The forecasting performance of mortality models
Tóm tắt
Mortality projections are of special interest in many applications. For example, they are essential in life insurances to determine the annual contributions of their members as well as for population predictions. Due to their importance, there exists a huge variety of mortality forecasting models from which to seek the best approach. In the demographic literature, statements about the quality of the various models are mostly based on empirical ex-post examinations of mortality data for very few populations. On the basis of such a small number of observations, it is impossible to precisely estimate statistical forecasting measures. We use Monte Carlo (MC) methods here to generate time trajectories of mortality tables, which form a more comprehensive basis for estimating the root-mean-square error (RMSE) of different mortality forecasts.
Tài liệu tham khảo
Babel, B., Bomsdorf, E., Schmidt, R.: Forecasting German mortality using panel data procedures. J. Popul. Econ. 21, 541–555 (2008)
Bell, W.R.: Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates. J. Off. Stat. 13, 279–303 (1997)
Boes, S., Pflaumer, P.: University student enrollment forecasts by analysis structural ratios using ARIMA-methods. Allg. Stat. Arch. 90, 253–271 (2006)
Bomsdorf, E., Trimborn, M.: Sterbetafel 2000. Modellrechnungen der Sterbetafel. ZVersWiss 81, 457–485 (1992)
Bomsdorf, E.: Neue Generationensterbetafeln für die Geburtsjahrgänge 1933–2003. Modellrechnungen für die Bundesrepublik Deutschland. Eul, Köln (2002)
Bomsdorf, E.: Rückgang der Bevölkerung—Zunahme der Pflegefälle: divergierende Entwicklungen in Deutschland bis 2050. AStA Wirtsch. Sozialstat. Arch. 4, 3–18 (2010)
Börsch-Supan, A., Heiss, F., Ludwig, A.: Pension reform, capital markets, and the rate of return. Ger. Econ. Rev. 4, 151–181 (2003)
Booth, H., Tickle, L.: Mortality modelling and forecasting: A review of methods. ADSRI Working Paper No. 3, Canberra (2008)
Booth, H., Maindonald, J., Smith, L.: Applying Lee–Carter under conditions of variable mortality decline. Population Studies 56, 325–336 (2002)
Booth, H., Hyndman, R.J., Tickle, L., de Jong, P.: Lee–Carter mortality forecasting: A multi-country comparison of variants and extensions. Demogr. Res. Monogr. 15, 289–310 (2006)
Brass, W.: A generation method for projecting death rates. In: Bechofer, F. (ed.) Population Growth and the Brain Drain, pp. 75–91. University Press, Edinburgh (1969)
Brass, W.: On the scale of mortality. In: Brass, W. (ed.) Biological Aspects of Demography, pp. 69–110. Taylor and Francis, London (1971)
Braun, H.: Geschichte der Lebensversicherung und der Lebensversicherungstechnik, 2nd edn. Duncker & Humblot, Berlin (1963)
Brouhns, N., Denuit, M., Vermunt, J.K.: A Poisson log-bilinear regression approach to the construction of projected lifetables. Insur. Math. Econ. 31, 373–393 (2002)
Coelho, E., Nunes, L.C.: Forecasting mortality in the event of a structural change. Paper presented on the European Population Conference 2010 in Vienna (Austria) (2009)
Carriére, J.F.: Parametric models for life tables. Trans.—Soc. Actuar. 44, 77–99 (1992)
Czado, C., Delwarde, A., Denuit, M.: Bayesian Poisson log-bilinear mortality projections. SFB 386 Paper No. 398, LMU München (2004)
Ewbank, D.C., Gomez de Leon, J.C. Stoto, M.A.: A reducible four parameter system of model life tables. Population Studies 37, 105–127 (1983)
Farr, W.: English Life Table. London (1864)
Forfar, D., McCutcheon, J., Wilkie, A.: On graduation by mathematical formula. J. Inst. Actuar. 115, 1–149 (1988)
Frier, B.: Roman life expectancy: Ulpian’s evidence. In: Harvard Studies in Classical Philology, vol. 86, pp. 213–251 (1982)
Gakidou, E., King, G.: Death by survey: Estimating adult mortality without selection bias from sibling survival data. Demography 43, 569–585 (2006)
Gompertz, B.: On the nature of the function expressive of the law of human mortality. Philos. Trans. R. Soc. Lond. 115, 513–585 (1825)
