Abstract
This paper introduces a gender specific model for the joint mortality projection of three countries (England and Wales combined, Scotland, and Northern Ireland) of the United Kingdom. The model, called 2-tier Augmented Common Factor model, extends the classical Lee and Carter [26] and Li and Lee [32] models, with a common time factor for the whole UK population, a sex specific period factor for males and females, and a specific time factor for each country within each gender. As death counts in each subpopulation are modelled directly, a Poisson framework is used. Our results show that the 2-tier ACF model improves the in-sample fitting compared to the use of independent LC models for each subpopulation or of independent Li and Lee models for each couple of genders within each country. Mortality projections also show that the 2-tier ACF model produces coherent forecasts for the two genders within each country and different countries within each gender, thus avoiding the divergence issues arising when independent projections are used. The 2-tier ACF is further extended to include a cohort term to take into account the faster improvements of the UK ‘golden generation’.
Highlights
The last three decades have witnessed tremendous developments in the area of mortality modelling and forecasting, beginning with the Lee-Carter (LC) proposed in [26]
Our results show that the 2-tier augmented common factor model (ACF) model improves the insample fitting compared to the use of independent LC models for each subpopulation or of independent Li and Lee models for each couple of genders within each country
The aim of this paper is to introduce an extension to the ACF model, which we call 2-tier ACF, where a common factor models the trend for the aggregated UK population, a sex specific factor captures the discrepancy between each gender and the total population, and a country/sex specific factor captures the discrepancy of a gender in a specific country from the overall trend of that gender
Summary
The last three decades have witnessed tremendous developments in the area of mortality modelling and forecasting, beginning with the Lee-Carter (LC) proposed in [26]. The aim of this paper is to introduce an extension to the ACF model, which we call 2-tier ACF, where a common factor models the trend for the aggregated UK population, a sex specific factor captures the discrepancy between each gender and the total population, and a country/sex specific factor captures the discrepancy of a gender in a specific country from the overall trend of that gender. This specification ensures to achieve coherence of forecasts in both dimensions - mortality by gender within each country and mortality by country within each gender. Due to the high volatility of mortality rates at the very old ages, we have excluded ages above 100 from the analysis
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