A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States

Abstract

We compare quantitatively eight stochastic models explaining improvements in mortality rates in England and Wales and in the United States. On the basis of the Bayes Information Criterion (BIC), we find that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males data best, while for U.S. males data, the Renshaw and Haberman (RH) extension to the Lee and Carter model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates under the RH model, calling into question its suitability for forecasting. A different extension to the CBD model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both datasets. This model also shows, for both datasets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects.

StMoMo: An R Package for Stochastic Mortality Modeling

“…This includes the original Lee-Carter model, the extensions of the Lee-Carter proposed in Haberman (2003, 2006), the original CBD model, and the extended CBD models of Cairns et al (2009). In addition, all the model structures considered in Renshaw (2011), Lovász (2011) and Van Berkum, Antonio, and Vellekoop (2016), as well as the models of Plat (2009), Aro andPennanen (2011), O'Hare andLi (2012), Börger, Fleischer, and Kuksin (2013) and Alai and Sherris (2014), are part of the GAPC class of models.…”

“…For this purpose, we use as a running example a comparison of several stochastic mortality models fitted to the England and Wales population. This example is in the spirit of the comparison exercises of Cairns et al (2009) ;Cairns, Blake, Dowd, Coughlan, Epstein, and Khalaf-Allah (2011), Haberman and Renshaw (2011) and Lovász (2011), allowing us to show how several of the analysis performed in these papers can easily be replicated using StMoMo. The structure of the paper is as follows.…”

“…Specifically, it assumes that, for a given year, the logit of the one-year death probability is a linear function of age, and treats the intercept and slope parameters across years as stochastic processes. Cairns et al (2009) considered three extensions to the original CBD model by incorporating combinations of a quadratic age term and a cohort effect term. Plat (2009) combined features of the CBD and the Lee-Carter models to produce a model that is suitable for full age ranges and captures the cohort effect.…”

“…The ilc package (Butt, Haberman, and Shang 2014) implements the Renshaw and Haberman (2006) cohort extension of the Lee-Carter model together with the Lee-Carter model under a Poisson regression framework. The R functions referred to as "LifeMetrics" available at http://www.macs.hw.ac.uk/~andrewc/lifemetrics/ implement the original CBD model and the three extended CBD models considered in Cairns et al (2009), along with the LeeCarter model (using Poisson maximum likelihood), the traditional age-period-cohort model (see , Osmond 1985) and the Renshaw and Haberman (2006) model.…”

Impact of different mortality forecasting methods and explicit assumptions on projected future life expectancy: The case of the Netherlands

“…In addition to the forecasting approach, these include the measure to be forecasted, the specification of an underlying data model, and the specific forecasting method. Among the most important issues that must be taken into account when assessing a forecasting method are the amount of subjectivity, robustness, and whether the outcomes will be logical (e.g., Cairns et al 2009Cairns et al , 2011). An example of a logical outcome is the plausibility of the projected agesex profiles of the death rates.…”