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

Abstract

In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities.

Notes

Delwarde et al. (2006) have considered a similar parametrisation in the simultaneous modeling of mortality in five developed countries.

The seven deprivations domains with their percentage participation in the index are (1) income deprivation (22.5%), (2) employment deprivation (22.5%), (3) health deprivation and disability (13.5%), (4) education, skills, and training deprivation (13.5%), (5) barriers to housing and services (9.3%), (6) crime (9.3%), and (7) living environment deprivation (13.5%).

For example, the stratified Lee-Carter model (11) requires the estimation of k values of α _x , m values of α _g , k values of β _x , and n values of κ _t , totaling 2k+m+n parameters, but since the parameters have to satisfy the constraints ∑ _x β _x =1, ∑ _t κ _t =0, and ∑ _g α _g =0, the effective number of parameters is ν=2k+m+n−3. For the relative model with age-period-cohort reference we take v′ as the number of parameters in the reference population equation (16) less 4 to account for constraints (19)–(21) and (26), and v as the number of parameters that appear exclusively in the subpopulation equation (17) less 2 for constraints (22) and (23).

As opposed to a period approach, a cohort approach makes full allowance for the future evolution of mortality rates. Thus, the annuity rate for an individual of subpopulation g age x in year t is computed using mortality rates μ _xtg , μ _x+1,t+1,g , μ _x+2,t+2,g …, μ_{110,t+110−x,g} .