Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting : a penalized log-likelihood approach
(2007) Statistical Modelling : an international journal — Vol. 7, p. 29-48 (2007)
Files
pdfdocument.pdf
Restricted Access - Adobe PDF
- 222.73 KB
Details
- Authors
- Abstract
- Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp({alpha}x + ßx{kappa}t ). The log of the time series of age-specific death rates is thus expressed as the sum of an age-specific component {alpha}x that is independent of time and another component that is the product of time-varying parameter {kappa}t reflecting the general level of mortality, and an age-specific component ßx that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. This model is fitted to historical data. The resulting estimated {kappa}t 's are then modeled and projected as stochastic time series using standard Box–Jenkins methods. However, the estimated ßx's exhibit an irregular pattern in most cases, and this produces irregular projected life tables. This article demonstrates that it is possible to smooth the estimated ßx's in the Lee–Carter and Poisson log-bilinear models for mortality projection. To this end, penalized least-squares/maximum likelihood analysis is performed. The optimal value of the smoothing parameter is selected with the help of cross validation.
- Affiliations
Louvain School of Management
Citations
Delwarde, A., Eilers, P. H. C., & Denuit, M. (2007). Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting : a penalized log-likelihood approach. Statistical Modelling : an international journal, 7, 29-48. https://doi.org/10.1177/1471082X0600700103 (Original work published 2007)