On age-period-cohort parametric mortality rate projections

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract: An augmented version of the Lee-Carter modelling approach to mortality forecasting, extended to include an age modulated cohort index in addition to the standard age modulated period index is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail. Permanent repository link(i) H0: log{mu(x,t)} = alpha(x) + kappa(t) + iota(t-x)(ii) H0: log{mu(x,t)} = alpha(x) + iota(t-x) + kappa(t) (iii) H0: log{mu(x,t)} = kappa(t) + iota(t-x) + alpha(x) England & Wales 1961 male mortality experience, ages 0-99. Linear structure H0: comprising main age-period-cohort effects fitted in different orders, as specified in the above captions. Main age effect (1st column), main period effect (2nd column), main cohort effect (3rd column). Single stage fitting process, with different model formulae. Reduction factor parameter patterns, with beta parameter smoothing. beta vs age period 1961-1997 1965 1970 1975 1980 1985 1990 1995 beta vs age period 1961-1999 1965 1970 1975 1980 1985 1990 1995 1965 1970 1975 1980 1985 1990 1995 -of-birth: 1902, 1910, 1918, 1926, 1934, 1942. 4% annuity a(x,t) 1965 1970 1975 1980 1985 1990 1995 Evolving biennial (1997, 99, 01, 03, 05, 2007) life expectancy and 4% fixed rate annuity predictions, by cohort trajectory: presented in decreasing sequence, for individuals aged 65, 70, 75, 80 respectively.Fig 1.Prediction intervals by bootstrapping the time series prediction error and selecting 2.5, 50, 97.5 percentiles. 4% annuity a(x,t) Evolving biennial (1997, 99, 01, 03, 05, 2007) life expectancy and 4% fixed rate annuity predictions, by cohort trajectory: presented in decreasing sequence, for individuals aged 65, 70, 75, 80 respectively. Prediction intervals by simulation and selecting 2.5, 50, 97.5 percentiles using Algorithm 1 and Algorithm 2, with and without allowance for time series parameter error (pe). 4% annuity a(x,t) 1On age-period-cohort parametric mortality rate projections. AbstractAn augmented version of the Lee-Carter modelling approach to mortality forecasting, extended to include an age modulated cohort index in addition to the standard age modulated period index is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail.

StMoMo: An R Package for Stochastic Mortality Modelling

“…To simulate the period index, κ t , StMoMo implements a multivariate adaptation of Algorithm 2 in Haberman and Renshaw (2009) without provision for parameter error 15 , while to simulate the cohort index, γ t−x , function simulate uses the equivalent S3 method for objects of class "Arima" provided by the package forecast. For example, the code below produces 500 simulated trajectories for the next 50 years of the six stochastic mortality models fitted previously to the England and Wales male mortality experience:…”

On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England

“…The presence of a mild curvature in κ ′ t complicates its forecasting. Although second order ARIMA models should produce good time series fits, Haberman and Renshaw (2009) argue against the use of this approach as it tends to produce excessively wide prediction intervals. Therefore, we instead follow Haberman and Renshaw (2009) and curtail the time series at a perceived point of departure from linearity.…”

StMoMo: An R Package for Stochastic Mortality Modeling

“…In order to simulate the period index, κ t , in package StMoMo we implement a multivariate adaptation of Algorithm 2 in Haberman and Renshaw (2009) without provision for parameter error, 14 while to simulate the cohort index, γ t−x , 15 function simulate uses the equivalent S3 method for objects of class 'Arima' provided by the package forecast. For example, the code below produces 500 simulated trajectories for the next 50 years of the six stochastic mortality models fitted previously to the England and Wales male mortality experience:…”