Carter Model Research Articles

Modeling and prediction of age-specific mortality rates using the Lee–Carter model

BACKGROUND: High mortality remains one of the most significant health concerns in Russia. One of the priorities of the state policy is to reduce mortality rates among the working-age population and increase life expectancy. Predicting population mortality rates serves as a valuable tool for effectively allocating the available resources. AIM: To perform mathematical modeling and prediction of mortality rates of the population of the Orenburg region using the Lee–Carter model. MATERIAL AND METHODS: The age- and sex-specific mortality rates and the population size of the Orenburg region for the period 1991–2020 was used as a study base. The Lee–Carter method was applied to model and predict population mortality. By deriving key parameters, a random walk model with drift was developed, and an accuracy assessment was performed. RESULTS: The Lee-Carter model has been utilized to analyze the mortality rates of the male population in the Orenburg region. Through this modeling process, an accuracy rate of 87% was achieved, providing a reliable basis for long-term prediction. Mortality forecasts have been generated up to the year 2035, allowing for a comprehensive evaluation of future trends in the region. CONCLUSION: The analysis of the results indicates that the pandemic's impact on population mortality is expected to be short-term. In the upcoming years, the mortality rate of the male population in the Orenburg region is projected to continue decreasing.

Unifying mortality forecasting model: an investigation of the COM–Poisson distribution in the GAS model for improved projections

Forecasting mortality rates is crucial for evaluating life insurance company solvency, especially amid disruptions caused by phenomena like COVID-19. The Lee–Carter model is commonly employed in mortality modelling; however, extensions that can encompass count data with diverse distributions, such as the Generalized Autoregressive Score (GAS) model utilizing the COM–Poisson distribution, exhibit potential for enhancing time-to-event forecasting accuracy. Using mortality data from 29 countries, this research evaluates various distributions and determines that the COM–Poisson model surpasses the Poisson, binomial, and negative binomial distributions in forecasting mortality rates. The one-step forecasting capability of the GAS model offers distinct advantages, while the COM–Poisson distribution demonstrates enhanced flexibility and versatility by accommodating various distributions, including Poisson and negative binomial. Ultimately, the study determines that the COM–Poisson GAS model is an effective instrument for examining time series data on mortality rates, particularly when facing time-varying parameters and non-conventional data distributions.

Structural analysis of reverse mortgages in Taiwan

This study investigated the framework of reverse mortgage (RM) programs in Taiwan, with a particular emphasis on the perspectives of both debtors and creditors. Employing the Lee–Carter model, the research estimated mortality rates in Taiwan while utilizing the theoretical framework to analyze various aspects of RM. House prices were assessed using the house price index as a foundational metric for estimating prices, along with lump-sum loanable amounts and RM considerations. Empirical analysis was conducted on debtors’ loans and incomes and financial institutions’ perspectives. The study delved into parameters such as maximum loanable amounts and income replacement ratios for debtors based on demographic factors such as sex, age, and occupation. Furthermore, the structure of RM programs was scrutinized from the viewpoint of financial institutions, considering factors such as rental income, remaining house value, creditor insurance protection, premium expenses, and creditor profitability. A series of simulations were performed to gauge the effects of different variables on the outcomes. The normal distribution of the house price index (HPI), as verified through the Anderson-Darling (AD) test and Kolmogorov–Smirnov (KS) test, bolstered the theoretical findings. This study’s primary contribution lies in its comprehensive exploration of the structure and advantages of RMs from the dual perspectives of debtors and creditors, a departure from insights from previous research predominantly focused on financial institutions. This research can aid debtors and creditors in evaluating RM programs and making informed decisions regarding asset allocation, thereby facilitating the selection of more suitable programs tailored to debtor characteristics.

