Demography

, Volume 50, Issue 6, pp 2037–2051 | Cite as

Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections

Article

Abstract

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, a phenomenon we call “rotation.” We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. We simplify the problem by focusing on the relative magnitude of death rates at two ages (0 and 15–19) while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations, including those that currently have very high life expectancies. Detailed examples are given using data from Japan and the United States.

Keywords

Mortality age pattern Long-term projection Extended Lee-Carter method Mortality forecasting Extrapolation 

References

  1. Bongaarts, J. (2005). Long-range trends in adult mortality: Models and projection methods. Demography, 42, 23–49.CrossRefGoogle Scholar
  2. Booth, H. (2006). Demographic forecasting: 1980 to 2005 in review. International Journal of Forecasting, 22, 547–581.CrossRefGoogle Scholar
  3. Chu, C. Y. C., Chien, H.-K., & Lee, R. D. (2008). Explaining the optimality of U-shaped age-specific mortality. Theoretical Population Biology, 73, 171–180.CrossRefGoogle Scholar
  4. Fisher, R. A. (1930). The genetical theory of natural selection. Oxford, UK: The Clarendon press.Google Scholar
  5. Galley, C., & Woods, R. (1999). On the distribution of deaths during the first year of life. Population: An English Selection, 11, 35–59.Google Scholar
  6. Girosi, F., & King, G. (2008). Demographic forecasting. Princeton: Princeton University Press.Google Scholar
  7. Hamilton, W. D. (1966). The moulding of senescence by natural selection. Journal of Theoretical Biology, 12, 12–45.CrossRefGoogle Scholar
  8. Horiuchi, S., & Wilmoth, J. R. (1995, April). The aging of mortality decline. Paper presented at the annual meeting of the Population Association of America, San Francisco, CA.Google Scholar
  9. Kannisto, V., Lauritsen, J., Thatcher, A. R., & Vaupel, J. W. (1994). Reductions in mortality at advanced ages: Several decades of evidence from 27 countries. Population and Development Review, 20, 793–810.CrossRefGoogle Scholar
  10. Lee, R. (2000). The Lee-Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal, 4, 80–93.CrossRefGoogle Scholar
  11. Lee, R. D. (2003). Rethinking the evolutionary theory of aging—Transfers, not births, shape senescence in social species. Proceedings of the National Academy of Sciences, 100, 9637–9642.CrossRefGoogle Scholar
  12. Lee, R. (2008). Sociality, selection, and survival: Simulated evolution of mortality with intergenerational transfers and food sharing. Proceedings of the National Academy of Sciences, 105, 7124–7128.CrossRefGoogle Scholar
  13. Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
  14. Lee, R., & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38, 537–549.CrossRefGoogle Scholar
  15. Li, N., & Gerland, P. (2011, April). Modifying the Lee-Carter method to project mortality changes up to 2100. Paper presented at the annual meeting of the Population Association of America, Washington, DC.Google Scholar
  16. Li, N., & Lee, R. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42, 575–594.CrossRefGoogle Scholar
  17. Liu, L., Johnson, H. L., Cousens, S., Perin, J., Scott, S., Lawn, J. E., . . . Black, R. E. (2012). Global, regional, and national causes of child mortality: An updated systematic analysis for 2010 with time trends since 2000. Lancet, 379, 2151–2161.Google Scholar
  18. Patton, G. C., Coffey, C., Sawyer, S. M., Viner, R. M., Haller, D. M., Bose, K., . . . Mathers, C. D. (2009). Global patterns of mortality in young people: a systematic analysis of population health data. Lancet, 374, 881–892. doi:10.1016/S0140-6736(09)60741-8
  19. Raftery, A., Chunn, J., Gerland, P., & Ševčíková, H. (2013). Bayesian probabilistic projections of life expectancy for all countries. Demography, 50, 77–801.CrossRefGoogle Scholar
  20. Rao, C., Adair, T., & Kinfu, Y. (2011). Using historical vital statistics to predict the distribution of under-five mortality by cause. Clinical Medicine & Research, 9, 66–74.CrossRefGoogle Scholar
  21. Shang, H. L., Booth, H., & Hyndman, R. (2011). Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods. Demographic Research, 25(article 5), 173–214. doi:10.4054/DemRes.2011.25.5 CrossRefGoogle Scholar
  22. Soneji, S., & King, G. (2011). The future of death in America. Demographic Research, 25(article 1), 1–38. doi:10.4054/DemRes.2011.25.1 CrossRefGoogle Scholar
  23. Tuljapurkar, S., Li, N., & Boe, C. (2000). A universal pattern of mortality decline in the G7 countries. Nature, 405, 789–792.CrossRefGoogle Scholar
  24. United Nations. (2010). World population prospects: The 2006 revision, volume III: Analytical report. New York: Department of Economic and Social Affairs, Population Division.Google Scholar
  25. University of California at Berkeley & Max Planck Institute for Demographic Research. (2012). Human Mortality Database (HMD). Retrieved from www.mortality.org or www.humanmortality.de

Copyright information

© Population Association of America 2013

Authors and Affiliations

  1. 1.Population DivisionUnited NationsNew YorkUSA
  2. 2.Departments of Demography and EconomicsUniversity of California at BerkeleyBerkeleyUSA

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