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 twoperiod
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.
Keywords. Altruism, inter vivos transfers, consumption–savings decision, differential
games.
JEL classification. C73, D1, D64, E21.