IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp129-143.html
   My bibliography  Save this article

An age-at-death distribution approach to forecast cohort mortality

Author

Listed:
  • Basellini, Ugofilippo
  • Kjærgaard, Søren
  • Camarda, Carlo Giovanni

Abstract

Mortality forecasting has received increasing interest during recent decades due to the negative financial effects of continuous longevity improvements on public and private institutions’ liabilities. However, little attention has been paid to forecasting mortality from a cohort perspective. In this article, we introduce a novel methodology to forecast adult cohort mortality from age-at-death distributions. We propose a relational model that associates a time-invariant standard to a series of fully and partially observed distributions. Relation is achieved via a transformation of the age-axis. We show that cohort forecasts can improve our understanding of mortality developments by capturing distinct cohort effects, which might be overlooked by a conventional age–period perspective. Moreover, mortality experiences of partially observed cohorts are routinely completed. We illustrate our methodology on adult female mortality for cohorts born between 1835 and 1970 in two high-longevity countries using data from the Human Mortality Database.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:129-143
    DOI: 10.1016/j.insmatheco.2020.01.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300159
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.01.007?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marie-Pier Bergeron-Boucher & Vladimir Canudas-Romo & James E. Oeppen & James W. Vaupel, 2017. "Coherent forecasts of mortality with compositional data analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 37(17), pages 527-566.
    2. Vladimir M. Shkolnikov & Dmitri A. Jdanov & Evgeny M. Andreev & James W. Vaupel, 2011. "Steep Increase in Best‐Practice Cohort Life Expectancy," Population and Development Review, The Population Council, Inc., vol. 37(3), pages 419-434, September.
    3. Siu Lan Karen Cheung & Jean-Marie Robine & Fred Paccaud & Alfio Marazzi, 2009. "Dissecting the compression of mortality in Switzerland, 1876-2005," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(19), pages 569-598.
    4. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    5. A. Roger Thatcher & Siu Lan Karen Cheung & Shiro Horiuchi & Jean-Marie Robine, 2010. "The compression of deaths above the mode," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(17), pages 505-538.
    6. 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.
    7. Currie, Iain D., 2020. "Constraints, the identifiability problem and the forecasting of mortality," Annals of Actuarial Science, Cambridge University Press, vol. 14(2), pages 537-566, September.
    8. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    9. Väinö Kannisto, 2000. "Measuring the compression of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(6).
    10. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    11. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    12. Vladimir Shkolnikov & Evgeny M. Andreev & Alexander Begun, 2003. "Gini coefficient as a life table function," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 8(11), pages 305-358.
    13. Richards, S. J. & Kirkby, J. G. & Currie, I. D., 2006. "The Importance of Year of Birth in Two-Dimensional Mortality Data," British Actuarial Journal, Cambridge University Press, vol. 12(1), pages 5-38, March.
    14. Ugofilippo Basellini & Carlo Giovanni Camarda, 2019. "Modelling and forecasting adult age-at-death distributions," Population Studies, Taylor & Francis Journals, vol. 73(1), pages 119-138, January.
    15. Pfaff, Bernhard, 2008. "VAR, SVAR and SVEC Models: Implementation Within R Package vars," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i04).
    16. Smits, Jeroen & Monden, Christiaan, 2009. "Length of life inequality around the globe," Social Science & Medicine, Elsevier, vol. 68(6), pages 1114-1123, March.
    17. James Vaupel & Hans Lundstrom, 1994. "Longer Life Expectancy? Evidence from Sweden of Reductions in Mortality Rates at Advanced Ages," NBER Chapters, in: Studies in the Economics of Aging, pages 79-102, National Bureau of Economic Research, Inc.
    18. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    19. 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.
    20. 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.
    21. Camarda, Carlo G., 2012. "MortalitySmooth: An R Package for Smoothing Poisson Counts with P-Splines," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i01).
    22. 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.
    23. 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.
    24. Ørnulf Borgan & Nico Keilman, 2019. "Do Japanese and Italian Women Live Longer than Women in Scandinavia?," European Journal of Population, Springer;European Association for Population Studies, vol. 35(1), pages 87-99, February.
    25. Vladimir Canudas-Romo, 2010. "Three measures of longevity: Time trends and record values," Demography, Springer;Population Association of America (PAA), vol. 47(2), pages 299-312, May.
    26. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    27. Han Lin Shang & Heather Booth & Rob Hyndman, 2011. "Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(5), pages 173-214.
    28. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    29. 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.
    30. Nadine Ouellette & Robert Bourbeau, 2011. "Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(19), pages 595-628.
    31. Chiou, Jeng-Min & Müller, Hans-Georg, 2009. "Modeling Hazard Rates as Functional Data for the Analysis of Cohort Lifetables and Mortality Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 572-585.
    32. Chiara Gigliarano & Ugofilippo Basellini & Marco Bonetti, 2017. "Longevity and concentration in survival times: the log-scale-location family of failure time models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 254-274, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. van Raalte, Alyson A & Basellini, Ugofilippo & Camarda, Carlo Giovanni & Nepomuceno, Marília & Myrskylä, Mikko, 2022. "The dangers of drawing cohort profiles from period data: a research note," SocArXiv frkcw, Center for Open Science.
    2. 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.
    3. Héctor Pifarré i Arolas & José C. Andrade Santacruz & Mikko Myrskylä, 2023. "An overlapping cohorts perspective of lifespan inequality," MPIDR Working Papers WP-2023-046, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. Alyson van Raalte & Ugofilippo Basellini & Carlo Giovanni Camarda & Marília R. Nepomuceno & Mikko Myrskylä, 2022. "The dangers of drawing cohort profiles from period data: a research note," Working Papers ayadh-ohbnm4x3q6cor1, French Institute for Demographic Studies.
    5. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2023. "Intergenerational actuarial fairness when longevity increases: Amending the retirement age," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 161-184.
    6. Carlo G. Camarda & Ugofilippo Basellini, 2021. "Smoothing, Decomposing and Forecasting Mortality Rates," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 569-602, July.
    7. Shang, Han Lin & Haberman, Steven & Xu, Ruofan, 2022. "Multi-population modelling and forecasting life-table death counts," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 239-253.

