Identifying structural breaks in stochastic mortality models

O'Hare, Colin and Li, Youwei (2014): Identifying structural breaks in stochastic mortality models. Forthcoming in: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B. Mechanical Engineering

Abstract

In recent years the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and hence quantify the costs of providing for future ageing populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort and forecast these trends into the future using standard statistical methods. These approaches rely on the assumption that structural breaks in the trend do not exist or do not have a significant impact on the mortality forecasts. Recent literature has started to question this assumption. In this paper we carry out a comprehensive investigation of the presence or otherwise of structural breaks in a selection of leading mortality models. We find that structural breaks are present in the majority of cases. In particular, where there is a structural break present we find that allowing for that improves the forecast result significantly.

• Item Type: MPRA Paper
• Language: English
• Keywords: Mortality; stochastic models; forecasting; structural breaks
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance ; Insurance Companies ; Actuarial Studies; G - Financial Economics > G2 - Financial Institutions and Services > G23 - Non-bank Financial Institutions ; Financial Instruments ; Institutional Investors; J - Labor and Demographic Economics > J1 - Demographic Economics > J11 - Demographic Trends, Macroeconomic Effects, and Forecasts

References

[1] Bai, J., and Perron, P. (1998), Estimating and Testing Linear Models With Multiple Structural Changes, Econometrica, 66, 47-78.

[2] Bai, J., and Perron, P. (2003), Computation and Analysis of Multiple Structural Change Models, Journal of Applied Econometrics, 18, 1-22.

[3] Booth, H., Maindonald, J., and Smith, L. (2002), Applying Lee-Carter under conditions of variable mortality decline.Population Studies 56, 325-336.

[4] Booth, H., and Tickle, L. (2008), Mortality modeling and forecasting: A review of methods, Annals of actuarial science. 3, 3-43.

[5] Brouhns, N., Denuit, M., and Vermunt, J.K. (2002), A Poisson log-bilinear approach to the construction of projected lifetables. Insurance: Mathematics and Economics 31(3), 373-393.

[6] Brown R.L., Durbin J., Evans J.M. (1975), Techniques for testing constancy of regression relationships over time, Journal of the Royal Statistical Society, Series B, 37, 149-163.

[7] Cairns, A.J.G., Blake, D., and Dowd, K. (2006), A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73, 687-718.

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

[9] Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., and Khalaf-Allah, M. (2011), Mortality density forecasts: An analysis of six stochastic mortality models.Insurance: Mathematics and Economics 48, 355-367.

[10] Carter, L. R., and Prskawetz., A. (2001), Examining Structural Shifts in Mortality Using the Lee-Carter Method. Working Paper WP 2001-007,Max Planck Institute for Demographic Research.

[11] Chu, C.S., Hornik, K., Kuan, C.M. (1995),MOSUM tests for parameter constancy, Biometrika, 82, 603-617.

[12] Clayton, D. and Schifflers, E. (1987), Models for temporal variation in cancer rates. II: Age-period-cohort models. Statistics in Medicine, 6, 469-481.

[13] Coelho, E. and Nunes, L. C. (2011), Forecasting mortality in the event of a structural change. Journal of the Royal Statistical Society: Series A (Statistics in Society), 174, 713-736.

[14] Currie, I.D. (2006), Smoothing and forecasting mortality rates with P-splines.Presentation to the Institute of Actuaries. Available at: http://www.ma.hw.ac.uk/ iain/research.talks.html.

[15] Currie, I.D. (2011),Modelling and forecasting the mortality of the very old. ASTIN Bulletin, 41, 419-427.

[16] Delwarde, A., Denuit, M., and Eilers, P. (2007), Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: A penalized log-likelihood approach. Statistical Modelling, 7, 29-48.

[17] De Jong, P., and Tickle, L. (2006), Extending the Lee-Carter model of mortality projection. Mathematical Population Studies, 13, 1-18.

[18] Girosi, F., and King, G. (2005), A reassessment of the Lee-Carter mortality forecasting method, Working Paper, Harvard University.

[19] Harris, D., Harvey, D. I., Leybourne, S. J. and Taylor, A. M. R. (2009), Testing for a unit-root in the presence of a possible break in trend. Econmetric Theory, 25, 1545-1588.

[20] Harvey, D. I., Leybourne, S. J. and Taylor, A.M. R. (2009), Simple, robust and powerful tests of the changing trend hypothesis. Econmetric Theory, 25, 995-1029.

[21] Kannisto, V., Lauristen, J., Thatcher, A.R., and Vaupel. J.W. (1994), Reduction in Mortality at Advanced Ages: Several Decades of Evidence from 27 Countries. Population Development Review, 20, 793-810.

[22] Koissi, M.C., Shapiro, A.F., and Hognas, G. (2005), Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Interval. Insurance: Mathematics and Economics, 38, 1-20.

[23] Kuan, C.M., and Hornik, K. (1995), The generalized fluctuation test: A unifying view, Econometric Reviews, 14, 135-161.

[24] Lee, R.D., and Carter, L.R. (1992), Modeling and Forecasting U. S. Mortality, Journal of the American Statistical Association, 87(419), 659-671.

[25] Lee, R. D., and Miller, T. (2001), Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 537-549.

[26] Li, J.S.H., Chan, W.S., and Cheung, S.H. (2011), Structural Changes in the Lee-Carter Mortality Indexes: Detection and Implications, North American Actuarial Journal, 15, 13-31.

[27] O’Hare, C., and Li, Y. (2012), Explaining young mortality, Insurance: Mathematics and Economics, 50(1), 12-25.

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

[29] Ploberger,W., and Kr¨amer,W. (1992), The CUSUM test with OLS residuals, Econometrica, 60, 271-285.

[30] Renshaw, A.E., and Haberman, S. (2003), Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255-272.

[31] Renshaw, A.E., and Haberman, S. (2006), A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556-70.

[32] Tuljapurkar, S., and Boe, C. (1998), Mortality Change and Forecasting: How Much and How Little Do We Know? North American Actuarial Journal, 2, 13-47.

[33] Vaupel, J.W. (1997), The Remarkable Improvements in Survival at Older Ages. Philosophical Transactions of the Royal Society of London, B 352, 1799-1804.

[34] Zeileis, A. (2000), p-values and alternative boundaries for CUSUM tests. Working Paper 78, SFB Adaptive Information Systems and Modelling in Economics and Management Science, http://www.wu-wien.ac.at/am/wp00.htm#78.

[35] Zeileis, A., Kleiber C., Kramer W., and Hornik K. (2003), Testing and Dating of Structural Changes in Practice, Computational Statistics and Data Analysis, 44, 109-123.

[36] Zeileis, A. (2005), A Unified Approach to Structural Change Tests Based onML Scores, F Statistics and OLS Residuals. Econometric Reviews, 24, 445-466.

[37] Zivot, E., and Andrews, D. (1992), Further Evidence of the Great Crash, the Oil-Price Shock and the Unit- Root Hypothesis. Journal of Business and Economic Statistics, 10, 251-270.