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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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15288.

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Date of creation: Aug 2009
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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), September.
  2. Ryan D. Edwards, 2008. "The Cost of Uncertain Life Span," NBER Working Papers 14093, National Bureau of Economic Research, Inc.
  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. 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.
  5. Shripad Tuljapurkar & Carl Boe, . "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.
  6. Edwards Ryan D, 2009. "The Cost of Cyclical Mortality," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, March.
  7. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer, vol. 42(1), pages 23-49, February.
  8. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer, vol. 16(3), pages 439-454, August.
  9. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
  10. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer, vol. 36(4), pages 475-495, November.
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Cited by:
  1. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.

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