This paper investigates a high-dimensional vector-autoregressive (VAR) model in mortality modeling and forecasting. We propose an extension of the sparse VAR (SVAR) model fitted on the log-mortality improvements, which we name “spatially penalized smoothed VAR” (SSVAR). By adaptively penalizing the coefficients based on the distances between ages, SSVAR not only allows a flexible data-driven sparsity structure of the coefficient matrix but simultaneously ensures interpretable coefficients including cohort effects. Moreover, by incorporating the smoothness penalties, divergence in forecast mortality rates of neighboring ages is largely reduced, compared with the existing SVAR model. A novel estimation approach that uses the accelerated proximal gradient algorithm is proposed to solve SSVAR efficiently. Similarly, we propose estimating the precision matrix of the residuals using a spatially penalized graphical Lasso to further study the dependency structure of the residuals. Using the UK and France population data, we demonstrate that the SSVAR model consistently outperforms the famous Lee–Carter, Hyndman–Ullah, and two VAR-type models in forecasting accuracy. Finally, we discuss the extension of the SSVAR model to multi-population mortality forecasting with an illustrative example that demonstrates its superiority in forecasting over existing approaches.

In this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

We propose a new inference strategy for general population mortality tables based on annual population and death estimates, completed by monthly birth counts. We rely on a deterministic population dynamics model and establish formulas that link the death rates to be estimated with the observables at hand. The inference algorithm takes the form of a recursive and implicit scheme for computing death rate estimates. This paper demonstrates both theoretically and numerically the efficiency of using additional monthly birth counts for appropriately computing annual mortality tables. As a main result, the improved mortality estimators show better features, including the fact that previous anomalies in the form of isolated cohort effects disappear, which confirms from a mathematical perspective the previous contributions by Richards, Cairns et al., and Boumezoued.

This paper proposes a spatial-temporal autoregressive model for the mortality surface, where mortality rates of each age depend on the historical values of itself (temporality) and the neighbouring ages (spatiality). The mortality dynamics is formulated as a large, first order vector autoregressive model which encompasses standard factor models such as the Lee and Carter (1992) model. Sparsity and smoothness constraints are then introduced, based on the idea that the nearer the two ages, the more important the dependence between mortalities at these ages. Our model has several novelties. First, it ensures that in the long-run, mortality rates at different ages do not diverge. Second, it provides a natural explanation of the so-called cohort effect without identifiability difficulties. Third, the model is easily extended to the multiple-population case in a coherent way. Finally, the model is associated with a closed form, non-parametric estimation method: the penalized least square, which ensures spatial smoothness of the age-dependent parameters. Using US and UK mortality data, we find that our model produces reasonable projected mortality profile in the long-run, as well as satisfying short-run out-of-sample forecast performance.

The aim of the present article was to study the prevalence and the heritability of the initiation of breastfeeding in the Netherlands. The study was carried out in 5,581 participants from the Netherlands Twin Register, and included female twins, their sisters and mothers. All of the participants were born between 1911 and 1991. Breastfeeding was self-reported by the participants, and its prevalence was estimated conditional on birth cohort (born before 1955, 1955–1964, 1965–1974, 1975, or later). To estimate the heritability, we conducted extended twin-family modeling using the SEM package OpenMx in R. Mothers of twins had lower prevalence to initiate breastfeeding and the prevalence of initiation of breastfeeding increased with birth cohort: among mothers of twins 66% in the oldest (pre-1955) to 74% in the youngest (post-1974) and among mothers, who were twins themselves or sisters of twins, 79% in the oldest (pre-1955) to 85% in the youngest (post-1974). When accounting for prevalence differences between mothers of twins and other women, heritability of initiation of breastfeeding was 70%. However, the familial resemblance for sister and mother-daughter pairs was clearly lower than for DZ twin pairs, but as the number of non-twin sisters was relatively low, this observation did not lead to a significant contribution of a special shared twin environment.

Some studies with children have shown that there is no semantic priming at short stimulus onset asynchrony (SOA) in lexical decision and naming tasks for homographs. The predictions of spreading activation theories might explain this missing effect. There may be differences in children's and adults' memory structures. We have explored this hypothesis. The development of memory structure representations for homographs was measured by a Pathfinder algorithm. In Experiment 1, the three dependent variables were: the number of links in the network, closeness measures (C), and distances between nodes. Results revealed developmental differences in network structure representations in adults and children. In Experiment 2, results revealed that these differences were not due to the cohort effect. In Experiment 3, the relationship between associative strength, as measured by associative norms, and distances, as measured by Pathfinder algorithm, was explored. The results of these three experiments and empirical research from semantic priming experiments show that these differences in memory structure representations could be one of the sources of the missing semantic priming effect in children.

