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Extending the Lee Carter Model: a Three-way Decomposition

Russolillo, M., Giordano, G. & Haberman, S. (2011). Extending the Lee Carter Model: a Three-way Decomposition. Scandinavian Actuarial Journal, 2011(2), pp. 96-117. doi: 10.1080/03461231003611933


In this paper, we focus on a Multidimensional Data Analysis approach to the Lee-Carter (LC) model of mortality trends . In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker 3 model. The suggested methodology allows us to obtain combined estimates for the three modes: i) time, ii) agegroups and iii) different populations. From the results obtained by the Tucker 3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model’s goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares ten European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Scandinavian Actuarial Journal on 2011, available online:
Publisher Keywords: Biplot, Mortality Forecasting, Singular Value Decomposition, Tucker3 model.
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:
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