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Variance in death and its implications for modeling and forecasting mortality

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  • Shripad Tuljapurkar

    (Stanford University)

  • Ryan Edwards

    (University of California, Berkeley)

Abstract

The slope and curvature of the survivorship function reflect the considerable amount of variance in length of life found in any human population. This is due in part to the well-known variation in life expectancy between groups: large differences in race, sex, socioeconomic status, or other covariates. But within-group variance is large even in narrowly defined groups, and changes substantially and inversely with the group average length of life. We show that variance in length of life is inversely related to the Gompertz slope of log mortality through age, and we reveal its relationship to variance in a multiplicative frailty index. Our findings bear a variety of implications for modeling and forecasting mortality. In particular, we examine how the assumption of proportional hazards fails to account adequately for differences in subgroup variance, and we discuss how several common forecasting models treat the variance in the temporal dimension.

Suggested Citation

  • Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    • Handle: RePEc:dem:demres:v:24:y:2011:i:21
    DOI: 10.4054/DemRes.2011.24.21
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    References listed on IDEAS

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    Cited by:

    1. Debón, A. & Chaves, L. & Haberman, S. & Villa, F., 2017. "Characterization of between-group inequality of longevity in European Union countries," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 151-165.
    2. Meyer, Patrick & Ponthiere, Gregory, 2020. "Threshold ages for the relation between lifetime entropy and mortality risk," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 1-7.
    3. Patrick Meyer & Gregory Ponthiere, 2020. "Human lifetime entropy in a historical perspective (1750–2014)," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 14(1), pages 129-167, January.
    4. Tomasz Wrycza, 2014. "Variance in age at death equals average squared remaining life expectancy at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(50), pages 1405-1412.
    5. Ahbab Mohammad Fazle Rabbi & Stefano Mazzuco, 2021. "Mortality Forecasting with the Lee–Carter Method: Adjusting for Smoothing and Lifespan Disparity," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 97-120, March.
    6. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    7. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    8. Duncan Gillespie & Meredith Trotter & Shripad Tuljapurkar, 2014. "Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 1003-1017, June.
    9. Michal Engelman & Hal Caswell & Emily Agree, 2014. "Why do lifespan variability trends for the young and old diverge? A perturbation analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(48), pages 1367-1396.
    10. Richard G. Rogers & Robert A. Hummer & Justin M. Vinneau & Elizabeth M. Lawrence, 2020. "Greater mortality variability in the United States in comparison with peer countries," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(36), pages 1039-1056.
    11. Glenn Firebaugh & Francesco Acciai & Aggie Noah & Christopher Prather & Claudia Nau, 2014. "Why Lifespans Are More Variable Among Blacks Than Among Whites in the United States," Demography, Springer;Population Association of America (PAA), vol. 51(6), pages 2025-2045, December.
    12. Mathias Voigt & Antonio Abellán & Julio Pérez & Diego Ramiro, 2020. "The effects of socioeconomic conditions on old-age mortality within shared disability pathways," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-17, September.
    13. Aburto, José Manuel & Basellini, Ugofilippo & Baudisch, Annette & Villavicencio, Francisco, 2022. "Drewnowski’s index to measure lifespan variation: Revisiting the Gini coefficient of the life table," Theoretical Population Biology, Elsevier, vol. 148(C), pages 1-10.
    14. Claudia Nau & Glenn Firebaugh, 2012. "A New Method for Determining Why Length of Life is More Unequal in Some Populations Than in Others," Demography, Springer;Population Association of America (PAA), vol. 49(4), pages 1207-1230, November.
    15. Milevsky, Moshe A., 2020. "Swimming with wealthy sharks: longevity, volatility and the value of risk pooling," Journal of Pension Economics and Finance, Cambridge University Press, vol. 19(2), pages 217-246, April.
    16. Aburto, José Manuel & Kristensen, Frederikke Frehr & Sharp, Paul, 2021. "Black-white disparities during an epidemic: Life expectancy and lifespan disparity in the US, 1980–2000," Economics & Human Biology, Elsevier, vol. 40(C).
    17. Jos'e Manuel Aburto & Ugofilippo Basellini & Annette Baudisch & Francisco Villavicencio, 2021. "Drewnowski's index to measure lifespan variation: Revisiting the Gini coefficient of the life table," Papers 2111.11256, arXiv.org.
    18. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.
    19. Nico Keilman, 2019. "Mortality shifts and mortality compression in period and cohort life tables," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(40), pages 1147-1196.
    20. Sergei Scherbov & Dalkhat Ediev, 2016. "Does selection of mortality model make a difference in projecting population ageing?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 34(2), pages 39-62.
    21. Kashnitsky, Ilya & de Beer, Joop & van Wissen, Leo, 2017. "Decomposition of regional convergence in population aging across Europe," OSF Preprints ykqbv, Center for Open Science.
    22. Nico Keilman & Dinh Q. Pham & Astri Syse, 2018. "Mortality shifts and mortality compression. The case of Norway, 1900-2060," Discussion Papers 884, Statistics Norway, Research Department.
    23. Jose Manuel Aburto & Jesús-Adrián Alvarez & Francisco Villavicencio & James W. Vaupel, 2019. "The threshold age of the lifetable entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(4), pages 83-102.

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    More about this item

    Keywords

    inequality; entropy; proportional hazards;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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