Abstract

This article links parameterized model mortality schedules with time series methods to develop forecasts of U.S. mortality to the year 2000. The use of model mortality schedules permits a relatively concise representation of the history of mortality by age and sex from 1900 to 1985, and the use of modern time series methods to extend this history forward to the end of this century allows for a flexible modeling of trend and the accommodation of changes in long-run mortality patterns. This pilot study demonstrates that the proposed procedure produces medium-range forecasts of mortality that meet the standard tests of accuracy in forecast evaluation and that are sensible when evaluated against the comparable forecasts produced by the Social Security Administration.

The text of this article is only available as a PDF.

References

Ascher, W. (
1978
).
Forecasting: An Appraisal for Policy Makers
.
Baltimore, Md.
:
Johns Hopkins University Press
.
Bohara, A. K., Bradley, M., & McNown, R. F. (
1987
).
New evidence on targets for monetary policy
.
Southern Economic Journal
,
53
,
591
604
. 10.2307/1058756
Boulier, B. L., & Paqueo, V. B. (
1988
).
On the theory and measurement of the determinants of mortality
.
Demography
,
25
,
249
263
. 10.2307/2061292
Box, G. E. P., & Jenkins, G. M. (
1976
).
Time Series Analysis, Forecasting and Control
.
San Francisco
:
Holden-Day
.
Brass, W. (
1971
).
On the scale of mortality
. In Brass, W. (Ed.),
Biological Aspects of Demography
(pp.
86
110
).
London
:
Taylor and Francis
.
Carter, L. R., & Lee, R. D. (
1986
).
Joint forecasts of U.S. marital fertility, nuptiality, births and marriages using time series models
.
Journal of the American Statistical Association
,
81
,
902
911
. 10.2307/2289058
Coale, A. J., & Demeny, P. (
1966
).
Regional Model Life Tables and Stable Populations
.
Princeton, N.J.
:
Princeton University Press
.
Coale, A. J., & McNeil, D. R. (
1972
).
The distribution by age of the frequency of first marriage in a female cohort
.
Journal of the American Statistical Association
,
67
,
743
749
. 10.2307/2284631
Coale, A. J., & Trussell, T. J. (
1974
).
Model fertility schedules: Variations in the age structure of childbearing in human populations
.
Population Index
,
40
,
185
206
. 10.2307/2733910
Crimmins, E. M. (
1981
).
The changing pattern of American mortality decline, 1940–77, and its implications for the future
.
Population and Development Review
,
7
,
229
254
. 10.2307/1972622
Easterlin, R. A. (
1980
).
Birth and Fortune
.
New York
:
Basic Books
.
Efron, B., & Gong, G. (
1983
).
A leisurely look at the bootstrap, the jackknife, and cross validation
.
American Statistician
,
37
,
36
48
. 10.2307/2685844
Heligman, L., & Pollard, J. H. (
1980
).
The age pattern of mortality
.
journal of the Institute of Actuaries
,
107
,
49
80
.
Keyfitz, N. (
1982
).
Choice of function for mortality analysis: Effective forecasting depends on a minimum parameter representation
.
Theoretical Population Biology
,
21
,
329
352
. 10.1016/0040-5809(82)90022-3
Keyfitz, N. 1985. Demography in the twenty-first century: The uses of forecasting. Pp. 59-81 in Proceedings of the IUSSP International Population Conference (Vol. 1). Liege: International Union for the Scientific Study of Population.
Kling, J. L., & Bessler, D. A. (
1985
).
A comparison of multivariate forecasting procedures for economic time series
.
International Journal of Forecasting
,
1
,
5
24
. 10.1016/S0169-2070(85)80067-4
Land, K. C. (
1986
).
Methods for population forecasts: A review
.
Journal of the American Statistical Association
,
81
,
888
901
. 10.2307/2289057
Land, K. C, & McMillan, M. M. (
1980
).
A macrodynamic analysis of changes in mortality indexes in the United States, 1940–1975: Some preliminary results
.
Social Indicators Research
,
7
,
1
46
. 10.1007/BF00305590
Lee, R. D. (
1974
).
Forecasting births in post-transition populations: Stochastic renewal with serially correlated fertility
