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Structural Changes in the Lee-Carter Mortality Indexes

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  • Johnny Li
  • Wai-Sum Chan
  • Siu-Hung Cheung

Abstract

In recent years mortality has improved considerably faster than had been predicted, resulting in unforeseen mortality losses for annuity and pension liabilities. Actuaries have considered various models to make stochastic mortality projections, one of which is the celebrated Lee-Carter model. In using the Lee-Carter model, mortality forecasts are made on the basis of the assumed linearity of a mortality index, parameter kt, in the model. However, if this index is indeed not linear, forecasts will tend to be biased and inaccurate. A primary objective of this paper is to examine the linearity of this index by rigorous statistical hypothesis tests. Specifically, we consider Zivot and Andrews’ procedure to determine if there are any structural breaks in the Lee-Carter mortality indexes for the general populations of England and Wales and the United States. The results indicate that there exists a statistically significant structural breakpoint in each of the indexes, suggesting that forecasters should be extra cautious when they extrapolate these indexes. Our findings also provide sound statistical evidence for some demographers’ observation of an accelerated mortality decline after the mid-1970s.

Suggested Citation

  • Johnny Li & Wai-Sum Chan & Siu-Hung Cheung, 2011. "Structural Changes in the Lee-Carter Mortality Indexes," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 13-31.
    • Handle: RePEc:taf:uaajxx:v:15:y:2011:i:1:p:13-31
    DOI: 10.1080/10920277.2011.10597607
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Reese, Simon, 2015. "Asymptotic Inference in the Lee-Carter Model for Modelling Mortality Rates," Working Papers 2015:16, Lund University, Department of Economics.
    3. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2017. "Cohort effects in mortality modelling: a Bayesian state-space approach," Papers 1703.08282, arXiv.org.
    4. Colin O’hare & Youwei Li, 2017. "Modelling mortality: are we heading in the right direction?," Applied Economics, Taylor & Francis Journals, vol. 49(2), pages 170-187, January.
    5. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    6. Li, Johnny Siu-Hang & Liu, Yanxin, 2021. "Recent declines in life expectancy: Implication on longevity risk hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 376-394.
    7. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    8. Wang, Pengjie & Pantelous, Athanasios A. & Vahid, Farshid, 2023. "Multi-population mortality projection: The augmented common factor model with structural breaks," International Journal of Forecasting, Elsevier, vol. 39(1), pages 450-469.

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