We provide the analytical explanation of the interactions between precautionary saving and liquidity constraints. The effects of liquidity constraints and risks are similar because both stem from the same source: a concavification of the consumption function. Since a more concave consumption function exhibits heightened prudence, both constraints and risks strengthen the precautionary saving motive. In addition, we explain the apparently contradictory results that constraints and risks in some cases intensify, but in other cases weaken the precautionary saving motive. The central insight is that the effect of introducing an additional constraint or risk depends on whether it interacts with preexisting constraints or risks. If it does not interact with any preexisting constraints or risks, it intensifies the precautionary motive. If it does interact, it may reduce the precautionary motive in earlier periods at some levels of wealth.

我们提供了预防性储蓄与流动性约束之间相互作用的分析解释。流动性约束和风险的影响是相似的，因为两者都源于同一个来源：消费函数的凹化。由于更凹的消费函数表现出更高的审慎性，约束和风险都加强了预防性储蓄的动机。此外，我们解释了在某些情况下约束和风险加剧，但在其他情况下削弱了预防性储蓄动机的明显矛盾的结果。核心观点是引入额外约束或风险的效果取决于它是否与先前存在的约束或风险相互作用。如果它不与任何预先存在的限制或风险相互作用，就会强化预防动机。在某些财富水平上减少早期的预防动机。