Graunt, J.: Natural and political observations mentioned in a following index and made upon the bills of mortality. London (1662)
Greene, W.H.: Econometric Analysis. Prentice-Hall, Upper Saddle River (2002)
Hansen, H.: Qualitätsvergleiche von Prognosemodellen für die Sterblichkeit mit Schwerpunkt auf dem deutschen Spezialfall “Wiedervereinigung”. Books on Demand, Norderstedt (2010)
Hansen, H., Pflaumer, P.: Zur Prognose der Lebenserwartung in Deutschland: Ein Vergleich verschiedener Verfahren. AStA Wirtsch. Sozialstat. Arch. 5, 203–219 (2011)
Hartmann, M.: Past and recent attempts to model mortality at all ages. J. Off. Stat. 3, 19–36 (1987)
Hatzopoulos, P., Haberman, S.: A parameterized approach to modeling and forecasting mortality. Insur. Math. Econ. 44, 103–123 (2009)
Heligman, L., Pollard, J.H.: The age pattern of mortality. J. Inst. Actuar. 107, 49–80 (1980)
Henderson, R.: Mortality Laws and Statistics. Wiley, London (1915)
Human Mortality Database: University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). http://www.mortality.org/ (2010). Accessed on 14 January 2010
Hyndman, R.J.: The R-package demography: Forecasting mortality, fertility, migration and population data. Available on http://robjhyndman.com. Downloaded on 15 February 2009
Keyfitz, N., Caswell, H.: Applied Mathematical Demography, 3rd edn. Springer, Berlin (2005)
Koissi, M.C., Shapiro, A., Högnas, G.: Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insur. Math. Econ. 38, 1–20 (2006)
Lee, R., Carter, L.: Modelling and forecasting the time series of U.S. mortality. J. Am. Stat. Assoc. 87, 659–671 (1992)
Lee, R., Miller, T.: Evaluating the performance of the Lee–Carter method for forecasting mortality. Demography 38, 537–549 (2001)
Lütkepohl, H.: Introduction to Multiple Time Series Analysis. Springer, Berlin (1991)
Menning, S.: Lebenserwartung und Mortalität im Alter—ein Überblick. In: Informationsdienst Altersfragen, vol. 2 (2006)
Oeppen, J., Vaupel, J.: Broken limits to life expectancy. Science 296, 1029–1031 (2002)
Olivieri, A.: Uncertainty in mortality projections: An actuarial perspective. Insur. Math. Econ. 29, 231–245 (2001)
Pflaumer, P.: Stochastische Bevölkerungsmodelle zur Analyse der Auswirkungen demographischer Prozesse auf die Systeme der sozialen Sicherung. Allg. Stat. Arch. 70, 52–74 (1986)
Pflaumer, P.: Confidence intervals for population projections based on Monte Carlo methods. Int. J. Forecast. 4, 135–142 (1988)
Reichmuth, W., Sarferaz, S.: Bayesian demographic modeling and forecasting: An application to U.S. mortality. SFB 649 Discussion Paper No. 52, HU Berlin (2008)
Shang, H.L., Hyndman, R.J., Booth, H.: A comparison of ten principal component methods for forecasting mortality rates. Working paper No. 8, Monash University (Australia), Department of Econometrics and Business Statistics (2010)
Skiadas, Ch., Skiadas, Ch.: Properties of a stochastic model for life table data: Exploring life expectancy limits. Available on http://www.arxiv.org (2010)
Statistisches Bundesamt: Periodensterbetafeln für Deutschland. Wiesbaden (2006)
Statistisches Bundesamt: Bevölkerung Deutschlands bis 2060: 12. koordinierte Bevölkerungsvorausberechnung. Berlin (2009)
Tong, H., Han, Y., Liu, Y.: Bayesian estimation and MCMC sampling for the mortality probability model of population. Paper Presented on the 1st IEEE International Conference on Bioinformatics and Biomedical Engineering 2007 in Wuhan (China) (2007)
Vaupel, J., Kistowski, K.G.: Der bemerkenswerte Anstieg der Lebenserwartung und sein Einfluss auf die Medizin. Bundesgesundheitsbl. Gesundheitsforsch. Gesundheitsschutz 48, 586–592 (2005)
Wilmoth, J., Horiuchi, S.: Rectangularization revisited: Variability of age at death within human populations. Demography 36(4), 475–495 (1999)
Wittstein, J.: The mathematical law of mortality. J. Inst. Actuar. 24, 152–173 (1883)
Wynder, E.L.: A corner of history: John Graunt, 1620–1674, the father of demography. Prev. Med. 4, 85–88 (1975)