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Modelling and forecasting mortality improvement rates with random effects

Renshaw, A. E. & Haberman, S. ORCID: 0000-0003-2269-9759 (2021). Modelling and forecasting mortality improvement rates with random effects. European Actuarial Journal, 11(2), pp. 381-412. doi: 10.1007/s13385-021-00274-1


A common feature in the modelling and extrapolation of the trends in mortality rates over time, based on fitted parametric structures, has tended to involve the treatment of a structured fitted main effects period component (with possibly a cohort component) as a random effects time series. In this paper, we follow the lead of Haberman and Renshaw (Insurance Math Econ 50:309–333, 2012) and other authors in modelling and forecasting mortality improvement rates over time, rather than mortality rates. In this context, we assume linear parametric structures for mortality improvement rates, and we examine the feasibility of modelling the main period effects (and possibly any cohort effects) as a random effect from the outset. We argue that this leads to a more unified approach to model fitting and extrapolation.

Publication Type: Article
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Publisher Keywords: Mortality improvements, Random efects modelling, Hierarchical generalised linear modelling, Age heteroscedasticity, Mortality forecasting
Subjects: G Geography. Anthropology. Recreation > GF Human ecology. Anthropogeography
H Social Sciences > HD Industries. Land use. Labor
H Social Sciences > HF Commerce
H Social Sciences > HN Social history and conditions. Social problems. Social reform
Departments: Bayes Business School > Actuarial Science & Insurance
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