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**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 |

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\textit{R. D. Lee} and \textit{L. R. Carter}, J. Am. Stat. Assoc. 87, No. 419, 659--675 (1992; Zbl 1351.62186)

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