2 The model

We integrate investment in financial information in a standard model of intertemporal choice. The model emphasizes that, like other forms of human capital, financial information can be accumulated, and that the decision to invest in financial sophistication has costs and benefits. On the costs side, investing in financial sophistication requires time and monetary resources. On the benefits side, financial sophistication allows consumers to access better investment opportunities, thereby raising the return on each euro saved. To the best of our knowledge, Arrow (Reference Arrow1987) was the first to propose, in a theoretical model, the idea that investors can increase the payoff from their financial portfolios by acquiring information on the rate of return. The assumption is consistent with many empirical studies showing that there is substantial dispersion in portfolio returns across households, and that portfolio performance is associated with financial sophistication and investors' experience (see for instance Calvet et al., Reference Calvet, Campbell and Sodini2007). In Section 5, we discuss this literature in more detail.

We illustrate the role of financial sophistication in a multi-period model with endogenous saving and investment in financial information.Footnote ¹ The setup is a partial equilibrium model, and neglects any asset pricing implication.Footnote ² More specifically, we consider an intertemporal model in which consumers live for T periods (from 0 to T − 1) and die at the end of period T − 1, so that they consume their entire wealth and income in the final period T − 1. The return to saving is the interest rate factor R _t+1, which is paid at the beginning of each period on wealth transferred from period t to period t + 1. We assume that the gross rate of return depends on the level of financial sophistication according to:

(1) $$R_{t + 1} = f\,(\Phi _{t + 1} ).$$

Raising the stock of financial information allows consumers to access better investment opportunities and/or save on transaction costs and fees, so that f′(Φ _t+1) > 0. It is also plausible, but not necessary for our argument, to assume $f^{\prime\prime} (\Phi _{t + 1} ) \le 0$ , that is either constant or decreasing returns to financial sophistication. Each period, financial information can be acquired at a price p, depreciates at a rate δ and evolves according to:

$$\Phi _{t + 1} = (1 - \delta )\Phi _t + \varphi _t, $$

where φ _t is the gross-investment in financial information. The initial stock of information Φ₀ is what people know about finance before entering the labor market. Therefore the initial stock is related to schooling decisions and parental background, neither of which we model explicitly. We assume that earnings y _t are uncertain, and denote wealth and consumption by A _t and c _t and the discount factor by β.

The value function of the optimization problem is:

$$V_0 (A_0, \Phi _0 ) = \mathop {\max} \limits_{\left\{ {c_t, \Phi _{t + 1}} \right\}} E_0 \sum\limits_{t = 0}^{T - 1} \beta ^t u(c_t ),$$

where u(c _t ) is the period utility function. The value function satisfies the recursion:

$$V_t (A_t, \Phi _t ) = \mathop {\max} \limits_{\left\{ {c_t, \Phi _{t + 1}} \right\}} \left[ {u(c_t ) + \beta E_t V_{t + 1} (A_{t + 1}, \Phi _{t + 1} )} \right],$$

where

$$A_{t + 1} = f(\Phi _{t + 1} )[A_t + y_t - c_t - p\Phi _{t + 1} + p(1 - \delta )\Phi _t ].$$

Appendix A shows that the Euler equation of the problem is

(2) $$u{\rm ^{\prime}}(c_t ) = \beta f\,(\Phi _{t + 1} )E_t u{\rm ^{\prime}}(c_{t + 1} )$$

and that Φ _t+1 evolves according to the following recursion:

(3) $$[s_t f{\rm ^{\prime}}(\Phi _{t + 1} ) - pf(\Phi _{t + 1} )] + p(1 - \delta ) = 0,\quad {\rm for}\quad t \le T - 3,$$

(4) $$pf(\Phi _{t + 1} ) - s_t f{\rm ^{\prime}}(\Phi _{t + 1} ) = 0,\quad {\rm for}\quad t = T - 2,$$

where s _t is cash-on-hand and is defined as s _t  = [A _t  + y _t  − c _t  − pΦ _t+1 + p(1 − δ)Φ _t ].

