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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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    References listed on IDEAS

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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), September.
    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 & 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.
    4. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Edwards Ryan D, 2009. "The Cost of Cyclical Mortality," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, March.
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    Citations

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    Cited by:

    1. 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.
    2. 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, May.
    3. repec:eee:insuma:v:75:y:2017:i:c:p:151-165 is not listed on IDEAS
    4. 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.
    5. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    6. 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, January.

    More about this item

    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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