This is apparently a classic:
http://www.jstor.org/fcgi-bin/jstor/listjournal.fcg/01621459/di985993/98p0117d
"Modeling and Forecasting U. S. Mortality"
Ronald D. Lee, Lawrence R. Carter
Journal of the American Statistical Association,
Vol. 87, No. 419. (Sep., 1992), pp. 659-671.
Abstract
Time series methods are used to make long-run forecasts, with confidence
intervals, of age-specific mortality in the United States from 1990 to 2065.
First, the logs of the age-specific death rates are modeled as a linear
function of an unobserved period-specific intensity index, with parameters
depending on age. This model is fit to the matrix of U.S. death rates, 1933
to 1987, using the singular value decomposition (SVD) method; it accounts
for almost all the variance over time in age-specific death rates as a
group. Whereas $e_0$ has risen at a decreasing rate over the century and has
decreasing variability, $\mathbf{k}(t)$ declines at a roughly constant rate
and has roughly constant variability, facilitating forecasting.
$\mathbf{k}(t)$, which indexes the intensity of mortality, is next modeled
as a time series (specifically, a random walk with drift) and forecast. The
method performs very well on within-sample forecasts, and the forecasts are
insensitive to reductions in the length of the base period from 90 to 30
years; some instability appears for base periods of 10 or 20 years, however.
Forecasts of age-specific rates are derived from the forecasts of
$\mathbf{k}$, and other life table variables are derived and presented.
These imply an increase of 10.5 years in life expectancy to 86.05 in 2065
(sexes combined), with a confidence band of plus 3.9 or minus 5.6 years,
including uncertainty concerning the estimated trend. Whereas 46% now
survive to age 80, by 2065 46% will survive to age 90. Of the gains forecast
for person-years lived over the life cycle from now until 2065, 74% will
occur at age 65 and over. These life expectancy forecasts are substantially
lower than direct time series forecasts of $e_0$, and have far narrower
confidence bands; however, they are substantially higher than the forecasts
of the Social Security Administration's Office of the Actuary.
Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323
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