Stochastic impatience and the separation of time and risk preferences

We study how the separation of time and risk preferences relates to a property called Stochastic Impatience. We show that, within a broad class of models, Stochastic Impatience holds if and only if risk aversion and the inverse elasticity of intertemporal substitution are sufficiently close. In the models of Epstein and Zin (1989) and Hansen and Sargent (1995), Stochastic Impatience is violated for commonly used parameters. Our result also provides a simple, one-question test for the separation of time and risk preferences.