Equation (2) is the standard Euler equation for consumption, and states that the marginal rate of substitution between consumption in any two periods equals the interest rate factor, which in turn depends on the stock of financial information. Equation (3) states that in equilibrium the marginal return from financial information, s _t f′(Φ _t+1) equals the cost of information, p[f(Φ _t+1) − (1 − δ)]. Note also that in our model the interest rate is non-stochastic. However, the model can be easily extended to the case of stochastic returns, with the modification that the error term of the Euler equation includes also the covariance between the interest rate and consumption growth.

We can immediately verify that if the utility function is isoelastic, after taking logs, equation (2) can be written as:

(5) $$\Delta \ln c_{t + 1} = \sigma \,\ln \,\beta + \sigma \,\ln \,f(\Phi _{t + 1} ) + {\rm \epsilon} _{t + 1}, $$

where σ is the elasticity of intertemporal substitution and ε _t+1 is a composite error term, which includes the conditional variance of consumption growth and innovation in consumption (the difference between realized and expected consumption). The expression indicates that consumption growth is positively correlated with the stock of financial information, to an extent that depends on the elasticity of substitution σ. It is important to notice that the omission of the conditional variance term in the estimation of (5) is likely to lead to a downward bias in the estimate of the impact of financial sophistication on consumption growth (the σ parameter). To see why, note that in the model higher financial sophistication leads to higher returns and higher cash-on-hand. This reduces the need for precautionary saving, the conditional variance of consumption and the expected growth rate of consumption.Footnote ³

Equation (5) provides the framework of our empirical analysis. The equation is an equilibrium condition because both Δ ln c _t+1 and Φ _t+1 are endogenous variables. To make it operational we need to use instruments that are correlated with the stock of financial information, but uncorrelated with the consumption innovation term of the Euler equation.

3 Data

Estimation of the Euler equation (5) requires panel data on consumption and a measure of financial sophistication. The panel included in the 2006–10 Survey of Household Income and Wealth (SHIW) meets this requirement. It offers widely used indicators of financial sophistication, an annual measure of non-durable consumption that is not affected by seasonality factors, and detailed demographic, income and wealth data. The SHIW is a biannual survey of a representative sample of the Italian population conducted by the Bank of Italy covering about 8,000 households and 24,000 individuals. Details of the questionnaire, sample design, response rates and comparison of survey data with macroeconomic data are provided in Faiella et al. (Reference Faiella, Gambacorta, Iezzi and Neri2008), Bartiloro et al. (Reference Bartiloro, Cappelletti, D'Amuri, Gamba-corta, Iezzi, Magri, Neri and Rondinelli2010), and Biancotti et al. (Reference Biancotti, D'Amuri, Gambacorta, Ilardi, Neri and Rondinelli2012).

The SHIW includes a rotating panel component: in each survey, about 45% of the households are also interviewed 2 years later.Footnote ⁴ Most importantly for the present study, the 2008 and 2010 SHIW contains three core questions on financial sophistication: interest rate compounding, portfolio diversification and understanding of mortgage contracts (the wording of the questions is reported in Appendix B). The first two questions are the same questions as posed in the US Health and Retirement Survey (HRS); together with a question on understanding the difference between nominal and real interest rates, they have become a standard tool to measure financial sophistication (Lusardi and Mitchell, Reference Lusardi and Mitchell2011). The question on understanding mortgage contracts is one of two questions posed in the 2009 National Financial Capability Survey (Lusardi, Reference Lusardi2011). Therefore our indicators include three out of the five standard questions on financial sophistication.Footnote ⁵ In 2008, the SHIW includes also information on the interest rate at which respondents think they can invest their assets; we will use this information in Section 5.

Table 1 reports the distribution of the financial sophistication indicators, merging 2008 and 2010 data. It is apparent that a considerable number of respondents have limited understanding of financial matters: 72.7% correctly answered the compound interest question, 64.8% gave right answers the mortgage question, but only 48.5% correctly answered the diversification question. Overall, there were only 32.8% of correct answers to all the questions. The pattern agrees with the evidence in Lusardi and Mitchell (Reference Lusardi and Mitchell2011), who use international data to show that financial illiteracy is widespread even in countries with well developed financial markets, such as Germany, the Netherlands, Sweden, Japan, Italy, New Zealand and the USA. They report also that, in each of these countries, less well-educated people, women and older people are less well informed than the average. Table 1 also shows that financial sophistication is strongly correlated with parental education, and with the individual having a college degree in economics; we use these background variables as an instrument for Φ _t+1 in the Euler equation.

