Precautionary Saving and Consumption Smoothing Across Time and Possibilities

This paper examines how aversion to risk and intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Kreps-Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive which generalizes to these more general preferences the concept of "prudence" introduced by Kimball [l990b] to these more general preferences. For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for the strength of the precautionary saving motive to decline with wealth and for a change in risk preferences alone to increase the strength of the precautionary saving motive.