Projecting delay and compression of mortality

Abstract

Background: Although mortality delay (the shift of the age-at-death distribution to older ages) and mortality compression (less variability in the age at death) are the key dynamics that drove past mortality trends, they have seldom been included in mortality projections. Objective: We compare the projections of a new parametric mortality model that captures delay and compression of mortality (CoDe) with projections based on the well-known Lee-Carter (LC) model. Data and methods: We compare the two models' properties and in-sample and out-of-sample performance using data from 1960 to 2014 for French, Japanese, and American women and men. Results: The CoDe model has less parameters to describe the shape of the age pattern, but more parameters to describe the changes in the age pattern, provides extrapolation to higher ages, allows to estimate the modal age at death, does not assume the exponential decline of rates across all ages, decomposes the delay and compression effect, and can serve as a diagnostic tool. While the LC model provides a better fit at younger ages, the CoDe model provides a better fit at older ages. The LC model consistently projects a slowdown of mortality delay and thus of the increase in life expectancy at birth, whereas the CoDe model can project a continuation of delay and thus a steady increase in life expectancy. Conclusion: Projecting mortality by including mortality delay and compression can result in better forecast performance than using the LC model, especially when the modal age at death increases linearly.

A Three-Component Approach to Model and Forecast Age-at-Death Distributions

“…On the other hand, the 3C-STAD parameters capture and disentangle the shifting and compression mortality dynamics. The recently proposed model of Bardoutsos et al (2018) is another example of projection methodology that satisfies these features.…”

A validation workflow for mortality forecasting

“…Since the introduction of the Lee-Carter model in 1992 (Lee and Carter, 1992), several extensions have been proposed (Booth et al, 2006;Booth and Tickle, 2008;Basellini et al, 2022). For example, considering the advancement of survival improvements to increasingly older ages (Rau et al, 2008), more recent approaches account for trends in rates of mortality improvement and in the distribution of ages at death (Haberman and Renshaw, 2012;Li et al, 2013;Ševčíková et al, 2016;de Beer et al, 2017;Bardoutsos et al, 2018;Basellini and Camarda, 2019;Camarda, 2019). Other methodological trends in mortality forecasting are to account for health behaviour such as smoking, obesity and alcohol consumption (Vogt et al, 2017;Janssen et al, 2013;Wang and Preston, 2009;Janssen et al, 2021) and for mortality developments in benchmark countries (Li and Lee, 2005;Hyndman et al, 2013;Raftery et al, 2013).…”

Markov-Switching Bayesian Vector Autoregression Model in Mortality Forecasting

“…The methodology described above, which fits a cross-sectional parametric model to mortality data and then forecasts parameter values, has long been used, for example, in McNown and Rogers (1989), Thompson et al (1989), Avraam et al (2014), Njenga and Sherris (2020), Fu et al (2022), and Bardoutsos et al (2018). The fitted parameters help to visualize mortality trends and reveal structural changes.…”

“…The fitted parameters help to visualize mortality trends and reveal structural changes. One approach to mortality projection uses ARIMA models to forecast each parameter separately (see McNown and Rogers (1989), Fu et al (2022), and Bardoutsos et al (2018)). The forecast accuracy can depend on the age-specific parametric model used.…”