Liquidity constraints and precautionary saving

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.