on Φ _it is larger in countries with relatively low replacement rates such as Germany (a 1 standard deviation increase in Φ₀ leads to an increase in Φ _it of 0.20) than in countries with higher replacement rates (0.16 in Italy).

Column 2 in Table 2 includes health status and log disposable income to rule out that the effect of Φ _i0 on Φ _it is due simply to the correlation between Φ _i0 and these variables. The coefficients of health status and log income are positive and statistically different from zero, whereas the other coefficients are not affected. In the next regression (column 3), we check the stability of the results replacing the age variable with a full set of age dummies. The pattern of the estimated coefficients of the age dummies (not reported for brevity) indicates that the stock of financial literacy falls during retirement, while the coefficients of the other variables are unaffected. Of course, in cross-sectional data we cannot distinguish between age and cohort effects, and therefore an interpretation of the age dummies in terms of cohort effects (literacy is higher for younger generations) would be equally possible. The other three regressions in Table 2 repeat the estimation using data from Wave 2. The size and significance of the coefficients is very similar to Wave 1. In particular, the coefficient of Φ _i0 ranges between 0.25 and 0.27 and is precisely estimated, whereas the coefficient of the interaction between Φ _i0 and ρ _c is negative, confirming the model's prediction that a more generous social security system attenuates the effect of Φ _i0.Footnote ²¹

5.2 Stockholding

Models I and II predict that the decision to invest in stocks and financial literacy are positively correlated. We study direct and total stockholding separately; the latter includes stocks owned through managed investment accounts and mutual funds. We use the same specification as for financial literacy, relating stock-market participation to demographic variables, education, indicators of household resources and – most importantly for the present study – the initial stock of literacy Φ _i0.

The results for direct and total stockholding are reported in Tables 3 and 4, respectively. Each of the two tables reports separate results for Waves 1 and 2. The regressions indicate that both direct and total stockholding fall with age, a result consistent with many other studies (see the survey by Guiso and Sodini, Reference Guiso, Sodini, Constantinides, Harris and Stulz2013). The results are similar for direct and total stockholding and for the two waves of SHARE, and imply that every 10 years stockholding falls by about 2%.Footnote ²² Introducing age as a linear variable does not affect any of our results, as shown in Tables 3 and 4 columns 3 and 6 where a set of age dummies replaces the linear age term. The coefficient of the female dummy is negative but imprecisely estimated, possibly because financial literacy captures part of the gender gap in stockholding, as argued in a recent paper by Almenberg and Dreber (Reference Almenberg and Dreber2011).

Table 3. Direct stock−market participation

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

Table 4. Direct and indirect stock-market participation

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

Singles are 9% less likely to invest in stocks than couples (the omitted category). But being single is correlated with household resources. In fact, controlling for income and wealth reduces the effect by a factor of roughly 3. High-school and college graduates are, respectively, 4.7 and 14.5 percentage points more likely than high-school drop-outs to hold stocks directly. The coefficient of initial literacy (Φ _i0) is positive and statistically different from zero: an increase of one standard deviation of Φ _i0 is associated with an increase in stockholding of about 5 percentage points, and the result is quite stable across specifications. Results for total stockholding (Table 4) are similar. These results are consistent with Model II which predicts that financial literacy triggers participation by reducing entry costs.

The coefficient of the replacement rate is negative in all regressions for direct stockholding, and in all but one regressions for total stockholding. In most specifications, however, the coefficient is not statistically different from zero. The coefficient of the interaction term (Φ _i0 × ρ _ic  ) is negative and significant (ξ ₂ < 0), showing that a higher replacement rate attenuates the effect of Φ _i0 on stockholding, consistent again with Model II. The effect is similar across specifications and definitions of stockholding (direct or total), meaning that a 1% increase in the replacement rate reduces the effect of Φ _i0 on stock-ownership by about 0.06 percentage points.

The effect of Φ _i0 on direct stockownership varies with the replacement rate, and countries with relatively low replacement rates display stronger effects. For instance, in Germany a one standard deviation increase in Φ _i0 increases participation by 3 percentage points, whereas for Italy the increase is only 1.5 points.

5.3 Risky asset share

Our final set of results refers to the share of assets invested in stocks. In this case, we also use two definitions of stockholding (direct and total). Model I shows that financial literacy might affect not only stock-market participation but also the share of risky assets, allowing people to invest in assets with higher returns, whereas Model II predicts no relation. We estimate a Tobit model for the financial asset share invested in stocks and find no effect of financial literacy on the risky asset share (at conventional significance levels), regardless of the definition of the share (direct stockholding as in Table 5, or total stockholding as in Table 6). Combined with the evidence on stock-market participation, the results lend support to models (such as Model II) where literacy affects the decision to own stocks but not the asset share invested.

Table 5. Asset shares – direct stockholding

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

Table 6. Asset shares – direct and indirect stockholding

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

Note that, compared to stock-market participation, asset shares are more volatile and more difficult to predict. Most of the estimated coefficients, while reasonably signed, are not precisely estimated, with the notable exception of the high-school and college dummies, which suggests a positive relation between education and the share of risky assets.

According to standard portfolio theory with CRRA, the share of assets invested in risky assets should be independent of wealth. Our results instead reveal a positive relation between household resources and share of risky assets, suggesting that exposure to stock-market risk tends to be higher for the wealthy. The dummy for singles is negative and statistically different from zero but the effect is much reduced if we control for household resources (income and wealth). Better health status is also positively associated with a higher share of risky assets, consistent with the argument that people exposed to background risks (such as health) tend to limit exposure to risks that can be avoided.

The regressions in Tables 5 and 6 also indicate that the coefficient of Φ _i0 is never statistically different from zero. We therefore use Φ _i0 as the identifying variable in a selectivity-model of the share of risky assets, assuming that Φ _i0 affects the participation decision but not the asset share. The main advantage of the selectivity model with respect to the Tobit model is that we can focus on the conditional asset share, i.e., restrict attention to the sample of actual stockholders. The model also allows us to distinguish between the extensive and intensive margins (respectively the decision to invest in stocks and the amount invested). The results are reported in Tables 7 and 8.

Table 7. Conditional asset shares – direct stockholding

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. λ is the inverse Mills ratio. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

Table 8. Conditional asset shares – direct and stockholding

Note: All regressions include a full set of country dummies. Wave 1 was collected in 2004 and Wave 2 in 2006/2007. λ is the inverse Mills ratio. *p < 0.1, **p < 0.05, ***p < 0.01 (standard errors in parentheses).

The selectivity model confirms many of the results of the Tobit regressions, in particular that household resources affect conditional asset shares, the positive effect of age, gender, and being single. The pattern of the coefficients of the age dummies (not reported in columns 3 and 6 for brevity) suggest that the age profile of the conditional asset share is hump-shaped. The selectivity model is also consistent with non-random selection since in most specifications, the coefficient of the inverse Mills ratio is statistically different from zero for both direct and total stockholding.