We develop a tractable way to solve for equilibrium quantities and asset prices in a class of real business cycle models featuring Epstein-Zin preferences and affine dynamics for productivity growth and volatility. The method relies on log-linearization and exploits the log-normality of all the quantities. It is an easy substitute for more involved numerical techniques, such as higher order perturbation methods, and allows for easy implementation and analytical results. We show explicitly the link with perturbation techniques and find that the quantitative difference between the two is insignificant for several models of interest.

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