Table 1. Fraction of correct answers to questions on financial sophistication

Note: The table reports the fraction of correct answers to the questions on interest rate compounding, risk diversification and mortgage contract questions, by selected characteristics of the respondent and of the respondent's parents. For the wording of questions see Appendix B. The sample is drawn from the 2008 and 2010 SHIW for a total of 8,743 observations.

Our panel includes 4,345 households interviewed in 2006 and 2008, and 4,621 households interviewed in 2008 and 2010. Defining an ‘observation’ as two years of data, this corresponds to 8,966 potential observations. We drop cases where the household head changed, and those with inconsistent data on age, gender or education, missing information on consumption, missing indicators of financial sophistication or where growth rate of consumption exceeds 100% (in absolute value). The final sample includes 8,743 observations (4,234 in 2006–08, 4,509 in 2008–10). Since in many cases we have only one observation per household, we test primarily if the cross-sectional variation in consumption growth is explained by the cross-sectional variation in financial sophistication.

Table 2 reports descriptive statistics for the main variables used in the estimation. The average yearly growth rate of non-durable consumption is 1.2%, but the average conceals considerable sample heterogeneity (the standard deviation of consumption growth is 0.276). The sample average of the financial sophistication indicator is 1.86, which means that on average people gave the correct answer to less than two questions. Our sample selection rules do not affect average income (9.97 before selection vs. 9.99 in Table 2), family size, fraction of household heads with a college degree in economics (1.2%), and the fraction of heads whose fathers and mothers have a college degree (2.3% and 0.8%, respectively). Average age is slightly lower in the selected sample in comparison with the original sample (58.01 vs. 60.01 years).

Table 2. Sample statistics

Note: The table reports sample statistics for the variables used in the estimation. The sample is drawn from the 2008 and 2010 SHIW for a total of 8,743 observations.

The main limitation of our dataset is that the panel is relatively short. Even though over long periods of time the forecast error in consumption growth should be zero on average, in the case of short panels it might not be. In some specifications therefore we augment the regression with regional dummies and group dummies to control, at least partly, for the effect of aggregate and group-specific shocks on the forecast error.

4 Empirical results

Our theoretical model delivers an equilibrium relation between consumption growth and financial sophistication. However, it is important to stress that this is not a causal relation, because financial sophistication and consumption are both endogenous variables, and are jointly determined in the optimization problem. Ordinary Least Squares (OLS) estimation of the Euler equation therefore will yield inconsistent estimates. To address the endogeneity problem, we rely on an IV strategy, using four background education variables as instruments for financial sophistication: whether the respondent has a college degree, whether the respondent has a degree in economics and whether one of the respondent's parents has a college degree. As we shall see, the four instruments are strongly correlated with financial sophistication. Our identification assumption is that the instruments are not correlated with the error term of the Euler equation, and in particular with heterogeneity in individual preferences. The assumption would be violated if parents' education is related to children's rate of time preferences. We find this channel rather implausible. If education or parents' education shifts the utility function, what appears in the first-order condition of the problem is the change in education (which for adults is zero), not the level of education. An alternative possibility is that education is associated with household resources and borrowing constraints. In the robustness analysis, we control for this possibility using household disposable income and sample splits by wealth.

Two previous studies use an IV approach to address the endogeneity between financial sophistication and choice variables such as wealth, saving and portfolio composition. Christiansen et al. (Reference Christiansen, Joensen and Rangvid2008) use a large register-based panel dataset containing detailed information on Danish investors' educational attainment and financial and socioeconomic variables. The authors show that stockholding increases if individuals have completed an economics education program and if an economist becomes part of the household. To sort out the double causality between portfolio choice and the decision to become an economist, Christiansen et al. (Reference Christiansen, Joensen and Rangvid2008) use better access to education due to the establishment of a new university, as an instrument for economics education. Behrman et al. (Reference Behrman, Mitchell, Soo and Bravo2012) use an IV approach to isolate the causal effects of financial sophistication on wealth accumulation and wealth components in Chile, using as instruments school attendance and family background.Footnote ⁶ Other recent studies acknowledge the endogeneity of financial sophistication with respect to saving decisions and point out that the incentives to invest in financial information can affect the relation between financial sophistication and saving; see Delavande et al. (Reference Delavande, Rohwedder and Willis2008), Willis (Reference Willis2009), Calvet et al. (Reference Calvet, Campbell and Sodini2009) and Lusardi et al. (Reference Lusardi, Michaud and Mitchell2013).

