Family altruism and long-term care insurance

Abstract

The aim of this paper is to analyse long-term care (LTC) insurance purchase decisions by parents who expect to receive assistance from altruistic children. We first propose a simple theoretical model in which we show that the effect of children’s altruism on parents’ insurance decisions is ambiguous and depends on a number of factors: the degree of substitutability between informal and formal care, the degree of parental altruism, and the curvature of the utility functions. We then run an empirical test using data from the U.S., France, Spain, Germany and Israel, and proxy altruism with assistance provided to healthy parents. We find that the effect of children’s altruism is negative in Germany and Israel but not significant in the United States, France and Spain, which possibly suggests that the different forces identified in the theoretical model offset each other.

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Notes

  1. 1.

    Informal care is defined as the time spent by relatives in caring for a dependent. It includes talking with the dependent, nursing and helping the dependent with various domestic tasks.

  2. 2.

    See Costa-Font and Courbage (2015), who show evidence consistent with family crowding out. They do not find robust evidence of public sector crowding out.

  3. 3.

    Bonsang (2009) finds that formal and informal care are substitutes as long as LTC needs are low and an unskilled type of care is required.

  4. 4.

    For a study on France, see Courbage and Roudaut (2008). For a study on Spain, see Jimenez-Martin et al.(2016).

  5. 5.

    Informal care is expressed in terms of time, whereas formal care and earnings w(1−a) are expressed in monetary terms. In other words, we normalise the price of formal care to 1.

  6. 6.

    To keep the model as simple as possible, we only focus on the child’s assistance in time, a. More generally, we could have allowed the child to choose between providing informal care and paying for the parent’s formal care as in Pestieau and Sato (2008). In that case, the relative importance of informal versus formal care depends on the substitutability of the two types of care and on the opportunity cost of providing informal care, measured by w.

  7. 7.

    This can also be thought of in terms of “q-substitutes” and “q-complements” as in Seidman (1989).

  8. 8.

    Alternatively, the problem could be solved in terms of insurance compensation b. This would not impact the results.

  9. 9.

    Dependence is widely defined as having two or more limitations in activities of daily living (ADL). It concerns bathing, eating, dressing, walking across a room, getting in or out of bed and using the toilet. To qualify for LTC insurance benefits in the U.S., one must be recognised as unable to perform two or more ADLs. A nurse employed by a third-party administrator conducts the evaluations of ADL limitations (Frank 2012) just as for Medicaid. The same thresholds exist in Europe (see SCOR 2012; Zuchandke et al. 2012). However, a person having a limitation with one ADL still depends on the help of others, particularly on their children’s help, even if they are not eligible for private LTC insurance benefits. This is why we use the threshold of zero ADL limitations to define a non-dependent parent.

  10. 10.

    Examples of help to non-dependent parents can be help in managing money, help with chores, errands and transportation.

  11. 11.

    Providing informal aid should not necessarily be equated with the presence of altruism since, as discussed in the introduction, caregiving can also be driven by other motives such as exchange or family norms. However, it seems that altruism is the prevailing motivation in many countries (see Klimaviciute et al. 2017).

  12. 12.

    Individuals have been ranked according to quartiles of income created for each country separately.

  13. 13.

    In order to control for the quid pro quo motive of aid, in Appendix 2 we added to our regressions the fact that during the same period the parents made a financial transfer to at least one of their children. We observe that the relationship between children’s altruism and insurance is still negative in Germany and in Israel. In these two countries we do not observe any effect from downward transfer from the parent to a child. This variable has a negative and significant effect on private LTC insurance in the U.S. It is statistically significant and positive in Spain. The absence of effect of a child’s help on owning an LTC insurance is still observed in the other countries. However, if we pool data from different waves of HRS (2004, 2006, 2008 and 2010), we also obtain a negative and significant link between children’s altruism and insurance in the U.S.

  14. 14.

    We also run linear probability models in order to test the robustness of the results. The results are similar but not presented.

  15. 15.

    Our result for the U.S. is similar to Mellor (2001), who found no statistically significant effect of informal caregiving on private insurance.

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Acknowledgements

We are grateful to two anonymous referees for their excellent comments. Financial support from the Belgian Science Policy Office (BELSPO) research project CRESUS and the “Chaire Marché des risques et création de valeur” of the FdR/SCOR is gratefully acknowledged.

