The impact of multiple structural changes on mortality predictions. (English) Zbl 1401.91221

Summary: Most mortality models proposed in recent literature rely on the standard ARIMA framework (in particular: a random walk with drift) to project mortality rates. As a result the projections are highly sensitive to the calibration period. We therefore analyse the impact of allowing for multiple structural changes on a large collection of mortality models. We find that this may lead to more robust projections for the period effect but that there is only a limited effect on the ranking of the models based on backtesting criteria, since there is often not yet sufficient statistical evidence for structural changes. However, there are cases for which we do find improvements in estimates and we therefore conclude that one should not exclude on beforehand that structural changes may have occurred.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62P25 Applications of statistics to social sciences


Full Text: DOI


[1] Andrews, D. (1992). Tests for parameter instability and structural change with unknown change point. Econometrica61 (4), 821-856. · Zbl 0795.62012
[2] Bai, J. & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica66 (1), 47-78. · Zbl 1056.62523
[3] Bai, J. & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics18 (1), 1-22.
[4] Barrieu, P., Bensusan, H., Karoui, N. E., Hillairet, C., Loisel, S., Ravanelli, C. & Salhi, Y. (2012). Understanding, modelling and managing longevity risk: key issues and main challenges. Scandinavian Actuarial Journal3, 203-231. · Zbl 1277.91073
[5] Booth, H., Maindonald, J. & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies56 (3), 325-336.
[6] Bots, M. & Grobbee, D. (1996). Decline of coronary heart disease mortality in the Netherlands from 1978 to 1985: Contribution of medical care and changes over time in presence of major cardiovascular risk factors. Journal of Cardiovascular Risk3 (3), 271-276.
[7] Brouhns, N., Denuit, M. & Vermunt, J. (2002). A poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics31 (3), 373-393. · Zbl 1074.62524
[8] Cairns, A., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance73 (4), 687-718.
[9] Cairns, A., Blake, D. & Dowd, K. (2008). Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal2-3, 79-113. · Zbl 1224.91048
[10] Cairns, A., Blake, D., Dowd, K., Coughlan, G., Epstein, D. & Khalaf-Allah, M. (2011). Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics48 (3), 355-367. · Zbl 1231.91179
[11] Cairns, A., Blake, D., Dowd, K., Coughlan, G., 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 Journal13 (1), 1-35.
[12] Chow, G. (1960). Tests of equality between sets of coefficients in two linear regressions. Econometrica28 (3), 591-605. · Zbl 0099.14304
[13] Coelho, E. & Nunes, L. (2011). Forecasting mortality in the event of a structural change. Journal of the Royal Statistical Society174 (3), 713-736.
[14] Coelho, E. & Nunes, L., (2013). Cohort effects and structural changes in the mortality trend. Working paper. Available online at: http://www.unece.org/leadmin/DAM/stats/documents/ece/ces/ge.11/2013/WP_5.1.pdf.
[15] Currie, I., (2006). Smoothing and forecasting mortality rates with P-splines. Talk given at the Institute of Actuaries. Available online at: http://www.ma.hw.ac.uk/ iain/research/talks.html.
[16] Denuit, M. & Goderniaux, A., (2005). Closing and projecting lifetables using log-linear models. Bulletin of the Swiss Association of Actuaries1, 29-49. · Zbl 1333.62251
[17] Dowd, K., Cairns, A., Blake, D., Coughlan, G., Epstein, D. & Khalaf-Allah, M. (2010). Backtesting stochastic mortality models: An ex post evaluation of multiperiod-ahead density forecasts. North American Actuarial Journal14 (3), 281-298.
[18] Gneiting, T. & Raftery, A. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association102 (477), 359-378. · Zbl 1284.62093
[19] Haberman, S. & Renshaw, A. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics48 (1), 35-55.
