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Deterministic and stochastic trends in the Lee-Carter mortality model

Author

Listed:
  • Laurent Callot

    (VU University Amsterdam, the Tinbergen Institute and CREATES)

  • Niels Haldrup

    (Aarhus University and CREATES)

  • Malene Kallestrup Lamb

    (Aarhus University and CREATES)

Abstract

The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies to a random walk model with age specific drift components. But restricting the adjustment mechanism of the stochastic and linear trend components to be identical may be a too strong simplification. In fact, the presence of a stochastic trend component may itself result from a bias induced by properly fitting the linear trend that characterizes mortality data. We find empirical evidence that this feature of the Lee-Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee-Carter model will otherwise over estimate the reduction of mortality for the younger age groups and will under estimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee-Carter model instead of a one-factor model should be formulated as a two (or several)-factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee-Carter model in various directions.

Suggested Citation

  • Laurent Callot & Niels Haldrup & Malene Kallestrup Lamb, 2014. "Deterministic and stochastic trends in the Lee-Carter mortality model," CREATES Research Papers 2014-44, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-44
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    References listed on IDEAS

    as
    1. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    2. 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.
    3. Ronald Lee, 2000. "The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(1), pages 80-91.
    4. Booth, H. & Tickle, L., 2008. "Mortality Modelling and Forecasting: a Review of Methods," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 3-43, September.
    5. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
    6. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    7. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    8. Arthur Renshaw & Steven Haberman, 2003. "Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137, January.
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    Cited by:

    1. Hans Oluf Hansen, 2015. "Modeling and projecting mortality. A new model of heterogeneity and selection in survivorship," Discussion Papers 15-16, University of Copenhagen. Department of Economics.
    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. Hunt, Andrew & Villegas, Andrés M., 2015. "Robustness and convergence in the Lee–Carter model with cohort effects," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 186-202.
    4. 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.
    5. Gisou Díaz-Rojo & Ana Debón & Jaime Mosquera, 2020. "Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes," Mathematics, MDPI, vol. 8(11), pages 1-17, November.

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    More about this item

    Keywords

    Mortality modelling; factor models; principal components; stochastic and deterministic trends;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J1 - Labor and Demographic Economics - - Demographic Economics
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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