Marius D. Pascariu

The prediction of human longevity levels in the future by direct forecasting of life expectancy offers numerous advantages, compared to methods based on extrapolation of age-specific death rates. However, the reconstruction of accurate life tables starting from a given level of life expectancy at birth, or any other age, is not straightforward. Model life tables have been extensively used for estimating age patterns of mortality in poor-data countries. We propose a new model inspired by indirect estimation techniques applied in demography, which can be used to estimate full life tables at any point in time, based on a given value of life expectancy at birth. Our model relies on the existing high correlations between levels of life expectancy and death rates across ages. The methods presented in this paper are implemented in a publicly available R package.

In the last three decades, considerable progress in mortality forecasting has been achieved, with new and more sophisticated models being introduced. Most of these forecasting models are based on the extrapolation of past trends, often assuming linear (or log-linear) development of mortality indicators, such as death rates or life expectancy. However, this assumption can be problematic in countries where mortality development has not been linear, such as in Denmark. Life expectancy in Denmark experienced stagnation from the 1980s until the mid-1990s. To avoid including the effect of the stagnation, Denmark’s official forecasts are based on data from 1990 only. This chapter is divided into three parts. First, we highlight and discuss some of the key methodological issues for mortality forecasting in Denmark. How many years of data are needed to forecast? Should linear extrapolation be used? Second, we compare the forecast performance of 11 models for Danish females and males and for period and cohort data. Finally, we assess the implications of the various forecasts for Danish society, and, in particular, their implications for future lifespan variability and age at retirement.

The age-at-death distribution is a representation of the mortality experience in a population. Although it proves to be highly informative, it is often neglected when it comes to the practice of past or future mortality assessment. We propose an innovative method to mortality modeling and forecasting by making use of the location and shape measures of a density function, i.e. statistical moments. Time series methods for extrapolating a limited number of moments are used and then the reconstruction of the future age-at-death distribution is performed. The predictive power of the method seems to be net superior when compared to the results obtained using classical approaches to extrapolating age-specific-death rates, and the accuracy of the point forecast (MASE) is improved on average by 33% respective to the state-of-the-art, the Lee–Carter model. The method is tested using data from the Human Mortality Database and implemented in a publicly available R package.

Female and male life expectancies have converged in most industrialized societies in recent decades. To achieve coherent forecasts between females and males, this convergence needs to be considered when forecasting sex-specific mortality. We introduce a model forecasting a matrix of the age-specific death rates of sex ratio, decomposed into two age profiles and time indices—before and after age 45—using principal component analysis. Our model allows visualization of both age structure and general level over time of sex differences in mortality for these two age groups. Based on a prior forecast for females, we successfully forecast male mortality convergence with female mortality. The usefulness of the developed model is illustrated by its comparison with other coherent and independent models in an out-of-sample forecast evaluation for 18 countries. The results show that the new proposal outperformed the other models for most countries.