IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v81y2018icp51-70.html
   My bibliography  Save this article

Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland

Author

Listed:
  • Fuino, Michel
  • Wagner, Joël

Abstract

Due to the demographic changes and population aging occurring in many countries, the financing of long-term care (LTC) poses a systemic threat. The scarcity of knowledge about the probability of an elderly person needing help with activities of daily living has hindered the development of insurance solutions that complement existing social systems. In this paper, we consider two models: a frailty level model that studies the evolution of a dependent person through mild, moderate and severe dependency states to death and a type of care model that distinguishes between care received at home and care received in an institution. We develop and interpret the expressions for the state- and time-dependent transition probabilities in a semi-Markov framework. Then, we empirically assess these probabilities using a novel longitudinal dataset covering all LTC needs in Switzerland over a 20-year period. As a key result, we are the first to derive dependence probability tables by acuity level, gender and age for the Swiss population. We find that the transition probabilities differ significantly by gender, age and time spent in the frailty level and type of care states.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:81:y:2018:i:c:p:51-70
    DOI: 10.1016/j.insmatheco.2018.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717305346
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2018.05.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Janssen, J. & de Dominicis, R., 1984. "Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 157-165, July.
    2. Gentili, Elena & Masiero, Giuliano & Mazzonna, Fabrizio, 2017. "The role of culture in long-term care arrangement decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 186-200.
    3. Joan COSTA‐FONT & Christophe Courbage & Katherine Swartz, 2015. "Financing Long‐Term Care: Ex Ante, Ex Post or Both?," Health Economics, John Wiley & Sons, Ltd., vol. 24(S1), pages 45-57, March.
    4. Pitacco, Ermanno, 1995. "Actuarial models for pricing disability benefits: Towards a unifying approach," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 39-62, April.
    5. Jacques Janssen & Raimondo Manca, 2001. "Numerical Solution of non-Homogeneous Semi-Markov Processes in Transient Case," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 271-293, September.
    6. Francesca Colombo, 2012. "Typology of Public Coverage for Long-Term Care in OECD Countries," Palgrave Macmillan Books, in: Joan Costa-Font & Christophe Courbage (ed.), Financing Long-Term Care in Europe, chapter 2, pages 17-40, Palgrave Macmillan.
    7. Jeffrey R. Brown & Amy Finkelstein, 2009. "The Private Market for Long‐Term Care Insurance in the United States: A Review of the Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(1), pages 5-29, March.
    8. Govorun, Maria & Latouche, Guy & Loisel, Stéphane, 2015. "Phase-type aging modeling for health dependent costs," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 173-183.
    9. Karlsson, Martin & Mayhew, Les & Plumb, Robert & Rickayzen, Ben, 2006. "Future costs for long-term care: Cost projections for long-term care for older people in the United Kingdom," Health Policy, Elsevier, vol. 75(2), pages 187-213, January.
    10. 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.
    11. Tian Zhou‐Richter & Mark J. Browne & Helmut Gründl, 2010. "Don't They Care? Or, Are They Just Unaware? Risk Perception and the Demand for Long‐Term Care Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 715-747, December.
    12. Tomas, Julien & Planchet, Frédéric, 2013. "Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 573-589.
    13. Beatrix Eugster & Rafael Lalive & Andreas Steinhauer & Josef Zweimüller, 2011. "The Demand for Social Insurance: Does Culture Matter?," Economic Journal, Royal Economic Society, vol. 121(556), pages 413-448, November.
    14. Luís Meira-Machado & Jacobo Uña-Álvarez & Somnath Datta, 2015. "Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model," Computational Statistics, Springer, vol. 30(2), pages 377-397, June.
    15. Biessy, Guillaume, 2017. "Continuous-Time Semi-Markov Inference Of Biometric Laws Associated With A Long-Term Care Insurance Portfolio," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 527-561, May.
    16. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    17. Tomas, Julien & Planchet, Frédéric, 2015. "Prospective mortality tables: Taking heterogeneity into account," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 169-190.
    18. Jacobo de Uña-Álvarez & Luís Meira-Machado, 2015. "Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study," Biometrics, The International Biometric Society, vol. 71(2), pages 364-375, June.
    19. D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
    20. Helms, Florian & Czado, Claudia & Gschlößl, Susanne, 2005. "Calculation of LTC Premiums Based on Direct Estimates of Transition Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 455-469, November.
    21. Jason Brown & Mark Warshawsky, 2013. "The Life Care Annuity: A New Empirical Examination of an Insurance Innovation That Addresses Problems in the Markets for Life Annuities and Long-Term Care Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 677-704, September.
    22. Czado, Claudia & Rudolph, Florian, 2002. "Application of survival analysis methods to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 395-413, December.
    23. D. J. Pritchard, 2006. "Modeling Disability in Long-Term Care Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 48-75.
    24. Levantesi, Susanna & Menzietti, Massimiliano, 2012. "Managing longevity and disability risks in life annuities with long term care," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 391-401.
    25. Król, Agnieszka & Saint-Pierre, Philippe, 2015. "SemiMarkov: An R Package for Parametric Estimation in Multi-State Semi-Markov Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i06).
