Long-term care and lazy rotten kids
This paper studies the determination of informal long-term care (family aid) to de- pendent elderly in a worst case scenario concerning the harmonyof family relations. Children are purely sel sh, and neither side can make credible commitments (which rules out e¢ cient bargaining). The model is based on Beckers rotten kid speci ca- tion except that it explicitly accounts for the sequence of decisions. In Beckers world, with a single good, this setting yields e¢ ciency. We show that when family aid (and long-term care services in general) are introduced the outcome is likely to be ine¢ cient. Still, the rotten kid mechanism is at work and ensures that a positive level of aid is provided as long as the bequest motive is operative. We identify the ine¢ ciencies by comparing the laissez-faire (subgame perfect) equilibrium to the rst-best allocation. We initially assume that families are identical ex ante. However, the case where dyn- asties di¤er in wealth is also considered. We study how the provision of long-term care (LTC) can be improved by public policies under various informational assumptions. In- terestingly, crowding out of private aid by public LTC is not a problem in this setting. With an operative bequest motive, public LTC will have no impact on private aid. More amazingly still, when the bequest motive is (initially) not operative, public insurance may even enhance the provision of informal aid.
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