×

An analysis of period and cohort mortality shocks in international data. (English) Zbl 1461.91255

Summary: This article uses Bayesian maximum a posteriori (BMAP) estimation to fit a cohort-based mortality model that applies the Gompertz mortality law to fixed cohorts across different periods (rather than the more usual application to fixed periods across different cohorts). Period effects are then estimated as residuals. In this approach, cohort effects can be viewed as a proxy for causes of death with long latency, which have become relatively more important in recent decades in richer countries. We estimate the model independently using male and female adult population mortality data in 31 countries. We are able to associate historical events with many of the observed period and cohort shocks, most notably the 1918 flu epidemic, and find striking geographical and cultural correlations in the results. We find that after 1960, the variance of period mortality shocks has declined by an average factor of 5 in most of the countries we examine. Over the same period, cohort shocks appear to have become a more important factor causing changes in mortality than period shocks. We also find that period and cohort shocks appear to be driven by different underlying factors. Our results have important implications for stochastic mortality modeling, and may explain why stochastic mortality models that rely largely on period mortality shocks struggle to generate sufficient variation in mortality rates. Our results will also be useful to those who construct reinsurance portfolios, those who issue or trade longevity-linked securities, and those who study the origins of human mortality.

MSC:

91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abdi, H.; Williams., L. J., Principal component analysis, Wiley Interdisciplinary Reviews: Computational Statistics, 2, 433-59 (2010)
[2] Abdullah, A., R. Wolfe, J. U. Stoelwinder, M. De Courten, C. Stevenson, H. L. Walls, and A. Peeters. 2011. The number of years lived with obesity and the risk of all-cause and cause-specific mortality. International Journal of Epidemiology, 40 (4):985-96.
[3] Almond, D., Is the 1918 influenza pandemic over? Long-term effects of in utero influenza exposure in the post-1940 us population, Journal of Political Economy, 114, 672-712 (2006)
[4] Åström, D. O.; Forsberg, B.; Ebi, K. L.; Rocklöv., J., Attributing mortality from extreme temperatures to climate change in Stockholm, Sweden, Nature Climate Change, 3, 1050 (2013)
[5] Barker, D. J., The fetal and infant origins of adult disease, British Medical Journal, 301, 1111 (1990)
[6] Barker, D. J. 1995. The fetal and infant origins of disease. European Journal of Clinical Investigation, 25:457-63. doi:.
[7] Barker, D. J, J. G. Eriksson, T. Forsén, and C. Osmond. 2002. Fetal origins of adult disease: Strength of effects and biological basis. International Journal of Epidemiology, 31 (6):1235-39. doi:.
[8] Blake, D.; MacMinn, R.; Li, J. S.-H.; Hardy., M., Longevity risk and capital markets: The 2012-2013 update, North American Actuarial Journal, 18, 1-13 (2014) · Zbl 1458.00030
[9] Bradley, W.; Massey, A.; Logan, W.; Semple, A.; Benjamin, B.; Grist, N.; Simpson, R.; Hope, I.; Mitman, M.; Smith, R., Discussion: Influenza 1951, Proceedings of the Royal Society of Medicine, 44, 789-801 (1951)
[10] Cairns, A. J.; Blake, D.; Dowd., K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 687-718 (2006)
[11] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich., I., 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 (2009)
[12] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Khalaf-Allah., M., Bayesian stochastic mortality modelling for two populations, ASTIN Bulletin: The Journal of the IAA, 41, 29-59 (2011)
[13] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Khalaf-Allah., M., A gravity model of mortality rates for two related populations, North American Actuarial Journal, 15, 2, 334-56 (2011) · Zbl 1228.91032
[14] Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah., M., Mortality density forecasts: An analysis of six stochastic mortality models, Insurance: Mathematics and Economics, 48, 3, 355-67 (2011)
[15] Caldwell, J. C., Cultural and social factors influencing mortality levels in developing countries, Annals of the American Academy of Political and Social Science, 510, 1, 44-59 (1990)
[16] Calle, E. E., C. Rodriguez, K. Walker-Thurmond, and M. J. Thun. 2003. Overweight, obesity, and mortality from cancer in a prospectively studied cohort of US adults. New England Journal of Medicine348 (17):1625-38.
