Social Security benefits are the main source of retirement income for the majority of retirees. But in Section 4, we show that many respondents—including those close to their expected claiming age—exhibit uncertainty about the level of benefits they expect to receive. The theoretical model we presented in Section 2 indicates that individuals who face more uncertainty in their Social Security benefits invest a smaller fraction of their wealth in risky assets. In this section, we investigate this premise empirically. To this end, we estimated a reduced-form model, taking into consideration the uncertainty that individuals face with respect to both the uncertainty related to their eligibility for benefits and that related to the benefit amount, i.e., the distribution of benefits unconditional
We estimated an equation of the form:
denotes the fraction of wealth held in stocks by the household in which individual i
denotes the standard deviation of i
’s subjective distribution of Social Security benefits, Zi
denotes individual and household characteristics, and εi
is an unobserved random term. On average, individuals in our sample hold 14% of their total assets in stocks; the median is 3% (). Forty-five percent of the households in which our respondents live do not hold any stocks. (Note that the fraction of wealth invested in stocks is a household-level variable from the HRS 2006 core survey).25
In addition to uncertainty about their own future benefits, married individuals in our sample may have uncertainty about their spouse’s Social Security benefits. However, we do not have any information on this variable.
As we explained in Section 3.2, information is available on the distribution of Social Security unconditional on the expected claiming age (i.e., the distribution of p1bA1 + p2bA2 in the model) for some respondents, and for other respondents, conditional on an expected claiming age (the distribution of bA1, for example, if the respondent reports the most likely claiming age as expected claiming age and p1 > p2). In this simple framework, answers about bA1 should capture the uncertainty associated with b. In practice, an individual who delays claiming may work longer. As a result of the additional years of earnings, his PIA may increase. But because there may be uncertainty about future earnings close to retirement (i.e., in w in our model), this individual may exhibit more uncertainty about future Social Security benefits conditional on claiming late than conditional on claiming early. As such, the standard deviation of the distribution unconditional on a claiming age—which supposedly also captures uncertainty about lifetime earnings for all potential claiming ages—would better capture the uncertainty that individuals consider when making their portfolio choice than would the standard deviation of the distribution conditional on a claiming age.
However, using the standard deviation of the distribution unconditional on the expected claiming age poses some econometric challenges. By definition, this standard deviation depends on the subjective distribution of stock market returns, because those influence the retirement age, which is not precisely measured in the HRS. As a result, it may be correlated with the random term εi. To deal with this issue, one could use an instrumental variable approach, but we do not have a suitable instrument. Instead, we used the standard deviation of the distribution of Social Security benefits conditional on a claiming age. The underlying assumption is that this uncertainty, which depends on factors such as the probability of reform, is exogenous to unobservable variables that influence portfolio choice. But this standard deviation may underestimate the overall uncertainty that individuals face. Consequently our estimate may provide a lower bound of the effect of uncertainty about future Social Security benefits on portfolio choice.
Our theoretical framework suggests a number of other covariates we should include in our reduced-form model. People’s subjective beliefs about stock market returns are critical to their portfolio choice. We used (1) the elicited subjective probability that the price of mutual fund shares invested in blue chip stocks, such as those in the Dow Jones Industrial Average, will increase faster than the cost of living over the next 10 years, (2) the subjective probability that it will increase by 8 percent or more per year on average over the next 10 years, and to complement these measures (3) the subjective probability that there will be an economic recession within the next 10 years.
Risk-aversion is another important factor in portfolio choice and we used it too as a covariate. The HRS includes a categorical measure of risk-aversion derived from a set of questions where the respondent is asked to choose between two jobs, where one guarantees the current family income and the other offers a chance to increase income, but also carries the risk of income loss. As we point out in Section 2, the time horizon may additionally be important, so we controlled for age and a measure of subjective survival expectations relative to the life table (i.e., the ratio of the subjective probability of being alive at age 75 to the probability given by the life table). We used education as a covariate as well, because a more educated individual may be more able to insure his risky investment with labor income. Finally, we controlled for the level of total wealth, including expected Social Security entitlements. We created an indicator for total bequeathable wealth (above and below the median in our sample, referred to as “other wealth” in ) and an indicator for Social Security wealth as measured by the mean of the fitted distribution of Social Security benefits (above and below the median), and interacted the two. We also included an indicator for whether the individual has an employer pension.
