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The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study

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Demography

Abstract

Several recent studies suggest that individual subjective survival forecasts are powerful predictors of both mortality and behavior. Using 15 years of longitudinal data from the Health and Retirement Study, I present an alternative view. Across a wide range of ages, predictions of in-sample mortality rates based on subjective forecasts are substantially less accurate than predictions based on population life tables. Subjective forecasts also fail to capture fundamental properties of senescence, including increases in yearly mortality rates with age. To shed light on the mechanisms underlying these biases, I develop and estimate a latent-factor model of how individuals form subjective forecasts. The estimates of this model’s parameters imply that these forecasts incorporate several important sources of measurement error that arguably swamp the useful information they convey.

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Notes

  1. This sampling design is intended to match that of the over-50 population represented by the Current Population Survey (CPS) to facilitate comparisons between the two data sets.

  2. Yearly life tables record the probability of surviving to age x + 1 conditional on reaching age x, based on actual mortality rates in that year. Letting d x,t be the number of people who die between age x and age x + 1 in a given year t, and letting l x,t be the number of people alive at age x in that year, this probability equals . A researcher might use year t life tables to compute a probability of living to age S conditional on reaching age R as but the actual ex post survival probability equals . As an example, one might calculate the probability that a person aged 60 in 1992 lives to age 62 by multiplying the 1992 one-year survival rate for those aged 60 by the 1992 one-year survival rate for those aged 61. This will understate the true two-year survival rate if the probability of living to age 62 conditional on reaching age 61 increases between 1992 and 1993. More generally, survival probabilities based on a given year’s life tables will understate the true probability of survival to age x if age-specific survival probabilities increase over time.

  3. Among respondents of gender g in year t, the sample fraction that is age x is Pr(age = x | g, t). Therefore, to match the within-gender age distribution in 2006 to that found in 1992, for example, respondents of gender g aged x are weighted by . Table 1 reports weighted survival probabilities for all years in the table based on the age distribution among HRS respondents in 1992.

  4. Oeppen and Vaupel (2002) showed that “best-performance” longevity—that is, the life expectancy of the longest-lived ethnicities or nationalities—has steadily increased by roughly 2.5 years per decade since 1840. Whereas other authors, such as Olshansky et al. (2005), predicted stagnation and even declines in longevity within the next century, Oeppen and Vaupel (2002) demonstrated that such predictions have commonly been made (and subsequently proven wrong) in the past 160 years, arguing that there is no compelling reason to believe that the trend should end now.

  5. In the 1995 wave of the AHEAD, individual respondents were asked about the same target ages as they were in 1993, so that those aged 72–76 were given a target age of 85, those aged 77–81 were given a target age of 90, and so on. In all following waves, the mapping between a respondent’s age and the target age reverted to that used in 1993: for example, those aged 70–74 were given a target age of 85.

  6. The 1993 AHEAD included persons younger than 70 who were spouses of respondents who were 70 or older, but I exclude these individuals from the figure because the resulting samples are both small and nonrepresentative of the U.S. population at these ages.

  7. By comparison, Hurd and McGarry (2002) estimated that a 1-percentage-point increase in the SSFs is associated with a 0.016-percentage-point increase in the likelihood of actually surviving from Wave 1 to Wave 2 of the HRS. This estimate is much smaller than that found here for two reasons. First, Hurd and McGarry’s (2002) dependent variable captures survival over only a two-year period, compared with up to 14 years in the models considered earlier. Second, their sample includes only those younger than 65 in Wave 1. As a result, the probability of death in their estimation sample was roughly 1.7 % , compared with 53 % in the sample used in columns 1 and 2 of Table 2, and 27 % in the sample used in columns 3 and 4.

  8. The estimates shown in Table 2 are not necessarily inconsistent with the findings of authors such as Smith et al. (2001), who argued that SSFs are useful for predicting individual variation in mortality. Conditional on a respondent’s age and gender, SSFs are more informative than forecasts based on life tables by definition because published life table values are constant within age-gender cells.

  9. Although it is unlikely that respondents consult life tables when thinking about their own survival prospects, this information is publically available; the Centers for Disease Control and Prevention provides detailed age- and gender-specific population life tables on its website (http://www.cdc.gov/nchs/products/life_tables.htm).

  10. In describing possible reasons why optimism increases with age, Mirowsky (1999:978) speculated that “. . . the simplest explanation is that continuing survival encourages greater optimism at older ages because it seems increasingly remarkable.”

