Multi-population mortality modelling and forecasting: a hierarchical credibility regression approach
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Multi‑population mortality modelling and forecasting: a hierarchical credibility regression approach Apostolos Bozikas1,2 · Georgios Pitselis1 Received: 17 August 2019 / Revised: 6 July 2020 / Accepted: 24 September 2020 © EAJ Association 2020
Abstract This paper proposes a multi-level hierarchical credibility regression approach to model multi-population mortality data. Future mortality rates are derived using extrapolation techniques, while the forecasting performances between the proposed model, the original Lee–Carter model and two Lee–Carter extensions for multiple populations are compared for both genders of three northern European countries with small populations (Ireland, Norway, Finland). Empirical illustrations show that the proposed method produces more accurate forecasts than the Lee–Carter model and its multi-population extensions. Keywords Multi-level hierarchical credibility regression · Multi-population mortality modelling · Lee–Carter
1 Introduction During the last decades, mortality has significantly declined in most developed countries around the world, mainly due to the continuous improvement of living conditions and the evolution of medical science and technology. Eventually, the decline in mortality creates higher financial responsibilities for governments and annuity providers. Consequently, finding ways to manage the mortality dynamics of a population is a very important step in building a sustainable health and pension system. In this spirit, actuaries and demographers are focused on the development of novel methods to model and forecast the mortality rates of a population. In the literature, several methods have been proposed in order to capture the mortality trends of a population. Lee and Carter [35] presented a pioneer method to forecast the mortality of the total population in the United States, by decomposing
* Apostolos Bozikas [email protected] 1
University of Piraeus, Piraeus, Greece
2
National and Kapodistrian University of Athens, Athens, Greece
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the mortality rates into age and period parameters. Cairns et al. [9] proposed the CBD model, particularly designed for higher ages. We can also find many variations of these methods. To refer to some of them, Renshaw and Haberman [46] extended the Lee–Carter model by including a cohort effect, while Plat [44] proposed a model which combines preferable characteristics of the Lee–Carter [35] and the CBD [9] models. Hyndman and Ullah [31] used functional data analysis and penalized regression splines to model mortality data and Hatzopoulos and Haberman [28, 29] proposed some mortality modelling approaches under the framework of generalized linear models. Moreover, Apicella et al. [2] proposed a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by using an affine model such as the Cox-Ingersoll-Ross process and various out-ofsample validation methods. Since Wilson [58] observed a global convergence in mortality, accountin
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