Hyperbolic utility discounting has emerged as a leading alternative to exponential discounting because it can explain time-inconsistent behaviors. Intuitively, hyperbolic discounting should play a crucial role in intergenerational models characterized by intertemporal trade-offs. In this paper, we incorporate hyperbolic discounting into a dynamic model in which parents are altruistic towards their children. Agents live for four periods and choose levels of consumption, fertility, investment in their children’s human capital, and bequests to maximize discounted utility. In the steady state, hyperbolic discounting decreases fertility, increases human capital investment, and shifts consumption towards younger ages. These effects are more pronounced in the time-consistent problem (in which agents cannot commit to a course of action) than in the commitment problem, which can be interpreted as realized and intended actions, respectively. The preference-based discrepancy between intended fertility and realized fertility has important implications for the empirical literature that compares the two.

双曲线效用折扣已成为指数折扣的主要替代方法，因为它可以解释时间不一致的行为。直觉上，双曲线贴现应该在以时间折衷为特征的代际模型中发挥关键作用。在本文中，我们将双曲折现纳入一个动态模型，在该模型中，父母对孩子无私。代理人生活了四个时期，他们选择了消费水平，生育能力，对子女人力资本的投资以及遗嘱以最大化折价效用。在稳定状态下，双曲线贴现会降低生育能力，增加人力资本投资，并使消费转向年轻年龄段。这些影响在时间一致的问题（代理无法采取行动的过程）中比在承诺问题中更为明显，在承诺问题中，这可以分别解释为已实现的行动和预期的行动。预期生育率与实际生育率之间基于偏好的差异对比较两者的经验文献具有重要意义。