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Multistate Actuarial Models of Functional Disability

Author

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  • Joelle H. Fong
  • Adam W. Shao
  • Michael Sherris

Abstract

Long-term-care (LTC) costs are expected to significantly increase over the coming decades as the Baby Boom generation nears retirement. Recent policy discussions in the United State have focused on expanding the private LTC insurance market so as to alleviate some of the pressure on public programs. An important and fundamental input to the pricing of LTC insurance products is a set of age- and sex-specific functional status transition rates that can flexibly take into account alternative benefit trigger specifications. We apply generalized linear models to evaluate disability transitions for individuals in old age based on a large sample of U.S. elderly. We estimate a multistate model for LTC insurance applications and find significant differences in disability rate patterns and levels between our set of estimates and those separately estimated using an earlier approach developed by the Society of Actuaries. Our results suggest that the elderly face a 10% chance of becoming LTC disabled only at ages past 90, rather than in their 80s. Furthermore, age patterns of recovery are found to differ significantly between the sexes. We also show that these estimates of transition probability are sensitive to the definition of “LTC disability,” which has implications for the design of benefit triggers for private and public LTC insurance programs.

Suggested Citation

  • Joelle H. Fong & Adam W. Shao & Michael Sherris, 2015. "Multistate Actuarial Models of Functional Disability," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(1), pages 41-59, January.
  • Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:41-59
    DOI: 10.1080/10920277.2014.978025
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    Cited by:

    1. Carlos Vidal-Meliá & Manuel Ventura-Marco & Juan Manuel Pérez-Salamero González, 2018. "Social Insurance Accounting for a Notional Defined Contribution Scheme Combining Retirement and Long-Term Care Benefits," Sustainability, MDPI, vol. 10(8), pages 1-36, August.
    2. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    3. Xu, Mengyi & Alonso-García, Jennifer & Sherris, Michael & Shao, Adam W., 2023. "Insuring longevity risk and long-term care: Bequest, housing and liquidity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 121-141.
    4. Carlos Vidal-Meliá & Manuel Ventura-Marco & Juan Manuel Pérez-Salamero González, 2018. "Actuarial accounting for a notional defined contribution scheme combining retirement and longterm care benefits," Documentos de Trabajo del ICAE 2018-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    5. Shi, Tianxiang & Lee, Yung-Tsung, 2021. "Prepayment risk in reverse mortgages: An intensity-governed surrender model," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 68-82.
    6. Martin Eling & Omid Ghavibazoo, 2019. "Research on long-term care insurance: status quo and directions for future research," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(2), pages 303-356, April.
    7. Deng, Yuanyuan & Fang, Hanming & Hanewald, Katja & Wu, Shang, 2023. "Delay the Pension Age or Adjust the Pension Benefit? Implications for Labor Supply and Individual Welfare in China," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 1192-1215.
    8. Michael Sherris, 2021. "On Sustainable Aged Care Financing in Australia," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 54(2), pages 275-284, June.
    9. Mengyi Xu & Jennifer Alonso Garcia & Michael Sherris & Adam Shao, 2022. "Insuring Longevity Risk and Long-Term Care: Bequest, Housing and Liquidity," ULB Institutional Repository 2013/340821, ULB -- Universite Libre de Bruxelles.
    10. Jiwook Jang & Siti Norafidah Mohd Ramli, 2018. "Hierarchical Markov Model in Life Insurance and Social Benefit Schemes," Risks, MDPI, vol. 6(3), pages 1-17, June.
    11. Franca Glenzer & Bertrand Achou, 2019. "Annuities, long-term care insurance, and insurer solvency," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(2), pages 252-276, April.
    12. Javier Pla-Porcel & Manuel Ventura-Marco & Carlos Vidal-Meliá, 2017. "How do unisex life care annuities embedded in a pay-as-you-go retirement system affect gender redistribution?," Documentos de Trabajo del ICAE 2017-11, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    13. Guibert, Quentin & Planchet, Frédéric, 2018. "Non-parametric inference of transition probabilities based on Aalen–Johansen integral estimators for acyclic multi-state models: application to LTC insurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 21-36.
    14. William Lim & Gaurav Khemka & David Pitt & Bridget Browne, 2019. "A method for calculating the implied no-recovery three-state transition matrix using observable population mortality incidence and disability prevalence rates among the elderly," Journal of Population Research, Springer, vol. 36(3), pages 245-282, September.
    15. Manuel L. Esquível & Nadezhda P. Krasii & Gracinda R. Guerreiro, 2024. "Estimation–Calibration of Continuous-Time Non-Homogeneous Markov Chains with Finite State Space," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
    16. Long Xia & Lulu Chai & Hanyu Zhang & Zhaohui Sun, 2022. "Mapping the Global Landscape of Long-Term Care Insurance Research: A Scientometric Analysis," IJERPH, MDPI, vol. 19(12), pages 1-19, June.
    17. Mi, Hong & Fan, Xiaodong & Lu, Bei & Cai, Liming & Piggott, John, 2020. "Preparing for population ageing: Estimating the cost of formal aged care in China," The Journal of the Economics of Ageing, Elsevier, vol. 17(C).
    18. Manuel L. Esquível & Gracinda R. Guerreiro & Matilde C. Oliveira & Pedro Corte Real, 2021. "Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care," Risks, MDPI, vol. 9(2), pages 1-17, February.
    19. Qiqi Wang & Katja Hanewald & Xiaojun Wang, 2022. "Multistate health transition modeling using neural networks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 475-504, June.
    20. Shao, Adam W. & Chen, Hua & Sherris, Michael, 2019. "To borrow or insure? Long term care costs and the impact of housing," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 15-34.

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