How do subjective mortality beliefs affect the value of social security and the optimal claiming age?

One of the central predictions of the life-cycle model of savings behavior is that consumption, savings, and annuitization decisions are influenced by subjective mortality beliefs. These decisions should be influenced not only by how long the individual expects to live but also by the degree of uncertainty regarding the individual’s age of death. At one extreme, an individual who can forecast his age of death with certainty will value an annuity at the present value of the income stream to the age of death. This is because he can decumulate unannuitized wealth over a period ending with his date of death. At the other extreme, an individual with the same life expectancy but who is highly uncertain as to his age of death will value an annuity at considerably more than its expected present value because he will otherwise need to substantially reduce his consumption to guard against the perceived high risk of outliving his wealth.

Social Security provides benefits in the form of an inflation-indexed annuity. An individual who delays claiming receives an increase in his monthly benefit with delay being equivalent to an annuity purchase. He can be thought of as returning this month’s check to the Social Security Administration in return for an increase in his lifetime income. The value of delay will be greater for those individuals with greater life expectancy. It will also be greater for those who are most uncertain as to their age of death. Sun and Webb (2010) show that, given plausible preference parameters, it is optimal for households with population average annual mortality risk to delay claiming until age 68. Yet most households claim benefits at age 62 or soon thereafter, even when they have sufficient financial assets to postpone claiming until after retirement.Making use of data from the Health and Retirement Study (HRS), this paper assesses whether individuals’ subjective mortality beliefs exhibit systematic biases, and whether any such biases might contribute to the prevalence of early claiming of Social Security benefits. Starting in 1992, individuals in the HRS have been asked to assess their probabilities of surviving to ages 75 and 85. Previous research (Hurd and McGarry 1995, 2002) has shown that responses vary appropriately with risk factors and predict mortality during a two-year period. A substantial portion of the individuals interviewed in 1992 have now either died or reached age 75, providing an opportunity for us to extend research by comparing subjective mortality beliefs with actual survival to age 75. We show that self-assessed survival probability strongly predicts actual survival, but that it is statistically insignificant after controlling for observable health status and socioeconomic characteristics, indicating that responses do not incorporate private mortality information. We show that, on average, men form unbiased estimates of their survival probabilities, but that women understate their survival probabilities by 10 percentage points. We also show that, relative to the predictions of an econometric model based on observable health and socioeconomic status, those who survive to age 75 understated their survival probabilities by more than those who die by that age. We find that the ability to form accurate and unbiased estimates of the probability of surviving to age 75 is generally uncorrelated with socio-economic or health status.The responses suffer from focal point bias, with considerable bunching of responses at zero, 50, 100 percent, and so on. It is not clear how to treat these responses. Do individuals literally mean that they rate their survival probability at zero or 100 percent, or somewhere close to these numbers? In 2008, individuals who gave focal-point responses were asked follow-up questions designed to elicit information regarding their underlying beliefs. We find that although individuals who are unable to provide any estimate of their survival probabilities are significantly more likely to be members of minorities, be in poor health, and to have less than a high school education, there are few consistent and significant differences in either socio-economic characteristics or mortality rates between those who state that their estimates are precise, and those who say that they are approximations.

Previous research into subjective mortality beliefs has focused on whether people are capable of forming unbiased estimates of their life expectancy, and has not considered the question of whether people can accurately quantify the degree of uncertainty surrounding their age of death. We find some evidence that households not only underestimate their longevity, but also exhibit greater confidence in their ability to forecast their age of death, relative to estimates that assume they experience the average mortality rate of individuals of their age, gender, and birth cohort. We cannot infer from this finding that people are excessively confident. It is likely that individuals do possess information that enables them to improve on the confidence intervals that would be obtained from the use of life tables.We recover annual survival probabilities from subjective mortality beliefs and use these annual survival probabilities to calculate optimal Social Security claiming strategies. We show that although the subjective survival probabilities differ substantially from the predictions of life tables, they have little effect on optimal strategies. These theoretical calculations are consistent with empirical studies (Coile, Diamond, Gruber, and Jousten, 2002, Hurd, Smith, and Zissimopoulos, 2004) showing that subjective mortality beliefs appear to have little effect on the claiming decision.

The remainder of the paper is organized as follows. In Section 1, we review previous research. In Section 2, we analyze HRS respondents’ self-assessed survival probabilities, identify biases, and recover subjective annual survival probabilities from individuals’ responses. In Section 3, we present a theoretical model of the Social Security claiming decision, and consider how the optimal claiming age might be affected by subjective mortality beliefs. Section 4 concludes.