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Identifiability in age/period mortality models

Published online by Cambridge University Press:  02 June 2020

Andrew Hunt Open the ORCID record for Andrew Hunt [Opens in a new window]  and
David Blake
Andrew Hunt*
Affiliation:
Cass Business School, City University London, London, UK
David Blake
Affiliation:
Pensions Institute, Cass Business School, City University London, London, UK
*
*Corresponding author. Pacific Life Re, London. E-mail: andrew.hunt@pacificlifere.com
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Abstract

As the field of modelling mortality has grown in recent years, the number and importance of identifiability issues within mortality models has grown in parallel. This has led both to robustness problems and to difficulties in making projections of future mortality rates. In this paper, we present a comprehensive analysis of the identifiability issues in age/period mortality models in order to first understand them better and then to resolve them. To achieve this, we discuss how these identification issues arise, how to choose identification schemes which aid our demographic interpretation of the models and how to project the models so that our forecasts of the future do not depend upon the arbitrary choices used to identify the historical parameters estimated from historical data.

Keywords

Mortality modellingAge/period modelsIdentificationProjectionC15C51C53
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 461 - 499
Copyright
© Institute and Faculty of Actuaries 2020

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References

Aro, H. & Pennanen, T. (2011). A user-friendly approach to stochastic mortality modelling. European Actuarial Journal 1(S2), 151–167. Available online at the address http://www.springerlink.com/index/10.1007/s13385-011-0030-4CrossRefGoogle Scholar
Booth, H., Maindonald, J. & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325–336. Available online at the address http://www.ncbi.nlm.nih.gov/pubmed/12553330CrossRefGoogle ScholarPubMed
Brouhns, N., Denuit, M. M. & Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005(3), 212–224. Available online at the address http://www.tandfonline.com/doi/abs/10.1080/03461230510009754CrossRefGoogle Scholar
Brouhns, N., Denuit, M. M. & Vermunt, J. (2002a). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373–393.Google Scholar
Brouhns, N., Denuit, M. M. & Vermunt, J. K. (2002b). Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 2, 105–130.Google Scholar
Cairns, A. J. G., Blake, D. & Dowd, K. (2006a). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Cairns, A. J. G., Blake, D. & Dowd, K. (2006b). Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin, 36(1), 79–120.CrossRefGoogle Scholar
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D. & Khalaf-Allah, M. (2011). Mortality density forecasts: an analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48(3), 355–367. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668710001484Google Scholar
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., 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 Journal, 13(1), 1–35.CrossRefGoogle Scholar
Callot, L., Haldrup, N. & Lamb, M. K. (2014). Deterministic and stochastic trends in the Lee-Carter mortality model, technical report, Aarhus University.Google Scholar
Carter, R. & Lee, D. (1992). Modeling and forecasting US sex differentials. International Journal of Forecasting, 8, 393–411.CrossRefGoogle Scholar
Currie, I. D. (2014). On fitting generalized linear and non-linear models of mortality. Scandinavian Actuarial Journal (Forthcoming).Google Scholar
Czado, C., Delwarde, A. & Denuit, M. M. (2005). Bayesian Poisson log-bilinear mortality projections. Insurance: Mathematics and Economics, 36(3), 260–284.Google Scholar
D’Amato, V., Lorenzo, E. D., Haberman, S., Russolillo, M. & Sibillo, M. (2011). The Poisson log-bilinear Lee-Carter model: applications of efficient bootstrap methods to annuity analyses. North American Actuarial Journal, 15(2), 315–333. Available online at the address http://www.soa.org/library/journals/north-american-actuarial-journal/2011/no-2/naaj-2011-vol15-no2-damato.pdfCrossRefGoogle Scholar
Debón, A., Martinez-Ruiz, F., Montes, F., Martínez-Ruiz, F. & Montes, F. (2010). A geostatistical approach for dynamic life tables: the effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327–336. Available online at the address http://dx.doi.org/10.1016/j.insmatheco.2010.07.007http://www.sciencedirect.com/science/article/pii/S0167668710000843Google Scholar
Debón, A., Montes, F., Mateu, J., Porcu, E. & Bevilacqua, M. (2008). Modelling residuals dependence in dynamic life tables: a geostatistical approach. Computational Statistics & Data Analysis, 52(6), 3128–3147. Available online at the address http://www.sciencedirect.com/science/article/pii/S0167947307003040CrossRefGoogle Scholar
Haberman, S. & Renshaw, A., 2009. On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45(2), 255–270.Google Scholar
Haberman, S. & Renshaw, A. (2011.) A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35–55. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668710001022Google Scholar
