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Mortality Modelling and Forecasting: a Review of Methods

Published online by Cambridge University Press:  10 May 2011

H. Booth  and
L. Tickle
H. Booth
Affiliation:
Australian Demographic and Social Research Institute, Coombs Building 9, Australian National University, ACT 0200, Australia., Email: heather.booth@anu.edu.au
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Abstract

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Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee–Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee–Carter age-period-cohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

Keywords

MortalityForecastingModellingLee–CarterGLMp-splinesExtrapolationUncertaintyCohortDecompositionCause of DeathSoftware
Type
Papers
Information
Annals of Actuarial Science , Volume 3 , Issue 1-2 , September 2008 , pp. 3 - 43
Copyright
Copyright © Institute and Faculty of Actuaries 2008

References

Ahlburg, D.A. (1995). Simple versus complex models: evaluation, accuracy, and combining. Mathematical Population Studies, 5(3), 281–290.CrossRefGoogle ScholarPubMed
Ahlburg, D.A. & Vaupel, J.W. (1990). Alternative projections of the U.S. population. Demography, 27(4), 639–652.CrossRefGoogle ScholarPubMed
Alders, M. & De Beer, J. (2005). An expert knowledge approach to stochastic mortality forecasting in the Netherlands. In (Keilman, N., ed.) Perspectives on mortality forecasting (Vol. II. Probabilistic models, pp39–64). Swedish Social Insurance Agency, Stockholm.Google Scholar
Alderson, M. & Ashwood, F. (1985). Projection of mortality rates for the elderly. Population Trends, 42, 22–29.Google Scholar
Alho, J.M. (1990). Stochastic methods in population forecasting. International Journal of Forecasting, 6(4), 521–530.CrossRefGoogle ScholarPubMed
Alho, J.M. (1991). Effect of aggregation on the estimation of trend mortality. Mathematical Population Studies, 2, 53–67.CrossRefGoogle Scholar
Alho, J.M. (1992). Estimating the strength of expert judgement: the case of U.S. mortality forecasts. Journal of Forecasting, 11, 157–167.CrossRefGoogle Scholar
Alho, J.M. (1998). A stochastic forecast of the population of Finland (Reviews No. 1998/4). Statistics Finland, Helsinki.Google Scholar
Alho, J.M. (2003). Experiences from forecasting mortality in Finland. In (Bengtsson, T. & Keilman, N., eds.) Perspectives on mortality forecasting (Vol. I. Current practice, 29–40). Swedish Social Insurance Agency, Stockholm.Google Scholar
Alho, J.M. (2005). Remarks on the use of probabilities in demography and forecasting. In (Keilman, N., ed.) Perspectives on mortality forecasting (Vol. II. Probabilistic models, 27–38). Swedish Social Insurance Agency, Stockholm.Google Scholar
Alho, J.M. & Spencer, B.D. (1985). Uncertain population forecasting. Journal of the American Statistical Association, 80, 306–314.CrossRefGoogle ScholarPubMed
Alho, J.M. & Spencer, B.D. (1990). Error models for official mortality forecasts. Journal of the American Statistical Association, 85(411), 609–616.CrossRefGoogle ScholarPubMed
Alho, J.M. & Spencer, B.D. (2005). Statistical Demography and Forecasting. Springer, New York.Google Scholar
Alho, J.M., Alders, M., Cruijsen, H., Keilman, N., Nikander, T. & Pham, D.Q. (2006). New forecast: population decline postponed in Europe. Statistical Journal for the United Nations Economic Commission for Europe, 23(1), 1–10.CrossRefGoogle Scholar
Babel, B., Bomsdorf, E. & Schmidt, R. (2008). Forecasting German mortality using panel data procedures. Journal of Population Economics, 21(3), 541–555.CrossRefGoogle Scholar
Bell, W. (1997). Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates. Journal of Official Statistics, 13(3), 279–303.Google Scholar
Bell, W.R. & Monsell, B.C. (1991). Using principal components in time series modeling and forecasting of age-specific mortality rates. Paper presented at the American Statistical Association 1991 Proceedings of the Social Statistics Section.Google Scholar
Bengtsson, T. & Keilman, N. (eds.) (2003). Perspectives on mortality forecasting (Vol. I. Current practice). Swedish National Social Insurance Board, Stockholm.Google Scholar
Benjamin, B. & Pollard, J.H. (1980). The analysis of mortality and other actuarial statistics. Heinemann, London.Google Scholar
Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (2004). Annual report. Washington DC.Google Scholar
Boleslawski, L. & Tabeau, E. (2001). Comparing theoretical age patterns of mortality beyond the age of 80. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (127–155). Kluwer Academic Publishers, Dordrecht.Google Scholar
Bongaarts, J. (2005). Long-range trends in adult mortality: models and projection methods. Demography, 42(1), 23–49.CrossRefGoogle ScholarPubMed
Bongaarts, J. (2006). How long will we live? Population and Development Review, 32(4), 605–628.CrossRefGoogle Scholar
Bongaarts, J. & Feeney, G. (2002). How long do we live? Population and Development Review, 28(1), 13–29.CrossRefGoogle Scholar
Bongaarts, J. & Feeney, G. (2003). Estimating mean lifetime. Proceedings of the National Academy of Sciences, 100(23), 13127–13133.CrossRefGoogle ScholarPubMed
Bongaarts, J. & Feeney, G. (2006). The quantum and tempo of life-cycle events. Vienna Yearbook of Population Research 2006, 115–151.CrossRefGoogle Scholar
Booth, H. (2004). On the importance of being uncertain: forecasting population futures for Australia. People and Place, 12(2), 1–12.Google Scholar
Booth, H. (2006). Demographic forecasting: 1980 to 2005 in review. International Journal of Forecasting, 22, 547–581.CrossRefGoogle Scholar
Booth, H. & Tickle, L. (2003). The future aged: new projections of Australia's elderly population. Australasian Journal on Ageing, 22(4), 196–202.CrossRefGoogle Scholar
Booth, H. & Tickle, L. (2004). Beyond three score years and ten: prospects for longevity in Australia. People and Place, 12(1), 15–27.Google Scholar
Booth, H., Maindonald, J. & Smith, L. (2001). Age-time interactions in mortality projection: applying Lee–Carter to Australia (Working Papers in Demography No. 85). Australian National University, Canberra.Google Scholar
Booth, H., Maindonald, J. & Smith, L. (2002). Applying Lee–Carter under conditions of variable mortality decline. Population Studies, 56(3), 325–336.CrossRefGoogle ScholarPubMed
Booth, H., Tickle, L. & Smith, L. (2005). Evaluation of the variants of the Lee–Carter method of forecasting mortality: a multi-country comparison. In (Dharmalingam, A. & Pool, I., eds.) New Zealand Population Review, Special Issue on Stochastic Population Projections, 31(1), 13–37.Google Scholar
Booth, H., Hyndman, R.J., Tickle, L. & De Jong, P. (2006). Lee–Carter mortality forecasting: a multi-country comparison of variants and extensions. Demographic Research, 15(9), 289–310.CrossRefGoogle Scholar
Box, G., Jenkins, G.M. & Reinsel, G.C. (1994). Time series analysis: forecasting and control (3rd ed.). Prentice Hall, Englewood, NJ.Google Scholar
Brass, W. (1971). On the scale of mortality. In (Brass, W., ed.) Biological aspects of demography (69–110). Taylor and Francis, London.Google Scholar
Brass, W. (1974). Perspectives in population prediction: illustrated by the statistics of England and Wales. Journal of the Royal Statistical Society, Series A, 137(4), 532–583.CrossRefGoogle Scholar
Brillinger, D.R. (1986). The natural variability of vital rates and associated statistics. Biometrics, 42 (December), 693–734.CrossRefGoogle ScholarPubMed
Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected life-tables. Insurance: Mathematics and Economics, 31, 373–393.Google Scholar
Brouhns, N., Denuit, M. & Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 3, 212–224.CrossRefGoogle Scholar
Buettner, T. & Zlotnik, H. (2005). Prospects for increasing longevity as assessed by the United Nations. Genus, LXI(1), 213–233.Google Scholar
Cairns, A.J.G. (2000). A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313–330.Google Scholar
Carriere, J.F. (1992). Parametric models for life tables. Transactions of the Society of Actuaries, 44, 77–99.Google Scholar
Carter, L.R. & Prskawetz, A. (2001). Examining structural shifts in mortality using the Lee–Carter method (MPIDR Working Paper No. WP 2001–007). Max Planck Institute for Demographic Research.Google Scholar
Caselli, G. (1996). Future longevity among the elderly. In (Caselli, G. & Lopez, A., eds.) Health and mortality among elderly populations. Clarendon Press, Oxford.CrossRefGoogle Scholar
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(340), 743–749.CrossRefGoogle Scholar