As it has become standard practice in the estimation of a Euler equation for consumption since Zeldes (Reference Zeldes1989), we control for individual preferences using age and the growth rate of family size (assuming that family size is exogenous and anticipated). The indicator of financial sophistication is entered as the sum of the three indicators (thus it ranges from 0 to 3), or as three separate dummy variables. We also include a time dummy to control for aggregate shocks that hit the Italian economy between 2008 and 2010.Footnote ⁷ As left-hand-side variable we use the growth rate of non-durable consumption (excluding the purchase of durable goods).

Note that we omit the conditional variance of consumption growth (which according to equation (5) appears in the error term). The omission is justified only if preferences are quadratic. In fact, if the utility function is isoelastic, households react to expected consumption risk by increasing the growth rate of consumption (lowering consumption in period t relative to period t + 1) to an extent that depends on the degree of prudence. Empirically, it is difficult to find suitable proxies for consumption risk. The consequence of this omission is more serious in excess sensitivity tests, where the equation is augmented by expected income growth. Insofar as consumption risk is correlated with E _i,t Δ ln y _it+1, the latter proxies for the omitted effect of consumption risk, generating spurious evidence of excess sensitivity. In our context, the omission of consumption risk is of less concern, because the main purpose of our analysis is to estimate the sensitivity of consumption growth with respect to financial sophistication, not to perform an excess sensitivity test.Footnote ⁸

4.1 Baseline results

Table 3 reports our baseline specification omitting the demographic variables. The first-stage regression displayed in the lower panel indicates that the coefficients of our instruments have the expected positive sign; two of the coefficients (college education and college degree in economics and fathers' education) are statistically different from zero at the 1% level and one at the 5% level. In particular, having a college degree improves the financial sophistication score by 0.4, having an economics degree improves the score by an additional 0.25, while father's college degree is associated with an increase in the score of 0.17. Overall, the four instruments are powerful: the Anderson canonical correlation statistic on the three instruments is 170 and the F-test on the excluded instruments is 42.9. Furthermore, the Sargan test (1.13) does not reject the null hypothesis that the overidentifying restrictions are valid. In the second specification, the negative coefficient of age in the first-stage regression suggests that younger respondents score better in terms of financial sophistication, other things equal.

Table 3. Growth rate of consumption and overall measure of financial sophistication

Note: The top panel reports IV estimation of the Euler equation. The bottom panel reports the first-stage results. One star indicates that the coefficient is statistically different from zero at the 10% level, two stars at the 5% level, three stars at the 1% level.

Turning to the Euler equation estimates (upper panel in Table 3), we see that the coefficient of financial sophistication is positive and statistically different from zero at the 5% level, thus confirming the model's implication on the correlation between financial sophistication and consumption growth. These estimates do not immediately point to a particular value of the EIS. However, in Section 5, we complement them considering explicitly the link between financial sophistication and the return to saving. The second specification in Table 3 adds demographic controls and a time dummy. The age and growth rate of family size coefficients are both positive and statistically different from zero. In particular, the coefficient of family size is usually interpreted as indication that consumers save (consumption growth is higher) in anticipation of an increase of family size. Results for financial sophistication are similar, with a slightly higher effect of sophistication (the coefficient is 0.061). The other two regressions of Table 3 restrict the sample to households with heads aged <65 years. Indeed, it may be more appropriate to focus attention on people in the labor force, who face rather different constraints and shocks to their resources (e.g., income and unemployment shocks) with respect to the elderly, for whom health shocks, bequest motives and survival risk play more important roles. We still find a strong positive correlation between the instruments and financial sophistication in the first-stage estimates. Furthermore, dropping the elderly, the coefficient of financial sophistication in the Euler equation is higher than in the baseline estimates (0.086 in column 3 and 0.073 in column 4).

