A Multiple State Model for Disability Using the Decomposition of Death Probabilities and Cross-Sectional Data

ABSTRACT

We split the components corresponding to the disability-free survival probability, and the disability survival probability. Our analysis is conducted for men and women separately, for age groups over 64 years. We discuss the estimation of a multiple state model under several scenarios when only a single survey of cross-sectional data is available. The conclusions are used to discuss the disability level of the Spanish elderly population and are helpful to develop welfare programs and insurance products.

Keywords:

• Disability-free
• Longevity
• Long-term care
• Transition probabilities

Mathematics Subject Classification:

• 62P05
• 91B30

Acknowledgments

The authors are grateful for the valuable suggestion from the participants in the 6th International Congress on Insurance: Mathematics and Economics held in Lisbon, July 15–17, 2002. This work has received support from the Spanish grants FFBVA 2PR01B018 SEJ2004-5052 (M.E.C.) and SEC01-2581.

Notes

Source: Projection of population for 1999 (INE, 1999). Encuesta sobre Discapacidades, Deficiencias y Estado de Salud (INE, 1999).

Source: Projection of population for 1999 (INE, 1999). Encuesta sobre Discapacidades, Deficiencias y Estado de Salud (INE, 1999).

Source: Movimiento Natural de la Población 1999 (INE, 2001).

k ₁ = 0.50; k ₂ = 0.75.

k ₁ = 0.5; k ₂ = 0.5.