A general procedure for constructing mortality models. (English) Zbl 1412.91045

Summary: Recently a large number of new mortality models have been proposed to analyze historic mortality rates and project them into the future. Many of these suffer from being over-parametrized or have terms added in an ad hoc manner that cannot be justified in terms of demographic significance. In addition, poor specification of a model can lead to period effects in the data being wrongly attributed to cohort effects, which results in the model making implausible projections. We present a general procedure for constructing mortality models using a combination of a toolkit of functions and expert judgment. By following the general procedure, it is possible to identify sequentially every significant demographic feature in the data and give it a parametric structural form. We demonstrate using U.K. mortality data that the general procedure produces a relatively parsimonious model that nevertheless has a good fit to the data.


91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography


Human Mortality
Full Text: DOI Link


[1] Aro, H.; Pennanen, T., A User-Friendly Approach to Stochastic Mortality Modelling, European Actuarial Journal, 1, 151-167, (2011)
[2] Booth, H.; Maindonald, J.; Smith, L., Applying Lee-Carter Under Conditions of Variable Mortality Decline, Population Studies, 56, 325-336, (2002)
[3] Brouhns, N.; Denuit, M.; Vermunt, J., A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables, Insurance: Mathematics and Economics, 31, 373-393, (2002) · Zbl 1074.62524
[4] Cairns, A.; 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)
[5] Cairns, A.; Blake, D.; Dowd, K., Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk, ASTIN Bulletin, 36, 79, (2006) · Zbl 1162.91403
[6] Cairns, A.; Blake, D.; Dowd, K.; Coughlan, G.; 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, 1-35, (2009)
[7] Campos, J.; Ericsson, N. R.; Hendry, D. F., General-to-Specific Modeling: An Overview and Selected Bibliography, (2005)
[8] Coelho, E.; Nunes, L. C., Forecasting Mortality in the Event of a Structural Change, Journal of the Royal Statistical Society A, 174, 713-736, (2011)
[9] Currie, I.; Durbán, M.; Eilers, P., Smoothing and Forecasing Mortality Rates, Statistical Modelling, 4, 279-298, (2004)
[10] D’Amato, V.; Lorenzo, E. D.; Haberman, S., The Poisson Log-Bilinear Lee-Carter Model: Applications of Efficient Bootstrap Methods to Annuity Analyses, North American Actuarial Journal, 15, 315-333, (2011)
[11] Debón, A.; Martinez-Ruiz, F.; Montes, F., A Geostatistical Approach for Dynamic Life Tables: The Effect of Mortality on Remaining Lifetime and Annuities, Insurance: Mathematics and Economics, 47, 327-336, (2010) · Zbl 1231.91173
[12] Debón, A.; Montes, F.; Mateu, J.; Porcu, E.; Bevilacqua, M., Modelling Residuals Dependence in Dynamic Life Tables: A Geostatistical Approach, Computational Statistics Data Analysis, 52, 3128-3147, (2008) · Zbl 1452.62760
[13] Dowd, K.; Cairns, A.; Blake, D.; Coughlan, G.; Epstein, D.; Khalaf-Allah, M., Evaluating the Goodness of Fit of Stochastic Mortality Models, Insurance: Mathematics and Economics, 47, 255-265, (2010) · Zbl 1231.91179
[14] Dowd, K.; Blake, D.; Cairns, A., Facing Up to Uncertain Life Expectancy: The Longevity Fan Charts, Demography, 47, 67-78, (2010)
[15] Finkelstein, M., Discussing the Strehler-Mildvan Model of Mortality, Demographic Research, 26, 191-206, (2012)
[16] Haberman, S.; Renshaw, A., On Age-Period-Cohort Parametric Mortality Rate Projections, Insurance: Mathematics and Economics, 45, 255-270, (2009) · Zbl 1231.91195
[17] Haberman, S.; Renshaw, A., Parametric Mortality Improvement Rate Modelling and Projecting, Insurance: Mathematics and Economics, 50, 309-333, (2012) · Zbl 1237.91129