Coale, A.J. & Guo, G. (1989). Revised regional model life tables at very low levels of mortality. Population Index, 55(4), 613–643.CrossRefGoogle ScholarPubMed
Coale, A.J. & Kisker, E.E. (1990). Defects in data on old-age mortality in the United States: new procedures for calculating schedules and life tables at the highest ages. Asian and Pacific Population Forum, 4(1), 1–31.Google Scholar
Congdon, P. (1993). Statistical graduation in local demographic analysis and projection. Journal of the Royal Statistical Society, 156(2), 237–270.CrossRefGoogle ScholarPubMed
Continuous Mortality Investigation Bureau (1990). Standard tables of mortality based on the 1979–1982 experiences, CMI report no. 10. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (1999). Standard tables of mortality based on the 1991–1994 experiences, CMI report no. 17. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (2002). An interim basis for adjusting the “92” series mortality projections for cohort effects, CMI Working paper no. 1. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (2004). Projecting future mortality: a discussion paper, CMI Working paper no. 3. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (2005). Projecting future mortality: towards a proposal for a stochastic methodology, CMI Working paper no. 15. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (2006). Stochastic projection methodologies: further progress and p-spline model features, example results and implications, CMI Working paper no. 20. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Continuous Mortality Investigation Bureau (2007). Stochastic projection methodologies: Lee–Carter model features, example results and implications, CMI Working paper no. 25. London: Institute of Actuaries and Faculty of Actuaries.Google Scholar
Crimmins, E.M. (1981). The changing pattern of American mortality decline, 1947–1977, and its implication for the future. Population and Development Review, 7(2), 229–254.CrossRefGoogle Scholar
Currie, D., Durban, M. & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.CrossRefGoogle Scholar
Czado, C., Delwarde, A. & Denuit, M. (2005). Bayesian Poisson logbilinear mortality projections. Insurance: Mathematics and Economics, 36, 260–284.Google Scholar
De Beer, J. (1989). Projecting age-specific fertility rates by using time-series methods. European Journal of Population, 5(1989), 315–346.CrossRefGoogle Scholar
De Beer, J. (1997). The effect of uncertainty of migration on national population forecasts: the case of the Netherlands. Journal of Official Statistics, 13(3), 227–243.Google Scholar
De Beer, J. (2000). Dealing with uncertainty in population forecasting. Statistics Netherlands, Department of Population, Voorburg.Google Scholar
De Beer, J. & Alders, M. (1999). Probabilistic population and household forecasts for the Netherlands. Working paper no. 45. Paper presented at the Joint ECE-Eurostat Work Session on Demographic Projections, 3–7 May 1999, Perugia, Italy.Google Scholar
De Jong, P. & Tickle, L. (2006). Extending Lee–Carter mortality forecasting Mathematical Population Studies, 13(1), 1–18.CrossRefGoogle Scholar
De Jong, P. & Marshall, C. (2007). Forecasting mortality using the Wang transform. ASTIN Bulletin, 37(1), 149–162.CrossRefGoogle Scholar
Denton, F., Feaver, C. & Spencer, B. (2005). Time series analysis and stochastic forecasting: an econometric study of mortality and life expectancy. Journal of Population Economics, 18(2), 203–227.CrossRefGoogle Scholar
Ewbank, D.C., Gomez de Leon, J.C. & Stoto, M.A. (1983). A reducible four-parameter system of model life tables. Population Studies, 37(1), 105–127.CrossRefGoogle ScholarPubMed
Forfar, D.O. (2004). Mortality laws. In (Teugels, J.L. & Sundt, B., eds.) Encyclopedia of actuarial science (1139–1145). Wiley, West Sussex.Google Scholar
Forfar, D.O. & Smith, D.M. (1987). The changing shape of English life tables. Transactions of the Faculty of Actuaries, 40, 98–134.CrossRefGoogle Scholar
Forfar, D.O., McCutcheon, J.J. & Wilkie, A.D. (1988). On graduation by mathematical formula. Journal of the Institute of Actuaries, 115(1), 97–245.CrossRefGoogle Scholar
Gage, T.B. & Mode, C.J. (1993). Some laws of mortality: how well do they fit? Human Biology, 65(3), 445–461.Google ScholarPubMed
Girosi, F. & King, G. (2006). Demographic forecasting. Cambridge University Press, Cambridge.Google Scholar
