Recursive utility functions control the investors relative risk aversion (RRA) and elasticity of intertemporal substitution (EIS) by different parameters. They are generalization of expected utility functions in which the RRA and the EIS are controlled by the same parameter. This is widely discussed in the empirical literature. Also, the timing of the resolution of uncertainty matters in recursive setting. Recursive utility functions are widely used in the literature in order to explain many macroeconomic issues like the equity premium puzzle, risk free rate puzzle, and stock market participation. We want to have a deep understanding about the effects and relations of the model parameters. We use the Epstein-Zin preferences on a binomial tree and find the analytical closed form solution for the optimal allocations in consumption, risk free and risky assets. We give numerical results for the effects of model parameters. Numerical results show that the dependence of consumption on RRA parameter is insignificant. Then, we extend our model by adding lifetime uncertainty. We check the interchangeability of EIS parameter, and the subjective time discount factor under different cases like incomplete markets and stochastic lifetime. Analytically, these two parameters are not interchangeable, but numerically they are under certain lifetime, complete and incomplete markets. However, accuracy is much smaller for the uncertain lifetime model. Then, we analyze the welfare loss of suboptimal allocations. We find that effect of suboptimal allocation in bond holdings is insignificant. The welfare loss is larger when the suboptimal allocation is in stock holdings and consumption, but it is still modest. Finally, we numerically show that a representative agent exists when the heterogeneity is in RRA or EIS parameter. However, this is not true when the heterogeneity is in subjective time discount factor or survival probability.
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