This study examined cognitive test performance of second- and third-generation Japanese American (JA) adults, a relatively homogeneous Asian American subgroup. Sixty-five JA and 65 non-Hispanic White (NHW) adults, ages between 45 and 91, were administered the Boston Naming Test-2 (BNT), Letter Fluency Test, Semantic Fluency Test, California Verbal Learning Test (CVLT), Brief Visuospatial Memory Test-Revised (BVMT-R), and Trail Making Test. Levels of acculturation, quality of educational attainment, and generation status in the United States, were also collected. There were no significant differences in the scores between the two groups on the tests administered. JA and NHW groups, however, differed in the patterns of the associations between some of the test performance and demographic variables. JA adults showed a stronger age-score relationship on BNT, CVLT, and the BVMT-R. Furthermore, second-generation JA adults performed lower than the third-generation adults even after controlling for basic demographic variables on CVLT and Trail Making Test. Acculturation on the other hand did not explain score differences once demographic variables were considered. Our results suggest the importance of considering unique history and characteristics of ethnic groups, and interactions of the aging process and culture on tasks with different cognitive demands. (JINS, 2013, 19, 1–9)

We propose a new method for two-dimensional mortality modelling. Our approach smoothes the data set in the dimensions of cohort and age using Bayesian smoothing splines. The method allows the data set to be imbalanced, since more recent cohorts have fewer observations. We suggest an initial model for observed death rates, and an improved model which deals with the numbers of deaths directly. Unobserved death rates are estimated by smoothing the data with a suitable prior distribution. To assess the fit and plausibility of our models we perform model checks by introducing appropriate test quantities. We show that our final model fulfils nearly all requirements set for a good mortality model.

Projections of future mortality typically used for funding pension scheme liabilities assume that future year-on-year decreases in mortality rates will slow rapidly, and that there is very limited potential for further decreases at the oldest ages. This paper considers the consistency of such projections with current trends in life expectancy. Particular focus is paid to whether future mortality should be subject to a minimum level of improvement to reflect general advances in medicine. Care is taken to exclude the additional increases in longevity arising from a concentration of positive health factors amongst the generation who are currently experiencing the ‘cohort effect’.

If historic trends continue into the future, then period life expectancy from age 65 in England & Wales will increase at 26 days p.a. for women and 41 days p.a. for men, with additional increases arising from the ‘cohort effect’. This is a faster rate of period increase in life expectancy than embedded in the interim cohort projections. One way to ensure that actuarial projections keep pace with the population trend is to subject projections to a minimum level of (geometric) improvement of at least 11/4% p.a. for men and 3/4% p.a. for women, at all older ages and in all future years.

Consideration is given to the possible impact of differences between the socio-economic profile of England & Wales and the membership of the pension schemes to whom the projections will be applied ultimately. This paper also highlights that the application of a single minimum value, independent of time and age, simplifies a more complex underlying pattern, but that minimum improvements of 11/4% p.a. for males and 3/4% p.a. for females represent an average of historic improvements in mortality seen in England & Wales.

The paper includes a survey of the history of the low levels of mortality seen currently. The survey includes some discussion on the potential for future improvements and considers topical issues, such as the potential impact of obesity on life expectancy projections (and, in turn, the minimum value applied to improvements).

The financial impact of subjecting projections of mortality improvement to a minimum value is quantified.

The purpose of the report is to achieve a greater understanding of the United Kingdom ‘cohort effect’ by exploring research in other fields and analysing population mortality data by cause of death in more detail. The ‘cohort effect’ in this context is the observed phenomenon that people born in the U.K. between 1925 and 1945 (centred on the generation born in 1931) have experienced more rapid improvement in mortality than generations born either side of this period.

In a Continuous Mortality Investigation (CMI) Bureau working paper published in 2002, a similar trend was noted in the mortality experience of male pensioners and males with life assurance policies. The CMI Bureau investigation showed peak rates of improvement for the cohort born in 1926. Interim projection bases for future mortality experience were produced as a result of the study. The projections made various assumptions about the extent to which the observed cohort effect would continue to shape the pattern of future mortality improvement.

This report suggests that it is highly likely that the cohort effect has been caused by a number of different factors in combination. Prevalence of smoking from one generation to the next has certainly been one such factor. Furthermore, an analysis of patterns of cigarette smoking suggests that there is a degree of inevitability in some element of likely future improvement, especially for mortality at older ages from conditions strongly linked to smoking.

However, trends in heart disease and breast cancer mortality suggest that smoking is not the only factor. The differences between lung cancer and heart disease trends by year of birth are especially interesting. The report shows that there are two ‘sub-cohorts’ of the 1925 to 1945 cohort: an earlier group where the improvements may be largely due to smoking; and a later one where other factors, such as diet in early life, may have played a greater role.

Historic patterns of smoking behaviour by socio-economic class provide an explanation for the five-year difference in the year of birth showing the fastest improvements, i.e. the difference between 1926 for the CMI Bureau investigation and 1931 for the general population. It is also notable that the second ‘sub-cohort’ of high improvement, applying to people born in the early 1940s, can be seen in both population and CMI experience.