    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. 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.
    2. 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.
    3. 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.
    4. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    5. Rizzi, Silvia & Kjærgaard, Søren & Bergeron Boucher, Marie-Pier & Camarda, Carlo Giovanni & Lindahl-Jacobsen, Rune & Vaupel, James W., 2021. "Killing off cohorts: Forecasting mortality of non-extinct cohorts with the penalized composite link model," International Journal of Forecasting, Elsevier, vol. 37(1), pages 95-104.
    6. Ahbab Mohammad Fazle Rabbi & Stefano Mazzuco, 2021. "Mortality Forecasting with the Lee–Carter Method: Adjusting for Smoothing and Lifespan Disparity," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 97-120, March.
    7. Apostolos Bozikas & Georgios Pitselis, 2018. "An Empirical Study on Stochastic Mortality Modelling under the Age-Period-Cohort Framework: The Case of Greece with Applications to Insurance Pricing," Risks, MDPI, vol. 6(2), pages 1-34, April.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    13. Rachel WINGENBACH & Jong-Min KIM & Hojin JUNG, 2020. "Living Longer in High Longevity Risk," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(1), pages 47-86, March.
    14. Marie-Pier Bergeron-Boucher & Søren Kjærgaard & James E. Oeppen & James W. Vaupel, 2019. "The impact of the choice of life table statistics when forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(43), pages 1235-1268.
    15. Carlo G. Camarda & Ugofilippo Basellini, 2021. "Smoothing, Decomposing and Forecasting Mortality Rates," European Journal of Population, Springer;European Association for Population Studies, vol. 37(3), pages 569-602, July.
    16. 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.
    17. Han Lin Shang & Steven Haberman, 2020. "Retiree Mortality Forecasting: A Partial Age-Range or a Full Age-Range Model?," Risks, MDPI, vol. 8(3), pages 1-11, July.
    18. 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.
    19. 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.
    20. Ainhoa-Elena Léger & Stefano Mazzuco, 2021. "What Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database," European Journal of Population, Springer;European Association for Population Studies, vol. 37(4), pages 769-798, November.

    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:eee:insuma:v:91:y:2020:i:c:p:129-143. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.