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Estimating the joint survival probabilities of married individuals


  • Sanders, Lisanne
  • Melenberg, Bertrand


We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared polynomials. Also based on a nonparametric comparison, we find that extending the independent Weibull distribution by a squared third order polynomial shows the best performance. We illustrate our model by calculating remaining life expectancies and annuity values. We find that the husbands life expectancy at birth is generally increasing with his wifes age of death and the wifes life expectancy at birth is generally increasing with her husbands age of death. Ignoring the dependence between the remaining lifetimes of spouses may lead to an underestimation of the value of a joint annuity and an overestimation of the value of a single-life annuity, but less than suggested on the basis of the previous literature.

Suggested Citation

  • Sanders, Lisanne & Melenberg, Bertrand, 2016. "Estimating the joint survival probabilities of married individuals," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 88-106.
  • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:88-106
    DOI: 10.1016/j.insmatheco.2015.12.006

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    References listed on IDEAS

    1. Kotlikoff, Laurence J & Spivak, Avia, 1981. "The Family as an Incomplete Annuities Market," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 372-391, April.
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    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    6. Wolfram Horneff & Raimond Maurer & Olivia Mitchell & Ivica Dus, 2006. "Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion," Working Papers wp124, University of Michigan, Michigan Retirement Research Center.
    7. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    8. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," Review of Economic Studies, Oxford University Press, vol. 32(2), pages 137-150.
    9. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
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    11. Shaked, Moshe, 1982. "A general theory of some positive dependence notions," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 199-218, June.
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    Cited by:

    1. Janice Compton & Robert A. Pollak, 2018. "The Life Expectancy of Older Couples and Surviving Spouses," Working Papers 2018-072, Human Capital and Economic Opportunity Working Group.

    More about this item


    Mortality; Life expectancy; Annuity; Non-parametrics; Joint survival;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • J10 - Labor and Demographic Economics - - Demographic Economics - - - General


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