A Method for the Forecasting of Mortality

  • Konstantinos N. Zafeiris
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE, volume 46)


In population projections the problem of the estimation of future mortality trends is of central importance. In this paper a new method serving this purpose is applied. After assuming the probabilities of death for large age groups ( n q x ), a relational technique is applied for the estimation of one-year death probabilities ( 1 q x ) of a full life table as proposed by Kostaki (Math Popul Stud 9(1):83–95, 2000). Afterwards, a smoothing procedure of the 1 q x values is used, based on a 9 parameters relational model originally developed by Heligman and Pollard (J Inst Actuar 107:47–80, 1980) and later on modified by Kostaki (Math Popul Stud 3(4):277–288, 1992) in combination with three subsequent cubic splines. After the age of 84 years the probabilities of death were extrapolated on the basis of the parameters of the last spline used. Results of the analysis indicate that the method applied was on one hand very effective and on the other quite parsimonious in terms of calculations, property which further enhances its applicability.


Mortality forecasts Heligman-Pollarnd Cubic splines Relational method 


  1. Andreev, K., Gu, D., & Gerland, P. (2013). Patterns of mortality improvement by level of life expectancy at birth. Paper presented at the annual meeting of the Population Association of America, New Orleans, LA.
  2. Booth, H. (2006). Demographic forecasting: 1980 to 2005. International Journal of Forecasting, 22, 547–581.CrossRefGoogle Scholar
  3. Booth, H., & Tickle, L. (2008). Mortality and modeling: A review of methods. Annals of Actuarial Science, 3(I/II), 3–43.CrossRefGoogle Scholar
  4. Calot, G. (1999). L’ analyse démographique conjoncturelle. In A. Kuijsten, H. de Gans, & H. de Feijter (Eds.), The joy of demography, édité en l’honneur de D.J. van de Kaa (pp. 295–323). La Haye: NethurD Publications.Google Scholar
  5. Calot, G., & Franco, A. (2001). The construction of life tables. In G. Wunsch, M. Mouchart, & J. Duchêne (Eds.), Life tables: Data, methods, models (pp. 31–75). Dordrecht: Kluwer.Google Scholar
  6. Calot, G., & Sardon, J.-P. (2004). Methodology for the calculation of Eurostat’s demographic indicators. Detailed report for the European Demographic Observatory, Office for Official Publication of the European Communities, Luxemburg.Google Scholar
  7. Garbero, A., & Sanderson, W. (2014). Forecasting mortality convergence up to 2100. In W. Lutz, W. P. Butz, & K. C. Samir (Eds.), World population and human capital in the 21st century (pp. 650–665). Oxford: Oxford University Press.Google Scholar
  8. Heligman, L., & Pollard, J. H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107, 47–80.CrossRefGoogle Scholar
  9. Kostaki, A. (1991). The Heligman – Pollard formula as a tool for expanding an abridged life table. Journal of Official Statistics, 7(3), 311–323.Google Scholar
  10. Kostaki, A. (1992). A nine parameter version of the Heligman-Pollard formula. Mathematical Population Studies, 3(4), 277–288.CrossRefGoogle Scholar
  11. Kostaki, A. (2000). A relational technique for estimating the age – specific mortality pattern from grouped data. Mathematical Population Studies, 9(1), 83–95.CrossRefGoogle Scholar
  12. Kostaki, A., & Lanke, J. (2000). Degrouping mortality data for the elderly. Mathematical Population Studies, 7(4), 331–341.CrossRefGoogle Scholar
  13. Kostaki, A., & Panousis, V. (2001). Expanding an abridged life table. Demographic Research, 5(1), 1–22.CrossRefGoogle Scholar
  14. Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
  15. Li, N., Lee, R., & Gerland, P. (2013). Extending the Lee-Carter Method to model the rotation of age patterns of mortality decline for long term projection. Demography, 50(6), 2037–2051.CrossRefGoogle Scholar
  16. Mathers, C. D., & Loncar, D. (2006). Projections of global mortality and burden of disease from 2002 to 2030. PLoS Medicine, 3(11), 2011–2030.CrossRefGoogle Scholar
  17. Murray, J. L., & Lopez, A. D. (1997). Alternative projections of mortality and disability by cause 1990–2020: Global burden of disease study. The Lancet, 349(9064), 1458–1504.CrossRefGoogle Scholar
  18. Office of the Chief Actuary. (2014). Mortality projections for social security programs in Canada. Actuarial study Nr. 12. Office of the Superintendent of Financial Institutions Canada. Available at:
  19. Pollard, J. H. (1987). Projection of age-specific mortality rates. Population Bulletin of the United Nations, 21–22, 55–69.Google Scholar
  20. Raftery, A. E., Lalic, N., & Gerland, P. (2012). Joint probabilistic projection of female and male life expectancy. Paper presented at the annual meeting of the Population Association of America, San Francisco, CA.Google Scholar
  21. Raftery, A. E., Chunn, J. L., Gerland, P., & Ševčíková, H. (2013). Bayesian probabilistic projections of life expectancy for all countries. Demography, 50, 777–801.CrossRefGoogle Scholar
  22. Sala-I-Martin, X. (1996). The classical approach to convergence analysis. The Economic Journal, 106, 1019–1036.CrossRefGoogle Scholar
  23. Samir, K.C., Potančoková, M., Bauer, R., Goujon, A., & Striessnig, E. (2013). Summary of data, assumptions and methods for new Wittgenstein Centre for Demography and Global Human Capital (WIC) population projections by age, sex and level of education for 195 countries to 2100 (Interim Report No. IR-13-018). Laxenburg: International Institute for Applied Systems Analysis.Google Scholar
  24. Stoeldraijer, L., van Duin, C., van Wissen, L., & Janssen, F. (2013). Impact of different mortality forecasting methods and explicit assumptions on projected future life expectancy: The case of the Netherlands. Demographic Research, 29(13), 323–354.CrossRefGoogle Scholar
  25. Torri, T., & Vaupel, J. W. (2012). Forecasting life expectancy in an international context. International Journal of Forecasting, 28(2), 519–531.CrossRefGoogle Scholar
  26. UNPP, United Nations, Department of Economic and Social Affairs, Population Division. (2015). World population prospects, the 2015 revision. Methodology of the United Nations population estimates and projections. New York: United Nations.Google Scholar
  27. Zafeiris, K. N., & Kostaki, A. (2017). Recent mortality trends in Greece. Communications in Statistics-Theory and Methods.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of P. Anthropology, Department of History and EthnologyDemocritus University of ThraceKomotiniGreece

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