Precautionary Saving and Consumption Smoothing Across Time and Possibilities

This Paper examines how aversion to risk and aversion to intertemporal substitution determines 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 the concept of ‘prudence’ introduced by Kimball (1990b). 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 a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.