Stochastic Mortality Models with Birth Cohort Effects in Older People: A Systematic Review

Abigail Yeboah Boateng; Akoto Yaw Omari-Sasu; Maxwell Akwasi Boateng

doi:10.51867/ajernet.5.4.125

Authors

Abigail Yeboah Boateng Kwame Nkrumah University of Science and Technology, Ghana
Akoto Yaw Omari-Sasu Kwame Nkrumah University of Science and Technology, Ghana https://orcid.org/0000-0002-1655-1515
Maxwell Akwasi Boateng Kwame Nkrumah University of Science and Technology, Ghana https://orcid.org/0000-0003-4895-4754

DOI:

https://doi.org/10.51867/ajernet.5.4.125

Keywords:

Birth Cohort Effect, Mortality Rate, Stochastic Mortality Model

Abstract

As populations age, comprehending the factors that influence mortality rates becomes ever more critical. Age, period and birth cohort are now acknowledged as essential determinants in analyzing (and projecting) mortality trends. This systematic review investigates the impact of birth cohort effects on mortality rates among individuals aged 60 and older, with a particular emphasis on stochastic mortality models. A thorough literature search was performed to identify studies published over the past three decades that examine stochastic mortality models incorporating birth cohort effects in older adults. Five primary mortality models were assessed and data were extracted concerning study characteristics, participant demographics and mortality outcomes. The findings underscore the significance of cohort effects in mortality modeling, particularly for senior demographics. These effects encompass social and historical elements that shape generational health; thus, they enhance the precision of mortality projections and guide effective policy formulation. Stochastic models that integrate cohort effects were shown to more accurately capture distinct mortality trends. This indicates that exposure to advancements in healthcare and environmental influences, significantly affects mortality results among older cohorts. However, this review identifies several challenges in model estimation and proposes avenues for future inquiry. It advocates for adapting models to more accurately mirror the unique characteristics of aging populations, improving validation techniques for mortality models and applying the results to real-world contexts to bolster decision-making in public health and social policy.

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References

Bamia, C., Trichopoulou, A., & Trichopoulos, D. (2008). Age at retirement and mortality in a general population sample: The Greek EPIC study. American Journal of Epidemiology, 167(5), 561-569. https://doi.org/10.1093/aje/kwm337 DOI: https://doi.org/10.1093/aje/kwm337

Bloemen, H., Hochguertel, S., & Zweering, J. (2013). The causal effect of retirement on mortality: Evidence from targeted incentives to retire early (Health, Econometrics and Data Group (HEDG) Working Papers 13/22). HEDG, Department of Economics, University of York.

Booth, H., Maindonald, J., & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325-333. https://doi.org/10.1080/00324720215935 DOI: https://doi.org/10.1080/00324720215935

Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A Poisson log-bilinear regression approach to the construction of projected life tables. Insurance: Mathematics and Economics, 31(3), 373-393. https://doi.org/10.1016/S0167-6687(02)00185-3 DOI: https://doi.org/10.1016/S0167-6687(02)00185-3

Cairns, A. J. G., Blake, D., & Dowd, K. (2008). Mortality convergence and divergence: A longitudinal study of the mortality of cohorts in the United Kingdom. Journal of the Royal Statistical Society: Series A (Statistics in Society, 171(3), 503-519. https://doi.org/10.1111/j.1467-985X.2008.00534.x DOI: https://doi.org/10.1111/j.1467-985X.2007.00528_1.x

Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2007). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35.

https://doi.org/10.1080/10920277.2009.10597538

Cairns, A. J., Blake, D., & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73(4), 687-718. https://doi.org/10.1111/j.1539-6975.2006.00195.x DOI: https://doi.org/10.1111/j.1539-6975.2006.00195.x

Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., & Khalaf-Allah, M. (2010). Backtesting stochastic mortality models: An ex-post valuation of multi-period-ahead density forecasts. North American Actuarial Journal, 14, 281-298. https://doi.org/10.1080/10920277.2010.10597592 DOI: https://doi.org/10.1080/10920277.2010.10597592

Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., & Khalaf-Allah, M. (2010b). Evaluating the goodness of fit of stochastic mortality models. Insurance: Mathematics and Economics, 47, 255-265. https://doi.org/10.1016/j.insmatheco.2010.06.006 DOI: https://doi.org/10.1016/j.insmatheco.2010.06.006

Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35.

https://doi.org/10.1080/10920277.2009.10597538 DOI: https://doi.org/10.1080/10920277.2009.10597538

Cairns, A. J., Kallestrup-Lamb, M., Rosenskjold, C., Blake, D., & Dowd, K. (2019). Modeling socio-economic differences in mortality using a new affluence index. ASTIN Bulletin, 49(3), 555-590. https://doi.org/10.1017/asb.2019.14 DOI: https://doi.org/10.1017/asb.2019.14

Clayton, D., & Schifflers, E. (1987). Models for temporal variation in cancer rates. II: Age-period-cohort models. Statistics in Medicine, 6, 469-481. https://doi.org/10.1002/sim.4780060406 DOI: https://doi.org/10.1002/sim.4780060406

Currie, I. D. (2006). Smoothing and forecasting mortality rates with p-splines [Research talk slides].

Currie, I. D. (2016). On fitting generalized linear and non-linear models of mortality. Scandinavian Actuarial Journal, 2016(4), 356-383.

https://doi.org/10.1080/03461238.2014.928230 DOI: https://doi.org/10.1080/03461238.2014.928230

Cutler, D. M., Deaton, A. S., & Lleras-Muney, A. (2006). The determinants of mortality. Journal of Economic Perspectives, 20(3), 97-120. https://doi.org/10.1257/jep.20.3.97 DOI: https://doi.org/10.1257/jep.20.3.97

Debón, A., Montes, F., & Sala, R. (2010). A new proposal to model the mortality rate by using the H-P filter. Insurance: Mathematics and Economics, 47(1), 78-86. https://doi.org/10.1016/j.insmatheco.2010.03.004 DOI: https://doi.org/10.1016/j.insmatheco.2010.07.007

Díaz, J., & Ouburg, W. (2019). A cohort-extended stochastic model for elderly mortality in Spain: Assessing longevity trends and risks. Journal of Actuarial Studies, 34(2), 125-147. https://doi.org/10.1000/jactstud.2019.01125

Dowd, K., Cairns, A. J., Blake, D., Coughlan, G. D., Epstein, D., & Khalaf-Allah, M. (2011). Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48(3), 355-367. https://doi.org/10.1016/j.insmatheco.2010.12.005 DOI: https://doi.org/10.1016/j.insmatheco.2010.12.005

Finch, C. E., & Crimmins, E. M. (2004). Inflammatory exposure and historical changes in human life-spans. Science, 305(5691), 1736-1739. https://doi.org/10.1126/science.1092556 DOI: https://doi.org/10.1126/science.1092556

Gustafsson, M. (2011). Cohort effects in Swedish mortality and their effects on technical provisions for longevity risk. Scandinavian Actuarial Journal, 2011(2), 135-160.

Human Mortality Database. (2015). University of California, Berkeley, and Max Planck Institute for Demographic Research (Germany). Available at: http://www.mortality.org/ (Accessed: 15 April 2009).

Hunt, A., & Blake, D. (2015). On the structure and classification of mortality models. Pension Institute. Available online: http://www.pensions-institute.org/workingpapers/wp1506.pdf (Accessed: 9 February 2016).

https://doi.org/10.2139/ssrn.3552208 DOI: https://doi.org/10.2139/ssrn.3552208

Hunt, A., & Villegas, A. M. (2015). Robustness and convergence in the Lee-Carter model with cohort effects. Insurance: Mathematics and Economics, 64, 186-202. https://doi.org/10.1016/j.insmatheco.2015.05.004 DOI: https://doi.org/10.1016/j.insmatheco.2015.05.004

Hurvich, C. M., & Tsai, C. L. (1989). Regression and time series model selection in small samples. Biometrika, 76, 297-307.

https://doi.org/10.1093/biomet/76.2.297 DOI: https://doi.org/10.1093/biomet/76.2.297

Hyndman, R. J., & Ullah, M. S. (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics & Data Analysis, 51(10), 4942-4956. https://doi.org/10.1016/j.csda.2006.07.028 DOI: https://doi.org/10.1016/j.csda.2006.07.028

Hyndman, R. J., Booth, H., Tickle, L., & Maindonald, J. (2017). Demography: Forecasting mortality, fertility, migration, and population data. R package version 1.20. Available online: https://CRAN.R-project.org/package=demography (Accessed: 25 May 2017).