[18] Haberman, S.; Renshaw, A., Modelling and Projecting Mortality Improvement Rates Using a Cohort Perspective, Insurance: Mathematics and Economics, 53, 150-168, (2013) · Zbl 1284.91236
[19] Hobcraft, J.; Menken, J.; Preston, S. H., Age, Period and Cohort Effects in Demography: A Review, Population Index, 48, 4-43, (1982)
[20] Huang, J. Z.; Shen, H.; Buja, A., The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions, Journal of the American Statistical Association, 104, 1609-1620, (2009) · Zbl 1205.62072
[21] Human Mortality Database, (2012), Technical University of California, Berkeley, and Max Planck Institute for Demographic Research
[22] Hunt, A.; Blake, D., Identification in Age/Period Mortality Models, (2013)
[23] Hunt, A.; Blake, D., Identification in Age/Period/Cohort Mortality Models, (2013)
[24] Hunt, A.; Blake, D., On the Structure and Classification of Mortality Models, (2013)
[25] Hyndman, R.; Ullah, M., Robust Forecasting of Mortality and Fertility Rates: A Functional Data Approach, Computational Statistics & Data Analysis, 51, 4942-4956, (2007) · Zbl 1162.62434
[26] Koissi, M.; Shapiro, A.; Hognas, G., Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Interval, Insurance: Mathematics and Economics, 38, 1-20, (2006) · Zbl 1098.62138
[27] Lee, R. D., The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications, North American Actuarial Journal, 4, 80-93, (2000) · Zbl 1083.62535
[28] Lee, R. D.; Carter, L. R., Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association, 87, 659-671, (1992) · Zbl 1351.62186
[29] Li, J. S.-H.; Chan, W., Outlier Analysis and Mortality Forecasting: The United Kingdom and Scandinavian Countries, Scandinavian Actuarial Journal, 2005, 187-211, (2005) · Zbl 1092.91050
[30] Li, J. S.-H.; Chan, W.; Cheung, S., Structural Changes in the Lee-Carter Mortality Indexes: Detection and Implications, North American Actuarial Journal, 15, 13-31, (2011)
[31] Liu, X.; Braun, W. J., Investigating Mortality Uncertainty Using the Block Bootstrap, Journal of Probability and Statistics, 1-15, (2010)
[32] Mitchell, D.; Brockett, P.; Mendoza-Arriaga, R.; Muthuraman, K., Modeling and Forecasting Mortality Rates, Insurance: Mathematics and Economics, 52, 275-285, (2013) · Zbl 1284.91259
[33] Murphy, M., The “Golden Generations” in Historical Context, British Actuarial Journal, 15, 151-184, (2009)
[34] O’Hare, C.; Li, Y., Explaining Young Mortality, Insurance: Mathematics and Economics, 50, 12-25, (2012) · Zbl 1235.91102
[35] Pitacco, E.; Denuit, M.; Haberman, S.; Olivieri, A., Modelling Longevity Dynamics for Pensions and Annuity Business, (2009), Oxford: Oxford University Press, Oxford · Zbl 1163.91005
[36] Plat, R., On Stochastic Mortality Modeling, Insurance: Mathematics and Economics, 45, 393-404, (2009) · Zbl 1231.91227
[37] Renshaw, A.; Haberman, S., Lee-Carter Mortality Forecasting with Age-Specific Enhancement, Insurance: Mathematics and Economics, 33, 255-272, (2003) · Zbl 1103.91371
[38] Renshaw, A.; 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
[39] Richards, S. J., Detecting Year-of-Birth Mortality Patterns with Limited Data, Journal of the Royal Statistical Society A, 171, 279-298, (2008)
[40] Shkolnikov, V.; Andreev, E.; Begun, A. Z., Gini Coefficient as a Life Table Function, Demographic Research, 8, 305-358, (2003)
[41] Willets, R., Mortality in the Next Millennium, (1999)
[42] Willets, R., The cohort Effect: Insights and Explanations, British Actuarial Journal, 10, 833-877, (2004)
[43] Wilmoth, J., Variation in Vital Rates by Age, Period and Cohort, Sociological Methodology, 20, 295-335, (1990)
[44] Yang, S. S.; Yue, J. C.; Huang, H., Modeling Longevity Risks Using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models, Insurance: Mathematics and Economics, 46, 254-270, (2010) · Zbl 1231.91254
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