IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v51y2024i33.html
   My bibliography  Save this article

A Bayesian model for age at death with cohort effects

Author

Listed:
  • Matteo Dimai

    (Università degli Studi di Trieste (UNITS))

  • Marek Brabec

    (Akademie věd České Republiky)

Abstract

Background: Ongoing mortality trends affect the distribution of age at death, typically described by parametric models. Cohort effects can markedly perturb the distribution and reduce the fit of such models, and this needs to be specifically taken into account. Objective: This study examines the integration of cohort effects in a three-component parametric model for the age-at-death distribution, applying it to data with significant cohort effects. Methods: We employed a mixture model with a half-normal and two skew-normal components, adapted to a Bayesian framework to include multiplicative cohort effects. The model was applied to data from five Italian regions, with cohort effects estimated for the 1915–1925 cohorts. Results: Incorporating cohort effects significantly improved the model’s fit. A notable finding of the comprehensive model is the shift in Italy from premature to middle-age mortality components over time. Our results also demonstrate the tendency for mortality structures to spatially homogenize over time in Italy. Conclusions: The study underscores the importance of including cohort effects in mortality models in order to provide a more detailed picture of mortality trends. Contribution: This work introduces a novel application of a Bayesian mixture model with cohort effects, offering enhanced tools for demographic analysis and new insights into the evolution of mortality components in Italy. This approach is general but fully formalized and hence it can be readily used for demographic studies in other regions as well.

Suggested Citation

  • Matteo Dimai & Marek Brabec, 2024. "A Bayesian model for age at death with cohort effects," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(33), pages 1017-1058.
  • Handle: RePEc:dem:demres:v:51:y:2024:i:33
    DOI: 10.4054/DemRes.2024.51.33
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol51/33/51-33.pdf
    Download Restriction: no

    File URL: https://libkey.io/10.4054/DemRes.2024.51.33?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Andrew Hunt & David Blake, 2014. "A General Procedure for Constructing Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 116-138.
    2. Emanuele Aliverti & Stefano Mazzuco & Bruno Scarpa, 2022. "Dynamic modelling of mortality via mixtures of skewed distribution functions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1030-1048, July.
    3. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    4. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    5. Willets, R. C., 2004. "The Cohort Effect: Insights and Explanations," British Actuarial Journal, Cambridge University Press, vol. 10(4), pages 833-877, October.
    6. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    7. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    8. Andrew Hunt & David Blake, 2021. "On the Structure and Classification of Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 215-234, February.
    9. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    10. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    11. 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.
    12. Monica Alexander & Emilio Zagheni & Magali Barbieri, 2017. "A Flexible Bayesian Model for Estimating Subnational Mortality," Demography, Springer;Population Association of America (PAA), vol. 54(6), pages 2025-2041, December.
    13. Christina Bohk-Ewald & Marcus Ebeling & Roland Rau, 2017. "Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts," Demography, Springer;Population Association of America (PAA), vol. 54(4), pages 1559-1577, August.
    14. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    15. Carfora, M.F. & Cutillo, L. & Orlando, A., 2017. "A quantitative comparison of stochastic mortality models on Italian population data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 198-214.
    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. 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. Ugofilippo Basellini & Søren Kjærgaard & Carlo Giovanni Camarda, 2020. "An age-at-death distribution approach to forecast cohort mortality," Working Papers axafx5_3agsuwaphvlfk, French Institute for Demographic Studies.
    3. Basellini, Ugofilippo & Kjærgaard, Søren & Camarda, Carlo Giovanni, 2020. "An age-at-death distribution approach to forecast cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 129-143.
    4. 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.
    5. Redondo Lourés, Cristian & Cairns, Andrew J.G., 2021. "Cause of death specific cohort effects in U.S. mortality," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 190-199.
    6. 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.
    7. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    8. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    9. Guibert, Quentin & Lopez, Olivier & Piette, Pierrick, 2019. "Forecasting mortality rate improvements with a high-dimensional VAR," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 255-272.
    10. 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.
    11. 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.
    12. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," BAFFI CAREFIN Working Papers 1505, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    13. 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.
    14. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.
    15. Massimiliano Menzietti & Maria Francesca Morabito & Manuela Stranges, 2019. "Mortality Projections for Small Populations: An Application to the Maltese Elderly," Risks, MDPI, vol. 7(2), pages 1-25, March.
    16. Li, Johnny Siu-Hang & Zhou, Rui & Hardy, Mary, 2015. "A step-by-step guide to building two-population stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 121-134.
    17. David Atance & Alejandro Balbás & Eliseo Navarro, 2020. "Constructing dynamic life tables with a single-factor model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 787-825, December.
    18. 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.
    19. Paola Biffi & Gian Clemente, 2014. "Selecting stochastic mortality models for the Italian population," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 255-286, October.
    20. 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.

    More about this item

    Keywords

    mortality; Bayesian approach; age at death; cohort effects; Italy;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    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:dem:demres:v:51:y:2024:i:33. 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: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    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.