Joint mortality modelling and forecasting: a new joint model based on the Wang transform

Mortality models are mathematical approaches used to facilitate understanding and analysis of mortality patterns and trends, and to provide a basis for mortality forecasting. In an environment in which mortality is continuing to decline, there is considerable interest in developing mortality models that are flexible enough to capture variations in mortality by age, time and various other factors, and robust enough to produce reliable forecasts. Over recent years, there has been growing interest in the development of joint mortality models. Joint models aggregate similar populations to jointly fit and forecast mortality. Such models are able to incorporate the relationships among multiple populations and to ensure that forecast relationships remain reasonable over the long-term. However, existing models – both individual and joint – do suffer from shortcomings. This research develops a new model of mortality forecasting - the joint Wang transform (JWT) model - which aims to address shortcomings and improve upon existing models. As a joint model, the JWT model is able to capitalise on information from similar populations and to ensure that sensible relationships are maintained in the forecasts for such populations The JWT model allows for a flexible rate of mortality decline over time, which is more realistic than the fixed rate of mortality decline assumed in other widely-used methods. The JWT model has a simple form, reducing the risk of over-parameterization and of unreliable forecasts. The JWT model has flexibility yet builds in constraints, such as ensuring non-divergence of forecasts and hence appears to be appropriate for modelling and forecasting across multiple populations. This research applies the JWT model and seven existing individual and joint models to fit and forecast the mortality of 13 countries. The joint models are applied by pooling both "across country" separately for each sex, and "across sex" separately for each individual country. Model performance is evaluated by considering goodness of fit, forecasting accuracy, and ability to ensure a sensible relationship between forecasts of similar countries in the long-term (primarily avoiding forecast divergence). In the analyses of both data sets, the JWT model produces the best forecast accuracy of all eight models according to the evaluation measures. While the evaluation has been conducted only for a selection of developed countries and has compared only a selection of models, the strong performance of the JWT model suggests its potential for further use and evaluation.