Long-Term Care and Longevity

Abstract

The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe loss of autonomy. Because of the significant costs of long-term care (LTC) facilities, it is important to analyze the time spent in LTC state, as well as the probability of entering into this state during its lifetime, and how they evolve jointly with longevity across the different cohorts. Our paper considers such questions, when lifetime data are available, but LTC data are either unavailable, or available on too short periods, or too aggregated, or unreliable, as it is frequently the case.

We specify joint structural models of LTC, mortality, and longevity, and explain why parameters of these models are identifiable from only the lifetime data under reasonable assumptions. More precisely, we model the potential entry into LTC as a latent state, which creates a dynamic unobserved heterogeneity in the population when only the lifetime is observed. The methodology is applied to the cohort mortality data of French males, first with a deterministic trend and then with a dynamic and stochastic common latent factor. Prediction formulas for the hypothetical date of entry into LTC or the time spent in this state are then provided and illustrated using the same dataset.

Keywords: Longevity, Long-Term Care (LTC), Semi-Competing Risks, Treatment effect, Unobserved Heterogeneity, Dynamic Frailty, Partial Observability, Identi

JEL Classification: C1