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Individual Uncertainty About Longevity

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Demography

Abstract

This article presents an assessment of individual uncertainty about longevity. A survey performed on 3,331 French people enables us to record several survival probabilities per individual. On this basis, we compute subjective life expectancies (SLE) and subjective uncertainty regarding longevity (SUL), the standard deviation of each individual’s subjective distribution of her or his own longevity. It is large and equal to more than 10 years for men and women. Its magnitude is comparable to the variability of longevity observed in life tables for individuals under 60, but it is smaller for those older than 60, which suggests use of private information by older respondents. Our econometric analysis confirms that individuals use private information—mainly their parents’ survival and longevity—to adjust their level of uncertainty. Finally, we find that SUL has a sizable impact, in addition to SLE, on risky behaviors: more uncertainty on longevity significantly decreases the probability of unhealthy lifestyles. Given that individual uncertainty about longevity affects prevention behavior, retirement decisions, and demand for long-term care insurance, these results have important implications for public policy concerning health care and retirement.

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Notes

  1. Post and Hanewald (2013) make an indirect estimation of subjective uncertainty on the basis of saving behavior.

  2. Being a smoker increases the risk of lung cancer, which reduces the length of life dramatically. Because the onset of cancer is not certain, this may increase personal uncertainty on longevity.

  3. The latter are analyzed in a companion paper (Luchini et al. 2017).

  4. This constraint was also imposed in Delavande and Kohler (2009) but is not found in HRS.

  5. The response rate is similar for men (86.6 %) and women (85.5 %) and decreases with age. Detailed statistics regarding response rates are given in the online appendix.

  6. See Bahrami et al. (2011). The classification is detailed in the online appendix.

  7. The sample can be deemed representative of the French population (Schokkaert et al. 2014).

  8. Table A1 and Fig. A2 in the online appendix give more details.

  9. All variables presented in Table 1 are based on self-reporting.

  10. This difference in the proportion of deceased fathers and mothers results in part from the fact that husbands are generally older than their wives.

  11. To check that the options we propose are not too constraining, we compared our elicited probabilities to those observed in Wave 2 of SHARE, which uses only one open question requiring a probability between 0 % and 100 %. We found that only 5 % of respondents gave a probability that does not belong to our list of 14 values.

  12. Elicited probabilities for men, however, might suffer from a bias toward 0.5.

  13. The curves derive from locally weighted scatterpoint smoothing. For readability, confidence intervals are provided for men only.

  14. Actually, France is one of the countries with the largest gender gap in LE at birth. It amounts to 6.7 years in 2010, compared with 3.9 in the United Kingdom, 5 in the United States, and 6 in Japan.

  15. We find the same results using French data from SHARE (Wave 2). Men and women underestimate their survival probabilities, with no significant difference between them. In fact, the underestimation might be even greater, given that official statistics are based on 2009 mortality rates and do not incorporate future progress in longevity.

  16. The distribution of SLE is close to the normal distribution, with skewness equal to –0.7 and kurtosis equal to 3.3.

  17. This does not rule out variations in level of uncertainty across individuals, as shown in Fig. 3 and in the next section.

  18. For people aged 51–60, the corresponding figures are [57.9, 97.1] for the average CI, 63.5 for the third quartile of the lower bound, and 91.9 for the first quartile of the upper bound.

  19. We can also exhibit graphs of the SUL distribution for a unique level of SLE.

  20. This one-shot model can be easily extended to a life cycle perspective.

  21. Investigations detailed in the online appendix (Section 4) led us to reject the possibility of selection bias and not to reject the exogeneity of SAHi for the SLEi and SULi equations. Hence, we rely on a GLS estimator that allows for heteroskedasticity and correlations between the disturbances of Eqs. (5a)–(5c). Notice, however, that we perform the exogeneity test assuming that only SAH might be non-exogenous, which is rather contradictory with the idea that there are causations in multiple directions.

  22. Means-tested free complementary health insurance.

  23. The classification of illnesses (N, C, A, or AC) was not communicated to the respondents, nor was the information that a given illness does or does not shorten or threaten life.

  24. Endogeneity of lifestyle may also play a role if some of the less-healthy women are more careful about their weight.

  25. Mothers’ survival and longevity have a more limited impact, which might be explained by the fact that a mother’s death generally occurs later in individuals’ lives. In our sample, two-thirds of mothers, but less than one-half the fathers are still alive (Table 1).

  26. While controlling for all the regressors, we find that SUL residuals are an inverse U-shaped function of SLE residuals. This results partly from the definition of our indicators (see Fig. A9 in the online appendix).

  27. The results regarding complementary insurance are not conclusive, but enrollment is not much a matter of individual decision in France. One-half the population is covered by employer-provided plans, and 6 % of the population is covered for free by plans for low-income people.

  28. pt is the probability of being alive at period t, and pt – pt + l is the probability of dying at the end of period t. If pt = pt + l, there is no risk of dying in t. Hence, a constant pt sequence means that there are only two periods at which one can die: namely, the first and the last. This gives maximum dispersion to the distribution of ages at death. Contrary to Eq. (4), where the function pi(hi ; bi) was the subjective probability of different health states conditional on behavior, here pt(bl, . . . , bt – l) is the probability of being alive in t, conditional on behavior in previous periods. We consider only two health states: alive or dead.

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Acknowledgments

We are grateful to the four referees for their constructive suggestions. We would also like to thank for useful discussions Alain Trannoy, Frangois-Charles Wolff, Nicolas Jacquemet, Eric Bonsang, Emmanuel Thibault, and Pierre Pestieau; and participants at the Journee de la Chaire Sante (Paris, 2012), the Second Workshop TSE/IDEI on Long Term Care (Toulouse, 2012), the Seminar on Health Economics and Policy (Grindelwald, 2014), and the Workshop on Subjective Expectations and Probabilities in Economics and Psychology (Essex, 2014). We also thank France Mesle for information on life tables. We acknowledge financial support from the Health Chair–PSL, Universite Paris Dauphine, ENSAE and MGEN under the aegis of the Fondation du Risque.

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Authors and Affiliations

  1. Université Paris-Dauphine, PSL University, LEDa, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Brigitte Dormont & Anne-Laure Samson

  2. Woodrow Wilson School, Princeton University, Princeton, NJ, 08544, USA

    Marc Fleurbaey

  3. Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS, GREQAM, Centre de la Vieille Charité, 2 Rue de la Charité, 13002, Marseille, France

    Stéphane Luchini

  4. Department of Economics, KU Leuven, Naamsestraat 69 - bus 3565, 3000, Leuven, Belgium

    Erik Schokkaert

  5. CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Erik Schokkaert

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  1. Brigitte Dormont
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  2. Anne-Laure Samson
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  4. Stéphane Luchini
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Correspondence to Anne-Laure Samson.

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Dormont, B., Samson, AL., Fleurbaey, M. et al. Individual Uncertainty About Longevity. Demography 55, 1829–1854 (2018). https://doi.org/10.1007/s13524-018-0713-4

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