A Closed-form Solution for a Model of Precautionary Saving

Abstract

This paper analyses life-cycle consumption plans and distinguishes between temporal risk aversion and intertemporal substitution. The results assume that felicity functions are quadratic and that income follows a linear model with normally distributed errors. Stochastic dynamic programming then yields closed-loop linear decision rules. Certainty equivalence no longer holds, but instead households play a min-max strategy against nature. One finds a rationale for precautionary saving and a larger sensitivity of changes in consumption to income innovations.