Mortality improvements steady over 55 years

From: Robin Hanson (
Date: Mon Mar 27 2000 - 08:54:45 MST

This is apparently a classic:

"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.


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
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323

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