[20] Hainaut, D., (2012). Multi dimensional Lee-Carter model with switching mortality processes. Insurance: Mathematics and Economics50 (2), 236-246. · Zbl 1235.91091
[21] Harris, D., Harvey, D., Leybourne, S. & Taylor, A. (2009). Testing for a unit-root in the presence of a possible break in trend. Econometric Theory25, 1545-1588. · Zbl 1179.62120
[22] Harvey, D., Leybourne, S. & Taylor, A. (2009). Simple, robust and powerful tests of changing trend hypothesis. Econometric Theory25, 995-1029. · Zbl 1278.62135
[23] Janssen, F., Kunst, A. & Mackenbach, J. (2007). Variations in the pace of old-age mortality decline in seven European countries, 1950-1999: The role of smoking and other factors earlier in life. European Journal of Population23 (2), 171-188.
[24] Lee, R. & Carter, L. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association87 (419), 659-671. · Zbl 1351.62186
[25] Li, H., Waegenaere, A.D. & Melenberg, B., (2013). The choice of sample size for mortality forecasting: A Bayesian learning approach, Working paper. Tilburg University. · Zbl 1348.91162
[26] Li, J.-H., Chan, W.-S. & Cheung, S.-H. (2011). Structural changes in the Lee-Carter mortality indexes: Detection and implications. North American Actuarial Journal15 (1), 13-31.
[27] Lindbergson, M. (2001). Mortality among the elderly in Sweden 1988-1997. Scandinavian Actuarial Journal3, 79-94. · Zbl 0973.62106
[28] Lovász, E. (2011). Analysis of Finnish and Swedish mortality data with stochastic mortality models. European Actuarial Journal1, 259-289. · Zbl 1268.91083
[29] Milidonis, A., Lin, Y. & Cox, S. (2011). Mortality regimes and pricing. North American Actuarial Journal15 (2), 266-289. · Zbl 1228.91043
[30] Moreno-Serra, R. & Wagstaff, A. (2010). System-wide impacts of hospital payment reforms: Evidence from Central and Eastern Europe and Central Asia. Journal of Health Economics29 (4), 585-602.
[31] O’Hare, C. & Li, Y. (2011). Explaining young mortality. Insurance: Mathematics and Economics50 (1), 12-25. · Zbl 1235.91102
[32] O’Hare, C. & Li, Y., (2014). Identifying structural breaks in stochastic mortality models. Journal of Risk and Uncertainty in Engineering part B. Available online at SSRN: http://ssrn.com/abstract=2192208.
[33] Pitacco, E., Denuit, M., Haberman, S. & Olivieri, A. (2009). Modelling longevity dynamics for pensions and annuity business. New York: Oxford University Press. · Zbl 1163.91005
[34] Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics45 (3), 393-404. · Zbl 1231.91227
[35] Renshaw, A. & Haberman, S. (2003). Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics33 (2), 255-272. · Zbl 1103.91371
[36] Renshaw, A. & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics38 (3), 556-570. · Zbl 1168.91418
[37] Riebler, A., Held, L. & Rue, H. (2012). Estimation and extrapolation of time trends registry data - borrowing strength from related populations. The Annals of Applied Statistics6 (1), 304-333. · Zbl 1235.62030
[38] Sweeting, P. (2011). A trend-change extension of the Cairns-Blake-Dowd Model. Annals of Actuarial Science5 (2), 143-162.
[39] Vaupel, J. (1990). Relatives’ risks: frailty models of life history data. Theoretical population biology37 (1), 220-234. · Zbl 0695.62236
[40] Yao, Y.-C. (1988). Estimating the number of change-points via Schwarz’ criterion. Statistics & Probability Letters6 (3), 181-189. · Zbl 0642.62016
[41] Zeileis, A., Kleiber, C., Krämer, W. & Hornik, K. (2003). Testing and dating of structural changes in practice. Computational Statistics & Data Analysis44 (12), 109-123. · Zbl 1429.62307
[42] Zeileis, A., Leisch, F., Hornik, K. & Kleiber, C. (2002). Strucchange: An R package for testing for structural change in linear regression models. Journal of Statistical Software7 (2), 1-38.
[43] Zhao, Y. & Sweeting, P. (2012). Modelling the cohort effect in CBD models using a piecewise linear approach. Discussion paper. Pensions Institute.
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.