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

22 Pages Posted: 18 Oct 2018

See all articles by Saisai Zhang

Saisai Zhang

University of Waterloo

Mary R. Hardy

University of Waterloo

David Saunders

University of Waterloo

Date Written: September 25, 2018

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.

Keywords: Life-Cycle Investing, Epstein-Zin Preferences, Uncertain Lifetime, Consumption Smoothing, Elasticity of Intertemporal Substitution

JEL Classification: G10

Suggested Citation

Zhang, Saisai and Hardy, Mary R. and Saunders, David, Epstein-Zin Preferences in Life-Cycle Applications: Uncertain Lifetime and Consumption Smoothing (September 25, 2018). Available at SSRN: https://ssrn.com/abstract=3245960 or http://dx.doi.org/10.2139/ssrn.3245960

Saisai Zhang (Contact Author)

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Mary R. Hardy

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

David Saunders

University of Waterloo ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
(519) 888-4567 (Phone)

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