An Analytical Approach to Buffer-Stock Saving under Borrowing Constraints

Abstract

The profession has been longing for closed-form solutions to consumption functions under uncertainty and borrowing constraints. This paper proposes an analytical approach to solving general-equilibrium buffer-stock saving models with both idiosyncratic and aggregate uncertainties as well as liquidity constraints. It is shown analytically that an individual’s optimal consumption plan follows the rule of thumb: Consumption is proportional to a target level of wealth, with the marginal propensity to consume dependent on the state of the macroeconomy. I apply this method to address two long-standing puzzles in general equilibrium: the excess smoothness and excess sensitivity of consumption with respect to income changes. Some of my findings sharply contradict the conventional wisdom.