Mortality Forecasts Research Articles

Estimation of a semiparametric multiplicative density model

This paper discusses the estimation of a semiparametric structured density model that is very useful in forecasting the density on a region where the data are not observed. The model has many applications in actuarial science and mortality forecasting. It has a multiplicative structure with both parametric and nonparametric components that can be estimated based on the data at hand. The problem of estimating the parametric component is nonstandard since the information about the parametric component can be gathered through the derivative of the nonparametric components that are hard to estimate. We propose a simple procedure of estimating the parametric component, which may be used to construct estimators of the nonparametric components. We show that our estimator is consistent with a certain rate and also that it works quite well for finite sample sizes.

A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes

Mortality forecasts are critically important inputs to the consideration of a range of demographically-related policy challenges facing governments in more developed countries. While methods for jointly forecasting mortality for sub-populations offer the advantage of avoiding undesirable divergence in the forecasts of related populations, little is known about whether they improve forecast accuracy. Using mortality data from ten populations, we evaluate the data fitting and forecast performance of the Poisson common factor model (PCFM) for projecting both sexes’ mortality jointly against the Poisson Lee–Carter model applied separately to each sex. We find that overall the PCFM generates the more desirable results. Firstly, the PCFM ensures that the projected male-to-female ratio of death rates at each age converges to a constant in the long run. Secondly, using out-of-sample analysis, we find that the PCFM provides more accurate projection of the sex ratios of death rates, with the advantage being greater for longer-term forecasts. Thus the PCFM offers a viable and sensible means for coherently forecasting the mortality of both sexes. There are also significant financial implications in allowing for the co-movement of mortality of females and males properly.

Inference pitfalls in Lee–Carter model for forecasting mortality

Forecasting mortality is of importance in managing longevity risks for insurance companies and pension funds. Some widely employed models are the so-called Lee–Carter model and its extensions, which involve a two-step estimation procedure. Empirical findings from using the Lee–Carter model and its extensions prefer an ARIMA(p,1,q) model for modeling the dynamics of the logarithms of mortality rates, which is called mortality index and is a key element in forecasting mortality rates and managing longevity risks. In this paper we prove that the proposed two-step estimation procedure in Lee and Carter (1992) cannot detect the true dynamics of the mortality index in general, which means that future mortality projections based on the two step inference procedure for Lee–Carter model and its extensions are questionable.

Life Cycles and Mortality

In this paper we extend the consumption-investment life cycle model for an uncertain-lived agent, proposed by Richard (1974), to allow for flexible labor supply. We further study the consumption, labor supply and portfolio decisions of an agent facing age-dependent mortality risk, as presented by UK actuarial life tables spanning the time period from 1951-2060 (including mortality forecasts). We find that historical changes in mortality produces significant changes in portfolio investment (more risk taking), labour (decrease of hours) and consumption level (shift to higher level), but no explicit effect on consumption growth was found due to the full insurance against loss of life.

Small Area Forecasts of Cause-Specific Mortality: Application of a Bayesian Hierarchical Model to US Vital Registration Data

SummaryMortality forecasts are typically limited in that they pertain only to national death rates, predict only all-cause mortality or do not capture and utilize the correlation between diseases. We present a novel Bayesian hierarchical model that jointly forecasts cause-specific death rates for geographic subunits. We examine its effectiveness by applying it to US vital statistics data for 1979–2011 and produce forecasts to 2024. Not only does the model generate coherent forecasts for mutually exclusive causes of death, but also it has lower out-of-sample error than alternative commonly used models for forecasting mortality.

Model selection for forecasting mortality rates

The increasing life expectancy, driven mainly by improvements in sanitation, housing and education, is a positive change for individuals and a substantial social achievement but, at the same time, the implications for public spending need to be properly evaluated. Forecasting mortality appears indeed a key issue in different fields of insurance and financial markets as pricing annuity, evaluating mortality-linked securities and quantifying longevity risk. Lee-Carter proposed in 1992 a model widely used in order to forecast mortality rates. Actuarial literature has subsequently provided several extensions with the aim to correct some weaknesses of the original model. The purpose of this paper is to compare a range of both new and existing methodologies proposed over years. The study pays considerable attention to both consistency with historical data and robustness relative to the range of data employed in order to find a good balance between the goodness of fit, the simplicity of the model and the robustness of projections. At this regard, several nested methods are here compared by an application to five different countries and by analyzing several data-sets. Results confirm that some models perform better than others, but no single model can be defined as the best method. Furthermore the original version of Lee-Carter provides a good fit when a cohort effect is not significant leading to the strictest confidence interval.

Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data

The stochastic mortality model given by Lee and Carter (1992) has been used in literature for fitting and forecasting the human mortality. We have modeled mortality rates of Indian population using the Lee-Carter (LC) model based on decade-wise data available separately for Indian female and male populations in the form of life tables for the period 1901-2011. The Singular Value Decomposition (SVD) approach is used for estimation of the parameters of the LC model. Forecasted values of time dependent parameter of the LC model are obtained for next five decades using best fitted auto regressive integrated moving average (ARIMA) model. Forecasted values of life expectancy at different ages with 95% confidence intervals are also reported for the next five decades. As an application, using forecasted mortality rates for the next five decades, net single premium for whole life and term insurance, actuarial present values of life annuities for some selected ages are also evaluated

Incorporating the Bühlmann credibility into mortality models to improve forecasting performances

In this paper, we incorporate the Bühlmann credibility into three mortality models (the Lee–Carter model, the Cairns–Blake–Dowd model, and a linear relational model) to improve their forecasting performances, as measured by the MAPE (mean absolute percentage error), using mortality data for the UK. The results show that the MAPE reduction ratios for the three mortality models with the Bühlmann credibility are all significant. More importantly, the MAPEs under the three mortality models with the Bühlmann credibility are very close to each other for each age and forecast year. Thus, by incorporating the Bühlmann credibility we are able to converge the forecasting MAPEs resulting from the three different mortality models to a lower and more consistent level. Moreover, we provide a credibility interpretation with an individual time trend for age x and a group time trend for all ages. Finally, we apply the forecasted mortality rates both with and without the Bühlmann credibility to the net single premiums of life insurance products, and compare the corresponding MAPEs.

Two‐Dimensional Kernel Smoothing of Mortality Surface: An Evaluation of Cohort Strength

Accurate mortality forecasts are of primary interest to insurance companies, pension providers and government welfare systems owing to the rapid increase in life expectancy during the past few decades. Existing mortality models in the literature tend to project future mortality rates by extracting the observed patterns in the mortality surface. Patterns found in the cohort dimension have received a considerable amount of attention and are included in many models of mortality. However, to our knowledge very few studies have considered an evaluation and comparison of cohort patterns across different countries. Moreover, the answer to the question of how the incorporation of the cohort effect affects the forecasting performance of mortality models still remains unclear. In this paper we introduce a new way of incorporating the cohort effect at the beginning of the estimation stage via the implementation of kernel smoothing techniques. Bivariate standard normal kernel density is used and we capture the cohort effect by assigning greater weights along the diagonals of the mortality surface. Based on the results from our empirical study, we compare and discuss the differences in cohort strength across a range of developed countries. Further, the fitting and forecasting results demonstrate the superior performance of our model when compared to some well‐known mortality models in the literature under a majority of circumstances. Copyright © 2016 John Wiley & Sons, Ltd.

Circulation : Clinical Summaries

<i>Circulation</i> : Clinical Summaries

Modeling Future Cardiovascular Disease Mortality in the United States: National Trends and Racial and Ethnic Disparities.

Accurate forecasting of cardiovascular disease mortality is crucial to guide policy and programming efforts. Prior forecasts often have not incorporated past trends in rates of reduction in cardiovascular disease mortality. This creates uncertainties about future trends in cardiovascular disease mortality and disparities. To forecast US cardiovascular disease mortality and disparities to 2030, we developed a hierarchical bayesian model to determine and incorporate prior age, period, and cohort effects from 1979 to 2012, stratified by age, sex, and race, which we combined with expected demographic shifts to 2030. Data sources included the National Vital Statistics System, Surveillance, Epidemiology, and End Results (SEER) single-year population estimates, and US Bureau of Statistics 2012 national population projections. We projected coronary disease and stroke deaths to 2030, first on the basis of constant age, period, and cohort effects at 2012 values, as is most commonly done (conventional), and then with the use of more rigorous projections incorporating expected trends in age, period, and cohort effects (trend based). We primarily evaluated absolute mortality. The conventional model projected total coronary and stroke deaths by 2030 to increase by ≈18% (67 000 additional coronary deaths per year) and 50% (64 000 additional stroke deaths per year). Conversely, the trend-based model projected that coronary mortality would decrease by 2030 by ≈27% (79 000 fewer deaths per year) and stroke mortality would remain unchanged (200 fewer deaths per year). Health disparities will be improved in stroke deaths but not coronary deaths. After prior mortality trends and expected demographic shifts are accounted for, total US coronary deaths are expected to decline, whereas stroke mortality will remain relatively constant. Health disparities in stroke but not coronary deaths will be improved but not eliminated. These age, period, and cohort approaches offer more plausible predictions than conventional estimates.

