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

• 成果类型: Article; Early Access
• 署名作者: Ebert, Sebastian; Karehnke, Paul
• 署名单位: Ruprecht Karls University Heidelberg; heSam Universite; ESCP Business School
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0739
• 发表日期: 2024
• 关键词: expected utility; equity premium; aversion; uncertainty; consumption; ORDER; attitudes; substitution; RESOLUTION; demand

摘要

Prudence is widely known for inducing saving in response to future risk- precautionary saving. In this paper, we revisit this important implication by providing definitions of first- and second-order prudence that parallel Segal and Spivak's [Segal U, Spivak A (1990) First order versus second order risk aversion. J. Econom. Theory 51:111-125] 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 we propose. In equilibrium, first-order prudent preferences predict realistically low risk-free rates, thereby resolving the so-called risk-free rate puzzle.