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Extending the Lee–Carter model: a three-way decomposition

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  • Maria Russolillo
  • Giuseppe Giordano
  • Steven Haberman

Abstract

In this paper, we focus on a Multi-dimensional 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 Tucker3 model. The suggested methodology allows us to obtain combined estimates for the three modes: (1) time, (2) age groups and (3) different populations. From the results obtained by the Tucker3 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 10 European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation.

Suggested Citation

  • Maria Russolillo & Giuseppe Giordano & Steven Haberman, 2011. "Extending the Lee–Carter model: a three-way decomposition," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2011(2), pages 96-117.
    • Handle: RePEc:taf:sactxx:v:2011:y:2011:i:2:p:96-117
    DOI: 10.1080/03461231003611933
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    Cited by:

    1. Francesca Perla & Salvatore Scognamiglio, 2023. "Locally-coherent multi-population mortality modelling via neural networks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 157-176, June.
    2. Zhang, Xuanming & Huang, Fei & Hui, Francis K.C. & Haberman, Steven, 2023. "Cause-of-death mortality forecasting using adaptive penalized tensor decompositions," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 193-213.
    3. Matteo Lizzi, 2024. "A Contrast-Tree-Based Approach to Two-Population Models," Risks, MDPI, vol. 12(10), pages 1-17, September.

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