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Modeling mortality with a Bayesian vector autoregression

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  • Njenga, Carolyn Ndigwako
  • Sherris, Michael

Abstract

Parametric mortality models capture the cross section of mortality rates. These models fit the older ages better, because of the more complex cross section of mortality at younger and middle ages. Dynamic parametric mortality models fit a time series to the parameters, such as a Vector-auto-regression (VAR), in order to capture trends and uncertainty in mortality improvements. We consider the full age range using the Heligman and Pollard (1980) model, a cross-sectional mortality model with parameters that capture specific features of different age ranges. We make the Heligman–Pollard model dynamic using a Bayesian Vector Autoregressive (BVAR) model for the parameters and compare with more commonly used VAR models. We fit the models using Australian data, a country with similar mortality experience to many developed countries. We show how the Bayesian Vector Autoregressive (BVAR) models improve forecast accuracy compared to VAR models and quantify parameter risk which is shown to be significant.

Suggested Citation

  • Njenga, Carolyn Ndigwako & Sherris, Michael, 2020. "Modeling mortality with a Bayesian vector autoregression," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 40-57.
    • Handle: RePEc:eee:insuma:v:94:y:2020:i:c:p:40-57
    DOI: 10.1016/j.insmatheco.2020.05.011
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    1. Richards, S. J. & Currie, I. D. & Ritchie, G. P., 2014. "A Value-at-Risk framework for longevity trend risk," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 116-139, March.
    2. Michel Denuit & Esther Frostig, 2008. "First-Order Mortality Basis for Life Annuities," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(2), pages 75-89, December.
    3. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk †Abstract of the London discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 157-167, March.
    4. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    5. Wolfgang Reichmuth & Samad Sarferaz, 2008. "Bayesian Demographic Modeling and Forecasting: An Application to U.S. Mortality," SFB 649 Discussion Papers SFB649DP2008-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    7. Petros Dellaportas & Adrian F. M. Smith & Photis Stavropoulos, 2001. "Bayesian analysis of mortality data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 275-291.
    8. Börger, Matthias & Schupp, Johannes, 2018. "Modeling trend processes in parametric mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 369-380.
    9. John C. Robertson & Ellis W. Tallman, 1999. "Vector autoregressions: forecasting and reality," Economic Review, Federal Reserve Bank of Atlanta, vol. 84(Q1), pages 4-18.
    10. Donald McNeil & T. Trullell & John Turner, 1977. "Spline interpolation of demographic oata," Demography, Springer;Population Association of America (PAA), vol. 14(2), pages 245-252, May.
    11. 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.
    12. Brandt, Patrick T. & Freeman, John R., 2006. "Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis," Political Analysis, Cambridge University Press, vol. 14(1), pages 1-36, January.
    13. Wai-Sum Chan & Johnny Li & Jackie Li, 2014. "The CBD Mortality Indexes: Modeling and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 38-58.
    14. Peter Congdon, 1993. "Statistical Graduation in Local Demographic Analysis and Projection," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(2), pages 237-270, March.
    15. Lee, Ronald D., 1992. "Stochastic demographic forecasting," International Journal of Forecasting, Elsevier, vol. 8(3), pages 315-327, November.
    16. Carlos Wong-Fupuy & Steven Haberman, 2004. "Projecting Mortality Trends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 56-83.
    17. Summers, Peter M., 2001. "Forecasting Australia's economic performance during the Asian crisis," International Journal of Forecasting, Elsevier, vol. 17(3), pages 499-515.
    18. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk †Abstract of the Edinburgh discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 140-156, March.
    19. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    20. Michel Denuit & Esther Frostig, 2009. "Life Insurance Mathematics with Random Life Tables," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 339-355.
    21. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
    22. Peng, Roger, 2008. "A Method for Visualizing Multivariate Time Series Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(c01).
    23. Robert McNown & Andrei Rogers, 1989. "Forecasting Mortality: A Parameterized Time Series Approach," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 645-660, November.
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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. Wanying Fu & Barry R. Smith & Patrick Brewer & Sean Droms, 2023. "Markov-Switching Bayesian Vector Autoregression Model in Mortality Forecasting," Risks, MDPI, vol. 11(9), pages 1-23, August.

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    More about this item

    Keywords

    Mortality; Parameter risk; Vector auto-regression; Bayesian vector auto-regression; Heligman–Pollard model;
    All these keywords.

    JEL classification:

    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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