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Appendices

Appendix 1

In this appendix we derive the comparative statics result \(\frac{\partial P}{\partial \gamma }\). We have

$$\frac{\partial P}{\partial \gamma } = \frac{{\frac{{\partial EU_{P} }}{\partial P\partial \gamma }}}{{ - SOC_{P} }},$$
(4)

where SOCP < 0 is the second-order condition for P and \(\frac{{\partial EU_{P} }}{\partial P\partial \gamma }\) is obtained by deriving the FOC (2) with respect to γ. In particular, we have

$$\begin{aligned} \frac{{\partial EU_{P} }}{\partial P\partial \gamma } = & - \pi H_{ma} \frac{\partial a}{\partial \gamma } + \frac{{H_{ma} \frac{\partial a}{\partial \gamma }}}{1 + \lambda } + \pi H_{aa} \frac{\partial a}{\partial \gamma }\frac{\partial a}{\partial m}\left( {\frac{1}{{\left( {1 + \lambda } \right)\pi }} - 1} \right) + \pi H_{a} \frac{{\partial \left( {\frac{\partial a}{\partial m}} \right)}}{\partial \gamma }\left( {\frac{1}{{\left( {1 + \lambda } \right)\pi }} - 1} \right) \\ & \; + \pi \beta u^{\prime\prime}\left( c \right)w^{2} \frac{\partial a}{\partial \gamma }\frac{\partial a}{\partial m}\left( {\frac{1}{{\left( {1 + \lambda } \right)\pi }} - 1} \right) - \pi \beta u^{\prime}\left( c \right)w\frac{{\partial \left( {\frac{\partial a}{\partial m}} \right)}}{\partial \gamma }\left( {\frac{1}{{\left( {1 + \lambda } \right)\pi }} - 1} \right). \\ \end{aligned}$$

Using the fact that \(\frac{\partial a}{\partial m} = \frac{{\gamma H_{am} }}{{ - \Delta_{a} }}\) with \(\Delta_{a} = \gamma H_{aa} + w^{2} u^{\prime\prime}\left( c \right)\) and that \(H_{am} = H_{ma}\) and rearranging the first three terms, together with (4), we get the result in Eq. (3).

The expression for \(\frac{\partial a}{\partial \gamma }\) is derived using (1), while \(\frac{{\partial \left( {\frac{\partial a}{\partial m}} \right)}}{\partial \gamma }\) is obtained by deriving \(\frac{\partial a}{\partial m} = \frac{{ - \gamma H_{am} }}{{\gamma H_{aa} + w^{2} u^{\prime\prime}\left( c \right)}}\) with respect to γ.

Appendix 2

Probit models of LTC insurance with dependence (quid pro quo motive)

  U.S. France Germany Spain Israel
Children’s help − 0.015 (0.019) − 0.021 (0.031) − 0.033** (0.013) 0.002 (0.017) − 0.132*** (0.047)
In couple 0.029*** (0.006) 0.000 (0.020) 0.001 (0.011) 0.003 (0.010) − 0.069** (0.034)
Woman 0.034*** (0.006) 0.027* (0.016) 0.002 (0.007) 0.009 (0.007) − 0.013 (0.025)
Age
 50/64 − 0.096*** (0.009) − 0.058*** (0.026) 0.020 (0.020) 0.023* (0.013) 0.064 (0.043)
 65/79 − 0.009 (0.008) 0.024 (0.025) 0.037* (0.020) 0.021* (0.013) 0.066 (0.041)
 80+ Ref. Ref. Ref. Ref. Ref.
Years of education 0.014*** (0.001) − 0.002 (0.002) 0.002 (0.001) 0.005*** (0.001) 0.015*** (0.003)
Income
 1st quartile − 0.065*** (0.008) − 0.005 (0.027) − 0.034*** (0.012) − 0.004 (0.003) − 0.169*** (0.037)
 2nd quartile − 0.060*** (0.008) 0.012 (0.023) − 0.051*** (0.011) − 0.033*** (0.010) − 0.176*** (0.033)
 3rd quartile − 0.046*** (0.007) 0.002 (0.021) − 0.014 (0.008) − 0.027*** (0.009) − 0.098*** (0.032)
 4th quartile Ref. Ref. Ref. Ref. Ref.
 Financial transfer − 0.024* (0.014) 0.003 (0.026) 0.013 (0.009) 0.049** (0.021) − 0.021 (0.076)
N 14,946 2792 3357 3927 1439
Pseudo-R2 0.055 0.012 0.048 0.083 0.052
  1. Heteroscedasticity-consistent standard errors in parentheses
  2. *p < 0.1, **p < 0.05, ***p < 0.01

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Klimaviciute, J., Pestieau, P. & Schoenmaeckers, J. Family altruism and long-term care insurance. Geneva Pap Risk Insur Issues Pract 44, 216–230 (2019). https://doi.org/10.1057/s41288-018-00117-3

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Keywords

  • Long-term care insurance
  • Altruism
  • Informal care