A systematic vector autoregressive framework for modeling and forecasting mortality

AbstractRecently, there is a new stream of mortality forecasting research using the vector autoregressive model with different sparse model specifications. They have been shown to be able to overcome some of the limitations of the more traditional factor models such as the Lee–Carter model. In this paper, we propose a more generalized systematic vector autoregressive framework for modeling and forecasting mortality. Under this framework, we progressively increase the sophistication of the diagonal parameters in the autoregressive matrix and formulate a range of model structures in a systematic fashion. They offer much flexibility for capturing the mortality patterns of different populations. The resulting models produce age coherent forecasts, and their parameters are reasonably interpretable for modelers, demographers, and industry practitioners. Using the mortality data of Australia, Japan, New Zealand, and Taiwan, we demonstrate that the proposed approach generates appropriate forecasts of mortality rates and life expectancies and produces very good performance in the fitting and out‐of‐sample analysis.

Modeling and forecasting mortality with economic, environmental and lifestyle variables

AbstractTraditional stochastic mortality models tend to extrapolate, to focus on identifying trends in mortality without explaining them. Those that do link mortality with other variables usually limit themselves to GDP. This article presents a novel stochastic mortality model that incorporates a wide range of variables related to economic, environmental and lifestyle factors to predict mortality. The model uses principal components derived from these variables, extending the Niu and Melenberg (Demography 51(5):1755–1773, 2014) model to variables other than GDP, and is applied to 37 countries from the Human Mortality Database. Model fit is superior to the Lee–Carter model for 18 countries. The forecasting accuracy of the proposed model is better than that of the Niu–Melenberg model for half of the countries analyzed under various jump-off years. The model highlights the importance of economic prosperity and healthy lifestyle choices in improving lifespan, while the effect of environmental variables is mixed. By clarifying the specific contributions of different factors and thus making trade-offs explicit, the model is designed to facilitate scenario building and policy planning.

Adding Shocks to a Prospective Mortality Model

This work proposes a simple model to take into account the annual volatility of the mortality level observed on the scale of a country like France in the construction of prospective mortality tables. By assigning a frailty factor to a basic hazard function, we generalise the Lee–Carter model. The impact on prospective life expectancies and capital requirements in the context of a life annuity scheme is analysed in detail.

Nonlinear Modeling of Mortality Data and Its Implications for Longevity Bond Pricing

Human mortality has been improving faster than expected over the past few decades. This unprecedented improvement has caused significant financial stress to pension plan sponsors and annuity providers. The widely recognized Lee–Carter model often assumes linearity in its period effect as an integral part of the model. Nevertheless, deviation from linearity has been observed in historical mortality data. In this paper, we investigate the applicability of four nonlinear time-series models: threshold autoregressive model, Markov switching model, structural change model, and generalized autoregressive conditional heteroskedasticity model for mortality data. By analyzing the mortality data from England and Wales and Italy spanning the years 1900 to 2019, we compare the goodness of fit and forecasting performance of the four nonlinear models. We then demonstrate the implications of nonlinearity in mortality modeling on the pricing of longevity bonds as a practical illustration of our findings.

Lee–Carter model: assessing the potential to capture gender-related mortality dynamics

AbstractWe investigate the ability of the Lee–Carter model to effectively estimate the gender gap ratio (GGR), the ratio between the male death rates over the female ones, by using a Cox–Ingersoll–Ross (CIR) process to provide a stochastic representation of the fitting errors. The novelty consists in the fact that we use the parameters characterizing the CIR process itself (long-term mean and volatility), in their intrinsic meanings, as quantitative measures of the long-term fitting attitude of the Lee–Carter model and synthetic indicators of the overall risk of this model. The analysis encompasses 25 European countries, to provide evidence-based indications about the goodness of fit of the Lee–Carter model in describing the GGR evolution. We highlight some stylized facts, namely systematic evidence about the fitting bias and the risk of the model across ages and countries. Furthermore, we perform a functional cluster analysis, allowing to capture similarities in the fitting performance of the Lee–Carter model among countries.