Haberman, S. & Renshaw, A. (2012). Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics, 50(3), 309–333. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668711001272Google Scholar
Hatzopoulos, P. & Haberman, S. (2009). A parameterized approach to modeling and forecasting mortality. Insurance: Mathematics and Economics, 44(1), 103–123. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668708001340Google Scholar
Human Mortality Database (2014). Human mortality database, technical report, University of California, Berkeley and Max Planck Institute for Demographic Research. Available online at the address www.mortality.orgGoogle Scholar
Hunt, A. & Blake, D. (2014). A general procedure for constructing mortality models. North American Actuarial Journal, 18(1), 116–138. Available online at the address http://www.pensions-institute.org/workingpapers/wp1301.pdfCrossRefGoogle Scholar
Hunt, A. & Blake, D. (2020a). Identifiability in age/period/cohort mortality models. Annals of Actuarial Science (Forthcoming).CrossRefGoogle Scholar
Hunt, A. & Blake, D. (2020b). On the structure and classification of mortality models. North American Actuarial Journal (Forthcoming).CrossRefGoogle Scholar
Hyndman, R. J., Booth, H. & Yasmeen, F. (2013). Coherent mortality forecasting: The product-ratio method with functional time series models. Demography, 50, 261–283.CrossRefGoogle ScholarPubMed
Hyndman, R. J. & Ullah, M. S. (2007). Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51(10), 4942–4956.CrossRefGoogle Scholar
Koissi, M., Shapiro, A. & Hognas, G. (2006). Evaluating and extending the Lee-Carter model for mortality forecasting: bootstrap confidence interval. Insurance: Mathematics and Economics, 38(1), 1–20.Google Scholar
Lee, R. D. & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Li, J. (2014). A quantitative comparison of simulation strategies for mortality projection. Annals of Actuarial Science, 8(02), 281–297. Available online at the address http://www.journals.cambridge.org/abstract{_}S1748499514000153CrossRefGoogle Scholar
Li, N. & Lee, R. D. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography, 42(3), 575–594.CrossRefGoogle ScholarPubMed
Liu, Y. & Li, J. S. -H. (2015). The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds. Insurance: Mathematics and Economics, 64, 135–150. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668715000864Google Scholar
McCullagh, P. & Nelder, J. (1983). Generalized Linear Models. Chapman and Hall, London, UK.CrossRefGoogle Scholar
Mitchell, D., Brockett, P. L., Mendoza-Arriaga, R. & Muthuraman, K. (2013). Modeling and forecasting mortality rates. Insurance: Mathematics and Economics, 52(2), 275–285. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668713000061Google Scholar
Murphy, K. M. & Topel, R. H. (2002). Estimation and inference in two-step econometirc models. Journal of Business & Economic Statistics, 20(1), 88–97.CrossRefGoogle Scholar
Nielsen, B. & Nielsen, J. P. (2014). Identification and forecasting in mortality models. The Scientific World Journal, Article ID 347043.CrossRefGoogle Scholar
Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45(3), 393–404. Available online at the address http://www.sciencedirect.com/science/article/pii/S0167668709000973Google Scholar
Reichmuth, W. & Sarferaz, S. (2008). Bayesian demographic modeling and forecasting: an application to U.S. mortality, technical report, Humbolt University, Berlin.Google Scholar
Renshaw, A. & Haberman, S. (2003a). Lee-Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections. Journal of the Royal Statistical Society: Series C (Applied Statistics), 52(1), 119–137.CrossRefGoogle Scholar
Renshaw, A. & Haberman, S. (2003b). Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255–272.Google Scholar
Renshaw, A. & Haberman, S. (2008). On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling. Insurance: Mathematics and Economics, 42(2), 797–816.Google Scholar
Renshaw, A., Haberman, S. & Hatzopoulos, P. (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2(2), 449–477.CrossRefGoogle Scholar
Renshaw, A. E. & Haberman, S. (2003c). On the forecasting of mortality reduction factors. Insurance: Mathematics and Economics, 32(3), 379–401.Google Scholar
Sithole, T., Haberman, S. & Verrall, R. (2000). An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data. Insurance: Mathematics and Economics, 27(3), 285–312.Google Scholar
Tuljapurkar, S., Li, N. & Boe, C. (2000). A universal pattern of mortality decline in the G7 countries. Nature, 405(6788), 789–792.CrossRefGoogle ScholarPubMed
Villegas, A. M. & Haberman, S. (2014). On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in England. North American Actuarial Journal, 18(1), 168–193. Available online at the address http://www.tandfonline.com/doi/abs/10.1080/10920277.2013.866034CrossRefGoogle Scholar
Wilmoth, J. R. (1990). Variation in vital rates by age, period and cohort. Sociological Methodology, 20, 295–335.CrossRefGoogle Scholar
Yang, S. S., Yue, J. C. & Huang, H. C. (2010). Modeling longevity risks using a principal component approach: a comparison with existing stochastic mortality models. Insurance: Mathematics and Economics, 46(1), 254–270. Available online at the address http://linkinghub.elsevier.com/retrieve/pii/S0167668709001309Google Scholar