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How do families behave dynamically? We provide a framework for studying economic problems in which family behavior is essential. Our key innovation is the inclusion of imperfectly altruistic agents in an otherwise standard consumption&-savings problem with exogenous income risk. This gives rise to altruistic transfers and strategic behavior in the consumption&-savings decision. We study the Markov-perfect equilibrium that arises from the limit of equilibria in a sequence of finite games. The equilibrium's transfer patterns are empirically plausible. Furthermore, agents overconsume relative to the social optimum. In contrast to two-period models, both the richer and the poorer players overconsume long before transfers actually occur. The poorer agent also faces incentives to engage in excessive risk-taking because losses from a gamble are absorbed by both while gains are enjoyed alone.
altruism; inter vivos transfers; consumption-savings decision; differential games