Golulapati, R., De Ravin, J.W. & Trickett, P.J. (1984). Projections of Australian mortality rates, 1981–2020 (Occasional paper no. 1983/2). Australian Bureau of Statistics.Google Scholar
Goss, S.C., Wade, A., Bell, F. & Dussault, B. (1998). Historical and projected mortality for Mexico, Canada, and the United States. North American Actuarial Journal, 2(4), 108–128.CrossRefGoogle Scholar
Government Actuary's Department (2001). National population projections: review of methodology for projecting mortality. Government Actuary's Department: London.Google Scholar
Government Actuary's Department (2006). National population projections 2004-based. Government Actuary's Department: London.Google Scholar
Guillot, M. (2003). The cross-sectional average length of life (CAL): a period mortality measure that reflects the experience of cohorts. Population Studies, 57(1), 41–54.CrossRefGoogle Scholar
Gutterman, S. & Vanderhoof, I.T. (1998). Forecasting changes in mortality: a search for a law of causes and effects. North American Actuarial Journal, 2(4), 135–138.CrossRefGoogle Scholar
Hannerz, H. (1999). Methodology and applications of a new law of mortality. Department of Statistics, University of Lund, Sweden, Lund.Google Scholar
Hannerz, H. (2001a). Presentation and derivation of a five-parameter survival function intended to model mortality in modern female populations. Scandinavian Actuarial Journal, 2001(2), 176–187.CrossRefGoogle Scholar
Hannerz, H. (2001b). Manhood trials and the law of mortality. Demographic Research, 4(Article 7), 185–202.CrossRefGoogle Scholar
Hannerz, H. (2001c). An extension of relational methods in mortality estimation. Demographic Research, 4(Article 10), 337–367.CrossRefGoogle Scholar
Hartmann, M. (1987). Past and recent attempts to model mortality at all ages. Journal of Official Statistics, 3(1), 19–36.Google ScholarPubMed
Harvey, A. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge.Google Scholar
Hauser, R.M. & Willis, R.J. (2005). Survey design and methodology in the Health and Retirement Study and the Wisconsin Longitudinal Study. In (Waite, L.J., ed.) Aging, health, and public policy: demographic and economic perspectives. Population council. Supplement to Population and Development Review, 30 (2004), New York.Google Scholar
Heathcote, C. & Higgins, T. (2001a). A regression model of mortality, with applications to the Netherlands. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemio logical perspective (59–82). Kluwer Academic Publishers, Dordrecht.Google Scholar
Heathcote, C. & Higgins, T. (2001b). Forecasting mortality from regression models: the case of the Netherlands. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiologicalperspective (83–103). Kluwer Academic Publishers, Dordrecht.Google Scholar
Heligman, L. & Pollard, J.H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107(1, No 434), 49–80.CrossRefGoogle Scholar
Himes, C.L., Preston, S.H. & Condran, G.A. (1994). A relational model of mortality at older ages in low mortality countries. Population Studies, 48, 269–291.CrossRefGoogle Scholar
Hollmann, F.W., Mulder, T.J. & Kallan, J.E. (2000). Methodology and assumptions for the population projections of the United States: 1999 to 2100. Working paper 38, Population Division, U.S. Bureau of the Census.Google Scholar
Hyndman, R.J. & Ullah, S. (2007). Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics and Data Analysis, 51, 4942–4956.CrossRefGoogle Scholar
Idler, E.L. & Benyamini, Y. (1997). Self-rated health and mortality: a review of twenty-seven community studies. Journal of Health and Social Behavior, 38(1), 21–37.CrossRefGoogle ScholarPubMed
Kannisto, V. (1994). Development of oldest-old mortality, 1950–1990: evidence from 28 developed countries. Odense University Press, Odense, Denmark.Google Scholar
Kannisto, V., Lauritsen, J., Thatcher, A.R. & Vaupel, J.W. (1994). Reductions in mortality at advanced ages: several decades of evidence from 27 countries. Population and Development Review, 20(4), 793–810.CrossRefGoogle Scholar
Keilman, N. (1990). Uncertainty in population forecasting: issues, backgrounds, analyses, recommendations. Swets & Zeitlinger, Amsterdam.Google Scholar
Keilman, N. (1997). Ex-post errors in official population forecasts in industrialized countries. Journal of Official Statistics, 13(3), 245–277.Google Scholar
