Mortality Improvement Rates: Modeling, Parameter Uncertainty, and Robustness

Rather than looking at mortality rates directly, a number of recent academic studies have looked at modeling rates of improvement in mortality when making mortality projections. Although relatively new in the academic literature, the use of mortality improvement rates has a long-standing tradition in actuarial practice when allowing for improvements in mortality from standard mortality tables. However, mortality improvement rates are difficult to estimate robustly, and models of them are subject to high levels of parameter uncertainty, because they are derived by dividing one uncertain quantity by another. Despite this, the studies of mortality improvement rates to date have not investigated parameter uncertainty due to the ad hoc methods used to fit the models to historical data. In this study, we adapt the Poisson model for the numbers of deaths at each age and year proposed in Brouhns, Denuit, and Vermunt to model mortality improvement rates. This enables models of improvement rates to be fitted using standard maximum likelihood techniques and allows parameter uncertainty to be investigated using a standard bootstrapping approach. We illustrate the proposed modeling approach using data for the England and Wales population. The methods used in this article are available in the R package iMoMo.