First-Order Prudence and Its Implications for Precautionary Savings and the Risk-Free Rate

First-order prudence Prudence is widely known for inducing saving in response to future risk—precautionary saving. In “First-Order Prudence and its Implications for Precautionary Savings and the Risk-Free Rate,” Sebastian Ebert and Paul Karehnke revisit this important implication by providing definitions of first- and second-order prudence that parallel Segal and Spivak’s (1990) definitions of first- and second-order risk aversion. Second-order prudence means that the decision-maker is almost prudent-neutral for small risks, whereas under first-order prudence, small risks remain a major concern. In the expected utility (EU) framework and when utility is smooth, prudence is second order. In that case, a small, positive-mean risk to future wealth reduces savings because of the consumption smoothing motive, but it can increase savings under first-order prudence. The latter is the case for non-EU theories, such as rank-dependent or reference-dependent utility, but also in the EU framework with a novel utility function that the authors propose. They further show that, in equilibrium, first-order prudent preferences predict realistically low risk-free rates, thereby resolving the so-called risk-free rate puzzle.