Keilman, N. (ed.). (2005). Perspectives on mortality forecasting (Vol. II. Probabilistic models). Swedish Social Insurance Agency, Stockholm.Google Scholar
Keilman, N., Pham, D.Q. & Hetland, A. (2002). Why population forecasts should be probabilistic — illustrated by the case of Norway. Demographic Research, 6(15), 409–453.CrossRefGoogle Scholar
Keyfitz, N. (1982). Choice of function for mortality analysis: effective forecasting depends on a minimum parameter representation. Theoretical Population Biology, 21(3), 329–352.CrossRefGoogle Scholar
Keyfitz, N. (1991). Experiments in the projection of mortality. Canadian Studies in Population, 18(2), 1–17.CrossRefGoogle Scholar
Koissi, M.-C. & Shapiro, A.F. (2006). Fuzzy formulation of the Lee–Carter model for mortality forecasting. Insurance: Mathematics and Economics, 39, 287–309.Google Scholar
Koissi, M.-C., Shapiro, A.F. & Hognas, G. (2006). Evaluating and extending the Lee–Carter model for mortality forecasting: bootstrap confidence interval. Insurance: Mathematics and Economics, 38, 1–20.Google Scholar
Kostaki, A. (1988). Contributions to the methodology and application of the Heligman–Pollard formula. University of Lund, Lund.Google Scholar
Kunst, A.E., Mackenbach, J.P., Lautenbach, H., Oei, F.B. & Bijlsma, F. (2002). Gains in life expectancy by eliminating major causes of death: revised estimates taking into account competing causes of death. In (Wunsch, G., Mouchart, M. & Duchene, J., eds.) The life table: modelling survival and death (191–207). Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
Le Bras, H. (2005). Mortality tempo versus removal of causes of mortality: opposite views leading to different estimations of life expectancy. Demographic Research, 13(25), 615–640.CrossRefGoogle Scholar
Lee, R.D. (1992). Stochastic demographic forecasting. International Journal of Forecasting, 8(3), 315–327.CrossRefGoogle ScholarPubMed
Lee, R.D. (1999). Probabilistic approaches to population forecasting. In (Lutz, W., Vaupel, J.W. & Ahlburg, D.A., eds.) Frontiers of population forecasting (156–190). Population Council. A supplement to Population and Development Review, 24, 1998, New York.Google Scholar
Lee, R.D. (2000). The Lee–Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal, 4(1), 80–93.CrossRefGoogle Scholar
Lee, R.D. & Carter, L.R. (1992). Modelling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Lee, R.D. & Tuljapurkar, S. (1994). Stochastic population forecasts for the United States: beyond high, medium, and low. Journal of the American Statistical Association, 89(428), 1175–1189.CrossRefGoogle ScholarPubMed
Lee, R.D. & Tuljapurkar, S. (2000). Population forecasting for fiscal planning: issues and innovations. In (Auerbach, A. & Lee, R., eds.) Population and fiscal policy (7–57). Cambridge University Press, Cambridge.Google Scholar
Lee, R.D. & Miller, T. (2001). Evaluating the performance of the Lee^Carter method for forecasting mortality. Demography, 38(4), 537–549.CrossRefGoogle Scholar
Li, S.-H. & Chan, W.-S. (2005). Outlier analysis and mortality forecasting: the United Kingdom and Scandinavian countries. Scandinavian Actuarial Journal, 3, 187–211.CrossRefGoogle Scholar
Li, S.-H., Hardy, M.R. & Tan, K.S. (forthcoming). Uncertainty in mortality forecasting: an extension to the classical Lee–Carter approach. ASTIN Bulletin.Google Scholar
Long, J.F. (1995). Complexity, accuracy, and utility of official population projections. Mathematical Population Studies, 5(3), 203–216.CrossRefGoogle Scholar
Lundstrom, H. & Qvist, J. (2004). Mortality forecasting and trend shifts: an application of the Lee–Carter model to Swedish mortality data. International Statistical Review, 72(1), 37–50.CrossRefGoogle Scholar
Lutz, W. & Scherbov, S. (1998). An expert-based framework for probabilistic national population projections: the example of Austria. European Journal of Population, 14(1), 1–17.CrossRefGoogle ScholarPubMed
Lutz, W. & Goldstein, J.R. (eds.) (2004). How to deal with uncertainty in population forecasting?, Reprint of articles appearing in International Statistical Review, 71(2) and 72(1).CrossRefGoogle Scholar
Lutz, W., Goldstein, J.R. & Prinz, C. (1996a). Alternative approaches to population projection. In (Lutz, W., ed.) The future population of the world. What can we assume today? (14–44). Earthscan, London.Google Scholar
