The Ricardian Equivalence Theorem, which is the proposition that changes in the timing of lump-sum taxes have no effect on assumption or capital accumulation, depends on the exist- of operative altruistic motives for intergenerational transfers. These transfers can be bequests from parents to children or gifts from children to parents. In order for the Ricardian Equivalence Theorem to hold, one of these transfer motives must be operative in the sense that the level of the transfer is not determined by a corner solution resulting from a binding non-negativity constraint This paper derives conditions that determine whether the bequest motive will be operative, the gift motive will be operative, or neither motive will be operative in a model in which consumers are altruistic toward their parents and their children.