Precautionary Savings and the Permanent Income Hypothesis

This paper derives the explicit solution of a dynamic stochastic optimal consumption problem for infinitely-lived agents whose preferences exhibit, in the presence of non-diversifiable labour income uncertainty, a constant elasticity of intertemporal substitution and constant absolute risk aversion. The constancy of the elasticity of intertemporal substitution, which implies that marginal utility at zero consumption is infinite, guarantees that the non-negativity constraint on consumption is never binding along the optimal path. The assumption of constant absolute risk aversion allows an explicit computation of human wealth, and provides a simple representation of the precautionary savings motive.