Epstein-Zin Preferences in Life-Cycle Applications: Uncertain Lifetime and Consumption Smoothing

Abstract

This paper provides an in-depth investigation of Epstein-Zin preferences under an uncertain lifetime. These models have been gaining popularity as normative preference models in life-cycle applications. Though extensively used, it is unclear if the preference models are well-understood by the users. To this end, this paper studies the decision-making under Epstein-Zin preferences. Specifically, analytical solutions for a simple consumption and savings problem are derived, isolating the impact of relative risk aversion (RRA), elasticity of intertemporal substitution (EIS), time discounting, and risks stemming from mortality, investment, and inflation. We investigate three Epstein-Zin preference models that differ in their treatment of mortality risk, and find that some lead to normatively implausible solutions. Importantly, we find that the EIS is not always monotone in its effect on consumption volatility over time, meaning that its interpretation can be ambiguous when considering an uncertain future lifetime. This has been misinterpreted in the literature to date. We also show that one particular Epstein-Zin specification is not necessarily a generalization of expected discounted utility maximization in the case of constant relative risk aversion, as many works wrongly claim.