.
Journal of the American Statistical Association
,
69
,
607
617
. 10.2307/2285990
Ljung, G. M., & Box, G. E. P. (
1978
).
On a measure of lack of fit in time series models
.
Biometrika
,
65
,
297
303
. 10.1093/biomet/65.2.297
Long, J. F. (
1984
).
U.S. national population projection methods: A view from four forecasting traditions
.
Insurance: Mathematics and Economics
,
3
,
231
239
. 10.1016/0167-6687(84)90027-1
McDonald, J. (
1979
).
A time series approach to forecasting Australian total live births
.
Demography
,
16
,
575
601
. 10.2307/2060937
McDonald, J. (
1981
).
Modeling demographic relationships: An analysis of forecast functions for Australian births
.
Journal of the American Statistical Association
,
76
,
782
792
. 10.2307/2287568
McNown, R. F. (
1986
).
On the uses of econometric models: A guide for policy makers
.
Policy Sciences
,
19
,
359
380
. 10.1007/BF00139521
Olshansky, S. J. 1987. On Forecasting Mortality. Unpublished manuscript (mimeo), National Opinion Research Center, University of Chicago.
Peters, S. C, & Freedman, D. A. (
1985
).
Using the bootstrap to evaluate forecasting equations
.
Journal of Forecasting
,
4
,
251
262
. 10.1002/for.3980040302
Preston, S. H. (
1976
).
Mortality Patterns in National Populations
.
New York
:
Academic Press
.
Rogers, A. (
1986
).
Parameterized multistate population dynamics and projections
.
Journal of the American Statistical Association
,
81
,
48
61
. 10.2307/2287967
Rogers, A., & Castro, L. (
1981
).
Model Migration Schedules
.
Laxenburg, Austria
:
International Institute for Applied Systems Analysis
.
Rogers, A., and F. Planck. 1983. Model: A General Program for Estimating Parameterized Model Schedules of Fertility, Mortality, Migration, and Marital and Labor Force Status Transitions, Working Paper 83-102. Laxenburg, Austria: International Institute for Applied Systems Analysis.
Rogers, A., and J. Watkins. 1986. Parameterized Projections of Regional Populations in the United States, Working Paper 86-5. Boulder: University of Colorado, Institute of Behavioral Science, Population Program.
Saboia, J. L. M. (
1974
).
Modeling and forecasting populations by time series—The Swedish case
.
Demography
,
11
,
483
492
. 10.2307/2060440
Saboia, J. L. M. (
1977
).
Autoregressive integrated moving average (ARIMA) models for birth forecasting
.
Journal of the American Statistical Association
,
72
,
264
270
. 10.2307/2286787
Siler, W. (
1983
).
Parameters of mortality in human populations with widely varying life spans
.
Statistics in Medicine
,
2
,
373
380
. 10.1002/sim.4780020309
Sims, C. A. (
1980
).
Macroeconomics and reality
.
Econometrica
,
48
,
1
48
. 10.2307/1912017
Sims, C. A. 1982. Policy analysis with econometric models. Brookings Papers on Economic Activity, 107-152.
Social Security Area Population Projections, 1987
. (
1987
).
Washington, D.C.
:
U.S. Office of the Actuary
.
Stoto, M. A. (
1988
).
Dealing with uncertainty: Statistics for an aging population
.
American Statistician
,
42
,
103
110
. 10.2307/2684481
Theil, H. (
1966
).
Applied Economic Forecasting
.
Amsterdam
:
North Holland
.
Thiele, T. N. (
1872
).
On a mathematical formula to express the rate of mortality throughout the whole of life
.
Journal of the Institute of Actuaries
,
16
,
313
329
.
Thompson, P. A., Bell, W., Long, J., & Miller, R. B. (
1987
).
Multivariate Time Series Projections of Parameterized Age-Specific Fertility Rates
.
Columbus
:
Ohio State University, College of Business
.
Tiao, G. C., & Box, G. E. P. (
1981
).
Modeling multiple time series with applications
.
Journal of the American Statistical Association
,
76
,
802
816
. 10.2307/2287575
Zaba, B. (
1979
).
The four parameter logit life table system
.
Population Studies
,
33
,
79
100
. 10.2307/2173867
Zellner, A., & Palm, F. (
1974
).
Time series analysis and simultaneous equations models
.
Journal of Econometrics
,
2
,
17
54
. 10.1016/0304-4076(74)90028-1