Forecasting age distribution of deaths across countries: Life expectancy and annuity valuation

Abstract

In this paper, we provide a comprehensive cross-country validation study of compositional mortality modeling and forecasting methods. Thus, we consider two one-to-one transformations: the cumulative distribution function and the centered log-ratio transformation in compositional data analysis. Between the two transformations, the cumulative distribution function provides a scale-free way to visualize the gender gap and cross-country heterogeneity in the probability of dying by sex and country. Drawing on age-specific period life-table death counts from 24 countries in the Human Mortality Database (2025), we assess and compare the point and interval forecast accuracy of the two transformations, using the same forecasting method. Enhancing the forecast accuracy of period life-table death counts is of significant value to demographers, who rely on such forecasts to estimate survival probabilities and life expectancy, and to actuaries, who use them to price annuities across various entry ages and maturities.

Figures (15)

• Figure 1: Rainbow plots of Australian age-specific life-table death counts from 1921 to 2021 in a single-year group. The oldest years are shown in red, with the most recent years in violet. Curves are ordered chronologically according to the colors of the rainbow.
• Figure 2: Image plot showing time stochastic dominance map between the probabilities of dying between Australian males and females from 1921 to 2021.
• Figure 3: A time series plot of the integral measure of the probabilities of dying between the Australian males and females from 1921 to 2021.
• Figure 4: Image plot showing time stochastic dominance map between the probabilities of dying between the UK and Australian males and females from 1921 to 2021.
• Figure 5: Time series plots of the integral measure of the probabilities of dying between the UK and Australian males and females from 1921 to 2021.