Lee-Carter Research Articles

Detecting Common Longevity Trends by a Multiple Population Approach

Recently the interest in the development of country and longevity risk models has been growing. The investigation of long-run equilibrium relationships could provide valuable information about the factors driving changes in mortality, in particular across ages and across countries. In order to investigate cross-country common longevity trends, tools to quantify, compare, and model the strength of dependence become essential. On one hand, it is necessary to take into account either the dependence for adjacent age groups or the dependence structure across time in a single population setting—a sort of intradependence structure. On the other hand, the dependence across multiple populations, which we describe as interdependence, can be explored for capturing common long-run relationships between countries. The objective of our work is to produce longevity projections by taking into account the presence of various forms of cross-sectional and temporal dependencies in the error processes of multiple populations, considering mortality data from different countries. The algorithm that we propose combines model-based predictions in the Lee-Carter (LC) framework with a bootstrap procedure for dependent data, and so both the historical parametric structure and the intragroup error correlation structure are preserved. We introduce a model which applies a sieve bootstrap to the residuals of the LC model and is able to reproduce, in the sampling, the dependence structure of the data under consideration. In the current article, the algorithm that we build is applied to a pool of populations by using ideas from panel data; we refer to this new algorithm as the Multiple Lee-Carter Panel Sieve (MLCPS). We are interested in estimating the relationship between populations of similar socioeconomic conditions. The empirical results show that the MLCPS approach works well in the presence of dependence.

Analysis of the Residual Structure of the Lee–Carter Model: The Case of Japanese Mortality

The Lee–Carter (LC) model, developed in the early 1990s, is internationally used for mortality rate projection and risk evaluation. When the LC model is applied to Japanese death rates, however, the residuals of the logarithm of age-specific death rates reveal a time series correlation, and “undulation” is observed in the residual phase on the age and year axes. Previous studies point out the possibility of a cohort effect in Japanese death rates, and one proposes a modified LC model incorporating the death deferred factor. In this paper, taking previous studies into account, we analyze the residual structure involved in the application of the LC model to Japanese death rates and propose the LC-VAR (LC Vector Autoregressive) model, which is an extended LC model, based on this analysis. In addition, we demonstrate examples of the application of the LC-VAR model to pension liability valuation and pricing single net premiums as well as cover the key points in mortality projections.

Testing the sustainability of the Slovenian (PAYG) pension system using the Leeâ Carter method

Assumptions about the future development of people’s longevity have a crucial impact on the long-term sustainability of the public pension system. The use of standard methods to estimate longevity has led to systematically underestimates of increase in longevity. We use the Lee–Carter (LC) model to forecast demographics projections for the Slovenian population which leads to results much closer to the actual development of mortality. The assumptions about people’s longevity made in the latest Eurostat projections from 2008 more closely resemble the results of the LC model than earlier versions of its population projections. However, they still project somewhat lower increases in longevity than our results using LC model. This translates to about 0.9 percentage points higher public pension expenditure in 2060 if we use our results about mortality development in the future instead of the Eurostat assumptions.

Extending the Lee–Carter model: a three-way decomposition

In this paper, we focus on a Multi-dimensional Data Analysis approach to the Lee–Carter (LC) model of mortality trends. In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker3 model. The suggested methodology allows us to obtain combined estimates for the three modes: (1) time, (2) age groups and (3) different populations. From the results obtained by the Tucker3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time-series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model's goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares 10 European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation.

An Empirical Study of Mortality Models in Taiwan

There has been a significant increase in the life expectancies of the Taiwanese population after the end of Second World War. Like in many developed countries, due to the prolonging life expectancy and lower fertility rates, the aging population has now become a major policy concern in Taiwan. The search for feasible methods for modeling the future mortality changes has become a popular issue in Taiwan. The Lee-Carter (LC) model, the reduction factor (RF) model and the age-period-cohort (APC) model are three frequently used methods for modeling future mortality dynamics. In this paper, we introduce these three models and discuss their respective pros and cons. We carry out an empirical study using these models based on Taiwan mortality experience. In addition, we make a comparison analysis of different models with different mortality experience in Japan, England and Wales, and the US.

An Empirical Study of Mortality Models in Taiwan

There has been a significant increase in the life expectancies of the Taiwanese population after the end of Second World War. Like in many developed countries, due to the prolonging life expectancy and lower fertility rates, the aging population has now become a major policy concern in Taiwan. The search for feasible methods for modeling the future mortality changes has become a popular issue in Taiwan. The Lee-Carter (LC) model, the reduction factor (RF) model and the age-period-cohort (APC) model are three frequently used methods for modeling future mortality dynamics. In this paper, we introduce these three models and discuss their respective pros and cons. We carry out an empirical study using these models based on Taiwan mortality experience. In addition, we make a comparison analysis of different models with different mortality experience in Japan, England and Wales, and the US.

Robust forecasting of mortality and fertility rates: A functional data approach

A new method is proposed for forecasting age-specific mortality and fertility rates observed over time. This approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. Ideas from functional data analysis, nonparametric smoothing and robust statistics are combined to form a methodology that is widely applicable to any functional time series data observed discretely and possibly with error. The model is a generalization of the Lee–Carter (LC) model commonly used in mortality and fertility forecasting. The methodology is applied to French mortality data and Australian fertility data, and the forecasts obtained are shown to be superior to those from the LC method and several of its variants.

Longevity and adjustment in pension annuities, with application to Finland

The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model.

Fuzzy formulation of the Lee–Carter model for mortality forecasting

In this paper, a fuzzy formulation of the Lee–Carter [Lee, R.D., Carter, L.R., 1992. Modeling and forecasting U.S. mortality. J. Amer. Statist. Assoc. 419 (87), 659–675] model is proposed. The standard Lee–Carter (LC) model, which uses singular value decomposition, assumes that the errors have a constant variance over all ages. This statement, however, does not often hold. The advantage of such a fuzzy approach is that the errors are viewed as fuzziness of the model structure; hence the homoscedasticity is not an issue.