Improving mortality forecasting using a hybrid of Lee–Carter and stacking ensemble model

BackgroundMortality forecasting is a critical component in various fields, including public health, insurance, and pension planning, where accurate predictions are essential for informed decision-making. This study introduces an innovative hybrid approach that combines the classical Lee–Carter model with advanced machine learning techniques, particularly the stack ensemble model, to enhance the accuracy and efficiency of mortality forecasts.ResultsThrough an extensive analysis of mortality data from Ghana, the hybrid model’s performance is assessed, showcasing its superiority over individual base models. The proposed hybrid Lee–Carter model with a stack ensemble emerges as a powerful tool for mortality forecasting based on the performance metrics utilized. Additionally, the study highlights the impact of incorporating additional base models within the stack ensemble framework to enhance predictive performance.ConclusionThrough this innovative approach, the study provides valuable insights into enhancing mortality prediction accuracy. By bridging classic mortality modeling with advanced machine learning, the hybrid model offers a powerful tool for policymakers, actuaries, and healthcare practitioners to inform decisions and plan for the future. The findings of this research pave the way for further advancements and improvements in mortality forecasting methodologies, thus contributing to the broader understanding and management of mortality risks in various sectors.

On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems

Runge–Kutta algorithms with adaptive step size control provide reliable tools for the solution of initial value problems. Most widespread within the vast family of Runge–Kutta methods are the diagonally implicit Runge–Kutta (DIRK) methods. In particular, the new low-order explicit last-stage diagonally implicit Runge–Kutta (ELDIRK) methods are investigated, combining implicit schemes with an additional explicit evaluation as an explicit last stage. This results in Butcher tableaus with two solutions of different convergence orders suitable for embedded methods, where the higher-order solution is achieved by additional explicit evaluations. Thus, the iterative solution of non-linear systems is omitted for the additional stage, presenting a major reduction in computational cost for the determination of a local error estimate. The key contribution is the application of the novel Butcher tableaus to phase-field problems, solved with the finite-element method, leading to substantial numerical investigations with an efficient approach for diagonally implicit Runge–Kutta schemes. The most important aspects are the extension towards fourth-order methods, the study of the convergence orders for the ELDIRK schemes, their respective stability regions and computational efficiency. A local error estimator is presented capturing the evolution of the phase-field problems, such that adaptive step size control for the new low-order embedded schemes based on an empirical approach for error estimation is achieved. A suitable parallel algorithm is presented with conclusive two-dimensional phase-field simulations based on a Kobayashi–Warren–Carter model including benchmarks for computational efficiency. The higher-order convergence suggested by the novel schemes is confirmed, and their effective results are demonstrated, resulting in a valuable semi-explicit addition to the family of Runge–Kutta time integration schemes.

Service Quality Preferences Among Customers at Islamic Banks in South Africa

Purpose: The objective of this study is to investigate the service quality preferences of Muslim customers considering demographic factors, specifically gender preferences. Theoretical framework: This study is guided by the dimensions in the SERVQUAL model including an additional dimension related to ‘compliance’ from the Carter Model. Design/Methodology/Approach: A quantitative, cross-sectional study was carried out to examine the preferences of customers concerning service quality at Islamic banks in South Africa. The data was analysed using descriptive and inferential statistics. Findings: The findings from the study show that ‘convenient operating times’, ‘providing prompt service to customers’, ‘having records that are accurate and without errors’, ‘staff keep to promises when timeframes are given regarding services to be complete’, ‘keeping customer information confidential’ ‘staff having the best interest of customers in mind’ and finally ‘the Islamic bank does not take interest on loans given’ are the most important items for both males and females regarding the various dimensions of service quality. The reported results also show no significant difference when it comes to service quality preferences between males and females. Research, Practical & Social implications: The results of this study have several practical implications. Firstly, Islamic banks can increase their market share by tailoring the quality of their service offerings to align with customer preferences. Secondly, Islamic banks should include as part of their advertising campaigns, the specific service quality offering most appealing to customers. Lastly, initiatives towards improving service quality should not be directed to a specific gender, rather initiatives must be inclusive of all customers, as the results of this study found no difference in service quality preferences regarding gender. Originality/Value: This is the first study to consider the role of gender concerning service quality preferences by customers of Islamic banks in South Africa.

