Long Term Care and Longevity

Christian Gourieroux and Yang Lu

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 signi cant
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 identi able from only the lifetime data. The methodology is
applied to the mortality data of French males, rst 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.

Keywords: Longevity, Long Term Care (LTC), Semi-Competing Risks, Unobserved
Heterogeneity, Dynam

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