Estimation of Uncertainty in Mortality Projections Using State-Space Lee-Carter Model

Rokas Gylys,Jonas Šiaulys

doi:10.3390/math8071053

Abstract

The study develops alternatives of the classical Lee-Carter stochastic mortality model in assessment of uncertainty of mortality rates forecasts. We use the Lee-Carter model expressed as linear Gaussian state-space model or state-space model with Markovian regime-switching to derive coherent estimates of parameters and to introduce additional flexibility required to capture change in trend and non-Gaussian volatility of mortality improvements. For model-fitting, we use a Bayesian Gibbs sampler. We illustrate the application of the models by deriving the confidence intervals of mortality projections using Lithuanian and Swedish data. The results show that state-space model with Markovian regime-switching adequately captures the effect of pandemic, which is present in the Swedish data. However, it is less suitable to model less sharp but more prolonged fluctuations of mortality trends in Lithuania.

Highlights

Mortality projections are used by insurance companies, pension providers and public policy makers for forecasting expected payments of benefits contingent on human lives as well as their distribution
Which shows that the variability in projected mortality rates can be considered to arise multiplicatively from three sources: variation in constant which represents the increase in mortality with age, variation in trend, mainly driven by the parameter κt, and the remaining random variation
The methods developed in the paper can be used in common mortality modelling situations when there is a major change in mortality development trend or major fluctuations in mortality are observed

Summary

Introduction

Mortality projections are used by insurance companies, pension providers and public policy makers for forecasting expected payments of benefits contingent on human lives (such as insurance benefits and pensions) as well as their distribution. Lee-Carter stochastic mortality model is one of the most popular models applied in practice for forecasting expected human mortality and its distribution. Lee and Carter [1] models mortality rates according to the following formula: log (m x,t ) = α x + κt β x + E x,t , (1). Where m x,t is central mortality rate (ratio of the number of deaths to the exposed to risk) for age x in year t, α x , κt , β x are parameters depending on age x or on year t, and E x,t are independent and identically distributed (i.i.d.) random residuals with zero means. Parameter κt , which might be interpreted as time varying

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