A case study examining Japanese mortality experience shows that strong cohort trends can be projected well into old age. This does not provide proof that the U.K. cohort effect will do the same. However, it does counter arguments that year of birth effects will inevitably wear off with age. It is especially interesting given recent epidemiological research linking early life experience with markers of ageing.

There are a number of reasons to believe that the U.K. cohort effect will have an enduring impact on rates of mortality improvement in future decades. These include historical patterns of smoking behaviour and the impact of early life experience on health in later life. There appears to be little evidence to support the idea that the width of the generation experiencing rapid improvement will reduce with time.

The main objective of this paper is to offer a detailed analysis of mortality change in the United Kingdom at the beginning the 21st century. Starting from an exploration of 20th century mortality trends, focusing in particular on the 1990s, underlying forces driving trends in longevity are discussed. These include the ‘cohort effect’ and the ‘ageing of mortality improvement’. International mortality statistics and trends are also analysed. The pace of medical advances is discussed, with specific focus on research into the ageing process and a potential treatment for cardiovascular disease. The paper also discusses the potential threat from infectious diseases.

The analysis of underlying trends suggests that life expectancy in retirement in the U.K. is likely to increase rapidly in the early part of the 21st century. Some scientists are also claiming that we will be seeing the fruits of anti-ageing research within just a few decades.

A core theme of the paper is that future projections should be grounded in as good an understanding of the past as possible. Different methods for projecting future rates of mortality are discussed, and it is noted that emphasis should be placed on the uncertainty surrounding projections.

The financial impact of using different assumptions for future mortality is explored. Significant differences in the cost of an annuity or pension arise from the use of the various projection bases.

Life assurance companies have already declared significant losses as a result of strengthening reserves on annuity portfolios. Taken together, future increases in life expectancy, increasing awareness of the risk of providing longevity insurance, changes in legislation and shortages in market capacity and capital, may well lead to worsening annuity rates.

It is difficult to assess the precise impact of future changes in life expectancy on final salary pension schemes. There is a lack of readily available information on the mortality assumptions being used in practice. It is therefore suggested that more disclosure in this area would be helpful. Employers sponsoring final salary schemes are making promises to their employees that extend up to 70 or 80 years into the future. Actuaries should be clear in spelling out to employers and trustees the nature of the risks behind the promises they are making. Future scheme design should reflect the possibility of substantial increases in life expectancy.

An over-riding implication of the anticipated increases in life expectancy is that people will remain in work for longer in the future. The age at which people retire will inevitably have to increase, and this trend will necessarily drive changes in all aspects of our society. As actuaries we have a vital role in helping to inform the wider debate.

This paper introduces a new framework for modelling the joint development over time of mortality rates in a pair of related populations with the primary aim of producing consistent mortality forecasts for the two populations. The primary aim is achieved by combining a number of recent and novel developments in stochastic mortality modelling, but these, additionally, provide us with a number of side benefits and insights for stochastic mortality modelling. By way of example, we propose an Age-Period-Cohort model which incorporates a mean-reverting stochastic spread that allows for different trends in mortality improvement rates in the short-run, but parallel improvements in the long run. Second, we fit the model using a Bayesian framework that allows us to combine estimation of the unobservable state variables and the parameters of the stochastic processes driving them into a single procedure. Key benefits of this include dampening down of the impact of Poisson variation in death counts, full allowance for paramater uncertainty, and the flexibility to deal with missing data. The framework is designed for large populations coupled with a small sub-population and is applied to the England & Wales national and Continuous Mortality Investigation assured lives males populations. We compare and contrast results based on the two-population approach with single-population results.

An understanding of the cosmic ray modulation of life processes is critical to space exploration, evolution and current medical science. Previous evidence has implicated a role for cosmic rays in US female cancer, involving a possible cross-generational foetal effect. This study explores the global nature of that effect by examining cancer time variations for population cohorts in five countries on three continents. Age–period–cohort analysis was used to separate cohort-related effects from period-related effects, generating time signatures for comparisons among both male and female populations in the United States (US), United Kingdom (UK), Australia (AU), Canada (CA) and New Zealand (NZ). The available cancer mortality data spanned most of the 20th century for US, UK and AU, with shorter periods for CA and NZ. The longest cohort series spanned 1825 to 1965 and exhibited two peaks of higher mortality likelihood approximately 75 years apart in all countries and in both sexes. The constancy of this oscillation on three continents and both hemispheres suggests the presence of a global environmental effect. To explore a possible source for this effect, the birth cohort oscillation is shown to correlate with the variations in background cosmic radiation one generation prior to the birth cohorts. This confirms an earlier study correlating human breast cancer mortality and galactic cosmic rays. A corroborating correlation is also noted between the latitude dependences of cancer incidence in 42 countries and the intensity of background cosmic rays. The role of germ cells as a possible target of this radiation is discussed, emphasizing the amplification that must occur to make this weak radiation relevant to human health. Germ cell timing for this effect has profound implications for evolution, long-distance space travel and the colonization of planets with high background radiation.