A credibility approach of the Makeham mortality law

Interest from life insurers to assess their portfolios’ mortality risk has considerably increased. The new regulation and norms, Solvency II, shed light on the need of life tables that best reflect the experience of insured portfolios in order to quantify reliably the underlying mortality risk. In this context and following the work of Buhlmann and Gisler (A course in credibility theory and its applications. Springer, New York, 2005) and Hardy and Panjer (ASTIN Bull 28(2):269–283, 1998), we propose a credibility approach which consists on reviewing, as new observations arrive, the assumption on the mortality curve. Unlike the methodology considered in Hardy and Panjer (1998) that consists on updating the aggregate deaths we have chosen to add an age structure on these deaths. Formally, we use a Makeham graduation model. Such an adjustment allows to add a structure in the mortality pattern which is useful when portfolios are of limited size so as to ensure a good representation over the entire age bands considered. We investigate the divergences in the mortality forecasts generated by the classical credibility approaches of mortality including Hardy and Panjer (1998) and the Poisson-Gamma model on portfolios originating from various French insurance companies.

Analysis and Forecasting of Population Mortality and Life Lost Trend due to Lung Cancer among Xiamen Residents

背景与目的近年来肺癌发病率和死亡率不断上升，已成为我国恶性肿瘤的首位死因。本研究旨在探讨厦门市居民肺癌死亡和减寿的变化趋势，以期为厦门市肺癌综合防治工作提供依据。方法收集整理2005年-2014年厦门市居民肺癌死亡资料计算死亡率、平均减寿年数（average potential life lost, AYLL）、死亡率年均变化百分比等评价指标，用GM（1, 1）模型对死亡率和AYLL进行预测。结果2005年-2014年，厦门市居民肺癌死亡率28.58/10万，年均上升4.86%，男性死亡率是女性的2.90倍；AYLL为7.8年，存在下降趋势。GM（1, 1）模型预测值与实际值平均相对误差2.16%-8.83%，预测2015年-2019年肺癌死亡率和AYLL值均有所上升。结论厦门市肺癌死亡率逐年升高，未来肺癌死亡率和人均减寿数都有上升趋势，应重视肺癌的预防控制工作。

Evaluation of an Early-Warning System for Heat Wave-Related Mortality in Europe: Implications for Sub-seasonal to Seasonal Forecasting and Climate Services.

Heat waves have been responsible for more fatalities in Europe over the past decades than any other extreme weather event. However, temperature-related illnesses and deaths are largely preventable. Reliable sub-seasonal-to-seasonal (S2S) climate forecasts of extreme temperatures could allow for better short-to-medium-term resource management within heat-health action plans, to protect vulnerable populations and ensure access to preventive measures well in advance. The objective of this study is to assess the extent to which S2S climate forecasts could be incorporated into heat-health action plans, to support timely public health decision-making ahead of imminent heat wave events in Europe. Forecasts of apparent temperature at different lead times (e.g., 1 day, 4 days, 8 days, up to 3 months) were used in a mortality model to produce probabilistic mortality forecasts up to several months ahead of the 2003 heat wave event in Europe. Results were compared to mortality predictions, inferred using observed apparent temperature data in the mortality model. In general, we found a decreasing transition in skill between excellent predictions when using observed temperature, to predictions with no skill when using forecast temperature with lead times greater than one week. However, even at lead-times up to three months, there were some regions in Spain and the United Kingdom where excess mortality was detected with some certainty. This suggests that in some areas of Europe, there is potential for S2S climate forecasts to be incorporated in localised heat–health action plans. In general, these results show that the performance of this climate service framework is not limited by the mortality model itself, but rather by the predictability of the climate variables, at S2S time scales, over Europe.

Phantoms Never Die: Living with Unreliable Population Data

SummaryThe analysis of national mortality trends is critically dependent on the quality of the population, exposures and deaths data that underpin death rates. We develop a framework that allows us to assess data reliability and to identify anomalies, illustrated, by way of example, using England and Wales population data. First, we propose a set of graphical diagnostics that help to pinpoint anomalies. Second, we develop a simple Bayesian model that allows us to quantify objectively the size of any anomalies. Two-dimensional graphical diagnostics and modelling techniques are shown to improve significantly our ability to identify and quantify anomalies. An important conclusion is that significant anomalies in population data can often be linked to uneven patterns of births of people in cohorts born in the distant past. In the case of England and Wales, errors of more than 9% in the estimated size of some birth cohorts can be attributed to an uneven pattern of births. We propose methods that can use births data to improve estimates of the underlying population exposures. Finally, we consider the effect of anomalies on mortality forecasts and annuity values, and we find significant effects for some cohorts. Our methodology has general applicability to other sources of population data, such as the Human Mortality Database.