Lutz, W., Sanderson, W. & Scherbov, S. (1996b). Probabilistic population projections based on expert opinion. In (Lutz, W., ed.) The future population of the world: what can we assume today? (397–428). Earthscan, London.Google Scholar
Lutz, W., Sanderson, W. & Scherbov, S. (1997). Doubling of world population unlikely. Nature, 387, 803–805.CrossRefGoogle ScholarPubMed
Lutz, W., Sanderson, W. & Scherbov, S. (1999). Expert-based probabilistic population projections. In (Lutz, W., Vaupel, J.W. & Ahlburg, D.A., eds.) Frontiers of population forecasting (139-155). Population Council. A Supplement to Population and Development Review, 24 (1998), New York.Google Scholar
Lutz, W., Sanderson, W. & Scherbov, S. (2001). The end of world population growth. Nature, 412, 543–545.CrossRefGoogle ScholarPubMed
Lutz, W., Sanderson, W. & Scherbov, S. (2004). The end of world population growth. In (Lutz, W. & Sanderson, W., eds.) The end of world population growth in the 21st century: new challenges for human capital formation and sustainable development. Earthscan, London.Google Scholar
McNown, R. & Rogers, A. (1989). Forecasting mortality: a parameterized time series approach. Demography, 26(4), 645–660.CrossRefGoogle ScholarPubMed
McNown, R. & Rogers, A. (1992). Forecasting cause-specific mortality using time series methods. International Journal of Forecasting, 8(3), 413–432.CrossRefGoogle Scholar
McNown, R., Rogers, A. & Little, J. (1995). Simplicity and complexity in extrapolative population forecasting models. Mathematical Population Studies, 5(3), 235–257.CrossRefGoogle Scholar
Manton, K.G., Patrick, C.H. & Stallard, E. (1980). Mortality model based on delays in progression of chronic diseases: alternative to cause elimination model. Public Health Reports, 95(6), 580–588.Google ScholarPubMed
Manton, K.G., Stallard, E. & Tolley, H.D. (1991). Limits to human life expectancy: evidence, prospects, and implications. Population and Development Review, 17(4), 603–637.CrossRefGoogle Scholar
Manton, K.G., Stallard, E. & Singer, B. (1992). Projecting the future size and health status of the U.S. elderly population. International Journal of Forecasting, 8(3), 433–458.CrossRefGoogle ScholarPubMed
Mode, C. J. & Busby, R.C. (1982). An eight-parameter model of human mortality — the single decrement case. Bulletin of Mathematical Biology, 44(5), 647–659.Google ScholarPubMed
Mode, C.J. & Jacobson, M.E. (1984). A parametric algorithm for computing model period and cohort human survival functions. International Journal of Biomedical Computing, 15, 341–356.CrossRefGoogle ScholarPubMed
Murphy, M.J. (1990). Methods of forecasting mortality for population projections. In population projections: trends, methods and uses. Occasional paper 38 (87–102). OPCS, London.Google Scholar
Murphy, M.J. (1995). The prospect of mortality: England and Wales and the United States of America, 1962–1989. British Actuarial Journal, 1, 331–350.CrossRefGoogle Scholar
Murray, C. & Lopez, A. (1997). Global mortality, disability, and the contribution of risk factors: global burden of disease study. The Lancet, 349(9063), 1436–1442.CrossRefGoogle ScholarPubMed
Oeppen, J. & Vaupel, J.W. (2002). Broken limits to life expectancy. Science, 296, 1029–1031.CrossRefGoogle ScholarPubMed
Olivieri, A. (2001). Uncertainty in mortality projections: an actuarial perspective. Insurance: Mathematics and Economics, 29, 231–245.Google Scholar
Olshansky, S.J. (1987). Simultaneous/multiple cause-delay (SIMCAD): an epidemiological approach to projecting mortality. Journal of Gerontology, 42(4), 358–365.CrossRefGoogle ScholarPubMed
Olshansky, S.J. (1988). On forecasting mortality. The Milbank Quarterly, 66(3), 482–530.CrossRefGoogle ScholarPubMed
Olshansky, S.J. & Carnes, B.A. (1997). Ever since Gompertz. Demography, 34(1), 1–15.CrossRefGoogle ScholarPubMed
Pedroza, C. (2006). A Bayesian forecasting model: predicting U.S. male mortality. Biostatistics, 7(4), 530–550.CrossRefGoogle ScholarPubMed
Pitacco, E. (2004). Survival models in a dynamic context: a survey. Mathematics and Economics, 35, 279–298.CrossRefGoogle Scholar
Pollard, J.H. (1987). Projection of age-specific mortality rates Population Bulletin of the United Nations 21–22, 55–69.Google Scholar
Pollard, J.H. (1998). Keeping abreast of mortality change. Actuarial and Demography Research Paper Series, No. 002/98.Google Scholar
