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Coherent modeling of mortality patterns for age-specific subgroups

  • Giuseppe Giordano
  • Steven Haberman
  • Maria RussolilloEmail author
Article

Abstract

The recent actuarial literature has shown that mortality patterns and trajectories in closely related populations are similar in some respects and that small differences are unlikely to increase in the long run. The common feeling is that mortality forecasts for individual countries could be improved by taking into account the patterns from a larger group. Starting from this consideration, we apply the three-way Lee–Carter model to a group of countries, by extending the bilinear LC model to a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. From a methodological point of view, there are several issues to deal with when focusing on such kind of data. In the presence of a three-way data structure, several choices on the pretreatment of the data could affect the whole modeling process. This kind of analysis is useful to assess the source of variation in the raw mortality data, before the extraction of the rank-one components by the LC model. The proposed procedure is used to extract an ad hoc time mortality trend parameter for age-specific subgroups. The results show that the proposed strategy leads to a more coherent description of mortality for age-specific subgroups.

Keywords

ANOVA Human Mortality Database Lee–Carter model Three-way data analysis Tucker-3 

JEL Classification

C220 C380 

Notes

References

  1. Bergeron-Boucher, M., Simonacci, V., Oeppen, J., Gallo, M.: Coherent modeling and forecasting of mortality patterns for subpopulations using multiway analysis of compositions: an application to Canadian provinces and territories. N. Am. Actuar. J. 22(1), 92–118 (2018)CrossRefGoogle Scholar
  2. D’Amato, V., Haberman, S., Piscopo, G., Russolillo, M.: Modelling dependent data for longevity projections. Insur. Math. Econ. 51, 694–701 (2012)CrossRefGoogle Scholar
  3. Hatzopoulos, P., Haberman, S.: Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data. Insur. Math. Econ. 52, 320–337 (2013)CrossRefGoogle Scholar
  4. Jackson, D.: Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches. Ecology 74(8), 2204–2214 (1993).  https://doi.org/10.2307/1939574 CrossRefGoogle Scholar
  5. Kroonenberg, P.M.: Three-Mode Principal Component Analysis. Theory and Applications. DSWO Press, Leiden (1983)Google Scholar
  6. Kroonenberg, P.M.: Applied Multi-way Data Analysis. Wiley, Hoboken (2008)CrossRefGoogle Scholar
  7. Lazar, D., Denuit, M.: A multivariate time series approach to projected life tables. Appl. Stoch. Models Bus. Ind. 25, 806–823 (2009)CrossRefGoogle Scholar
  8. Lee, R.D., Carter, L.R.: Modelling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87, 659–671 (1992)Google Scholar
  9. Li, N., Lee, R.: Coherent mortality forecasts for a group of populations: an extension of the Lee–Carter method. Demography 42(3), 575–594 (2005)CrossRefGoogle Scholar
  10. Njenga, C., Sherris, M.: Longevity risk and the econometric analysis of mortality trends and volatility. Asia Pac. J. Risk Insur. (2011).  https://doi.org/10.2202/2153-3792.1115 Google Scholar
  11. Russolillo, M., Giordano, G., Haberman, S.: Extending the Lee–Carter model: a three-way decomposition. Scand. Actuar. J. 2, 96–117 (2011)CrossRefGoogle Scholar
  12. Tucker, L.R.: The extension of factor analysis to three-dimensional matrices. In: Frederiksen, N., Gulliksen, H. (eds.) Contributions to Mathematical Psychology, pp. 110–182. Holt, Rinehart & Winston, New York (1964)Google Scholar
  13. Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31(3), 279–311 (1966)CrossRefGoogle Scholar
  14. Villegas, A., Haberman, S., Kaishev, V., Millossovich, P.: A comparative study of two population models for the assessment of basis risk in longevity hedges. ASTIN Bull. 47(3), 631–679 (2017)CrossRefGoogle Scholar
  15. Wilson, C.: On the scale of global demographic convergence 1950–2000. Popul. Dev. Rev. 27(1), 155–172 (2001)CrossRefGoogle Scholar

Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2019

Authors and Affiliations

  1. 1.Department of Economics and StatisticsUniversity of SalernoFiscianoItaly
  2. 2.Faculty of Actuarial Science and Insurance, Cass Business SchoolCity, University of LondonLondonUK
  3. 3.Department of Political and Social StudiesUniversity of SalernoFiscianoItaly

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