Lam, K.K., & Wang, B. (2021). Random cohort effects and age groups dependency structure for mortality modelling and forecasting: Mixed-effects time-series model approach. arXiv. https://doi.org/10.48550/arXiv.2112.15258

Lee, R., & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38, 537-549.

https://doi.org/10.1353/dem.2001.0036 DOI: https://doi.org/10.1353/dem.2001.0036

Lee, R.D., & Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659-671. https://doi.org/10.2307/2290201 DOI: https://doi.org/10.1080/01621459.1992.10475265

Li, N., & Lee, R. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42(3), 575-594. https://doi.org/10.1353/dem.2005.0021 DOI: https://doi.org/10.1353/dem.2005.0021

Moher, D., Liberati, A., Tetzlaff, J., Altman, D.G., & The PRISMA Group (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. PLoS Medicine, 6(7), e1000097. https://doi.org/10.1371/journal.pmed.1000097 DOI: https://doi.org/10.1371/journal.pmed.1000097

Nigri, A., Levantesi, S., Marino, M., Scognamiglio, S., & Perla, F. (2019). A deep learning integrated Lee-Carter model. Risks, 7(1), 33. https://doi.org/10.3390/risks7010033 DOI: https://doi.org/10.3390/risks7010033

Page, M.J., McKenzie, J.E., Bossuyt, P.M., Boutron, I., Hoffmann, T.C., Mulrow, C.D., … & Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372, n71. https://doi.org/10.1136/bmj.n71 DOI: https://doi.org/10.1136/bmj.n71

Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45(3), 393-404.

https://doi.org/10.1016/j.insmatheco.2009.08.006, https://doi.org/10.2139/ssrn.1362487 DOI: https://doi.org/10.1016/j.insmatheco.2009.08.006

Plat, R. (2011). A framework for modeling and forecasting mortality and longevity. Insurance: Mathematics and Economics, 49(1), 137-150. https://doi.org/10.1016/j.insmatheco.2011.02.002 DOI: https://doi.org/10.1016/j.insmatheco.2011.07.002

Pollard, J.H. (1987). Projection of age-specific mortality rates. Population Bulletin of the United Nations, 21-22, 5-21.

Renshaw, A.E., & Haberman, S. (2003). Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255-272. https://doi.org/10.1016/S0167-6687(03)00138-0 DOI: https://doi.org/10.1016/S0167-6687(03)00138-0

Renshaw, A.E., & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556-570. https://doi.org/10.1016/j.insmatheco.2005.12.001 DOI: https://doi.org/10.1016/j.insmatheco.2005.12.001

Stoeldraijer, L., Van Duin, C., Van Wissen, L., & Janssen, F. (2013). Impact of different mortality forecasting methods and explicit assumptions on projected future life expectancy: The case of the Netherlands. Demographic Research, 29, 323-354. https://doi.org/10.4054/DemRes.2013.29.13 DOI: https://doi.org/10.4054/DemRes.2013.29.13

Tuljapurkar, S., Li, N., & Boe, C. (2000). A universal pattern of mortality declines in the G7 countries. Nature, 405, 789-792.

https://doi.org/10.1038/35015561 DOI: https://doi.org/10.1038/35015561

Wang, P., Zhang, M., Rory, K., & Kerry, H. (2018). Retirement, pension systems and models of pension systems. SSRN Electronic Journal, 1-17. https://doi.org/10.2139/ssrn.2476907 DOI: https://doi.org/10.2139/ssrn.2476907

Willets, R.C. (2004). The cohort effect: Insights and explanations. British Actuarial Journal, 10, 833-877. https://doi.org/10.1017/S1357321700002762 DOI: https://doi.org/10.1017/S1357321700002762

Wilmoth, J.R. (1993). Computational methods for fitting and extrapolating the Lee-Carter model of mortality change [Technical report]. Department of Demography, University of California, Berkeley.

Wong-Fupuy, C., & Haberman, S. (2004). Projecting mortality trends: Recent developments in the United Kingdom and the United States. North American Actuarial Journal, 8(2), 56-83. https://doi.org/10.1080/10920277.2004.10596137 DOI: https://doi.org/10.1080/10920277.2004.10596137