Best Linear Predictors under Square Loss of the Fraction of Wealth held in Stocks
shows the best linear predictors of the fraction of wealth held in stocks under square loss. The first column uses the standard deviation of the fitted distribution of Social Security benefits unconditional
on claiming age as the measure of uncertainty, while the second column uses the standard deviation of the distribution conditional
on the expected claiming age. The second column therefore presents our preferred estimates, as conditioning on the expected claiming age reduces the problem of endogeneity. Focusing on this column, we find, as predicted by the theoretical model, that individuals with more uncertainty about their future Social Security benefits are less likely to hold a greater portion of their wealth in stocks, and the coefficient is statistically significant at 5%. All else equal, increasing the standard deviation from the 25th
to the 75th
percentile reduces the fraction of wealth held in stocks or bonds by 0.017.26
Turning to those expectations related to the stock market or economy, we see that individuals who report a higher subjective probability that the price of stocks will rise faster than the cost of living over the next 10 years, or a lower subjective probability of a recession, hold a higher fraction of their wealth in stocks. Contrary to what the model predicts, shows that older individuals have a higher share of their assets in stocks. This may be due to the fact that younger households may be more likely to face borrowing constraints, which may make risky financial investments less attractive to them (Campbell, 2006
). However, individuals with more education tend to hold a higher proportion of their assets in stocks. The coefficients associated with the measures of risk aversion here are not precisely estimated, which may be due to the fact that the hypothetical questions about job loss do not do a very good job of capturing risk-aversion related to financial investments.
also shows interesting patterns related to wealth: Those with high other (bequeathable) wealth and high Social Security wealth invest by far the largest proportion of their assets in stocks (almost 10 percentage points more than the other groups).
The coefficients associated with the standard deviations of the distribution of benefits unconditional on claiming age is much smaller in magnitude than the one for the distribution conditional on claiming age. This may suggest that endogeneity is indeed an issue with the unconditional distribution, and that using the distribution conditional on an expected claiming age mitigates that problem.
Overall, the results presented in Column 2 based on the conditional distribution favor the hypothesis that individuals who exhibit less uncertainty about their future Social Security benefits hold more risky investment portfolios. Under the assumption that using the conditional distribution eliminates the endogeneity problem and that no other omitted variables bias the estimated relationship, these relationships can be interpreted as causal. In that sense, our results suggest that our respondents act qualitatively as theory would predict. However, they do not allow us to determine whether individuals choose the optimal amount of risky investment given the Social Security benefits they expect.
It is possible, though, that these results could be driven by some omitted variables. This would happen if, for example, lower levels of uncertainty were positively correlated with higher financial literacy or cognitive ability (and thus better knowledge of Social Security rules), and, in turn, if individuals who are more financially savvy are more likely to hold a larger portion of their wealth in stocks. Our specification includes controls for gender and education, which have been found to be important indicators of financial literacy (Lusardi and Mitchell, 2007
But we cannot rule out that this may be an important variable whose effect is not fully captured by the controls for gender and education.
Another issue may be related to the correlation between expectations about stock market returns and Social Security benefits. Such a correlation would occur, for example, if people believed that a correlation exists between the growth of their earnings and returns on stocks, or that a Social Security reform that would reduce benefits is more likely to happen when stock returns are low. In , we find that individuals who report a higher probability of a recession within the next 10 years report a lower probability of eligibility, which may indicate that a positive correlation does exist between stock market returns and Social Security expectations. This correlation would be problematic for our analysis of portfolio choice if it were to vary systematically across individuals and influenced their portfolio choice. But at this point, we do not have the information on the joint subjective distribution of benefit amounts and stock market returns that would enable us to establish whether this is indeed the case.