Quasi-Hyperbolic Discounting under Recursive Utility and Consumption-Investment Decisions

Abstract

This paper examines an Epstein-Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process and consider a Merton's optimal consumption-investment problem for application. I show that a solution to the Hamilton-Jacobi-Bellman equation is the value function. The numerical comparative statics and mathematical analysis shows that, unlike in the constant relative risk aversion utility, present bias in the Epstein-Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, I show that the sophisticated agent's preproperation occurs if and only if his or her elasticity of intertemporal substitution in consumption is larger than one.

Keywords: Quasi-Hyperbolic Discounting, Epstein-Zin Utility, Consumption-Investment Problem, Beta-Delta Model, Recursive Utility

JEL Classification: D15, G11, G40