Recursive utility and parameter uncertainty

We explore how the Epstein–Zin utility captures an agent's sensitivity to parameter uncertainty. Our main result is a closed-form representation of the Epstein–Zin utility for an i.i.d. consumption process with unknown parameter, as the discount factor approaches 1. Using this representation, and under the usual assumption about the relationship between risk aversion and the attitude towards time smoothing, we show that the agent is averse to parameter uncertainty.