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.
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Notes
In this article, period 2005–2010 is simplified as 2008, which is a rounding up of the midpoint, 2007.5; and years ending with 3 and 8 are used to represent the corresponding five-year periods.
Death rates of abridged life tables in five-year period were obtained on December 2011 from National Statistic Offices and the University of California at Berkeley and the Max Planck Institute for Demographic Research (2012). These death rates are computed from the five-year-period deaths and exposures. The use of five-year period data is more parsimonious and allows us to compute more robust b(x) distributions, even for smaller populations.
There are two ways to compute the total person-years in the open age group, the first assuming that the population in this age group is stationary and the second assuming the death rate in this age group obeys a logistic model converging to 1. The HMD used the second, and we also use it to extend the age group to 130 years, at which death rates are close to 1.
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The authors thank Shripad Tuljapurkar and Carl Boe for their useful comments. The views expressed in this article are those of the authors and do not necessarily reflect those of the United Nations.
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Li, N., Lee, R. & Gerland, P. Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections. Demography 50, 2037–2051 (2013). https://doi.org/10.1007/s13524-013-0232-2
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DOI: https://doi.org/10.1007/s13524-013-0232-2