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Long Term Care and Longevity

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  • Christian Gourieroux

    ()
    (Crest, University of Toronto)

  • Yang Lu

    ()
    (SCOR and Crest)

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    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 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

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-16.

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    Length: 63
    Date of creation: Oct 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-16

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    Related research

    Keywords: Longevity; Long term care (LTC); Semi-competing risks; Unobserved heterogeneity; Dynamic frailty; Affine process; Partial Observability; Identification; Markov chain Monte-Carlo;

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    1. Gourieroux, C. & Monfort, A., 2008. "Quadratic stochastic intensity and prospective mortality tables," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 174-184, August.
    2. Christian Gouriéroux & Yang Lu, 2013. "Love and Death : A Freund Model with Frailty," Working Papers 2013-09, Centre de Recherche en Economie et Statistique.
    3. Darrell Duffie & Andreas Eckner & Guillaume Horel & Leandro Saita, 2009. "Frailty Correlated Default," Journal of Finance, American Finance Association, vol. 64(5), pages 2089-2123, October.
    4. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
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