IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1053-d378305.html
   My bibliography  Save this article

Estimation of Uncertainty in Mortality Projections Using State-Space Lee-Carter Model

Author

Listed:
  • Rokas Gylys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    Both authors contributed equally to this work.)

  • Jonas Šiaulys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    Both authors contributed equally to this work.)

Abstract

The study develops alternatives of the classical Lee-Carter stochastic mortality model in assessment of uncertainty of mortality rates forecasts. We use the Lee-Carter model expressed as linear Gaussian state-space model or state-space model with Markovian regime-switching to derive coherent estimates of parameters and to introduce additional flexibility required to capture change in trend and non-Gaussian volatility of mortality improvements. For model-fitting, we use a Bayesian Gibbs sampler. We illustrate the application of the models by deriving the confidence intervals of mortality projections using Lithuanian and Swedish data. The results show that state-space model with Markovian regime-switching adequately captures the effect of pandemic, which is present in the Swedish data. However, it is less suitable to model less sharp but more prolonged fluctuations of mortality trends in Lithuania.

Suggested Citation

  • Rokas Gylys & Jonas Šiaulys, 2020. "Estimation of Uncertainty in Mortality Projections Using State-Space Lee-Carter Model," Mathematics, MDPI, vol. 8(7), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1053-:d:378305
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1053/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1053/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fung, Man Chung & Peters, Gareth W. & Shevchenko, Pavel V., 2017. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Annals of Actuarial Science, Cambridge University Press, vol. 11(2), pages 343-389, September.
    2. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    4. Rokas Gylys & Jonas Šiaulys, 2019. "Revisiting Calibration of the Solvency II Standard Formula for Mortality Risk: Does the Standard Stress Scenario Provide an Adequate Approximation of Value-at-Risk?," Risks, MDPI, vol. 7(2), pages 1-24, May.
    5. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    6. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    7. 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.
    8. Sylvia Kaufmann, 2000. "Measuring business cycles with a dynamic Markov switching factor model: an assessment using Bayesian simulation methods," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 39-65.
    9. 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.
    10. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
    11. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    2. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    3. 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.
    4. Adrian Raftery & Jennifer Chunn & Patrick Gerland & Hana Ševčíková, 2013. "Bayesian Probabilistic Projections of Life Expectancy for All Countries," Demography, Springer;Population Association of America (PAA), vol. 50(3), pages 777-801, June.
    5. Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
    6. 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.
    7. Han Lin Shang & Rob J Hyndman & Heather Booth, 2010. "A comparison of ten principal component methods for forecasting mortality rates," Monash Econometrics and Business Statistics Working Papers 8/10, Monash University, Department of Econometrics and Business Statistics.
    8. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    9. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Estimating the term structure of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 492-504, April.
    10. 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.
    11. Konstantin A. Kholodilin, 2006. "Using the Dynamic Bi-Factor Model with Markov Switching to Predict the Cyclical Turns in the Large European Economies," Discussion Papers of DIW Berlin 554, DIW Berlin, German Institute for Economic Research.
    12. Alexander Tsyplakov, 2011. "An introduction to state space modeling (in Russian)," Quantile, Quantile, issue 9, pages 1-24, July.
    13. Katja Hanewald & Thomas Post & Helmut Gründl, 2011. "Stochastic Mortality, Macroeconomic Risks and Life Insurer Solvency," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(3), pages 458-475, July.
    14. Li, Johnny Siu-Hang, 2010. "Pricing longevity risk with the parametric bootstrap: A maximum entropy approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 176-186, October.
    15. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    16. 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.
    17. 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.
    18. Heather Booth & Rob J Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Monash Econometrics and Business Statistics Working Papers 13/06, Monash University, Department of Econometrics and Business Statistics.
    19. Ai Deng & Pierre Perron, 2006. "A comparison of alternative asymptotic frameworks to analyse a structural change in a linear time trend," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 423-447, November.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1053-:d:378305. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.