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Variance in Death and Its Implications for Modeling and Forecasting Mortality

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  • Shripad Tuljapurkar
  • Ryan D. Edwards

Abstract

Entropy, or the gradual decline through age in the survivorship function, reflects the considerable amount of variance in length of life found in any human population. Part is due to the well-known variation in life expectancy between groups: large differences according to race, sex, socioeconomic status, or other covariates. But within-group variance is very large even in narrowly defined groups, and it varies strongly 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 along the temporal dimension.

Suggested Citation

  • Shripad Tuljapurkar & Ryan D. Edwards, 2009. "Variance in Death and Its Implications for Modeling and Forecasting Mortality," NBER Working Papers 15288, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:15288
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    1. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    2. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    3. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    4. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    5. Ryan Edwards, 2013. "The cost of uncertain life span," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1485-1522, October.
    6. Shripad Tuljapurkar & Carl Boe, 1998. "Mortality Change and Forecasting," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 13-47.
    7. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    8. John Bongaarts & Griffith Feeney, 2002. "How Long Do We Live?," Population and Development Review, The Population Council, Inc., vol. 28(1), pages 13-29, March.
    9. Edwards Ryan D, 2009. "The Cost of Cyclical Mortality," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, March.
    10. Shripad Tuljapurkar, 1998. "Forecasting Mortality Change," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 127-134.
    11. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    12. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    13. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
    14. Shripad Tuljapurkar & Carl Boe, "undated". "Mortality Change and Forecasting: How Much and How Little Do We Know?," Pension Research Council Working Papers 98-2, Wharton School Pension Research Council, University of Pennsylvania.
    15. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    10. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    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. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    21. Alexander, Monica, 2018. "Deaths without denominators: using a matched dataset to study mortality patterns in the United States," SocArXiv q79ye, Center for Open Science.
    22. 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.
    23. 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.

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    JEL classification:

    • I1 - Health, Education, and Welfare - - Health
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • N3 - Economic History - - Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy

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