Pollard, J.H. & Valkovics, E.J. (1992). The Gompertz distribution and its applications. Genus, 48(3–4), 15–27.Google ScholarPubMed
Renshaw, A.E. (1991). Actuarial graduation practice and generalised linear and non-linear models. Journal of the Institute of Actuaries, 118, 295–312.CrossRefGoogle Scholar
Renshaw, A.E. & Haberman, S. (2000). Modelling for mortality reduction factors (Actuarial Research Paper No. 127). Department of Actuarial Science and Statistics, City University, London.Google Scholar
Renshaw, A.E. & Haberman, S. (2003a). Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255–272.Google Scholar
Renshaw, A.E. & Haberman, S. (2003b). Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections. Applied Statistics, 51(1), 119–137.Google Scholar
Renshaw, A.E. & Haberman, S. (2003c). On the forecasting of mortality reduction factors. Insurance: Mathematics and Economics, 32, 379–401.Google Scholar
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension of the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556–570.Google Scholar
Renshaw, A.E., Haberman, S. & Hatzoupoulos, P. (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2, 449–477.CrossRefGoogle Scholar
Rogers, A. (1992). Heterogeneity and selection in multistate population analysis. Demography, 29(1), 31–38.CrossRefGoogle ScholarPubMed
Rogers, A. & Planck, F. (1983). Model: a general program for estimating parameterized model schedules of fertility, mortality, migration, and marital and labor force status transitions. International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
Rogers, A. & Gard, K. (1991). Applications of the Heligman/Pollard model mortality schedule. Population Bulletin of the United Nations, 30, 79–105.Google Scholar
Rogers, A. & Little, J.S. (1994). Parameterizing age patterns of demographic rates with the multiexponential model schedule. Mathematical Population Studies, 4(3), 175–195.CrossRefGoogle ScholarPubMed
Sanderson, W.C. & Scherbov, S. (2005). Average remaining lifetimes can increase as human populations age. Nature, 435(7043), 811–813.CrossRefGoogle ScholarPubMed
Shaw, C. (1994). Accuracy and uncertainty of the national population projections for the United Kingdom. Population Trends, 77, 24–32.Google Scholar
Siler, W. (1983). Parameters of mortality in human populations with widely varying life spans. Statistics in Medicine, 2, 373–380.CrossRefGoogle ScholarPubMed
Sithole, T.Z., Haberman, S. & Verrall, R.J. (2000). An investigation into parametric models for mortality projections, with applications to immediate annuitants' and life office pensioners' data. Insurance: Mathematics and Economics, 27, 285–312.Google Scholar
Stoto, M.A. (1988). Dealing with uncertainty: statistics for an aging population. The American Statistician, 42(2), 103–110.CrossRefGoogle ScholarPubMed
Stoto, M.A. & Durch, J.S. (1993). Forecasting survival, health, and disability: report on a workshop. Population Development and Review, 19(3), 557–581.CrossRefGoogle Scholar
Tabeau, E. (2001). A review of demographic forecasting models for mortality. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (1–32). Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C. (eds.) (2001a). Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective. Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
Tabeau, E., Willekens, F. & van Poppel, F. (2002). Parameterisation as a tool in analysing age, period and cohort effects on mortality: a case study of the Netherlands. In (Wunsch, G., Mouchart, M. & Duchene, J., eds.) The life table: modelling survival and death (141–169). Kluwer Academic Publishers, Dordrecht.Google Scholar
Tabeau, E., Ekamper, P., Huisman, C. & Bosch, A. (2001b). Predicting mortality from period, cohort or cause-specific trends: a study of four European countries. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (159–187). Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
Thatcher, A., Kannisto, V. & Vaupel, J. (1998). The force of mortality at ages 80 to 120. In Odense Monographs on Population Aging 5. Odense University Press, Odense, Denmark.Google Scholar
Thatcher, A.R. (1999). The long-term pattern of adult mortality and the highest attained age. Journal of the Royal Statistical Society, Series A, Statistics in Society, 162(1), 5–43.CrossRefGoogle ScholarPubMed
