A Flexible Functional Form Approach to Mortality Modeling : Do We Need Additional Cohort Dummies?

There has been a rapid growth in life expectancy during the past twenty years, resulting in increased pressure on personal and public finances. The increasing amount of attention paid on longevity risk and funding for old has created the needs for precise mortality models and accurate future mortality forecasts. Orthogonal polynomials have been widely used in technical fields but there are very few applications in mortality modeling. In this paper we adopt a flexible functional form approach using two-dimensional Legendre orthogonal polynomials to fit and forecast mortality rates. Unlike the existing mortality models in the literature, the model we propose does not impose any restrictions on the age, time or cohort structure of the data and thus allows for different model designs for different countries' mortality experience. We conduct an empirical study using male mortality data from a range of developed countries and compare our model with well known mortality models in the literature. The fitting results show that the proposed model provides comparable fitting but with a much smaller number of parameters. We also show that the proposed model works well and produces clean residual plots without the incorporation cohort effect. Moreover, based on the 5-year-ahead forecasting results, it can be concluded that our model improves the overall accuracy of the future mortality forecast