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Incorporating structural changes in mortality improvements for mortality forecasting. (English) Zbl 1454.91198

Summary: In recent decades, there have been decreasing mortality improvements at younger ages but increasing mortality improvements at older ages in many countries. We propose a modified Lee-Carter method to allow for these structural changes, in which the entire data period is divided into more homogeneous subperiods and a unique set of age-specific parameters is incorporated for each subperiod. We consider a number of methods to project these age patterns into the future. Our results show that the new method can reasonably capture the underlying movements in the age patterns over time and can potentially improve the forecast accuracy of death rates and life expectancies. It is interesting to observe that the highest age sensitivity has been moving gradually to older ages and it is important to take this trend into account in mortality forecasting.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography

Software:

Human Mortality
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[1] Booth, H.; Maindonald, J.; Smith, L., Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336 (2002) · doi:10.1080/00324720215935
[2] Booth, H.; Tickle, L., Mortality modelling and forecasting: A review of methods, Annals of Actuarial Science, 3, 1-2, 3-43 (2008) · doi:10.1017/S1748499500000440
[3] Brouhns, N.; Denuit, M.; Vermunt, J. K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31, 373-393 (2002) · Zbl 1074.62524
[4] Carnes, B. A.; Olshansky, S. J., A realist view of aging, mortality, and future longevity, Population and Development Review, 33, 2, 367-381 (2007) · doi:10.1111/j.1728-4457.2007.00172.x
[5] Carter, L. R. & Prskawetz, A. (2001). Examining structural shifts in mortality using the Lee-Carter method. MPIDR Working Paper 2001-007.
[6] Coale, A.; Guo, G., Revised regional model life tables at very low levels of mortality, Population Index, 55, 4, 613-643 (1989) · doi:10.2307/3644567
[7] Coelho, E.; Nunes, L. C., Forecasting mortality in the event of a structural change, Journal of the Royal Statistical Society Series A, 174, 3, 713-736 (2011) · doi:10.1111/j.1467-985X.2010.00687.x
[8] Continuous Mortality Investigation (CMI) (2007). Stochastic projection methodologies: Lee-Carter model features, example results and implications. Working Paper 25.
[9] Currie, I. D., Smoothing constrained generalized linear models with an application to the Lee-Carter model, Statistical Modelling, 13, 1, 69-93 (2013) · Zbl 07257450 · doi:10.1177/1471082X12471373
[10] Delwarde, A.; Denuit, M.; Eilers, P., Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: A penalized log-likelihood approach, Statistical Modelling, 7, 1, 29-48 (2007) · Zbl 07257671 · doi:10.1177/1471082X0600700103
[11] Denuit, M.; Goderniaux, A. C., Closing and projecting lifetables using log-linear models, Bulletin of the Swiss Association of Actuaries, 1, 29-49 (2005) · Zbl 1333.62251
[12] Gampe, J.; Maier, H.; Gampe, J.; Jeune, B.; Vaupel, J. W.; Robine, J. M., Human mortality beyond age 110, Supercentenarians. Demographic Research Monographs, 219-230 (2010), Heidelberg: Springer-Verlag Berlin, Heidelberg
[13] Gavrilova, N.S., Gavrilov, L.A. & Krut’ko, V.N. (2017). Mortality trajectories at exceptionally high ages: A study of supercentenarians. Living to 100 Symposium. Society of Actuaries.
[14] Ginn, S. L.; Amaya, A. K.; Alexander, I. E.; Edelstein, M., Gene therapy clinical trials worldwide to 2017: An update, Journal of Gene Medicine, 20, 5, e3015 (2018) · doi:10.1002/jgm.3015
[15] Haberman, S.; Renshaw, A., A comparative study of parametric mortality projection models, Insurance: Mathematics and Economics, 48, 35-55 (2011)
[16] Hainaut, D., Multidimensional Lee-Carter model with switching mortality processes, Insurance: Mathematics and Economics, 50, 236-246 (2012) · Zbl 1235.91091
