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A principal component model for forecasting age- and sex-specific survival probabilities in Western Europe

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Abstract

The assessment of future mortality is of high importance in many areas where the allocation of future resources has to be planned in time, especially in social security and private life insurance. This contribution represents an extension of the classic forecasting approaches of Bell–Monsell and Lee–Carter. Based on a forecast of the first two principal components, age- and sex-specific survival probabilities for 18 Western European countries are predicted simultaneously until the year 2070. In addition to the correlations in the mortality trends between the age groups and the genders, international trends in mortality are captured as well. A major improvement in the classic Lee–Carter models is the adequate quantification of the uncertainty associated with the whole system of variables by stochastic simulation of all remaining principal components with simple time series models. The model’s easy applicability to further analyses is illustrated by forecasting the median life span as well as the resulting Gender Gap for Germany, France, and Italy.

Zusammenfassung

Die Einschätzung der zukünftigen Mortalität ist für viele Bereiche zur Planung der Ressourcenallokation von hoher Bedeutung, besonders in der Sozialversicherung und der privaten Lebensversicherung. Dieser Beitrag stellt eine Erweiterung der klassischen Prognoseansätze von Bell-Monsell und Lee-Carter dar, wobei auf Basis der Prognose der ersten zwei Hauptkomponenten die alters- und geschlechtsspezifischen Überlebenswahrscheinlichkeiten für 18 westeuropäische Länder simultan bis ins Jahr 2070 prognostiziert werden. Neben den Korrelationen, die bei den Mortalitätstrends zwischen den Altersgruppen und den beiden Geschlechtern bestehen, werden auch internationale Trends aufgefangen. Eine signifikante Verbesserung zu gängigen Lee-Carter-Modellen wird durch stochastische Simulation der verbleibenden Hauptkomponenten mit simplen Zeitreihenmodellen erreicht, wodurch sich die Unsicherheit im ganzen Variablensystem mit Prognoseintervallen angemessen quantifizieren lässt. Die Flexibilität des Modells für weiterführende Analysen wird anhand der Prognose der medianen Lebensspanne und des resultierenden Geschlechterunterschiedes in dieser Mortalitätskennziffer für Deutschland, Frankreich und Italien illustriert.

Notes

Acknowledgements

I would like to thank my colleagues Vladimir Canudas-Romo and Marius Pascariu from the Max-Planck Odense Center on Biodemography, as well as Ralph Rogalla from St. John’s University, for the discussion of an earlier version of this contribution at the annual meeting of the DVfVW in Berlin on March 16, 2017. Their valuable comments and advice significantly contributed in the improvement of this paper.

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Copyright information

© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2017

Authors and Affiliations

  1. 1.Center for Risk and Insurance, Demographic and Insurance Research CenterGottfried Wilhelm Leibniz Universität HannoverHannoverGermany

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