MODELING LONGEVITY RISK WITH GENERALIZED DYNAMIC FACTOR MODELS AND VINE-COPULAE

AbstractWe present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses generalized dynamic factor models fitted to the differences in the log-mortality rates. We compare their prediction performance with that of models previously described in the literature, including the traditional static factor model fitted to log-mortality rates. We also construct risk measures using vine-copula simulations, which take into account the dependence between the idiosyncratic components of the mortality rates. The methodology is applied to forecast mortality rates for a population portfolio for the UK and to estimate longevity and mortality risks.

Forecasting Longevity Gains for a Population with Short Time Series Using a Structural SUTSE Model: An Application to Brazilian Annuity Plans

In this article, a multivariate structural time series model with common stochastic trends is proposed to forecast longevity gains of a population with a short time series of observed mortality rates, using the information of a related population for which longer mortality time series exist. The state space model proposed here makes use of the seemingly unrelated time series equation and applies the concepts of related series and common trends to construct a proper model to predict the future mortality rates of a population with little available information. This common trends approach works by assuming the two populations’ mortality rates are affected by common factors. Further, we show how this model can be used by insurers and pension funds to forecast mortality rates of policyholders and beneficiaries. We apply the proposed model to Brazilian annuity plans where life expectancies and their temporal evolution are predicted using the forecast longevity gains. Finally, to demonstrate how the model can be used in actuarial practice, the best estimate of the liabilities and the capital based on underwriting risk are estimated by means of Monte Carlo simulation. The idiosyncratic risk effect in the process of calculating an amount of underwriting capital is also illustrated using that simulation.

Dynamics and forecast of morbidity and mortality from prostate cancer in St. Petersburg

The paper presents the characteristics of primary disease incidence, prevalence and mortality from prostate cancer among men's population of St. Petersburg (normal and age-standardized rates); analyzed their dynamics for 20 years; shows the calculated trend of these indicators up to 2020.

Bayesian Poisson log-bilinear models for mortality projections with multiple populations

Life insurers, pension funds, health care providers and social security institutions face increasing expenses due to continuing improvements of mortality rates. The actuarial and demographic literature has introduced a myriad of (deterministic and stochastic) models to forecast mortality rates of single populations. This paper presents a Bayesian analysis of two related multi-population mortality models of log-bilinear type, designed for two or more populations. Using a larger set of data, multi-population mortality models allow joint modelling and projection of mortality rates by identifying characteristics shared by all subpopulations as well as sub-population specific effects on mortality. This is important when modeling and forecasting mortality of males and females, regions within a country and when dealing with index-based longevity hedges. Our first model is inspired by the two factor Lee & Carter model of Renshaw and Haberman (2003) and the common factor model of Carter and Lee (1992). The second model is the augmented common factor model of Li and Lee(2005). This paper approaches both models in a statistical way, using a Poisson distribution for the number of deaths at a certain age and in a certain time period. Moreover, we use Bayesian statistics to calibrate the models and to produce mortality forecasts. We develop the technicalities necessary for Markov Chain Monte Carlo ([MCMC]) simulations and provide software implementation (in R) for the models discussed in the paper. Key benefits of this approach are multiple. We jointly calibrate the Poisson likelihood for the number of deaths and the times series models imposed on the time dependent parameters, we enable full allowance for parameter uncertainty and we are able to handle missing data as well as small sample populations. We compare and contrast results from both models to the results obtained with a frequentist single population approach and a least squares estimation of the augmented common factor model.

Impact of Economic Conditions and Crises on Mortality and its Predictability.

To investigate how economic conditions and crises affect mortality and its predictability in industrialized countries, we review the related literature, and we forecast mortality developments in Spain, Hungary, and Russia—three countries which have recently undergone major transformation processes following the introduction of radical economic and political reforms. The results of our retrospective mortality forecasts from 1991 to 2009 suggest that our model can capture major changes in long-term mortality trends, and that the forecast errors it generates are usually smaller than those of other well-accepted models, like the Lee-Carter model and its coherent variant. This is because our approach is capable of modeling (1) dynamic shifts in survival improvements from younger to older ages over time, as well as (2) substantial changes in long-term trends by optionally complementing the extrapolated mortality trends in a country of interest with those of selected reference countries. However, the forecasting performance of our model is limited (like that of every model): e.g., if mortality becomes extremely volatile—as was the case in Russia after the dissolution of the Soviet Union—generating a precise forecast will depend more on luck than on methodology and expert judgment. In general, we conclude that, on their own, recent economic changes appear to have minor effects on life expectancy in industrialized countries, but that the effects of these changes are greater if they occur in conjunction with other major social and political changes.