A Three-Component Approach to Model and Forecast Age-at-Death Distributions

Mortality forecasting has recently received growing interest, as accurate projections of future lifespans are needed to ensure the solvency of insurance and pension providers. Several innovative stochastic methodologies have been proposed in most recent decades, the majority of them being based on age-specific mortality rates or on summary measures of the life table. The age-at-death distribution is an informative life-table function that provides readily available information on the mortality pattern of a population, yet it has been mostly overlooked for mortality projections. In this chapter, we propose to analyse and forecast mortality developments over age and time by introducing a novel methodology based on age-at-death distributions. Our approach starts from a nonparametric decomposition of the mortality pattern into three independent components corresponding to Childhood, Early-Adulthood and Senescence, respectively. We then model the evolution of each component-specific death density with a relational model that associates a time-invariant standard to a series of observed distributions by means of a transformation of the age axis. Our approach allows us to capture mortality developments over age and time, and forecasts can be derived from parameters’ extrapolation using standard time series models. We illustrate our methods by estimating and forecasting the mortality pattern of females and males in two high-longevity countries using data of the Human Mortality Database. We compare the forecast accuracy of our model and its projections until 2050 with three other forecasting methodologies.

New Approaches to the Conceptualization and Measurement of Age and Ageing

People’s views on population ageing are influenced by the statistics that they read about it. The statistical measures in common use today were first developed around a century ago, in a very different demographic environment. For around two decades, we have been studying population ageing and have been arguing that its conventional portrayal is misleading. In this chapter, we summarize some of that research, which provides an alternative picture of population ageing, one that is more appropriate for twenty-first century. More details about our new view of population ageing can be found in. (Sanderson and Scherbov 2019). Population ageing can be measured in different ways. An example of this can found in the UN’s Profiles in Ageing, 2017. One way is to report on the forecasted increase in the number of people 60+ years old in the world.

Using Expert Elicitation to Build Long-Term Projection Assumptions

Most statistical agencies consult with experts in some manner prior to formulating their assumptions about the future. Expert judgment is valuable when there is either a lack of good data, insufficient knowledge about underlying causal mechanisms, or apparent randomness in trends. In this paper, we describe the expert elicitation protocol developed by Statistics Canada in 2018 to inform the development of projection assumptions. The protocol may be useful for projection makers looking to adopt a formal approach to eliciting expert judgments, or for producing probabilistic projections, where it is necessary to obtain plausible estimates of uncertainty for components of population growth.

Stochastic Population Forecasting: A Bayesian Approach Based on Evaluation by Experts

We suggest a procedure for deriving expert based stochastic population forecasts within the Bayesian approach. According to the traditional and commonly used cohort-component model, the inputs of the forecasting procedures are the fertility and mortality age schedules along with the distribution of migrants by age. Age schedules and distributions are derived from summary indicators, such as total fertility rates, male and female life expectancy at birth, and male and female number of immigrants and emigrants. The joint distributions of all summary indicators are obtained based on evaluations by experts, elicited according to a conditional procedure that makes it possible to derive information on the centres of the indicators, their variability, their across-time correlations, and the correlations between the indicators. The forecasting method is based on a mixture model within the Supra-Bayesian approach that treats the evaluations by experts as data and the summary indicators as parameters. The derived posterior distributions are used as forecast distributions of the summary indicators of interest. A Markov Chain Monte Carlo algorithm is designed to approximate such posterior distributions.

Forecasting Origin-Destination-Age-Sex Migration Flow Tables with Multiplicative Components

In this chapter, we show how multiplicative components that capture the underlying structures of migration flow tables can be used to inform forecasts of interstate migration in Australia. For our illustration, we decompose 5-year census migration flow tables by state or territory of origin, state or territory of destination, 5-year age group and sex for seven census time periods from 1981–1986 to 2011–2016. The components are described over time and then fitted with time series models to produce holdout sample forecasts of interstate migration with measures of uncertainty. Goodness-of-fit statistics and calibration are then used to identify the best fitting models. The results of this research provide (i) insights into the different migration patterns of an important aspect of subnational population growth in Australia and (ii) potential inputs for standard or multiregional cohort component projection models.

Post-transitional Demography and Convergence: What Can We Learn from Half a Century of World Population Prospects?

After the Demographic Transition, convergence towards similar fertility and mortality levels, is the prevailing hypothesis in UN World Population Prospects Revisions. This chapter questions this assumption of “weak convergence” comparing actual data with the forecasted fertility, mortality, and migration trends computed by UN over the last half century. The “weak convergence” during 1985–2015 is not confirmed in countries that had a Total Fertility Rate below 2.5 children per woman before 1985. Moreover, in the period 2000–2015 the differences between groups of homogeneous countries actually increase. Further research can identify new regularities in order to predict future trends more accurately.

European Mortality Forecasts: Are the Targets Still Moving?

Many statistical agencies routinely produce population forecasts, and revise these forecasts when new data become available, or when current demographic trends indicate that an update is necessary. When the forecaster strongly revises, from one forecast round to the next one, a forecast for a certain target year (for instance the life expectancy in 2050), this indicates large uncertainty connected to mortality predictions. The aim of this chapter is to shed more light on the uncertainty in mortality forecasts, by analysing the extent to which life expectancy predictions for 2030 and 2050 were revised in subsequent rounds of population forecasts published by statistical agencies in selected countries. It updates and extends earlier work that focused on United Nations and Eurostat forecasts published between 1994 and 2004 (Keilman et al. 2008). There the conclusion was that life expectancy forecasts for 18 European countries for the year 2050 had been revised upwards systematically, by around 2 years on average during the 10-year publication period. A recent analysis based on official population forecasts for Norway published in the period 1999–2018 led to the same conclusion (Keilman 2018). Here we will show that the period of upward revisions seems to have ended for some European countries.

Alternative Forecasts of Danish Life Expectancy

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.

Introduction

Future trends in population size, age structure, regional distribution, and other demographic variables are important for a wide range of planning situations. Hence, many statistical agencies and independent researchers compute demographic forecasts at various levels of detail. The primary aim of this book is to sketch new developments in the field of demographic forecasting. This chapter addresses various issues taken up by the authors of this volume. We discuss deterministic and probabilistic approaches to forecast uncertainty, Bayesian and frequentist perspectives, the role of experts compared to purely data driven methods, and ways to communicate forecast results to the users.

Bayesian Disaggregated Forecasts: Internal Migration in Iceland

Local-level demographic forecasts are in high demand. Constructing local-level forecasts requires confronting the problems of random variation and sparse data. Bayesian methods offer promising solutions to both these problems. We illustrate using the example of inter-regional migration in Iceland.