    26. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2011. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives," Journal of Finance, American Finance Association, vol. 66(2), pages 519-561, April.
    27. Ji, Min & Hardy, Mary & Li, Johnny Siu-Hang, 2012. "A Semi-Markov Multiple State Model for Reverse Mortgage Terminations," Annals of Actuarial Science, Cambridge University Press, vol. 6(2), pages 235-257, September.
    28. France Weaver, 2012. "Long-Term Care Financing in Switzerland," Palgrave Macmillan Books, in: Joan Costa-Font & Christophe Courbage (ed.), Financing Long-Term Care in Europe, chapter 15, pages 279-299, Palgrave Macmillan.
    29. Joan Costa-Font & Christophe Courbage (ed.), 2012. "Financing Long-Term Care in Europe," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-34919-3, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shemendyuk, Aleksandr & Wagner, Joël, 2024. "On the factors determining the health profiles and care needs of institutionalized elders," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 223-241.
    2. 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.
    3. Michel Fuino & Andrey Ugarte Montero & Joël Wagner, 2022. "On the drivers of potential customers' interest in long‐term care insurance: Evidence from Switzerland," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(3), pages 271-302, September.
    4. Joan Costa-Font & Christophe Courbage & Joël Wagner, 2019. "Long-term care insurance research and trajectory," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(2), pages 179-182, April.
    5. Fuino, Michel & Wagner, Joël, 2020. "Duration of long-term care: Socio-economic factors, type of care interactions and evolution," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 151-168.
    6. Manuel Ventura-Marco & Carlos Vidal-Meliá & Juan Manuel Pérez-Salamero González, 2022. "Life care annuities to help couples cope with the cost of long-term care," Documentos de Trabajo del ICAE 2022-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    7. 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.
    8. Chen, An & Fuino, Michel & Sehner, Thorsten & Wagner, Joël, 2022. "Valuation of long-term care options embedded in life annuities," Annals of Actuarial Science, Cambridge University Press, vol. 16(1), pages 68-94, March.
    9. Ugarte Montero, Andrey & Wagner, Joël, 2023. "On potential information asymmetries in long-term care insurance: A simulation study using data from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 230-241.
    10. 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.
    11. 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.
    12. Ventura-Marco, Manuel & Vidal-Meliá, Carlos & Pérez-Salamero González, Juan Manuel, 2023. "Joint life care annuities to help retired couples to finance the cost of long-term care," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 122-139.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Fuino, Michel & Wagner, Joël, 2020. "Duration of long-term care: Socio-economic factors, type of care interactions and evolution," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 151-168.
    4. 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.
    5. 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.
    6. Chen, An & Fuino, Michel & Sehner, Thorsten & Wagner, Joël, 2022. "Valuation of long-term care options embedded in life annuities," Annals of Actuarial Science, Cambridge University Press, vol. 16(1), pages 68-94, March.
    7. Joan Costa-Font & Martin Karlsson & Henning Øien, 2015. "Informal Care and the Great Recession," CINCH Working Paper Series 1502, Universitaet Duisburg-Essen, Competent in Competition and Health, revised Feb 2015.
    8. M. Martin Boyer & Philippe De Donder & Claude Fluet & Marie-Louise Leroux & Pierre-Carl Michaud, 2020. "Long-Term Care Insurance: Information Frictions and Selection," American Economic Journal: Economic Policy, American Economic Association, vol. 12(3), pages 134-169, August.
    9. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    10. 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.
    11. Joan Costa‐Font & Martin Karlsson & Henning Øien, 2016. "Careful in the Crisis? Determinants of Older People's Informal Care Receipt in Crisis‐Struck European Countries," Health Economics, John Wiley & Sons, Ltd., vol. 25(S2), pages 25-42, November.
    12. 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.
    13. Shang Wu & Hazel Bateman & Ralph Stevens & Susan Thorp, 2022. "Flexible insurance for long‐term care: A study of stated preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 823-858, September.
    14. Hsieh, Ming-hua & Wang, Jennifer L. & Chiu, Yu-Fen & Chen, Yen-Chih, 2018. "Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 246-254.
    15. Baione, Fabio & Levantesi, Susanna, 2014. "A health insurance pricing model based on prevalence rates: Application to critical illness insurance," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 174-184.
    16. M. Martin Boyer & Philippe De Donder & Claude Denys Fluet & Marie-Louise Leroux & Pierre-Carl Michaud, 2018. "A Canadian Parlor Room-Type Approach to the Long-Term Care Insurance Puzzle," CIRANO Working Papers 2018s-13, CIRANO.
    17. D'Amico, Guglielmo & Singh, Shakti & Selvamuthu, Dharmaraja, 2024. "Optimal investment-disinvestment choices in health-dependent variable annuity," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 1-15.
    18. Boumezoued, Alexandre & Karoui, Nicole El & Loisel, Stéphane, 2017. "Measuring mortality heterogeneity with multi-state models and interval-censored data," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 67-82.
    19. Martin Boyer & Philippe De Donder & Claude Fluet & Marie-Louise Leroux & Pierre-Carl Michaud, 2017. "Long-Term Care Insurance: Knowledge Barriers, Risk Perception and Adverse Selection," NBER Working Papers 23918, National Bureau of Economic Research, Inc.
    20. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:81:y:2018:i:c:p:51-70. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.