In the baseline specification, we construct the financial sophistication indicator adding one point for each question answered correctly. Since this procedure is rather arbitrary, in Table 4 we present estimates obtained introducing the three dummies separately and reporting estimates for the full sample (upper panel) and the sample that excludes the elderly (lower panel). In all regressions, the coefficient of the financial sophistication indicator is positive. The coefficients are also similar in size, ranging from 0.12 (when for the full sample we use the risk diversification question) to 0.27 (when for the ‘20–65’ sample we use the mortgage question).

Table 4. Financial sophistication indicators and consumption growth

Note: Both panels report IV estimation of the Euler equation. The top panel uses the whole sample, the bottom panel excludes the 65+. The definition of Φ _t+1 varies between columns, according to the column heading. Column heading ‘Interest rate question’ indicates that Φ _t+1 is a 0/1 dummy equal to 1 if the interest rate question is answered correctly; column heading ‘Risk diversification question’ that Φ _t+1 is a 0/1 dummy equal to 1 if the risk diversification question question is answered correctly; column heading ‘Mortgage contract question’ that Φ _t+1 is a 0/1 dummy equal to 1 if the mortgage question is answered correctly. One star indicates that the coefficient is statistically different from zero at the 10% level, two stars at the 5% level, three stars at the 1% level.

4.2 Robustness checks

In Table 5, we provide a further check for the stability of the results augmenting the Euler equation by a set of 19 regional dummies. The disturbance term ε _t+1 in equation (5) is a forecast error, the difference between realized and expected consumption growth. According to the permanent income hypothesis with rational expectations, the conditional expectation of a forecast error should be zero, i.e., E _t (ε _i,t+1). The empirical analog of this expectation is an average taken over long periods of time, rather than across a large number of households.

Table 5. Regressions with regional dummies

Note: The table reports IV estimation of the Euler equation. One star means 10% significantly different from zero, two stars 5%, three stars 1%. A full set of regional dummies is included. The left panel uses the whole sample, the right panel excludes the 65+.

As pointed out by Chamberlain (Reference Chamberlain, Griliches and Intriligator1984), there is no guarantee that the cross-sectional average of forecast errors will converge to zero as the dimension of the cross-section becomes larger. This typically happens in the presence of aggregate shocks which lead all households to revise expectations simultaneously. Even though the regression includes a time dummy, the approach is restrictive because it rules out aggregate shocks that are not evenly distributed in the population. Regional dummies can proxy for group-level shocks that might be correlated with other terms of the Euler equation, and checking the stability of the results is particularly useful if the panel is short (as in our case). However, it is apparent from the estimates in Table 5 that our estimates are unaffected by the inclusion of these dummies.Footnote ⁹

The Euler equation that we estimate so far assumes that markets are perfect, that consumers can freely move resources over time, and therefore that there are no borrowing constraints. In the presence of such constraints, consumption growth is affected by households' resources.Footnote ¹⁰ Thus in Table 6, we add to the baseline specification (the log of) lagged disposable income as a proxy for current resources. We find a negative income coefficient (as predicted by models with borrowing constraints) but the coefficient of the financial sophistication indicator is barely affected in this extended specification (0.079 in column 1 and 0.092 in column 2) even if we drop households where the respondent is over 65 (columns 3 and 4).Footnote ¹¹

Table 6. Regressions adding lagged diposable income

Note: The table reports IV estimation of the Euler equation. One star means 10% significantly different from zero, two stars 5%, three stars 1%. The left panel uses the whole sample, the right panel excludes the 65+. The left-hand side variable is the growth rate of non-durable consumption.

An alternative way to control for the presence of borrowing constraints is to focus on a sample of households that are unlikely to face such constraints. In Table 7, we implement Zeldes's (Reference Zeldes1989) classical approach and split the sample according to whether or not households have relatively high liquid assets (more than 3-months' income). In the high-wealth sample (about 62% of the total sample) the coefficient of financial sophistication is 0.067 (0.084 if we include demographic controls), while in the low-wealth sample the coefficient is not statistically different from zero. This result is remarkable, because the Euler equation fails in the presence of credit constraints, and should apply only to individuals who can smooth consumption over time.

