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International Tax and Public Finance

Erschienen in:

03.07.2019

Long-term care and myopic couples

verfasst von: Justina Klimaviciute

Erschienen in: International Tax and Public Finance | Ausgabe 1/2020

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Abstract

The paper proposes a theoretical model of long-term care (LTC) issues in the context of elderly spouses and studies public LTC policy optimal in that case. In particular, it focuses on myopia about the negative health effects of caregiving burden and, relatedly, on the interaction between this burden and the two spouses’ insurance coverage. Myopia results in an inefficiently high caregiving effort of the woman, who is the caregiver in the model. While under full information a linear caregiving tax can implement the first-best, unobservability of the woman’s caregiving might require the use of LTC insurance subsidies. Interestingly, myopia about negative caregiving effects implies a subsidy on the man’s but a tax on the woman’s insurance premium. Paradoxically, insurance against the woman’s LTC risk may be at odds with the protection of her health, which questions the popular tendency to emphasize more the importance of LTC insurance for women than for men.

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For instance, around half of all LTC users in the OECD countries are over 80 years old (Colombo et al. 2011).

A 90% increase is predicted assuming that age-specific disability rates will decline in the future, while a 115% increase is expected if these rates remain constant (European Commission 2009).

See, for instance, Colombo et al. (2011), Mausbach et al. (2007), Sansoni et al. (2004), and Shaw et al. (1999).

According to a survey in the USA, 88% of men and 72% of women expect that if they become disabled, their spouse will be their primary caregiver; 90% of men and 94% of women think that they will become primary caregivers if their spouse loses autonomy (The MetLife Mature Market Institute and AARP Health Care Options 2004).

See, for instance, American Council of Life Insurers (2014) and EHB Insurance Group (2010).

Elder Law Answers (2013) and Life Resources Group LLC (2015).

See the references in the two footnotes above.

For instance, life expectancy at birth of women in the EU member states was on average 82.2 years in 2012, compared with 76.1 years for men, which makes the gender gap of 6.1 years. The gender gap in life expectancy at age 65 was on average 3.6 years (OECD 2014b).

The difference between the man’s and the woman’s age in industrialized countries tends to be 2–3 years on average (OECD 2014a).

For instance, in the USA, 73% of men aged 75–84 were married in 2010, compared with only 38% of women. In contrast, 50% of women were widowed, compared with only 17% of men (Federal Interagency Forum on Aging-Related Statistics 2012). In addition, a study of nine European countries (Belgium, Czech Republic, Germany, Finland, France, Italy, Netherlands, Portugal and UK) has shown that in 2000, on average in these countries, 69% of disabled men aged 75–84 were married and 21% widowed, while among disabled women in the same age group only 25% were married and even 61% were widowed. The study has also provided a projection for the year 2030 according to which these differences between men and women should decrease but still remain considerable (Gaymu et al. 2008). Some more evidence can be found in the French data according to which 2 out of 3 dependent men had a healthy spouse in 2000, compared with only 1 dependent woman out of 4 (Duée and Rebillard 2006).

This result is somewhat similar in nature to Leroux (2011) where it is shown that when effort for increasing longevity is not contractible and not observable, then one way to correct that problem is to tax saving.

Even though the woman never becomes dependent in the first period, it is assumed that she can purchase LTC insurance (for the second period) only before the beginning of the first period and not later. An explanation for this could be that, even though she is still autonomous, in the first period the woman is already old and thus might be already ineligible for insurance because of her age and/or her health history (e.g. she might have had a stroke, etc).

In the case of autonomy, all the variables have a superscript “I” standing for “independence” as opposed to “dependence.

For simplicity, it is assumed that the utility functions of the two partners are the same when they are autonomous and when they are dependent. More generally, these functions could be assumed to be different, but this would not change the main results.

It can be argued that in the presence of unequal longevities, the use of classical utilitarianism might not be appropriate since it tends to redistribute resources from the short-lived towards the long-lived (see e.g. Leroux and Ponthière 2013). Leroux and Ponthière (2013) propose a remedy consisting in monetizing the advantage of a longer life and counting it as a part of the long-lived agents’ consumption. However, things are even more complicated in the present setting since the additional period of life is a period where the long-lived agent (the wife) can become dependent. Therefore, for simplicity, the analysis sticks to the classical utilitarian approach.

Equation (9) is obtained using Eq. (8) and the fact that \(\frac{\partial c_\mathrm{m}^{I}}{\partial s^{I}}+\frac{\partial c_\mathrm{f}^{I}}{\partial s^{I}}=-1\) which is proved in Appendix A.

Equation (12) is obtained using Eq. (11) and the fact that \(\frac{\partial c_\mathrm{m}^{D}}{\partial s^{D}}+\frac{\partial c_\mathrm{f}^{D}}{\partial s^{D}}=-1\) which is proved in Appendix A.

