Robustness and convergence in the Lee-Carter model with cohort effects

Interest in cohort effects in mortality data has increased dramatically in recent years, with much of the research focused on extensions of the Lee-Carter model incorporating cohort parameters. However, some studies find that these models are not robust to changes in the data or fitting algorithm, which limits their suitability for many purposes. It has been suggested that these robustness problems may be the result of an unresolved identifiability issue. In this paper, after investigating systemically the robustness of cohort extensions of the Lee-Carter model and the convergence of the algorithms used to fit it to data, we demonstrate the existence of such an identifiability issue and propose an additional approximate identifiability constraint which solves many of the problems found.