Table 7. Sample split by credit constraints indicator

Note: The table reports IV estimation of the Euler equation. One star means 10% significantly different from zero, two stars 5%, three stars 1%. The left panel uses the whole sample, the right panel excludes the 65+. For ‘Constrained households’ the ratio between financial wealth and monthly disposable income is smaller than than 3, for ‘Unconstrained households’ is larger than 3.

Before moving to the analysis of the correlation between financial sophistication portfolio performance, it is worth emphasizing that the validity of our results rests on the identification assumption that the education of parents has no direct effect on the growth rate of consumption. However, if time preference is heritable, one would expect that more highly educated parents would, on average, have more patient children. Therefore, we explore the robustness of the results using an alternative set of instruments, and exploiting a reform that increased compulsory school age in Italy. We thus replace education (for fathers, mothers and children) with indicators of whether fathers and mothers reached the relevant school age in 1962 (when compulsory age was raised to 14). The variability induced by the school reform is exogenous, but rather limited. Therefore, we complement the set of instruments noting that in the estimation of the Euler equation at t + 1 the variables dated t or before are (weakly) exogenous. This allows us to rely on financial literacy in 2008 as an instrument for financial literacy in 2010. The choice is well grounded also in light of the high correlation between financial literacy in the two subsequent waves of data, but reduces further the sample used for estimation. The results confirm the positive association between financial sophistication and the growth rate of consumption: depending on the specification and on the sample used the coefficient for Φ _t+1 ranges between 0.022 (0.010) and 0.033 (0.018).Footnote ¹²

5 Financial sophistication and portfolio performance

Our empirical results provide meaningful estimates of the EIS only under the assumption that financial sophistication is correlated with portfolio performance, and that more sophisticated individuals expect higher returns on their wealth. We can offer several pieces of evidence to corroborate our findings, and to show that financial sophistication is indeed correlated with portfolio performance.

The first evidence is that, at any point in time, there is substantial dispersion in portfolio returns, contrary to the assumption of standard intertemporal models in which all consumers have the same beliefs and purchase the same set of assets. Furthermore, part of portfolio performance is associated with financial sophistication. The evidence comes from detailed analysis of portfolio performance in Sweden, Germany, China, India and other countries for which extensive panel data on individual accounts are available.

Calvet et al. (Reference Calvet, Campbell and Sodini2007, Reference Calvet, Campbell and Sodini2009) uncover substantial heterogeneity in account performance using Swedish data, and find that part of the variability of returns across investors is explained by financial sophistication. In particular, they show that predictors of financial sophistication (such as wealth, income, occupation and education) are associated with higher Sharpe ratios, and that richer and more sophisticated households invest more efficiently. Hackethal et al. (Reference Hackethal, Haliassos and Jappelli2012) use data on German brokerage accounts and find that years of experience tend to contribute to higher returns. This is consistent with other studies indicating that the magnitude of investment mistakes decreases with sophistication and experience. Feng and Seasholes (Reference Feng and Seasholes2005) find that investor sophistication and trading experience eliminate the reluctance to realize losses.Footnote ¹³

Campbell et al. (Reference Campbell, Ramadorai and Ranishy2012) study investment strategies and performance of individual investors in Indian equities over the period 2002–2012.Footnote ¹⁴ Indian data provide no information on the demographic characteristics of investors, and therefore the authors cannot measure financial sophistication using information about investors, as in Calvet et al. (Reference Calvet, Campbell and Sodini2007, Reference Calvet, Campbell and Sodini2009) or direct survey evidence (as in Lusardi and Mitchell, Reference Lusardi and Mitchell2007 and in the present paper). Instead, Campbell et al. (Reference Campbell, Ramadorai and Ranishy2012) study learning by relating account age (length of time since the account was opened) and past portfolio mistakes, to the performance of each account; they find that account performance improves significantly with account age, that stocks whose individual investors have older accounts tend to outperform the value-weighted Indian stock market, and that the increase is monotonic in account age. The difference in performance between the oldest and youngest accounts is 35 to 40 basis points per month (about 20 basis points per month in their lower estimates with further controls). Since older accounts have a smaller tendency to underdiversify, lower turnover, and a smaller disposition effect, these results suggests that learning is important among Indian individual investors.