  11. Distinguishing this phenomenon is important, which is apparent among individuals of a given age forecasting their survival prospects to two different points in the future, from changes in forecasts over time for an individual. This latter source of variation does imply that individuals recognize, over time, that death rates increase with age. I return to this distinction at the end of this section.

  12. The use of a logarithmic specification introduces problems when P 75 and/or P 85 equal 0. In practice, I set P 85 equal to 0.01 when P 75 is positive but P 85 equals 0. I drop observations for which both P 75 and P 85 equal 0, but the results presented in Table 3 are insensitive to instead setting both P 75 and P 85 equal to 0.01 in these cases.

  13. A large experimental literature examines the sensitivity of survey responses to various factors, including the phrasing of questions, the order in which questions are asked, and interviewer cues on the social desirability of particular responses. This literature finds that subjective survey responses are particularly sensitive to these factors, possibly because subjective beliefs cannot be verbalized and may not even exist in a coherent form. Tanur (1992) and Sudman et al. (1996) provide excellent reviews of the experimental evidence.

  14. As noted by an anonymous reviewer, the item-reliability estimate of 0.714 is roughly comparable with that found among other subjective measures, such as self-rated health on a 5-point scale from “excellent” to “poor.” Zajacova and Dowd (2011) estimated reliability of self-rated health at 0.75 in NHANES data, and Crossley and Kennedy (2002) found similar reliabilities in the Australian National Health Survey.

  15. In models that include individual fixed effects, where Age it refers to individual i’s age at time t and denotes the fixed effects, I estimate that = –0.068 (0.024) when the SSF is P 75 and –0.072 (0.031) when the SSF is P 85. The corresponding estimates are 0.875 (0.002) and 0.602 (0.002), respectively, when I instead use actuarial survival probabilities as dependent variables.

  16. This structure allows for positive, negative, or zero correlation between g i and d i . Specifically,

  17. More concretely, I define , , and so on. I then choose the five parameters to minimize m 1 + m 2 + m 3 + m 4 + m 5 + m 6.

  18. Noise in SSFs also plays a large role in the results of Table 2, which shows that actuarial forecasts outperform SSFs in models of in-sample survival. As Eq. (10) shows, SSFs net of actuarial forecasts (SSF i – A i ) equal g i + d i + e i , so the coefficient on SSF i in a linear regression of survival (Y i ) on SSF i and A i will converge to cov(Y i , g i + d i + e i ) / var(g i + d i + e i ). If g i and e i are unrelated to actual survival, one can use the estimates in Table 4 to recover cov(Y i , d i ) / var(d i ), which is the coefficient on SSF i in this regression if SSFs included no errors (ignoring that the models underlying Table 2 are probits rather than linear regressions). Specifically, cov(Y i , d i ) / var(d i ) = [cov(Y i , g i + d i + e i ) / var(g i + d i + e i )] × [var(g i + d i + e i ) / var(d i )]. Because var(g i + d i + e i ) / var(d i ) = var(SSF i – A i ) / var(d i ) = 0.3448, the estimated effects of SSF i in Table 2 would roughly triple in magnitude if var(g i ) = var(e i ) = 0. I thank an anonymous referee for suggesting these ideas and bias corrections.

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Acknowledgements

I am grateful to seminar participants at Michigan State University, the University of Michigan, the W.E. Upjohn Institute for Employment Research, and the Michigan Retirement Research Center for helpful comments and suggestions. I am especially grateful for the financial support provided by the U.S. Social Security Administration through the Michigan Retirement Research Center, funded as part of the Retirement Research Consortium (Project ID #UM07-19). The opinions and conclusions expressed are solely those of the author and do not necessarily represent the opinions or policy of SSA or of any agency of the Federal Government.

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  1. Department of Economics, Michigan State University, 110 Marshall-Adams Hall, East Lansing, MI, 48824, USA

    Todd E. Elder

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Appendix

Appendix

Table 5 Average subjective and life table–based forecasts of survival to ages 75 and 85, by HRS wave and gender, unweighted
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Table 6 Age-specific 10- and 11-year survival probabilities and predicted survival probabilities from subjective forecasts, initial-year life tables, and target-year life tables
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Elder, T.E. The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study. Demography 50, 569–589 (2013). https://doi.org/10.1007/s13524-012-0164-2

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