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A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates

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  • Giacometti, Rosella
  • Bertocchi, Marida
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.

Abstract

With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortality rates and is still broadly used today. In this paper, we propose an alternative to the Lee–Carter model: an AR(1)–ARCH(1) model. More specifically, we compare the performance of these two models with respect to forecasting age-specific mortality in Italy. We fit the two models, with Gaussian and t-student innovations, for the matrix of Italian death rates from 1960 to 2003. We compare the forecast ability of the two approaches in out-of-sample analysis for the period 2004–2006 and find that the AR(1)–ARCH(1) model with t-student innovations provides the best fit among the models studied in this paper.

Suggested Citation

  • Giacometti, Rosella & Bertocchi, Marida & Rachev, Svetlozar T. & Fabozzi, Frank J., 2012. "A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 85-93.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:85-93
    DOI: 10.1016/j.insmatheco.2011.10.002
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    References listed on IDEAS

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    1. Alho, Juha M., 1990. "Stochastic methods in population forecasting," International Journal of Forecasting, Elsevier, vol. 6(4), pages 521-530, December.
    2. Angus S. Deaton & Christina Paxson, 2004. "Mortality, Income, and Income Inequality over Time in Britain and the United States," NBER Chapters, in: Perspectives on the Economics of Aging, pages 247-286, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.
    5. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    6. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    7. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
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    Cited by:

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    2. David Blake & Marco Morales & Jing Ai & Patrick L. Brockett & Linda L. Golden & Wei Zhu, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 319-343, April.
    3. Suryo Adi Rakhmawan & Tahir Mahmood & Nasir Abbas & Muhammad Riaz, 2024. "Unifying mortality forecasting model: an investigation of the COM–Poisson distribution in the GAS model for improved projections," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 800-826, October.
    4. Li, Hong & Shi, Yanlin, 2021. "Forecasting mortality with international linkages: A global vector-autoregression approach," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 59-75.
    5. Lingbing Feng & Yanlin Shi, 2018. "Forecasting mortality rates: multivariate or univariate models?," Journal of Population Research, Springer, vol. 35(3), pages 289-318, September.
    6. Doukhan, P. & Pommeret, D. & Rynkiewicz, J. & Salhi, Y., 2017. "A class of random field memory models for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 97-110.

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    More about this item

    Keywords

    Mortality rates; Lee–Carter model; Autoregression–autoregressive conditional heteroskedasticity model; AR(1)–ARCH(1) model;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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