A second piece of evidence comes from direct evidence available in the 2008 SHIW, but unfortunately not repeated in later years. Half of the sample was asked: At which interest rate (net of taxes) do you think you can invest without risk for a year (think of 1-year T-bills, or saving accounts)? The cross-sectional average of the 3,156 valid answers (excluding eight observations with implausible values exceeding 10%) is 2.47% (median is 2), with a standard deviation of 1.48. The scatter plot of the subjective interest rate is reported in Figure 1, showing that there is a mode at 2% and some bunching of responses, but also a quite reasonable distribution of the variable. The focus of the question is the riskless return, and we see this as a potential limitation. However, to the extent that the cross-sectional variability of the subjective expectation of the riskless return is related to the cross-sectional variability of the returns on risky financial assets, our exercise will also speak about the relation between financial sophistication and portfolio returns.

Figure 1. (Colour online) Subjective risk-free interest rate. Note. The figure plots the histogram of the subjective risk-free interest rate. The data are drawn from SHIW 2008, where half of the sample is asked: At which interest rate (not considering taxes) do you think you can invest without risk for a year (think of 1-year T-bills or saving accounts)?

Using the available measure of the riskless return, we can estimate a three equations system, where the first equation relates our set of instruments to Φ _t+1, the second links the reported interest rate to financial sophistication, and the third is the Euler equation for consumption, i.e., equation (5). Table 8 show the results form the estimation of the three equations system. The only complication is that data on the subjective risk-free rate are available only for 2008. Standard errors are adjusted for the presence of generated regressors, as suggested by Murphy and Topel (Reference Murphy and Topel2002) and Pagan (Reference Pagan1984).

Table 8. Growth rate of consumption, financial sophistication and subjective interest rate

Note: The table reports the results from the estimation of a system of three recursive equations. The first equation is estimated regressing Φ _t+1 against the set of instrument, z _t , which includes age, the growth rate of family size and four dummies for whether one has a degree in economics, one is college graduate, and the father and the mother are college graduate. The second equation is estimated regressing r _t+1 on the predicted value for Φ _t+1 from the first stage. In the third equation, the growth rate of consumption, Δ ln c _t+1, is regressed on the predicted value for r _t+1 from the second equation. Asymptotic standard errors in parentheses (see Murphy and Topel, Reference Murphy and Topel2002). One star means 10% significantly different from zero, two stars 5%, three stars 1%.

The bottom part of Table 8 reports a regression for financial sophistication for the 2008 sample. Results are qualitatively similar to the first-stage regression for the full sample reported in Table 3, except that the coefficients of most variables are less precisely estimated. The middle panel reports the relation between financial sophistication and the interest rate, showing that each point of the financial sophistication indicator is associated with 120 basis points increase of the risk-free rate. Since we do not observe risky returns, we cannot draw direct inference on the relation between financial sophistication and returns of risky assets. However, in the simplest case in which the equity premium does not vary across households with financial sophistication over and above the riskless return, our results suggest that financial sophistication is positively associated with portfolio returns.Footnote ¹⁵

The top panel reports the Euler equation for consumption, where consumption growth is regressed on the interest rate, taking into account the fact that the interest rate depends on financial sophistication, which is itself a choice variable. The interest rate coefficient is statistically different from zero, suggesting an EIS of 0.53 in column 1 (statistically different from zero at the 5% level) and 0.45 in column 2 (different from zero at the 10% level). If we drop the elderly, the values of the EIS are slightly higher (0.7 in column 3 and 0.65 in column 4).

To summarize, several papers show that in many countries financial sophistication, as measured by direct survey questions, investors' experience and education, is associated with higher portfolio returns. In addition, direct evidence available for a section of our survey shows that financial sophistication is an important determinant of the cross-sectional variability of (one-period ahead) subjective risk-free interest rates. With the important caveat that the question refers to the ‘risk-free rate’ and not to the overall portfolio return, we obtain plausible estimates of the EIS. These results increase our confidence that the positive correlation between consumption growth and financial sophistication we estimated in Section 4 is indeed linked to the EIS.