Maybe "honor thy father and thy mother": uncertain family aid and the design of social long term care insurance

We study the role and design of private and public insurance programs when informal care is uncertain. Children's degree of altruism is randomly distributed over some interval. Social insurance helps parents who receive a low level of care, but it comes at the cost of crowding out informal care. Crowding out occurs both at the intensive and the extensive margins. We consider three types of LTC policies: (i) a topping up (TU) scheme providing a transfer which is non exclusive and can be supplemented; (ii) an opting out (OO) scheme which is exclusive and cannot be topped up and (iii), a mixed policy combining these two schemes. TU will involve crowding out both at the intensive and the extensive margins, whereas OO will crowd out informal care solely at the extensive margin. However, OO is not necessarily the dominant policy as it may exacerbate crowding out at the extensive margin. The distortions of both policies can be mitigated by using an appropriately designed mixed policy.