Tuljapurkar, S. (1998). Forecasting mortality change: questions and assumptions. North American Actuarial Journal, 2(4), 127–134.CrossRefGoogle Scholar
Tuljapurkar, S. & Boe, C. (1998). Mortality change and forecasting: how much and how little do we know? North American Actuarial Journal, 2(4), 13–47.CrossRefGoogle Scholar
Tuljapurkar, S., Li, N. & Boe, C. (2000). A universal pattern of mortality decline in the G7 countries. Nature, 405, 789–792.CrossRefGoogle ScholarPubMed
United Nations (2004). World population to 2300. United Nations, New York.Google Scholar
Van Den Berg Jeths, A., Hoogenveen, R., De Hollander, G. & Tabeau, E. (2001). A review of epidemiological approaches to forecasting mortality and morbidity. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (33–56). Kluwer Academic Publishers, Dordrecht.Google Scholar
Van Genugten, M., Hoogenveen, R. & De Hollander, A. (2001). Incorporating risk factor epidemiology in mortality projections. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (189–204). Kluwer Academic Publishers, Dordrecht.Google Scholar
Van Hoorn, W. & De Beer, J. (2001). Projecting mortality in population forecasts in the Netherlands. In (Tabeau, E., Van Den Berg Jeths, A. & Heathcote, C., eds.) Forecasting mortality in developed countries: insights from a statistical, demographic and epidemiological perspective (205–226). Kluwer Academic Publishers, Dordrecht.Google Scholar
Vaupel, J.W. & Yashin, A.I. (1985). Heterogeneity's ruses: some surprising effects of selection on population dynamics. The American Statistician, 39(3), 176–185.CrossRefGoogle ScholarPubMed
Waldron, H. (2005). Literature review of long-term mortality projections. Social Security Bulletin, 66(1), 16–30.Google ScholarPubMed
Wang, S.S. (2000). A class of distortion operators for pricing financial and insurance risks. The Journal of Risk and Insurance, 67(2), 15–36.CrossRefGoogle Scholar
White, K.M. (2002). Longevity advanced in high-income countries, 1955–96. Population and Development Review, 28(1), 59–76.CrossRefGoogle Scholar
Willekens, F.J. (1990). Demographic forecasting; state-of-the-art and research needs. In (Hazeu, C.A. & Frinking, G.A.B., eds.) Emerging issues in demographic research (9–75). Elsevier Science.Google Scholar
Willekens, F.J. & Baydar, N. (1986). Age-period-cohort models for forecasting fertility (No. 45). NIDI, The Hague.Google Scholar
Willets, R.C. (2004). The cohort effect: insights and explanations. British Actuarial Journal, 10, 833–877.CrossRefGoogle Scholar
Willets, R.C., Gallop, A.P., Leandro, P.A., Lu, J.L.C., Macdonald, A.S., Miller, K.A., Richards, S.J., Robjohns, N., Ryan, J.P. & Waters, H.R. (2004). Longevity in the 21st century. British Actuarial Journal, 10, 685–898.CrossRefGoogle Scholar
Wilmoth, J.R. (1990). Variation in vital rates by age, period and cohort. Sociological Methodology, 20, 295–335.CrossRefGoogle Scholar
Wilmoth, J.R. (1993). Computational methods for fitting and extrapolating the Lee–Carter model of mortality change (Technical report). Department of Demography, University of California, Berkeley.Google Scholar
Wilmoth, J.R. (1995). Are mortality projections always more pessimistic when disaggregated by cause of death? Mathematical Population Studies, 5(4), 293–319.CrossRefGoogle ScholarPubMed
Wilmoth, J.R. (1996). Mortality projections for Japan: a comparison of four methods. In (Caselli, G. & Lopez, A., eds.) Health and mortality among elderly populations (266–287). Oxford University Press, New York.Google Scholar
Wilmoth, J.R. (2005). Some methodological issues in mortality projection, based on an analysis of the U.S. social security system. Genus, LXI(1), 179–212.Google Scholar
Wolf, D.A. (2004). Another variation on the Lee–Carter model. Paper presented at the Annual meeting of the Population Association of America, Boston.Google Scholar
Wong-Fupuy, C. & Haberman, S. (2004). Projecting mortality trends: recent developments in the United Kingdom and the United States. North American Actuarial Journal, 8(2), 56–83.CrossRefGoogle Scholar
Zaba, B. (1979). The four-parameter logit life table system. Population Studies, 33(1), 79–100.CrossRefGoogle ScholarPubMed
Zaba, B. & Paes, N. (1995). An alternative procedure for fitting relational model life tables. Genus, LI(1–2), 19–43.Google Scholar