[17] Heligman, L.; Pollard, J. H., The age pattern of mortality, Journal of the Institute of Actuaries, 107, 49-80 (1980) · doi:10.1017/S0020268100040257
[18] Ho, B. N.; Pfeffer, C. M.; Singh, A. T. K., Update on nanotechnology-based drug delivery systems in cancer treatment, Anticancer Research, 37, 5975-5981 (2017)
[19] Human Mortality Database (HMD). (2019). University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). Available at: www.mortality.org
[20] Koissi, M. C. & Shapiro, A. F. (2008). The Lee-Carter model under the condition of variables age-specific parameters. 43rd Actuarial Research Conference, Regina, Canada.
[21] Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, Journal of the American Statistical Association, 87, 419, 659-671 (1992) · Zbl 1351.62186
[22] Lee, R.; Miller, T., Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 4, 537-549 (2001) · doi:10.1353/dem.2001.0036
[23] Li, J., A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Population Studies, 67, 1, 111-126 (2013) · doi:10.1080/00324728.2012.689316
[24] Li, J., An application of MCMC simulation in mortality projection for populations with limited data, Demographic Research, 30, 1, 1-48 (2014) · doi:10.4054/DemRes.2014.30.1
[25] Li, N.; Lee, R., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42, 3, 575-597 (2005) · doi:10.1353/dem.2005.0021
[26] Li, H.; Li, J. S.H., Optimising the Lee-Carter approach in the presence of structural changes in time and age patterns of mortality improvements, Demography, 54, 1073-1095 (2017) · doi:10.1007/s13524-017-0579-x
[27] Li, H.; De Waegenaere, A.; Melenberg, B., The choice of sample size for mortality forecasting: A Bayesian learning approach, Insurance: Mathematics and Economics, 63, 153-168 (2015) · Zbl 1348.91162
[28] Li, J.; Li, J. S. H.; Tan, C. I.; Tickle, L., Assessing basis risk in index-based longevity swap transactions, Annals of Actuarial Science, 13, 1, 166-197 (2019) · doi:10.1017/S1748499518000179
[29] Li, J. S. H.; Chan, W. S.; Cheung, S. H., Structural changes in the Lee-Carter mortality indexes: Detection and implications, North American Actuarial Journal, 15, 1, 13-31 (2011) · doi:10.1080/10920277.2011.10597607
[30] Li, N.; Lee, R.; Gerland, P., Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections, Demography, 50, 2037-2051 (2013) · doi:10.1007/s13524-013-0232-2
[31] Li, N.; Lee, R.; Tuljapurkar, S., Using the Lee-Carter method to forecast mortality for populations with limited data, International Statistical Review, 72, 1, 19-36 (2004) · Zbl 1330.62349 · doi:10.1111/j.1751-5823.2004.tb00221.x
[32] Milidonis, A.; Lin, Y.; Cox, S. H., Mortality regimes and pricing, North American Actuarial Journal, 15, 2, 266-289 (2011) · Zbl 1228.91043 · doi:10.1080/10920277.2011.10597621
[33] Newman, S. J., Errors as a primary cause of late-life mortality deceleration and plateaus, PLOS Biology, 16, 12, e2006776 (2018) · doi:10.1371/journal.pbio.2006776
[34] O’Hare, C.; Li, Y., Identifying structural breaks in stochastic mortality models, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 1, 2, 021001 (2015) · doi:10.1115/1.4029740
[35] Renshaw, A.; Haberman, S., Lee-Carter mortality forecasting: A parallel generalized linear modelling approach for England and Wales mortality projections, Applied Statistics, 52, 1, 119-137 (2003) · Zbl 1111.62359
[36] Renshaw, A. E.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570 (2006) · Zbl 1168.91418
[37] Sinclair, D. A.; LaPlante, M. D., Lifespan: Why We Age – and Why We Don’t Have To (2019), London: Atria Books, London
[38] Van Berkum, F.; Antonio, K.; Vellekoop, M., The impact of multiple structural changes on mortality predictions, Scandinavian Actuarial Journal, 2016, 7, 581-603 (2016) · Zbl 1401.91221 · doi:10.1080/03461238.2014.987807
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