Stochastic Impatience and the Separation of Time and Risk Preferences

We study how the separation between time and risk preferences relates to a new behavioral property that generalizes impatience to stochastic environments: Stochastic Impatience. We show that Stochastic Impatience holds if and only if risk aversion is \not too high" relative to the inverse elasticity of intertemporal substitution. This result has implications for many known models. For example, in the models of Epstein and Zin (1989) and Hansen and Sargent (1995), Stochastic Impatience is violated for all commonly used parameters. If Stochastic Impatience is taken normatively, this suggests a limit on the amount of separation between time and risk preference; otherwise, it provides a simple one-question test for it.