Long-term care insurance with family altruism: Theory and empirics

This paper studies long-term care (LTC) insurance in the presence of family altruism. In the first, theoretical, part of the paper, we explore whether and how family solidarity affects the application to LTC of Arrow’s (1963) theorem of the deductible, which is shown to apply in models without family by a number of papers. We consider two tyes of family altruism, perfect and imperfect, and find that Arrow’s theorem generally holds, even though some departures from the standard model and some differences between the types of altruism exist. Oour analysis highlights a complex interplay between parents’ insurance and their children’s aid, which implies that a number of intuitive conjectures are not always verified. For instance, while one would expect the deductible to be increasing in the child’s degree of altruism, this is unambiguously verified only under certain conditions. Given the ambiguity of some results, in the second part of the paper, we resort, more generally, to an empirical test of the relation between LTC insurance and children’s altruism using the data from the Health and Retirement Study (HRS). Our findings suggest that children’s altruism has a negative impact on parents’ LTC insurance purchases, even though some results also point to this relationship being more complex than one might think.