[17] Campbell, J., Smallpox in aboriginal Australia, the early 1830s, Australian Historical Studies, 21, 336-58 (1985)
[18] Carson, C.; Hajat, S.; Armstrong, B.; Wilkinson., P., Declining vulnerability to temperature-related mortality in London over the 20th century, American Journal of Epidemiology, 164, 77-84 (2006)
[19] Case, A., and A. Deaton. 2017. Mortality and morbidity in the 21st century. Brookings Papers on Economic Activity2017 (1):397-476.
[20] Christidis, N.; Donaldson, G. C.; Stott., P. A., Causes for the recent changes in cold- and heat-related mortality in England and Wales, Climatic Change, 102, 539-53 (2010)
[21] Coughlan, G. D., M. Khalaf-Allah, Y. Ye, S. Kumar, A. J. Cairns, D. Blake, and K. Dowd. 2011. Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15 (2):150-76.
[22] Cutler, D.; Deaton, A.; Lleras-Muney., A., The determinants of mortality, Journal of Economic Perspectives, 20, 3, 97-120 (2006)
[23] Davis, R. E.; Knappenberger, P. C.; Michaels, P. J.; Novicoff., W. M., Changing heat-related mortality in the United States, Environmental Health Perspectives, 111, 1712 (2003)
[24] Doblhammer, G.; Van den Berg, G. J.; Lumey., L. H., A re-analysis of the long-term effects on life expectancy of the Great Finnish Famine of 1866-68, Population studies, 67, 3, 309-22 (2013)
[25] Dowd, K.; Cairns, A. J.; Blake, D.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah., M., Backtesting stochastic mortality models: an ex post evaluation of multiperiod-ahead density forecasts, North American Actuarial Journal, 14, 3, 281-98 (2010)
[26] European Union, Official Journal of the European Union, Commission Delegated Regulation (EU) 2015/35 (2015)
[27] European Union, Directive (EU) 2016/2341 of the European Parliament and of the Council of 14 December 2016 on the activities and supervision of institutions for occupational retirement provision (IORPs), Official Journal of the European Union (2016)
[28] Eurostat, Manual on government deficit and debt—Implementation of ESA, European Union, 2010 (2016)
[29] Fay, R.; Herriot., R., Estimates of income for small places: An application of James-Stein procedures to census data, Journal of the American Statistical Association, 74, 269-77 (1979)
[30] Fienberg, S. E.; Mason., M. W., Identification and estimation of age-period-cohort models in the analysis of discrete archival data,, Sociological Methodology, 10, 1-67 (1978)
[31] Franklin, T. B.; Russig, H.; Weiss, I. C.; Graff, J.; Linder, N.; Michalon, A.; Vizi, S.; Mansuyi., I. M., Epigenetic transmission of the impact of early stress across generations,, Biological Psychiatry, 68, 5, 408-15 (2010)
[32] Gompertz, B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society, 115, 513-85 (1825)
[33] Greene, W. H., Econometric analysis, Pearson Education (2003)
[34] Huijbregts, P.; Feskens, E.; Räsänen, L.; Fidanza, F.; Nissinen, A.; Menotti, A.; Kromhout., D., Dietary pattern and 20 year mortality in elderly men in Finland, Italy, and the Netherlands: Longitudinal cohort study, British Medical Journal, 315, 13-17 (1997)
[35] (2015)
[36] Jackson, J., France: The dark years, 1940-1944 (2003), New York, NY: Oxford University Press, New York, NY
[37] Kannisto, V.; Christensen, K.; Vaupel., J. W., No increased mortality in later life for cohorts born during famine, American Journal of Epidemiology, 145, 987-94 (1997)
[38] Kahn, L. B. 2010. The long-term labor market consequences of graduating from college in a bad economy. Labour Economics17 (2):303-16.
