An Irrelevance Theorem for Risk Aversion and Time-Varying Risk

2026-06-03

AI Summary

This study investigates how risk aversion and time-varying risk affect the elasticities of endogenous variables in macroeconomic models. By disentangling intertemporal preferences from risk preferences, distinguishing between first- and higher-order moment drivers, and assuming approximately linear constraints, the authors establish an irrelevance theorem. They rigorously demonstrate that when state variables do not influence higher-order moments, neither risk aversion nor time-varying risk impacts these elasticities. This result delineates the theoretical boundary within which risk effects vanish in standard macroeconomic frameworks and highlights that relaxing these assumptions can amplify the role of risk. The findings thus offer a principled foundation for developing more risk-sensitive macroeconomic models.

Abstract

We provide a theorem on the role of risk and risk attitudes in macroeconomic models that clarifies and extends the Tallarini (2000) separation result. Under (1) separation of intertemporal and risk preferences, (2) separation of drivers of first and higher moments in the model primitives, and (3) approximate linearity of constraints, risk aversion and time-varying risk are irrelevant for the elasticity of any endogenous variable with respect to state variables that don't drive variation in higher moments. We discuss how models generate a more prominent role for risk by ``breaking'' or ``adapting'' to the assumptions in the theorem.

Problem

• risk aversion
• time-varying risk
• macroeconomic models
• elasticity
• higher moments

Innovation

• irrelevance theorem
• risk aversion
• time-varying risk
• moment separation
• macroeconomic modeling