Risk and Intertemporal Preferences over Time Lotteries

TL;DR

This paper explores the incompatibility of Risk Averse over Time Lotteries with traditional utility models and introduces a new class of models that reconcile RATL with Stochastic Impatience, highlighting the potential role of Future Bias.

Contribution

It generalizes the incompatibility of RATL with key axioms and provides a new representation theorem accommodating RATL and SI simultaneously.

Findings

RATL is incompatible with Expected Discounted Utility models.

A new class of models satisfying RATL and SI is constructed.

RATL behavior may be explained by Future Bias rather than utility violations.

Abstract

This paper studies relations among axioms on individuals' intertemporal choices under risk. The focus is on Risk Averse over Time Lotteries (RATL), meaning that a fixed prize is preferred to a lottery with the same monetary prize but a random delivery time. Though surveys and lab experiments documented RATL choices, Expected Discounted Utility cannot accommodate any RATL. This paper's contribution is two-fold. First, under a very weak form of Independence, we generalize the incompatibility of RATL with two axioms about intertemporal choices: Stochastic Impatience (SI) and No Future Bias. Next, we prove a representation theorem that gives a class of models satisfying RATL and SI everywhere. This illustrates that there is no fundamental conflict between RATL and SI, and leaves open possibility that RATL behavior is caused by Future Bias.