Modeling Mortality with a Bayesian Vector Autoregression

Abstract

Mortality risk models have been developed to capture trends and common factors driving mortality improvement. Multiple factor models take many forms and are often developed and fitted to older ages. In order to capture trends from young ages it is necessary to take into account the richer age structure of mortality improvement from young ages to middle and then into older ages. The Heligman and Pollard (1980) model is a parametric model which captures the main features of period mortality tables and has parameters that are interpreted according to age range and effect on rates. Although time series techniques have been applied to model parameters in various parametric mortality models, there has been limited analysis of parameter risk using Bayesian techniques. This paper uses a Bayesian Vector Autoregressive (BVAR) model for the parameters of the Heligman-Pollard model and fits the model to Australian data. As VARmodels allow for dependence between the parameters of the Heligman-Pollard model they are flexible and better reflect trends in the data, giving better forecasts of the parameters. Forecasts can readily incorporate parameter uncertainty using the models. Bayesian Vector Autoregressive (BVAR) models are shown to significantly improve the forecast accuracy of VAR models for mortality rates based on Australian data. The Bayesian model allows for parameter uncertainty, shown to be a significant component of total risk.

Keywords: mortality, parameter risk, vector auto-regression, Bayesian, Heligman-Pollard model

JEL Classification: J11, C11, G22