Epstein–Zin preferences
In economics, Epstein–Zin preferences refers to a specification of recursive utility. A recursive utility function can be constructed from two components: a time aggregator that characterizes preferences in the absence of uncertainty and a risk aggregator that defines the certainty equivalent function that characterizes preferences over static gambles and is used to aggregate the risk associated with future utility. With Epstein–Zin preferences, the time aggregator is a linearly homogeneous CES aggregate of current consumption and the certainty equivalent of future utility. Specifically, the date-t utility index, formula_1, for a sequence of positive scalar consumptions  formula_2, that are potentially stochastic for time periods beyond date t, is defined recursively as the solution to the nonlinear stochastic difference equation where formula_4 is a real-valued certainty equivalent operator. The parameter formula_5 determines the marginal rate of time preference, formula_6, and the parameter formula_7 determines the elasticity of intertemporal substitution, formula_8. Epstein and Zin considered a variety of certainty equivalent operators, but a popular choice for both theoretical and empirical research has been formula_9, where formula_10 denotes the expected value of probability distribution of formula_11, conditional on information available to the planner in date t. The parameter  formula_12 encodes risk aversion, with smaller values of formula_13, other things equal, implying a stronger aversion to risk. The parameter restriction formula_14 results in a time-additive von Neumann–Morgenstern expected utility index. Importantly, unlike VNM utility functions (e.g. isoelastic utility), Epstein–Zin preferences allow the elasticity of intertemporal substitution (determined above by formula_15) to be unrelated to risk aversion (determined above by formula_13).