Blast from the past: The altruism model is richer than you think

Abstract

We provide the first full theoretical characterization of the standard two-period altruism model in a deterministic setting, thereby providing a coherent methodology for studying equilibria in this class of models. Under general conditions, policy and value functions are discontinuous; non-smoothness escalates one order higher than in one-player settings due to differing interests among players. We show that there exists a novel type of front-loaded transfer that enables the recipient to stay in autarky. The logic behind it challenges standard theory as it severs the link between transfer motives and first-order conditions. Our results revise qualitative predictions of dynamic altruism models and highlight that their computation demands global, not local, methods. Our results are robust to introducing income shocks and to varying assumptions on parent savings. Numerical experiments indicate that the correctly solved model features more front-loading of transfers than previously thought, accompanied by higher savings of transfer recipients.