Long Term Care and Longevity.

Summary The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe disability. Because of the significant costs of long term care facilities, it is important to analyze the time spent in long term care, as well as the probability of entering into this state during its lifetime, and how they evolve with longevity. Our paper considers such questions, when lifetime data are available, but long term care data are either unavailable, or too aggregated, or unreliable, as it is usually the case. We specify a joint structural model of long term care and mortality, and explain why parameters of such models are identifiable from only the lifetime data. The methodology is applied to the mortality data of French males, first with a deterministic trend and then with a dynamic factor process. Prediction formulas are then provided and illustrated using the same data. We show in particular that the expected cost of the long term care is increasing less fast than the residual life expectancy at age 50.