The Impact of Service Quality Using the Carter Model on Customer Satisfaction in Indonesian Islamic Banks

This study explores the impact of service quality, as evaluated using the CARTER model, on customer satisfaction at Bank Syariah Indonesia. Among the six initial hypotheses, only two were confirmed, yielding significant insights. Notably, the research revealed that neither sharia compliance nor tangible aspects significantly influenced customer satisfaction. Assurance and empathy also displayed no substantial impact. Conversely, two pivotal factors emerged as major drivers of customer satisfaction: reliability and responsiveness. This intriguing finding may be linked to a recent hacker attack on Bank Syariah Indonesia, which occurred a month before the study, although further research is required to confirm this hypothesis. Despite the rigor of the research procedures, some limitations emerged, including the use of online questionnaires via Google Forms, which hindered detailed explanations to respondents and potentially affected their understanding. Additionally, the study focused exclusively on the service quality components outlined by the CARTER model, neglecting other important variables like trust, awareness, and loyalty. In light of these findings, the study offers vital recommendations. Bank Syariah Indonesia is encouraged to focus more on the various components of the CARTER service quality model to potentially foster higher customer trust and loyalty. Furthermore, the bank should consider introducing flagship programs and comprehensive approaches to enhance customer satisfaction. Future researchers are encouraged to explore additional factors influencing customer satisfaction, such as product quality and brand image, and to expand the sample to include a more diverse range of respondents. In summary, this study summarizes its findings, limitations, and recommendations, providing valuable insights for Bank Syariah Indonesia and future researchers seeking to enhance their understanding of service quality and customer satisfaction in this context.

Should Selection of the Optimum Stochastic Mortality Model Be Based on the Original or the Logarithmic Scale of the Mortality Rate?

Stochastic mortality models seek to forecast future mortality rates; thus, it is apparent that the objective variable should be the mortality rate expressed in the original scale. However, the performance of stochastic mortality models—in terms, that is, of their goodness-of-fit and prediction accuracy—is often based on the logarithmic scale of the mortality rate. In this article, we examine whether the same forecast outcomes are obtained when the performance of mortality models is assessed based on the original and log scales of the mortality rate. We compare four different stochastic mortality models: the original Lee–Carter model, the Lee–Carter model with (log)normal distribution, the Lee–Carter model with Poisson distribution and the median Lee–Carter model. We show that the preferred model will depend on the scale of the objective variable, the selection criteria measure and the range of ages analysed.

Accounting for COVID-19-type shocks in mortality modeling: a comparative study

AbstractMortality shocks such as the one induced by the COVID-19 pandemic have substantial impact on mortality models. We describe how to deal with them in the period effect of the Lee–Carter model. The main idea is to not rely on the usual normal distribution assumption as it is not always justified. We consider a mixture distribution model based on the peaks-over-threshold method, a jump model, and a regime switching model and introduce a modified calibration procedure to account for the fact that varying amounts of data are necessary for calibrating different parts of these models. We perform an extensive empirical study for nine European countries, comparing the models with respect to their parameters, quality of fit, and forecasting performance. Moreover, we define five exemplary scenarios regarding the future development of pandemic-related mortality. As a result of our evaluations, we recommend the peaks-over-threshold approach for applications with a possibility of extreme mortality events.

Excess mortality associated with the COVID-19 pandemic during the 2020 and 2021 waves in Antananarivo, Madagascar

IntroductionCOVID-19-associated mortality remains difficult to estimate in sub-Saharan Africa because of the lack of comprehensive systems of death registration. Based on death registers referring to the capital city of Madagascar,...

A Preliminary Investigation of a Single Shock Impact on Italian Mortality Rates Using STMF Data: A Case Study of COVID-19

Mortality shocks, such as pandemics, threaten the consolidated longevity improvements, confirmed in the last decades for the majority of western countries. Indeed, just before the COVID-19 pandemic, mortality was falling for all ages, with a different behavior according to different ages and countries. It is indubitable that the changes in the population longevity induced by shock events, even transitory ones, affecting demographic projections, have financial implications in public spending as well as in pension plans and life insurance. The Short Term Mortality Fluctuations (STMF) data series, providing data of all-cause mortality fluctuations by week within each calendar year for 38 countries worldwide, offers a powerful tool to timely analyze the effects of the mortality shock caused by the COVID-19 pandemic on Italian mortality rates. This dataset, recently made available as a new component of the Human Mortality Database, is described and techniques for the integration of its data with the historical mortality time series are proposed. Then, to forecast mortality rates, the well-known stochastic mortality model proposed by Lee and Carter in 1992 is first considered, to be consistent with the internal processing of the Human Mortality Database, where exposures are estimated by the Lee–Carter model; empirical results are discussed both on the estimation of the model coefficients and on the forecast of the mortality rates. In detail, we show how the integration of the yearly aggregated STMF data in the HMD database allows the Lee–Carter model to capture the complex evolution of the Italian mortality rates, including the higher lethality for males and older people, in the years that follow a large shock event such as the COVID-19 pandemic. Finally, we discuss some key points concerning the improvement of existing models to take into account mortality shocks and evaluate their impact on future mortality dynamics.

