## Modeling and forecasting U.S. mortality. (With discussion).(English)Zbl 1351.62186

Summary: 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, $$k(t)$$ declines at a roughly constant rate and has roughly constant variability, facilitating forecasting. $$k(t)$$, 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 $$k$$, 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.

### MSC:

 62P20 Applications of statistics to economics 91B84 Economic time series analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M20 Inference from stochastic processes and prediction 91D20 Mathematical geography and demography

### Keywords:

demography; forecast; life expectancy; mortality; population; projection
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### References:

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