Liquidity Constraints and Precautionary Saving

Economists working with numerical solutions to the optimal consumption/saving problem under uncertainty have long known that there are quantitatively important interactions between liquidity constraints and precautionary saving behavior. This paper provides the analytical basis for those interactions. First, we explain why the introduction of a liquidity constraint increases the precautionary saving motive around levels of wealth where the constraint becomes binding. Second, we provide a rigorous basis for the oft-noted similarity between the effects of introducing uncertainty and introducing constraints, by showing that in both cases the effects spring from the concavity in the consumption function which either uncertainty or constraints can induce. We further show that consumption function concavity, once created, propagates back to consumption functions in prior periods. Finally, our most surprising result is that the introduction of additional constraints beyond the first one, or the introduction of additional risks beyond a first risk, can actually reduce the precautionary saving motive, because the new constraint or risk can hide' the effects of the preexisting constraints or risks.