Using graduation to modify the estimation of Lee-Carter model for small populations. (English) Zbl 1461.91263

Summary: Many mortality models, such as the Lee-Carter model, have unsatisfactory estimation in the case of small populations. Increasing population size is a natural choice to stabilize the estimation, if we can find a larger reference population that has a mortality profile similar to that of the small population. Aggregating historical data of the small populations is a fine candidate for the reference population. However, it is often not feasible in practice and we need to rely on other reference populations. In this study, we explore whether graduation methods can be used if the mortality profile of a small population differs from that of the reference population. To explore the appropriate occasion to use graduation methods, we create several mortality scenarios and similarity types between small and reference populations. We propose combining the graduation methods and mortality models, either graduating mortality rates first or applying the mortality model first, and determine whether they can improve the model fit. We use computer simulation to determine whether the proposed approach has better mortality estimation than the Lee-Carter model and the the Li-Lee model. We found that the Li-Lee model always has smaller estimation errors than the Lee-Carter model, and the proposed approach has smaller estimation errors than the Li-Lee model in most cases.


91G05 Actuarial mathematics
91D20 Mathematical geography and demography
Full Text: DOI


[1] Ahcan, A.; Medved, D.; Olivieri, A.; Pitacco., E., Forecasting mortality for small populations by mixing mortality data, Insurance: Mathematics and Economics, 54, 12-27 (2014)
[2] Booth, H.; Hyndman, R. J.; Tickle, L.; Jong., P. De, Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions, Demographic Research, 15, 289-310 (2006)
[3] Cairns, A. J. G.; Blake, D.; Dowd., K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 4, 687-718 (2006)
[4] Cairns, A. J. G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Khalaf-Allah., M., Bayesian stochastic mortality modelling for two populations, ASTIN Bulletin, 41, 1, 29-59 (2011)
[5] Chen, L.; Cairns, A. J. G.; Kleinow., T., Small population bias and sampling effects in stochastic mortality modelling, European Actuarial Journal, 7, 193-230 (2017) · Zbl 1394.91201
[6] Jarner, S. F.; Kryger, E. M., Modelling adult mortality in small populations: The SAINT model, ASTIN Bulletin, 41, 2, 377-418 (2011) · Zbl 1239.91128
[7] Kimerdorf, G. S.; Jones, D. A., Bayesian graduation, Transactions of the Society of Actuaries, 19, part 1, no. 54, 66-112 (1967)
[8] Klugman, S. A.; Panjer, H. H.; Willmot, G. E., Loss models: From data to decisions (2012), Hoboken, NJ: John Wiley & Sons, Hoboken, NJ · Zbl 1272.62002
[9] Lee, R. D.; Carter., L. R., Modeling and forecasting US mortality, Journal of the American Statistical Association, 87, 419, 659-71 (1992) · Zbl 1351.62186
[10] Lee, W. C., A partial SMR approach to smoothing age-specific rates, Annals of Epidemiology, 13, 2, 89-99 (2003)
[11] Lewis, E. B.; Burger, M. M.; Weber, R., Embryonic development, Part A: Genetics aspects, Control of body segment differentiation in Drosophila by the bithorax gene complex, 269-88 (1982), New York NY: Alan R. Liss, New York NY
[12] Li, N.; Lee., R., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42, 3, 575-94 (2005)
[13] London, R. L., Graduation: The revision of estimates (1985), New Hartford, CT: ACTEX, New Hartford, CT
[14] Renshaw, A. E.; Haberman., S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 3, 3, 556-70 (2006) · Zbl 1168.91418
[15] Wang, H. C.; Jin, S.; Yue, C. J., A simulation study of small area mortality projection, Journal of Population Studies, 45, 121-54 (2012)
[16] Wang, H. C.; Yue, C. J.; Chong., C. T., Mortality models and longevity risk for small populations, Insurance Mathematics and Economics, 78, 351-59 (2018) · Zbl 1400.91254
[17] Wiśniowski, A.; Smith, P. W. F.; Bijak, J.; Raymer, J.; Forster., J. J., Bayesian population forecasting: Extending the Lee-Carter method, Demography, 52, 3, 1035-59 (2015)
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.