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Modelling and forecasting mortality distributions in England and Wales using the Lee-Carter model

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  • Duolao Wang
  • Pengjun Lu

Abstract

Lee and Carter proposed in 1992 a non-linear model mxt = exp (ax + bx kt + εxt) for fitting and forecasting age-specific mortality rates at age x and time t. For the model parameter estimation, they employed the singular value decomposition method to find a least squares solution. However, the singular value decomposition algorithm does not provide the standard errors of estimated parameters, making it impossible to assess the accuracy of model parameters. This article describes the Lee-Carter model and the technical procedures to fit and extrapolate this model. To estimate the precision of the parameter estimates of the Lee-Carter model, we propose a binomial framework, whose parameter point estimates can be obtained by the maximum likelihood approach and interval estimates by a bootstrap approach. This model is used to fit mortality data in England and Wales from 1951 to 1990 and to forecast mortality change from 1991 to 2020. The Lee-Carter model fits these mortality data very well with R2 being 0.9980. The estimated overall age pattern of mortality ax is very robust whereas there is considerable uncertainty in bx (changes in the age pattern over time) and kt (overall change in mortality). The fitted log age-specific mortality rates have been declining linearly from 1951 to 1990 at different paces and the projected rates will continue to decline in such a way in the 30 years prediction period.

Suggested Citation

  • Duolao Wang & Pengjun Lu, 2005. "Modelling and forecasting mortality distributions in England and Wales using the Lee-Carter model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 873-885.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:9:p:873-885
    DOI: 10.1080/02664760500163441
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    Citations

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    Cited by:

    1. Salvatore Scognamiglio & Mario Marino, 2023. "Backtesting stochastic mortality models by prediction interval-based metrics," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3825-3847, August.
    2. Cristina Rueda-Sabater & Pedro Alvarez-Esteban, 2008. "The analysis of age-specific fertility patterns via logistic models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1053-1070.
    3. David McCarthy & David Miles, 2013. "Optimal Portfolio Allocation for Corporate Pension Funds," European Financial Management, European Financial Management Association, vol. 19(3), pages 599-629, June.
    4. Yaser Awad & Shaul K. Bar-Lev & Udi Makov, 2022. "A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach," Risks, MDPI, vol. 10(6), pages 1-17, 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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