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A multivariate time series approach to projected life tables

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  • Dorina Lazar
  • Michel M. Denuit

Abstract

The method of mortality forecasting proposed by Lee and Carter describes a time series of age‐specific log‐death rates as a sum of an independent of time age‐specific component and a bilinear term in which one of the component is a time‐varying factor reflecting general change in mortality and the second one is an age‐specific parameter. Such a rigid model structure implies that on average the mortality improvements for different age groups should be proportional, regardless of the calendar period: a single time factor drives the future death rates. This paper investigates the use of multivariate time series techniques for forecasting age‐specific death rates. This approach allows for relative speed of decline in the log death rates specific to the different ages. The dynamic factor analysis and the Johansen cointegration methodology are successfully applied to project mortality. The inclusion of several time factors allows the model to capture the imperfect correlations in death rates from 1 year to the next. The benchmark Lee–Carter model appears as a special case of these approaches. An empirical study is conducted with the help of the Johansen cointegration methodology. A vector‐error correction model is fitted to Belgian general population death rates. A comparison is performed with the forecast of life expectancies obtained from the classical Lee–Carter model. Copyright © 2009 John Wiley & Sons, Ltd.

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  • Dorina Lazar & Michel M. Denuit, 2009. "A multivariate time series approach to projected life tables," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 806-823, November.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:6:p:806-823
    DOI: 10.1002/asmb.781
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    References listed on IDEAS

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    2. Niels Haldrup & Carsten P. T. Rosenskjold, 2019. "A Parametric Factor Model of the Term Structure of Mortality," Econometrics, MDPI, vol. 7(1), pages 1-22, March.
    3. Arnold, Séverine & Glushko, Viktoriya, 2021. "Cause-specific mortality rates: Common trends and differences," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 294-308.
    4. A. Debòn & S. Haberman & F. Montes & E. Otranto, 2012. "Model effect on projected mortality indicators," Working Paper CRENoS 201215, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    5. Li, Hong & Lu, Yang, 2017. "Coherent Forecasting Of Mortality Rates: A Sparse Vector-Autoregression Approach," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 563-600, May.
    6. Bent Nielsen & J.P. Nielsen, 2010. "Identification and forecasting in the Lee-Carter model," Economics Series Working Papers 2010-W07, University of Oxford, Department of Economics.
    7. Giuseppe Giordano & Steven Haberman & Maria Russolillo, 2019. "Coherent modeling of mortality patterns for age-specific subgroups," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 189-204, June.
    8. Jarner, Søren F. & Jallbjørn, Snorre, 2020. "Pitfalls and merits of cointegration-based mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 80-93.
    9. Dorina Lazar & Anuta Buiga & Adela Deaconu, 2016. "Common Stochastic Trends in European Mortality Levels: Testing and Consequences for Modeling Longevity Risk in Insurance," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 152-168, June.
    10. Yahia Salhi & Stéphane Loisel, 2012. "Basis risk modelling: a co-integration based approach," Working Papers hal-00746859, HAL.
    11. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    12. Laurent Callot & Niels Haldrup & Malene Kallestrup-Lamb, 2016. "Deterministic and stochastic trends in the Lee–Carter mortality model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(7), pages 486-493, May.
    13. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    14. Yahia Salhi & Stéphane Loisel, 2017. "Basis risk modelling: a co-integration based approach," Post-Print hal-00746859, HAL.
    15. Hatzopoulos, P. & Haberman, S., 2011. "A dynamic parameterization modeling for the age-period-cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 155-174, September.
    16. Ana Debón & Steven Haberman & Francisco Montes & Edoardo Otranto, 2021. "Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model," IJERPH, MDPI, vol. 18(4), pages 1-16, February.
    17. Shang, Han Lin & Smith, Peter W.F. & Bijak, Jakub & Wiśniowski, Arkadiusz, 2016. "A multilevel functional data method for forecasting population, with an application to the United Kingdom," International Journal of Forecasting, Elsevier, vol. 32(3), pages 629-649.
    18. Han Lin Shang & Heather Booth & Rob Hyndman, 2011. "Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(5), pages 173-214.

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