[39] Kato, H., Mortality in children exposed to the A-bombs while in utero, 1945-1969, American Journal of Epidemiology, 93, 6, 435-42 (1971)
[40] Kohn, G. C., Encyclopedia of plague and pestilence: From ancient times to the present (2007), Facts On File, Inc
[41] Lee, R., The demographic transition: Three centuries of fundamental change, Journal of Economic Perspectives, 17, 167-90 (2003)
[42] Lee, R. D.; Carter., L. R., Modeling and forecasting us mortality, Journal of the American Statistical Association, 87, 659-71 (1992) · Zbl 1351.62186
[43] Lesthaeghe, R., A century of demographic and cultural change in western Europe: An exploration of underlying dimensions, Population and Development Review, 9, 411-35 (1983)
[44] Li, J. S.-H.; Chan, W.-S.; Zhou., R., Semicoherent multipopulation mortality modeling: The impact on longevity risk securitization, Journal of Risk and Insurance, 84, 1025-65 (2017)
[45] Li, J. S.-H.; Hardy., M. R., Measuring basis risk in longevity hedges, North American Actuarial Journal, 15, 177-200 (2011) · Zbl 1228.91042
[46] Li, J. S.-H.; Hardy, M. R.; Tan, K. S., Uncertainty in mortality forecasting: An extension to the classical Lee-Carter approach, ASTIN Bulletin: The Journal of the IAA, 39, 137-64 (2009) · Zbl 1203.91113
[47] Li, N.; Lee., R., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42, 575-94 (2005)
[48] MacMinn, R.; Brockett, P.; Blake., D., Longevity risk and capital markets, Journal of Risk and Insurance, 73, 551-57 (2006)
[49] Masters, R. K., E. N. Reither, D. A. Powers, Y. C. Yang, A. E. Burger, and B. G. Link. 2013. The impact of obesity on US mortality levels: The importance of age and cohort factors in population estimates. American Journal of Public Health, 103 (10):1895-1901.
[50] McKinsey (2014)
[51] Mulder, I.; Jansen, M. C.; Smit, H. A.; Jacobs, D. R. Jr.; Menotti, A.; Nissinen, A.; Fidanza, F.; Kromhout, D., Role of smoking and diet in the cross-cultural variation in lung-cancer mortality: The seven countries study, International Journal of Cancer, 88, 665-71 (2000)
[52] National Association of Insurance Commissioners, Longevity Risk (A/E) Subgroup—Conference call. National Association of Insurance Commissioners Life Actuarial Task Force Committee Document (2017)
[53] National Center for Health Statistics, Vital Statistics Online Data Portal, 2018. Public-use data file and documentation (2018)
[54] Oreopoulos, P., T. Von Wachter, and A. Heisz. 2012. The short and long-term career effects of graduating in a recession. American Economic Journal: Applied Economics4 (1):1-29.
[55] Organization for Economic Cooperation and Development, Pensions at a glance 2015 (2015), OECD Publishing
[56] Pearce, N., Traditional epidemiology, modern epidemiology, and public health, American Journal of Public Health, 86, 5, 678-83 (1996)
[57] Rousseeuw, P., A visual display for hierarchical classification, Delft University of Technology Reports of the Department of Mathematics and Informatics, 85, 5 (1985)
[58] Sparén, P., D. Vågerö, D. B. Shestov, S. Plavinskaja, N. Parfenova, V. Hoptiar, D. Paturot, and M. R. Galanti. 2004. Long term mortality after severe starvation during the siege of Leningrad: Prospective cohort study. British Medical Journal328 (7430):11.
[59] Szreter, S., The importance of social intervention in Britain’s mortality decline c.1850-1914: A re-interpretation of the role of public health, Society of Social History of Medicine, 1, 1, 1-38 (1988)
[60] Tan, K.; Blake, D.; MacMinn., R., Longevity risk and capital markets: The 2013-14 update, Insurance: Mathematics and Economics, 63, 1-11 (2015) · Zbl 1321.00138
[61] Van den Berg, G. J.; Lindeboom, M.; Portrait., R., Economic conditions early in life and individual mortality, American Economic Review, 96, 290-302 (2006)
[62] Vaupel, J.; Manten, K.; Stallard., E., The impact of heterogeneity in individual frailty on the dynamics of mortality,, Demography, 16, 3, 439-54 (1979)
[63] Wang, J. L.; Huang, H.; Yang, S. S.; Tsai., J. T., An optimal product mix for hedging longevity risk in life insurance companies: The immunization theory approach, Journal of Risk and Insurance, 77, 473-97 (2010)
[64] Willis Towers Watson, Global pension assets study. Willis Towers Watson (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.