An Interpretation of the Condition for Precautionary Saving: The Case of Greater Higher-Order Interest Rate Risk

Abstract

This paper shows that an increase in interest rate risk via (m, n)th-order stochastic dominance induces precautionary saving if, and only if, the measure of (k + 1)th-degree relative risk aversion exceeds k for all k = m, ..., n. This result has the following interpretation. On the one hand, the measures of (k + 1)th-degree relative risk aversion for all k = m, ..., n capture the prudence effect with respect to a risk increase via (m, n$th-order stochastic dominance, which favors precautionary saving. On the other hand, the thresholds, k = m, ..., n, measure the elasticity of the change in the kth moment of future income with respect to saving. The adverse changes in higher moments of future income for all k = m, ..., n when saving increases give rise to the risk aversion effect with respect to a risk increase via (m, n)th-order stochastic dominance, which limits precautionary saving. The necessary and sufficient condition for precautionary saving simply states that the prudence effect dominates the risk aversion effect, thereby making precautionary saving prevail.