In many policy areas it is essential to use the best estimates of life expectancy, but it is vital to most areas of pension policy. This paper presents the conceptual differences between static period and dynamic cohort mortality tables, estimates the differences in life expectancy for Portugal and Spain, and compares official estimates of both life expectancy estimates for Australia, the United Kingdom, and the United States for 1981, 2010, and 2060. These comparisons reveal major differences between period and cohort life expectancy in and between countries and across years. The implications of using wrong estimates for pension policy, including financial sustainability, are explored.

The Age-Period-Cohort-Improvement (APCI) model is a new addition to the canon of mortality forecasting models. It was introduced by Continuous Mortality Investigation as a means of parameterising a deterministic targeting model for forecasting, but this paper shows how it can be implemented as a fully stochastic model. We demonstrate a number of interesting features about the APCI model, including which parameters to smooth and how much better the model fits to the data compared to some other, related models. However, this better fit also sometimes results in higher value-at-risk (VaR)-style capital requirements for insurers, and we explore why this is by looking at the density of the VaR simulations.

This article proposes a neural-network approach to predict and simulate human mortality rates. This semi-parametric model is capable to detect and duplicate non-linearities observed in the evolution of log-forces of mortality. The method proceeds in two steps. During the first stage, a neural-network-based generalization of the principal component analysis summarizes the information carried by the surface of log-mortality rates in a small number of latent factors. In the second step, these latent factors are forecast with an econometric model. The term structure of log-forces of mortality is next reconstructed by an inverse transformation. The neural analyzer is adjusted to French, UK and US mortality rates, over the period 1946–2000 and validated with data from 2001 to 2014. Numerical experiments reveal that the neural approach has an excellent predictive power, compared to the Lee–Carter model with and without cohort effects.

The mortality data (registered deaths and population size) over the years 1961–2007 for the population of England and Wales and for Scotland were obtained from the Office for National Statistics (ONS) and from the Scottish Registrar General. This paper addresses the following questions:

(i) Is there statistical evidence for a cohort effect (i.e. a generation effect separate from the period effect) being present in the data?

(ii) Do both males and females exhibit similar cohort (generation) effects?

(iii) Are period effects (i.e. the improvement in mortality with time) more significant than cohort effects?

(iv) How should one allow, in forecasts of population mortality, for age, period and cohort effects?

(v) Is it sensible to combine male and female mortality experience to determine the period effect and the cohort effect?

(vi) How do the forecasts for the expectation of life at birth, using the Extended-Lee–Carter-Combined (ELCC) model (described in the paper) differ from the (2008 based) Office of National Statistics (ONS) forecasts of the expectation of life at birth?

Most of the methods of mortality forecasting have been assessed using performance on overall mortality, and few studies address the issue of identifying the appropriate forecasting models for specific causes of deaths. This study analyses trends and forecasts mortality rates for three major causes of death — lung cancer, influenza-pneumonia-bronchitis, and motor vehicle accidents — using Lee–Carter, Booth–Maindonald–Smith, Age-Period-Cohort, and Bayesian models, to assess how far different causes of death need different forecasting methods. Using data from the Twentieth and Twenty-First Century Mortality databases for England and Wales, results show major differences among the different forecasting techniques. In particular, when linearity is the main driver of past trends, Lee–Carter-based approaches are preferred due to their straightforward assumptions and limited need for subjective judgment. When a clear cohort pattern is detectable, such as with lung cancer, the Age-Period-Cohort model shows the best outcome. When complete and reliable historical trends are available the Bayesian model does not produce better results than the other models.

Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee–Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee–Carter age-period-cohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.