For this, we need to use Eqs. (11) and (12) and the fact that \(\frac{\partial c_\mathrm{m}^{D}}{\partial a_\mathrm{f}}+\frac{\partial c_\mathrm{f}^{D}}{\partial a_\mathrm{f}}=h^{\prime }(a_\mathrm{f})\) which is proved in Appendix A.

Equation (15) is obtained using the envelope theorem, Eqs. (8) and (11) and the fact (proved in Appendix A) that \(\frac{\partial c_\mathrm{m}^{I}}{\partial B_\mathrm{m}}+\frac{\partial c_\mathrm{f}^{I}}{\partial B_\mathrm{m}}=-\pi _\mathrm{m}\) and \(\frac{\partial c_\mathrm{m}^{D}}{\partial B_\mathrm{m}}+\frac{\partial c_\mathrm{f}^{D}}{\partial B_\mathrm{m}}=1-\pi _\mathrm{m}\).

Equation (16) is obtained using the envelope theorem, Eqs. (8) and (11) and the fact (proved in Appendix A) that \(\frac{\partial c_\mathrm{m}^{I}}{\partial B_\mathrm{f}}+\frac{\partial c_\mathrm{f}^{I}}{\partial B_\mathrm{f}}=-\pi _\mathrm{f}\) and \(\frac{\partial c_\mathrm{m}^{D}}{\partial B_\mathrm{f}}+\frac{\partial c_\mathrm{f}^{D}}{\partial B_\mathrm{f}}=-\pi _\mathrm{f}\).

One more possibility for the government could be to subsidize formal care services. However, with the present specification of the model, assuming that formal care (equal to \(L_\mathrm{m}-h(a_\mathrm{f})\)) is observable and can be subsidized would be inconsistent with the unobservability of informal care since the government then could easily infer the level of \(a_\mathrm{f}\). In a more complex model where the total amount of care is not exogenously given, it could be possible to introduce a subsidy on formal care. This subsidy could act as an additional policy instrument together with insurance subsidies, but it would not restore the first-best. As far as insurance is concerned, one could expect the presence of the same considerations as in the current model. Therefore, to focus on the interaction between caregiving and insurance, the analysis is based on the present (simpler) specification of the model and a policy directed only at insurance premiums is studied.

More generally, it is shown in Appendix D that the signs of these cross-derivatives are ambiguous. However, it is reasonable to expect these effects to be small (at least compared to the “own subsidy” effects).

All the relevant comparative statics are derived in Appendix D.

Women tend to provide more intensive and complex care than men (AARP Public Policy Institute 2007; Navaie-Waliser et al. 2002; Sinha 2013). Moreover, wives tend to be sole caregivers to their husbands while husbands are more likely to have assistance in their caregiving activities (Allen 1994; Feld et al. 2006; Katz et al. 2000; Stoller and Cutler 1992).

AARP Public Policy Institute. (2007). Women & Long-Term Care. AARP Public Policy Institute Fact Sheet, April 2007.

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American Council of Life Insurers. (2014). Who will pay for our long-term care? November 2014.

Cannuscio, C. C., Jones, C., Kawachi, I., Colditz, G. A., Berkman, L., & Rimm, E. (2002). Reverberations of family illness: A longitudinal assessment of informal caregiving and mental health status in the Nurses’ Health Study. American Journal of Public Health, 92(8), 1305–1311.CrossRef

Colombo, F., Llena-Nozal, A., Mercier, J., & Tjadens, F. (2011). Help wanted? Providing and paying for long-term care. OECD Health Policy Studies. Paris: OECD Publishing.CrossRef

Cremer, H., Pestieau, P., & Ponthière, G. (2012). The economics of long-term care: A survey. Nordic Economic Policy Review, 2, 107–148.

Duée, M., & Rebillard, C. (2006). La dépendance des personnes âgées : une projection en 2040. Données sociales: La société française. Insee.

EHB Insurance Group. (2010). Who really needs long-term care? www.ehbinsurancegroup.com/ltc.

Elder Law Answers. (2013). Which spouse should get long-term care insurance coverage? www.elderlawanswers.com/which-spouse-should-get-long-term-care-insurance-coverage-12321.

European Commission. (2009). The 2009 ageing report: Economic and budgetary projections for the EU-27 Member States (2008–2060). Joint report prepared by the European Commission (DG ECFIN) and the Economic Policy Committee (AWG).

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Titel: Long-term care and myopic couples
verfasst von: Justina Klimaviciute
Publikationsdatum: 03.07.2019
Verlag: Springer US
Erschienen in: International Tax and Public Finance / Ausgabe 1/2020
Print ISSN: 0927-5940
Elektronische ISSN: 1573-6970
DOI: https://doi.org/10.1007/s10797-019-09552-x

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