Oxidation behavior and mechanism of Al4O4C powders at 1000–1300 °C

The high temperature non–isothermal and isothermal oxidation behavior of Al4O4C powders were investigated in the temperature range of 1000 to 1300 °C. The phase composition, micro–structure evolution, and the thickness of the oxide scale were characterized. The Al4O4C powders showed a good oxidation resistance at 1000 and 1100 °C, owing to the generation of the dense nanoscale rod–like and worm–like α–Al2O3 layer. Density functional theory (DFT) calculation illustrated that Al4O4C performed a high–temperature stability due to the strong covalent bond. The grain sizes of α–Al2O3 increased evidently at 1200 °C, and the staggered growth of α–Al2O3 particles and their corresponding volume shrinkage dominated the generation of the porous surface structure of oxidized Al4O4C powders. Subsequently, the gas phase diffused quickly through these porous structures, and thus resulted in rapid and complete oxidation of Al4O4C powders at 1300 °C. The isothermal oxidation kinetics of Al4O4C powders can be accurately described by the Carter model, and their corresponding apparent activation energy was calculated to be 350.93 kJ/mol at 1000–1300 °C.

Kualitas Pelayanan Model CARTER Dan Pengaruhnya Terhadap Kepuasan Nasabah Bank Syariah Indonesia Kota Lhokseumawe Dengan Pendekatan SEM-PLS

This study aims to determine the effect of service quality with the CARTER model on customer satisfaction at Bank Syariah Indonesia in the city of Lhokseumawe. The sampling technique used was purposive sampling technique. The number of samples is 100 people who are in the city of Lhokseumawe. The research data were analyzed using PLS-SEM (Partial Least Square – Structural Equation Modeling) with SmartPLS 3 software. The results showed that the service quality of compliance, assurance, reliability, tangibles, empathy, and responsiveness had a positive influence on customer satisfaction of Islamic Banks. Indonesia in the city of Lhokseumawe. Only two variables have a positive and significant effect, namely compliance and responsiveness variables, the remaining four variables, namely assurance, reliability, tangibles, and empathy, have a positive but not significant effect. The implication of this research is to focus on compliance, assurance, reliability, tangibles, empathy, and responsiveness that can affect customer satisfaction at Bank Syariah Indonesia in the city of Lhokseumawe. The results of this study have differences and similarities with previous studies. The difference with previous research is that it uses the measurement of service quality with the Servqual dimension and the similarity that both use the CARTER dimension.

Bayesian model comparison for mortality forecasting

Abstract Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.

Managing Mortality and Aging Risks with a Time-Varying Lee-Carter Model.

Influential existing research has suggested that rather than being static, mortality declines decelerate at young ages and accelerate at old ages. Without accounting for this feature, the forecast mortality rates of the popular Lee-Carter (LC) model are less reliable in the long run. To provide more accurate mortality forecasting, we introduce a time-varying coefficients extension of the LC model by adopting the effective kernel methods. With two frequently used kernel functions, Epanechnikov (LC-E) and Gaussian (LC-G), we demonstrate that the proposed extension is easy to implement, incorporates the rotating patterns of mortality decline and is straightforwardly extensible to multi-population cases. Using a large sample of 15 countries over 1950-2019, we show that LC-E and LC-G, as well as their multi-population counterparts, can consistently improve the forecasting accuracy of the competing LC and Li-Lee models in both single- and multi-population scenarios.