Modeling and forecasting duration-dependent mortality rates

Mortality data of disabled individuals are studied and parametric modeling approaches for the force of mortality are discussed. Empirical observations show that the duration since disablement has a strong effect on mortality rates. In order to incorporate duration effects, different generalizations of the Lee–Carter model are proposed. For each proposed model, uniqueness properties and fitting techniques are developed, and parameters are calibrated to mortality observations of the German Pension Insurance. Difficulties with coarse tabulation of the empirical data are solved by an age–period-duration Lexis diagram. Forecasting is demonstrated for an exemplary model, leading to the conclusion that duration dependence should not be neglected. While the data shows a clear longevity trend with respect to age, significant fluctuations but no systematic trend is observed for the duration effects.